I have been missing a neat summary of Karl Popper´s scientific method. I have thought that a neat set of theorems representing his method would be useful – both as a guide for development and scrutiny of ideas. But also to be able to reveal weaknesses in any idea claimed to be true or accurate. This is an attempt to summarise Popper´s method into a set of theorems.
Update: 2017-10-11
The discussions in the comments section to this article led me out on an unforgettable journey. See the latest product of that journey here:
Principles of science and ethical guidelines for scientific conduct (v8.0)
These theorems are derived from Popper´s work, but I still think the theorems are original in the way they are phrased and presented.
The term “idea” is here meant to cover both simple ideas and more complex ideas such as models or theories about how things work.
The term “thing” is here meant to cover both human constructions and anything found in nature.
#1 There are no rules, whatsoever, related to how an idea might come about.
– Karl Popper; The logic of Scientific discovery
Chapter 2 Elimination of psychologism; Page 7 …
#2 An idea must be free from logical fallacies.
– Karl Popper; The logic of Scientific discovery;
Chapter 3 Deductive testing of theories; Section 2; Page 9
#3 An idea must be consistent and clearly distinguish events which are compatible with the idea and events which are not compatible with the idea.
– Karl Popper; The logic of Scientific discovery;
Chapter 24 Falsifiability and Consistency ; Page 72
#4 An idea must be well-defined – a well-defined concept in a well-defined context – and be both suitable and available for independent scrutiny and testing.
– Karl Popper; The logic of Scientific discovery;
Chapter 8 Scientific Objectivity and Subjective Conviction; Page 22 ..
#5 A test is a comparison of a deduced consequence of the idea with an observable event. To have the potential to increase our current ability to reliably predict outcomes, an idea must be testable now – both in principle and in practice.
– Karl Popper; The logic of Scientific discovery;
Chapter 24 Falsifiability and Consistency ; Page 72
#6 An idea must be possible to prove wrong. The idea must exclude a range of possible outcomes for a particular range of conditions. The more an idea prohibit from happening, the more powerful it is. An idea which allows everything is useless for reliable prediction.
– Karl Popper; The logic of Scientific discovery;
Chapter 6 Falsifiability as a Criterion of Demarcation; Page 18; Section 2
#7 Both the deduced outcome and the observed events may have statistical uncertainties associated with it. If the deduced outcome repeatedly differs from the observed events by more than the combined uncertainties, there is something wrong with the idea – or the test of it.
– Karl Popper; Realism and the aim of science
Chapter 4 Experimental tests and their repetition: Independence ; Section 12
#8 Both the deduced outcome and the observed events may have systematic errors associated with it. If the central estimate of the deduced outcome repeatedly differs from the mean value of the observed events – there is a systematic error with the idea – or the test of it.
Science or Fiction
#9 Even if the observed events seem to fit the the idea being tested – the idea might still be wrong. The observed events may also fit other ideas, more precise ideas or more powerful ideas – hence, even a successful test cannot be regarded as a conclusive evidence for the truth of the idea.
– Karl Popper; The logic of Scientific discovery;
Chapter 42 The methodological problem of simplicity ; Page 123; Section 3
#10 An idea is corroborated, and should be referred to, by the necessary consequences of it and the tests it has been exposed to and survived – and not by inductive reasoning in favor of it. The strive for truth is characterized by an urge to expose ideas to risky tests.
– Karl Popper; The logic of Scientific discovery;
Chapter 10 Corroboration, or how a theory stand up to tests
Copyleft ; “Science or Fiction” 2016-06-09; Please refer to the source.
All kinds of scrutiny will be welcomed – please leave a comment.
Science or Fiction´s Comments
For reference, I recommend reading the 26 first soothing pages of Popper´s original work: The logic of scientific discovery. In my view, these pages contain the essence.
Leave no doubt about it – I think Karl Popper´s ideas are great. Still, I am of the opinion that his work has a slight potential for improvement. That is why I attempt to simplify and build on his ideas.
First: I have always thought that one weakness with Popper´s work was that it lacks a neat summary of the scientific method he provided. It should be remembered that the Logic of Scientific discovery was written as a full argument to establish the idea´s Karl Popper had about the logic of Scientific Discovery. My “10 theorems for ideas about truth” is an attempt to provide a neat summary of the method he provided but also an attempt to improve a few minor issues I have with his work.
Second: The term falsification was used by Karl Popper, however, falsification can mean two different things: “The action of falsifying information” and “to prove wrong”. I have always had this feeling that it was a mistake by Karl Popper to use the term falsification because of the two very different meanings of the term. That is why I have avoided the term falsification in my “10 theorems for ideas about how things work”.
Third: I think Popper made a slight mistake in saying:
“According to my proposal, what characterises the empirical method is its manner of exposing to falsification, in every conceivable way, the system to be tested. Its aim is not to save the lives of untenable systems but, on the contrary, to select the one which is by comparison the fittest, by exposing them all to the fiercest struggle for survival.”
It seems to me that it didn´t occur to Popper that it might happen that none of the alternative systems survives testing, in which case we simply don´t know what truth is like and in which case it would be wrong to select any of the alternative systems.
I think what he should have said is something like:
What characterises the strive for knowledge, is the manner of trying to prove wrong, in every conceivable way, the system to be tested. The aim is not to save the lives of untenable systems but to expose them all to the fiercest struggle for survival. A system is corroborated, and should be acknowledged, by the severity of the tests it has been exposed to and survived – and not at all by inductive reasoning in favour of it.
Forth: An area where his work may now be improved is on the treatment of statistical uncertainties and systematic errors. We now have a widely accepted international standard for the expression of uncertainty: Guide to the expression of uncertainty in measurement (Freely available). This international standard was not available to Karl Popper at the time he wrote his works. I will by no means think that the last word has been said on uncertainties, but at least, the standard provides a thorough explanation of the terms “uncertainty” and “systematic error”. I have used these terms in 2 theorems.
Fifth: Karl Popper did not think that his method itself was possible to prove wrong. I´m not so sure about that. I think the method can be proven wrong simply by providing an example of one idea about how things work which is true but erroneously turned down as being false by Popper´s method or by the theorems here provided.
All in all, this Video covers it pretty well:
Revisions:
2016-09-21: Following the dialogue with Gnomish about the importance of definition of concept and context I updated theorem #4. to emphasise that a well-defined idea must be: a well-defined concept in a well-defined context
Science or fiction? 
popper’s stuff is sort of a hamfisted attempt at objectifying epistemology.
you want the condensed and correct source code for this?
http://bajafiles.com/f/vPPwJ
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Thanks! I will look into it 🙂
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I find Poppers method very useful and not at all clumsy.
Do you know about a more robust way to strive for knowledge than the method he propose?
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yes. the book you find at the link i posted is almost good enuff to code it in binary.
popper did have it right to focus on falsification as the operating function – but that’s just logic: self contradictions are false.
darwin’s recognition of this epistemological function was a bit off.
he said ‘survival of the fit’ but marginal fitness- mere adequacy – is sufficient for persistence.
the operating function is ‘extinction of the unfit’.
so, the gold standard for evolution is the same pattern as the gold standard for persistence of truth: self contradiction is false.
it gets better, though- and popper provided a good hint-
anything which is true can be proven (wheter it is convenient or economical or not- it’s not impossible)
and the corollary of that is ‘if it can not be proven, it is false’
that’s a bit more useful because it takes care of mysticism.
and i use punctuation when i want to – it’s an option for me. i know very well how to produce perfectly grammatical and syntactically correct english. but i type a lot and i don’t like using my little finger; it’s weak.
and i’ve been on internet long enuff i don’t obsess and go back correcting typos.
it’s not a function of literacy; it’s laziness/convenience.
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I´m only a bit into the book yet but I noted that it seem to be very well written.
«Darwin’s recognition of this epistemological function was a bit off. He said ‘survival of the fit’ but marginal fitness- mere adequacy – is sufficient for persistence. the operating function is ‘extinction of the unfit’.»
Fully agree – I have always thought that the principle is more like death of the unfit – or merely unlucky for that sake.
“so, the gold standard for evolution is the same pattern as the gold standard for persistence of truth.. ”
I also think that way. An idea might pass as true or not depending on the context. For most people it is sufficient to know that gravity exists. An engineer might need to use an estimate of 9.8 m/s^2 for gravity. For some purposes a more accurate value is required. A space rocket scientist might have to estimate it along a trajectory. An astro physicist might have to take velocity and relativity theory into consideration. A particle physicist might consider gravity differently.
Hence an idea might survive as being true depending on the context and depending on the consideration of those who are judging the truth of this idea. If an idea is merely adequate for the purpose it may survive – whether it is really worthy of survival or not.
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we may have to define some terms to get really into this. colloquial terms fail because of crappy definition.
for example: ‘consciousness is the act of identification’
that makes it possible to speak about consciousness without ambiguity – otherwise wut, amirite?
you’re there, tho.
‘logic is the act of non.contradictory identification’
when you get some good definitions that don’t contradict one another, you can really go to town and everything – i mean Everything – drops the cloak of confusion and becomes very clear.
thinking is something that can be learned. when rehearsed it can become a habit. when it’s a habit, you just find it second nature to make sense of everything – almost effortlessly.
enjoy the book. it’s the most important thing you will ever read qua ‘the nature of thinking’.
it will give you what you need to own your mind and use it at will with very low error rate.
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Thanks for the link – I will look into it and tell you what I think – it may take some time though. 🙂
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while it’s on my mind- and for no other reason than that i have it accessible atm and won’t have to dig it up later, allow me to list a few of the psychoviruses that afflict H. sapiens today:
1- there is no such thing as an absolute
(asserted as an absolute – see self contradiction? it’s false)
2- There’s no such thing as truth.
(asserted as truth – see self contradiction? it’s false)
3- You can’t know everything so you can’t really know anything.
(asserted as knowledge – see self contrdiction? it’s false)
the denizens of WUWT are fixated on popperian falsification and also the notion that ‘you can’t really prove anything’
go ahead and ask them to prove it. see self contradiction? it’s false.
for that reason they are idiotic. how do you splain to an idiot that he’s an idiot? you don’t – cuz idiot.
Death is Life (everlasting)
but death is the negation of life- see self contradiction? it is false.
try it – i’ll stop with the spoilers so you can have your fun.
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I think knowledge has nuances.
I can describe a test which demonstrates that an idea idea is wrong – then I know that the idea is wrong (or the test of it).
I can describe a test where the prediction of an idea is corroborated by observation – then I know that this idea has been corroborated by this test.
However, an idea about a quantitative relationship, will not be complete without a specification of the uncertainty range.
Hence, even if a quantitative idea, with it´s uncertainty specification, is corroborated by a test. I cannot know if another, so far unknown idea, can make more accurate predictions – maybe over a broader range of conditions – and hence be closer to truth.
I, think this interpretation is pretty much in line with Popper.
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truth exists in context.
without a specified context, a statement is not amenable to verification by logic.
this means that for any statement of truth, one must define the context in which it be true or else it can not be proven. if it can not be proven it is false.
must abstract principles. anecdotes will not serve.
a description is not a definition. a definition is a set of characteristics which distinguishes an entity from all other entities not in the set.
a definition of ‘green’ is NOT a list of every green thing you can think of.
it’is the set of distinguishing characteristics (greenness) only. it’s a matter of principles, not anecdotes.
a good definition of green might be ‘the reflection or emission of electromagnetic radiation Wavelength 495–570 nm or Frequency 526–606 THz
there is no ambiguity. there is no uncertainty. it is or it is not. the fundamental alternative in the universe.
be or not be. binary. not matter of opinion. not ambiguous, relative, statistical. true or false.
if it isn’t that clear, it’s not properly defined and that wont’ get you truth; it’ll get you confused.
the fundamental form of the law of implication is
if A then B
that has one corollary: if -B then -A
that’s all there is to that.
if it can’t be put in those terms, it is not amenable to validation and therefore can not represent truth.
the context (the if A – the predicate) may be understood – it may not be explicit- but it better exist or you don’t even have a reasonable statement. reason is the act of applying logic to draw conclusions from premises.
and that is also the basis of falsification. if NOT b, then NOT a.
it’s really simple but it’s not negotiable.
thinking can not be done any other way.
this is what puts the sapiens in our name.
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“a description is not a definition. a definition is a set of characteristics which distinguishes an entity from all other entities not in the set.”
Agree – “description” is to vague.
Regarding definitions I struggle to understand how Karl Popper could defend the following position.
“It is, I now think, the fact that most philosophers regard definitions as important, and that they have never taken my assurance seriously that I do regard them as unimportant. I neither believe that definitions can make the meaning of our words definite, nor do I think it worth bothering about whether or not we can define a term (though it may sometimes be moderately interesting that a term can be defined with the help of terms of a certain kind); for we do need undefined primitive terms in any case.”
– Karl Popper; The logic of scientific discovery
To me he seems to be on thin ice. I think just as you do that truth exists in context and I think that the context need to be well defined. just like the specific heat capacity for water depend on temperature without defining the temperature (context) the truth of a statement about the heat capacity for water cannot be judged.
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aye. you’re onto him now.
it’s not ‘thin ice’ – it’s his big lie.
he’s using ‘words’ to make his statements and he’s saying words have no definite meaning.
see a self contradiction? it’s false.
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I think you are right – thats why I used the phrase “well defined” in theorem #4.
However – even if he didn´t know everything – he knew something. He knew the law of implication – he knew that:
if A then B
has one corollary:
if -B then -A
He also knew that A has it´s context – and that the statement – A – is only valid within this context.
He understood that any attempt to extend the validity of A beyond this context is a kind of induction.
He also knew that induction is logically flawed.
And – he did understand the implications of his knowledge:
He understood that scrutiny and skepticism is mandatory for the strive for more accurate knowledge – mandatory for the strive for more precise predictions.
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yeah. he got some important things right.
what he got right is what i expect a child of 4 to get right.
he was way past that age.
when a child does something right it’s praiseworthy.
hell, when a child learns how to poop in the right place, he gets a nobel prize…lol – (do i need to label this as humor?)
when an old man achieves marginal continence, it’s not ad majorem gloriam sui.
plus, he never got there.
once you get there, nobody cares how; only that you did.
slow or quick – getting there is the thing.
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As you might have observed, my profession is within measurement. I enjoyed to observe that the first chapter in the Book by Ayn Rand was: Cognition and measurement». Anyhow – I take great pleasure in reading Ayn Rand «Introduction to Objectivist Epistemology»
Regarding definitions it seems that Ayn Rand got a better hang of it than Karl Popper.
Ayn Rand: (Introduction to Objectivist Epistemology. iBooks.)
«Words transform concepts into (mental) entities; definitions provide them with identity. (Words without definitions are not language but inarticulate sounds.) We shall discuss definitions later and at length.»
«as conceptual chain moves farther and farther away from perceptual concretes, the issue of verbal definitions becomes crucial. It is at this point that all hell breaks loose.
«Apart from the fact that the educational methods of most of his elders are such that, instead of helping him, they tend to cripple his further development, a child’s own choice and motivation are crucial at this point. There are many different ways in which children proceed to learn new words thereafter. Some (a very small minority) proceed straight on, by the same method as before, i.e., by treating words as concepts, by requiring a clear, first-hand understanding (within the context of their knowledge) of the exact meaning of every word they learn, never allowing a break in the chain linking their concepts to the facts of reality. Some proceed by the road of approximations, where the fog deepens with every step, where the use of words is guided by the feeling: “I kinda know what I mean.” Some switch from cognition to imitation, substituting memorizing for understanding, and adopt something as close to a parrot’s psycho-epistemology as a human brain can come—learning, not concepts nor words, but strings of sounds whose referents are not the facts of reality, but the facial expressions and emotional vibrations of their elders. And some (the overwhelming majority) adopt a precarious mixture of different degrees of all three methods.»
Karl Popper:
“It is, I now think, the fact that most philosophers regard definitions as important, and that they have never taken my assurance seriously that I do regard them as unimportant. I neither believe that definitions can make the meaning of our words definite, nor do I think it worth bothering about whether or not we can define a term (though it may sometimes be moderately interesting that a term can be defined with the help of terms of a certain kind); for we do need undefined primitive terms in any case.”
Ayn Rand vs. Karl Popper 1 – 0
Regarding the problem of induction – I think Ayn Rand quits where Karl Popper gets onto it:
Ayn Rand:
«(The problem of epistemology is: how to discover facts, how to discover what is. Its task is to formulate the proper methods of induction, the methods of acquiring and validating scientific knowledge.»
Karl Popper:
The first chapter of Karl Poppers work: The logic of scientific discovery is: «The problem of induction»
«According to a widely accepted view—to be opposed in this book — the empirical sciences can be characterized by the fact that they use ‘inductive methods’, as they are called. According to this view, the logic of scientific discovery would be identical with inductive logic, i.e. with the logical analysis of these inductive methods.»
Ayn Rand vs. Karl Popper 0 – 1
You mention about Popper that:
“what he got right is what i expect a child of 4 to get right.”
I think you are either underestimating the importance of Karl Popper´s work – or overestimating the capabilities of human cognition in general. It might be that you grasped the problem of induction and the implication for the strive for truth as a 4 year old kid – if that was really the case I would characterize you as a genius.
Anyhow – I think that the two most important flaw in human reasoning might very well be a tendency:
1. to be imprecise when defining concepts – and contexts
2. to overestimate the certainty of conclusions reached by inductive reasoning
All the Best
SoF
And thank you again for the link to Ayn Rand “Introduction to Objectivist Epistemology.”
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since you’ve noted that popper is all over this thing called ‘inductive logic’, i hope you will consider that rand was not enamored of this form of post-normal ideation for a reason.
she was all about deductive logic:
inductive logic is a system of rhetoric that purports to extend deductive logic to less-than-certain inferences. For valid deductive arguments the premises logically entail the conclusion, i.e., the truth of the premises guarantees of the truth of the conclusion.
simpler terms: popper is concerned with guessing; rand is concerned with proving.
i see the self contradictions in popper. he is, essentially, a mystic.
so when you give popper a point and none for rand in scoring the treatment of the subjunctive netherworld- you are actually damning popper and praising rand – because she would have none of it.
mysticism is not not not knowledge. guessing is not not not reason. that which is not is not not not.
popper’s epiphany about falsification is not his innovation – it’s the meat and potatoes of deduction. his discovery of supper is not a legitimate claim to bragging rights – he’s just ‘late to the meal’.
your conclusion:
Anyhow – I think that the two most important flaw in human reasoning might very well be a tendency:
1. to be imprecise when defining concepts – and contexts
2. to overestimate the certainty of conclusions reached by inductive reasoning
good shot. on track and ranging on target.
better definitions will improve the statements .
point 1 can be simplified – as long as you have a dictionary in the background .
point 2 can be rephrased, so:
guessing the guessiness of guesses reached by guessing.
so you are drawing a line of distinction between deduction and mysticism. that’s the border of sanity. you’ll like it here.
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“since you’ve noted that popper is all over this thing called ‘inductive logic’”
I´m not sure what you mean by that, but if you happen to mean that Popper endorsed inductive logic, I would say that It seems quite clear to me that Karl Popper opposed to any use of inductive methods within science. Critical rationalism is based on deducing necessary consequences of the idea, and checking if the necessary consequence materialize as it should. If the necessary consequences materialize as expected, we are entitled to state that the idea has so far passed this very test of it, but nothing more. There is no induction in that method.
Regarding definition I would say that both the concept (the idea) and the context for which the idea is valid would have to be defined far more extensively than found in a dictionary. Science is much about coming up with ideas about how things work, precise definition of new ideas about how things work cannot be found in a dictionary.
By the way – I said I would revert with my thoughts about Ayn Rand; Introduction to Objectivist Epistemology. I liked it a lot – I think Ayn Rand really managed to get to the core of measurement, cognition, concept formation and the importance of precise definitions. What I didn´t understand however was why the axiomatic concepts «“existence,” “identity” and “consciousness” is so important.
Anyway – thanks for the link – I took great pleasure in reading it, and I think Ayn Rand and Popper together provides a quite robust epistemology.
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all good. you’re thinking. your brain is working. eventually every such mechanism, with enough experience, will converge.
why is the concept of existence important?
to whom and for what, obviously, are hidden in that loaded question – part of the necessary context.
to rand, i speculate that part of the importance lies in that she was debunking then current idiocies from gurus infecting their victims with doubts so they could reap the benefit (of the doubt) – which means able to enslave – to exercise power. this first entails crippling any defense, and the attack node to hit is ‘critical thinking’.
it was a fashionable meme at the time- and still is – to ‘be uncertain that reality is real’
woody allen made jokes about it: “i told my rabbi i wasn’t sure if i really existed. so he punched me in the nose and asked ‘what hurts?’ “. and ‘relativism’ totally depends on ‘reality’ being whatever the hell the guru says it is, regardless of all proof to the contrary. so rand may be giving a little extra emphasis on it cuz of that.
however, being that it is the fundamental alternative in the universe: ‘existence or nonexistence’, it can hardly be given too much emphasis to be sure it’s understood. the reason for that is because it is the root and objective basis of morality. being as how living things can die, it’s this point where the standard of values is found – at the place where this fundamental alternative exists. morality being the science of choice in the face of alternatives, this is the fundamental choice. without choice, there is no morality, right?
but maybe she didn’t emphasize it enough, if you are wondering why she did…lol.
i hope i filled in anything she missed that works for you.
identity – well, the law of identity is the basis of all comprehension. it bears emphasis. identity is what definitions do for the abstractions called words which label the entities we identify.
(p.s. – you may find dictionaries wanting- and i would love to write a proper one for the sheer fun of it – but wherever you find an adequate definition – that’s where you found it. put it in a dictionary and your idea that dictionaries ‘can’t’ turns into ‘a dictionary does’ just that fast.
it’s self contradictory to say: ” would have to be defined far more extensively than found in a dictionary”.
and finally consciousness.
did you understand that ‘sensitive’ refers to sensory data – the afferent impulses of afferent neurons.
most of these never connect to the brain.
instead they are mediated by ‘perceptrons’ which are pre.processing neurons that reduce the numerous sensory data (by about 100 to 1 in the retina or auditory sense) and pass along the perceptual information to the brain. it is important to note that perceptions are snapshots of the state of the sensorium (preprocessed, too)
consciousness – the thing we think with – is the process of identification, i.e., the formation of concepts.
here, i note, that concepts are dependent on temporal separation for abstraction of cause and effect – the basis of any heirarchy of comprehension and the source of the weak implication we know as ‘the law of implication’ where falsification can be done.
heh- play with the ideas more- you’ve had an introduction but i don’t see that you’ve become particularly proficient – and don’t expect to without practice. anything you think, say or do is a rehearsal – what you rehearse, you get good at it. rehearse critical thinking enough and thinking becomes a habit – a habit is very easy to repeat any time and very hard to break. your consciousness is your means of survival. if your survival is a good thing for you – you know what to do. exercise your consciousness.
moar!
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Here is Ayn Rands definition of axiom:
«An axiomatic concept is the identification of a primary fact of reality, which cannot be analyzed, i.e., reduced to other facts or broken into component parts. It is implicit in all facts and in all knowledge. It is the fundamentally given and directly perceived or experienced, which requires no proof or explanation, but on which all proofs and explanations rest.»
I thought the potential absence of existence, identity and consciousness was pretty much falsified by René Descartes:
dubito, ergo cogito, ergo sum
I wouldn´t use the term axiom about “existence”, “identity” and “consciousness”. I would think that these concepts are simply ideas which have passed relevant tests.
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I own you an apology for being imprecise, without thinking very much about existence, identity and consciousness – I guess I kind of understood the importance – but as things get pretty absurd without these concepts – I just did not understand why Ayn Rand found it necessary to spend so much effort on these concepts.
Anyhow, I think your explanation makes sense: “part of the importance lies in that she was debunking then current idiocies”. I also guess that one reason why she found it so important to define these concepts as axioms, was that she needed these fundamental concepts in the epistemology she was constructing – hence she might have tried to prove these concepts true – and found that impossible.
In my view – I really don´t care if these concepts are “true” – as long as these concepts have passed relevant tests, the ideas about potential absence of these fundamentals concepts has been falsified or things gets absurd without them.
Regarding definitions and dictionaries: Ayn Rand defines a concept in the following way: «A concept is a mental integration of two or more units which are isolated according to a specific characteristic(s) and united by a specific definition.»
Hence, as an example, a scientific article will contain quite a few definitions – specific to the presented piece of work – to integrate units into concepts and their contexts.
I wouldn´t think that the term “dictionary” is proper term for that kind of definitions. My dictionary defines dictionary in the following way: “a book or electronic resource that lists the words of a language (typically in alphabetical order) and gives their meaning”. Hence the common use of the term dictionary is that it defines the meaning of words – and not typically the “integration of two or more units” into concepts and relevant contexts.
I think I see your point that the moment I define a concept in writing – I kind of write a dictionary at the same time – but that would make pretty much every written piece a “dictionary” – “dictionary” would then become pretty much a useless term.
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rand was not a biologist, psychologist, programmer or animal trainer.
her definition of ‘concept’ is simply inadequate because of that.
mine is based on neurophysiology and the root of epistemology, the law of implication.
observe how it is, itself, implicit by virtue of time, i.e., a cause always precedes its effect and never the other way ’round. sweet, eh?
also, an axiom is not unprovable – an axiom is the contrapositive of a self contradiction: it is self evidently true.
for the ‘cogito ergo sum’ (which is perfect) it is self evident that if there is thinking that somebody must exist to do it. there is no other possibility. and if it were not true, we could not say anything at all about it.
so an axiom is certainly provable but it just doesn’t really need to be on account of it’s bleedin obvious.
existence is not accurately characterized as ‘an idea that’s passed some relevant tests’. it’s impossible for any other option to exist (see how that works? any option that exists must prove existence- axiom!)
i note that your dictionary’s definition of dictionary is also inadequate because ‘meaning’ is a far cry from ‘definition’
if a dog snarls at you, you are probably very clear on the meaning. grunts, groans, snickers, sneers – all have meaning but none have a definition. the word for that is ‘semiotics’ and is distinct from ‘language’
so here’s the definition of ‘definition’: the set of characteristics which distinguishes an entity from all other entities – it’s identity.
i had rand with my mother’s milk, and i’ve not been stagnant, i stand on her shoulders and she was no midget at this.
are we having fun yet?
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I´m certainly having fun, many thanks for engaging with a novice. 🙂
By the way, I´m heading for fishing, just for you to know the reason for inadequate feed-back to your excellent comment. Have a nice weekend.
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I thought you might find this thought provoking, if you aren’t already familiar with it:
http://zimmer.csufresno.edu/~johnca/spch100/4-9-sapir.htm
one supreme example of ‘determinism’ i’ve discovered – much to my shock and consternation:
what color is the sun?
the almost universal tendency in america is to answer this incorrectly based strictly on ‘things one has heard’ and absolutely in contradiction of ‘what one has actually observed with his own eyes on a daily basis for decades’ or ‘what one can logically prove’
logically, we know what is the definition of ‘white’ and that it is the solar spectrum.
but everybody goes for the yellow crayon.
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“The fact of the matter is that the “real world” is to a large extent unconsciously built on the language habits of the group…We see and hear and otherwise experience very largely as we do because the language habits of our community predispose certain choices of interpretation.”
This reminds me about a definition of organization culture which I have found useful:
One helpful, though general, definition offered by Edgar Schein of MIT’s Sloan School of Management is that organizational culture is:
“a pattern of shared basic assumptions that the group learned as it solved its problems of external adaptation and internal integration, that has worked well enough to be considered valid and, therefore, to be taught to new members as the correct way to perceive, think, and feel in relation to those problems.”
I think it is pretty clear that what we perceive depends on what we are looking for. Language is our way to think and communicate about the world around us, hence language also affects how we perceive the world around us.
This also reminds about the summer I visited Barcelona with my kids. At La Rambla (The main street) I said to my kids that there were pickpockets. I knew, because I had been there once before – when a pickpocket failed, and was caught in action – by the victim. I proposed to my kids that we could try to see if we could spot one. Suddenly I spotted one and pointed him out to my kids. He crossed through a group which passed along the street – obviously without any good reason, other than to see if he could get into a situation where he could steel something. If I hadn´t been looking for a pickpocket I would not have noticed this guy.
I just think that we only see what we are looking for and are able to perceive. Our language plays a central role. Our basic assumptions influence what we perceive and what we think about it. Our basic assumptions are typically expressed in a language.
The following quote comes to mind:
«In the case of science – I think one of the things which makes it very difficult – is that it takes a lot of imagination – It´s really hard to imagine all the crazy things that things really are like!»
– Richard Feynman
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yup. your operating system has a metaphysical structure, too.
beyond the metaphors, it’s linnean taxonomic tree, of course.
the same structure can be expressed nicely in terms of set theory.
and what’s a dictionary, then, but a tree of linguistic venn diagrams?
here’s something fun:
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oops- didn’t complete the thought before striking POST…
so we looked at the first axiom: existence exists
after that we observed the second axiom: a thing is itself (the law of identity)
and just now i touched on the third axiom: a thing is a kind of thing.
words have definitions – not just emotional freight.
that’s how you know when somebody is trying to feed you reddish green bean bran.
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Thanks for that order of adjectives, I did not know about that. A polite native English speaker once told me that he understood perfectly well what I wrote – but he just wouldn´t write it the way I did. Anyhow – I gotta keep going. 🙂
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i found more on that:
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i just invented a new word: ‘plagiarism’
🙂
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I don´t get it – “plagiarism” isn´t a new word?
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think about it. it really is a funny joke.
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🙂 🙂 🙂
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did you see rud’s post on wuwt?
he says:
” And ‘truth’ cannot ever be proven (Gödel’s theorems)”
which i find offensively stupid and i challenged him on it but after a second’s consideration, i don’t want to touch that tarbaby. he would double down on the self contradiction and the lie cuz he’s a fraud by choice and inclination. none of them over there would become any wiser.
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I think you nailed it:
“truth is that which, in the defined context, cannot be contradicted. that’s the truth about truth”
That´s all there is to it.
Even if Rud got it wrong, he got a lot of things right too – I would not characterise him as a fraud in general.
Anyhow:
This is a truth about gravity: if I drop an object it will be attracted towards the earth.
This is also a truth about gravity:
300px-NewtonsLawOfUniversalGravitation.svg.png
Interestingly we do not seem to know the gravitational constant precisely (ref. Wikipedia on Gravitational constant):
«The gravitational constant appears in Newton’s law of universal gravitation, but it was not measured until seventy-one years after Newton’s death by Henry Cavendish with his Cavendish experiment, performed in 1798 … In modern units, the density that Cavendish calculated implied a value for G of 6.754×10−11 m3 kg−1 s−2.”
“The accuracy of the measured value of G has increased only modestly since the original Cavendish experiment. G is quite difficult to measure… Published values of G have varied rather broadly, and some recent measurements of high precision are, in fact, mutually exclusive. This led to the 2010 CODATA (Committee on data for science and technology) value by NIST (National Institute for Science and Technology) having 20% increased uncertainty than in 2006. For the 2014 update, CODATA reduced the uncertainty to less than half the 2010 value.”
«In the January 2007 issue of Science, Fixler et al. described a new measurement of the gravitational constant by atom interferometry, reporting a value of G = 6.693(34)×10−11 m3 kg−1 s−2. An improved cold atom measurement by Rosi et al. was published in 2014 of G = 6.67191(99)×10−11 m3 kg−1 s−2»
The difference between the estimate by Fixler et al. (2007) and Rosi et al. (2014) is 0,3 % !
The thing about quantitative theories is that there are measurement uncertainties and systematic errors, which may become reduced over time.
Can we say both that an estimate is true and that it has an uncertainty range?
I think so, and by your definition of truth, I think we can.
It cannot be contradicted that the Gravitational Constant in this theory is known to be within, say, a range of 2 % of a central estimate. Hence it is true, isn´t it?
Can we say that we know the true functional relationship, the true value of a constant and that we can never find a more accurate representation, or estimate, of how things work? Normally not.
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i note that you describe gravity as an ‘attractive force’.
why?
when you suck water up a straw- is it attracted to your mouth?
heh- maybe forces are all repulsive and ‘attractive force’ be oxymoron?
how can we find out?
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I describe gravity as an attractive force because my dictionary described it that way – and it has been a successful way of thinking.
Fluid in a (horizontal and uniform) pipe will tend to move towards a location with lower pressure.
I guess I could just as well have said that fluid will try to loose as much energy as it can as fast as it can.
Bernoulli made a very successful theory about fluid flow, the theory can be used to design systems which work the way intended.
I like the perspective of Richard Feynman on theories:
“The electron is a theory we use; it is so useful in understanding the way nature works that we can almost call it real.” – Richard Feynman
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in the example of the straw, there is no attraction-
air pressure is higher outside your mouth, so air pressure forces the liquid up the straw.
it is easy to show that this is so. a repulsive force pushes the liquid.
what if gravity is similar? a kind of brownian motion of infinitesimals that makes things move around except where they are shielded by mass from the battering.
how would one distinguish that explanation from the ‘attraction’ idea by experiment?
it’s still a puzzle to me, anyhow…
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Here is the picture (I hope)
Newton´s law of universal gravitation:
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yes, you can define a context and express a truth. it’s dropping the context where the trouble happens because there can be no validation of a statement or idea without the context.
and it’s a common dirty trick pulled on those who don’t know it’s a blunt instrument.
e.g.
who would argue against somebody who says “everybody should have enough to eat! – especially babies!'”
but there is no context to it. whose babies? where? does the food fall from the sky? who gets robbed to pay for it?
so by accepting that nonsense uncritically, the unwary person has simultaneously accepted any damn thing else – theft being the least insidious thing that emerges from the relativistic mists where the goatse mind gurus cast their spells – they have accepted nonsense as a superior argument – cuz they can’t prove otherwise! same way we know the spaghetti monster created the universe- except himself- cuz he wasn’t falling for any reductio ad absurdam fail!
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i found something on goedel’s incompleteness theorem
it is commonly used as a means of undermining the concept of truth, per se- one of the tools of the slaver in suborning his victims so they substitute his judgement for their own.
from https://en.wikipedia.org/wiki/Gödel%27s_incompleteness_theorems
“Gödel specifically cites … the liar paradox as semantical analogues to his syntactical incompleteness result in the introductory section of On Formally Undecidable Propositions in Principia Mathematica and Related Systems I.
The liar paradox is the sentence “This sentence is false.”
An analysis of the liar sentence shows that it cannot be true (for then, as it asserts, it is false), nor can it be false (for then, it is true)…”
i call this a spinner. here’s why.
you can make this statement with the simplest logic gate there is- the inverter.
simply plug the output back to the input.
if the input is 0, the output is 1 – and that goes back to the input to make it be 1 so the output will become 0.
when you do that in real life (and it is done because it’s useful!) you get an oscillator whose frequency is limited by the gate delay of the chip.
it is an oscillator.
now, static states consume little power but changing states consume much power.
a cmos circuit that doesn’t change consumes precious little power as the gates are capacitative – but when it’s clocking fast and changing states, yes- then there is a constant current flow charging and discharging the gates
the purpose of a spinner is to tie up the processing power of a brain by consuming energy uselessly- that causes lag in other processes – especially those required for critical thinking. that’s the purpose and use of a spinner.
and that’s what rud is infecting people with.
his intentions are irrelevant and i don’t care to guess about them.
the results he aims at are absolutely harmful to human minds.
and most importantly, what rud and other gurus deliberately don’t want to mention, goedel said:
“The truth of the sentence … may only be arrived at via a meta-analysis from outside the system. ”
in other words, what rud said was a lie.
Goedel did NOT say ‘there are unprovable things’
goedel was quite correct to observe that there are statements that require a larger context to resolve the truth of them.
and so, we simply state that the sentence ‘this statement is a lie’ is a self contradictory statement.
that’s all. simple. done. it’s resolved.
thus it’s safely neutered and can’t make your head spin.
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Thanks a lot for that very thoughtful and useful analysis. I like it a lot.
Makes me think about how much more time and energy it takes to point out deceptions than it takes to present them.
«A lie can travel half way around the world while the truth is putting on its shoes.»
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if there were a better argument for NAKED TRUTH, i don’t know what it is…lol
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🙂
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i have something new for you today.
i’m gonna describe something i call The Guinness Effect.
it’s human nature to remember limits (definition, btw, comes from the latin FINIS, meaning end – it’s what we do to digitize the analog universe so we can have discrete units we can use for thinking and logical computation. logic is not analog. to define is to set limits that bound a category)
people find it economical and useful to remember limits and the effect (i don’t know if anybody ever gave it a name before) is exploited by all and sundry. it’s a primary consideration for rhetorical persuasion, advertising and propaganda. it’s the basis of many ‘talking points’
the latest example that triggered my attention was:
“This was the hottest August in the 1880-2016 record, surpassing the previous record set in 2015”
ooh. superlative! i can see the EST! Everything else is less than the most!
by 0.09 F. such a small lie. because that is not a measurement – it’s an arithmetical artifact of averaging.
when i measure 1/8 but state it as 0.125 – that might fool somebody into thinking my ruler has graduations in 0.001 but no- no freakin way. but that’s another topic for another day…
i made an invention recently and i totally exploit the Guinness Effect.
my thing is the lightEST, fastEST, hottEST, smallEST, firstEST and mostEST.
that’s how it is to be advertised. Everything else is less than the most. mine is bestEST.
and if there were anything about it less than anybody else’s- i’d make the effort to seize the highEST ground even if it were merely for the talking point
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Fabulous! 🙂
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“and if there were anything about it less than anybody else’s- i’d make the effort to seize the highEST ground even if it were merely for the talking point”
Another effect, which might be related, is that it seems to be human nature to ignore negations – the word: “not” – like in:
” I admit that I did not live up to my high high moral standard”
Those who look for an apology in that statement might see it, those who don´t – and maybe even those who do look for an apology – may tend to perceive that I have high moral standards. (At least that is my claim, which might off course be unsupported).
Instructors in any sport will know that, and emphasize on showing and explaining how things are supposed to be done. If a sports instructor demonstrates how things are not supposed to be done, that´s exactly what the athletes will tend to do. That is why I tend underscore the word “not” whenever I have to use it.
Now, consider the statement by The National Snow and Ice Data Center NSIDC:
“A new record low September ice extent now appears to be unlikely”
That statement is part of the following:
“A cool and stormy Arctic in July
August 3, 2016
An extensive area of lower than average temperatures in the Central Arctic and the Siberian coast, attended by persistent low pressure systems in the same region, led to slightly slower than average sea ice decline through the month. The stormy pattern contributed to a dispersed and ragged western Arctic ice pack for July, with several polynyas beginning to form late in the month. A new record low September ice extent now appears to be unlikely.”
It is kind of deceiving isn´t it?
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yeah- that kind of squid ink is for obfuscation, for sure.
i remember the first time i twigged to the nature of words qua words.
my mom told me to go fetch something off the bedside table that was on top of a kleenex box.
i went in there and didn’t see it.
so i repeated to myself exactly what she said. cuz she never spoke falsely.
when i got to the part ‘on top of’ i looked ‘on top of’ and there it was.
i can’t really explain what it was i was doing before- but it wasn’t following the meaning of the words
and i didn’t find what was there until i did parse that sentence properly.
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Here is one kid who didn´t notice the word not – or don´t:
🙂
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Gnomish
following your input on Ayn Rand, I revised theorem #4. As mentioned above, I never bought into Karl Popper´s idea that definitions were not that important. I think precise definitions are extremely important, anything might pass scrutiny if the concept, or the context, is poorly defined. This is quite obvious, Karl Popper even says it himself:
“it is still impossible, for various reasons, that any theoretical system should ever be conclusively falsified. For it is always possible to find some way of evading falsification, for example by introducing ad-hoc an auxiliary hypothesis, or by changing ad hoc a definition. It is even possible without logical inconsistency to adopt the position of simply refusing to acknowledge any falsifying experience whatsoever. Admittedly, scientists do not usually proceed in this way, but logically such procedure is possible»
As mentioned above, I think Ayn Rand + Karl Popper might to be a powerful combination.
Anyhow, I still think it would be nice to have a set of theorems summarising a proper scientific method. I also think that something like that doesn’t really exist. I also think I got a somewhat decent starting point for such set. I also know that my proposal must be far from excellent.
However, I know that my theorems ain´t perfect, for all that I know, they ain´t even useful. However, I have been looking for some scrutiny. From what I have seen, I am convinced that you would be able to provide the kind of scrutiny I´m looking for. What I´m saying is that I would appreciate a lot if you would bother to expose these theorems to the kind of scrutiny I know you are capable off. Be my guest – if you like. Anything surviving your critical view it must be worth something, I will appreciate your input. 🙂
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can i put that on my CV? 🙂
sounds like an interesting and worthy project.
well… let me go thru them one at a time and get oriented-
i’ll try to make a preliminary comment-
this is gonna be ‘brainstorming’ and the rule for that is to collect ideas – they can be sorted and criticized later- first is to catch as many as possible in a net so there’s something to sort and criticize – that’s often the hardest part.
rule 1: hmm… sounds almost like acknowledgement of ‘brainstorming’?
rule 2: is a not too precise restatement of the law of identity. it’s saying ‘self contradictory statements are
false” logic is the practice of non-contradictory identification. so it’s it’s sort of low resolution
parsing that overlaps these 2 mutually consistent but conceptually distinguishable ideas
rule 3: is a poorly constructed version of the definition of definition.
how about i do just 3 at a time to break up the task into bite-size pieces? these rules will be building a foundation and a structure on top of it- so it won’t hurt to refine the elements as much as possible at the outset, do you think?
it looks like a definition of terms must be part of this, too. so maybe create a list of them as needed in parallel with creating the rules of science?
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you are, essentially, creating a metaphysical structure from the bottom up rather than top down. it’s a good plan to formalize the epistemological principles which will be used to validate anything you think up.
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Thanks so much for your response 🙂
If you think it is worth it, I would appreciate your effort a lot. Anyhow, we will have the fun of it. The number of theorems, or the structure doesn´t really matter to me. However, I think it might be an idea to keep it simple, being bullet proof won´t be possible – and probably not necessary. I still believe it would be worthwhile making the main principles of science easily available.
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have no faith. you will find that bulletproof is easy.
we’ll go past objectivism to absolutism and not miss a beat.
yah- i think it’s worth it – i can’t think of anything more important for a human than his own survival AS A HUMAN.
and so i’m gonna have to define human nature but i don’t want to put that in type, here, just yet.
you’ll understand why as we get further into it. be assured it’s easy. it just needs the definitions of the concepts to be used.
but one of the distinguishing characteristics of H. sapiens is that his basic too of survival is his reason.
and what you are proposing is on the order of a ‘cliff’s notes’ users’ manual for that.
how can that be trivial?
yeah, there may be a change in the number of rules – that may be a a somewhat arbitrary choice.
but i don’t see any problem with you outdoing popper without burning any braincells.
the ideas will be simple in concept, breathtaking in scope. that’s worthy.
nobody will care except those who are already there – but no matter. if you lived on a deserted island it would not be less important to understand, explicitly, how to use the mind for reasoning.
do i proceed with items 4 – 7 now or do you want to dissect the first 3 now?
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Feel free to address several rules at the time, for related rules that might necessary. However, it might be simplest for the discussion to address one rule at the time.
Regarding rule 1.
“There are no rules, whatsoever, related to how an idea might come about.”
My idea with rule number 1 is to emphasise that it doesn´t really matter what kind of method is used to arrive at the hypothesis, theory, idea or even device for that sake. What matters, is that the idea – once it is there – meets necessary criteria for being useful for reliable predictions.
This is the relevant section from The logic of scientific discovery.
“The initial stage, the act of conceiving or inventing a theory, seems to me neither to call for logical analysis nor to be susceptible of it. The question how it happens that a new idea occurs to a man— whether it is a musical theme, a dramatic conflict, or a scientific theory—may be of great interest to empirical psychology; but it is irrelevant to the logical analysis of scientific knowledge.”
As an analogy, I often have to relate to “black boxes” in my profession. However, these devices (“black boxes”) will have a stated capability within a stated range of conditions. Obviously, I have an idea about how they work, I understand the fundamental principles they work by, but I don´t know any details about how it came about or details about the software or electronics. I would never be able to verify that the instruments work within it´s stated capability by analysing every detail of it, and how it was invented or made. What I can do, however, is to take one of these devices and put it to an independent test. I can check whether this device works in accordance with it´s claimed capabilities. If it does, I can use it for reliable prediction, or actually measurement. (And yes, it might be a bit far-fetched, but I think that a measurement can be regarded as some kind of real time prediction. I see that it is a contradiction to use the term prediction about a measurement which is really an observation. One way out of that contradiction might be to think that the rules are about both reliable prediction and observation. )
By the way, I live in Europe, so you have an idea about when you might expect my responses. I also tend to let things rest or mature a bit before responding.
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A list of definitions seems necessary – it crossed my mind – but I abandoned it as I prioritised putting up the list of main principles. With your eventual contributions I guess it can be done.
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Regarding structure, I think the following structure may work:
– Rule
– Definitions
– Reason for the rule
I have been working a bit with rule #1 along these lines:
Rule #1:
«There are no rules related to how an idea might come about. The rules are there for judgement of the idea once it has been propounded.»
By rule is here meant: a requirement which is intended for judgement of the ability of an idea to provide reliable predictions or observations.
By idea is here meant: any idea, hypothesis, concept, model, theory, or device which proposes a functional relationship between two or more measurands.
By measurand is here meant: a well-defined physical quantity that can be characterised by an essentially unique value. If the phenomenon of interest can be represented only as a distribution of values or is dependent on one or more parameters, such as time, then the measurands required for its description are the set of quantities describing that distribution or that dependence.
By measurement is here meant: the identification of a quantitative relationship established by means of a standard that serves as a unit. Entities (and their actions) are measured by their attributes (length, weight, velocity, etc.) and the standard of measurement is a concretely specified unit representing the appropriate attribute. The requirements of a standard of measurement are: that it represent the appropriate attribute, that it be easily perceivable by man and that, once chosen, it remain immutable and absolute whenever used.
(Ref. Ayn Rand – Introduction to objectivist epistemology.)
Reason for rule #1:
There will be a vast number of ways by which an idea might come about. There will also be a vast number of possible errors which can be done while making an idea. Hence it will be near impossible to confirm the capabilities of an idea by analysis of how it is invented or made.
On the other hand, if the idea is put forward in an appropriate way it may be possible to test by observation whether the idea performs in accordance with its stated capabilities or not. Hence, the rules are there to judge whether an idea is put forward in a way which is appropriate for judgement of whether the idea is useful for reliable predictions or observation within it´s stated capabilities or not.
—
Hope you are right, in thinking that the quest might be achievable. I get this feeling that the more I write, the more words I have to use, the more definitions will be required.
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i don’t have a wordpress account to click LIKE for that but i sure do admire it.
you dropped the clutch and popped a wheelie on the road of reason just now…lol
i wane metaphorical- i mean your exposition was awesome. you KNOW wtf you are talking about.
it’s really fine. with that sort of reasoning i can admire my species.
that was really really well done. i want lots more of that, please.
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Thanks a lot. 🙂
Lets: “Head out on the highway”
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– Rule
– Definitions
– Reason for the rule
that’s a good scheme. i don’t see anything left out that matters.
i am completely convinced you will be able to reach any level of understanding you care to. you have all the necessary equipment and you know how to use it. it’s a thing of beauty.
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4 – truth exists in some context boils down to:
the process of deduction requires that statements be in the form of a logical proposition.
‘if A then B’ requires the ‘if A’ predicate to make it possible to validate.
and then, when you do that, you can invoke the corollary ‘if -B then -A’ to scratch popper’s itch.
note that time provides this relationship between cause and effect. it’s not a semantic trick.
‘prediction’ and ‘deduction’ seem indistinguishable…
5 – for a statement about the physical world must have a physical referent
6 – is a confabulation of the definition of definition with the law of implicaton
7 – statistics… i might not be much help here. in my view, statistics is a form of numerology because the premise is that one must ignore the individual case (and every individual thing is an individual case), it requires generalization of a population (ontological collectivism?) and can not be used for deduction because rule 5. the games you can play with ‘fuzzy logic’ and markoff chains do not produce a deductive chain.
i believe the demand for induction is proportional to the lack of understanding, i.e., it’s really an indication of lack of knowledge, not a new form of knowledge. There is really no physical referent behind ‘probability’ except ignorance. When you flip a coin, it comes down heads or tails. If you know enuff you can know the outcome. If you don’t know enough, you are gambling on it.
the I Ching was the earliest effort at formal attempt at ‘statistics’ (probabilities if you wish) of which i am aware. It may have been important to gamblers. It may have simply been ‘the book effect’ – but it was only based on counting in binary to 64. it explicitly listed all the possible combinations of 2^6. So another term for ‘probabilities’ is ‘possibilities’. With that small modification,, then, true deduction becomes possible.
There is no magic to it. Even tho peasants might be awed…lol
now i get to digress and describe ‘the book effect’
once upon a time there were few books. there were no printers. they had to be done by hand.
that made them costly.
few could afford one and few were literate.
when a man stood before them and cracked open a brick of a book- suddenly that man had words flowing thru him. he could talk for hours – a feat impossible to an ordinary person – why- it was as if the man were a conduit for a higher power that suffused him with thoughts and ideas all so impossibly well organized it boggled the peasants’ minds.
there was a use for that kind of book. it gave you amazing power of loquacity you could easily claim as divine.
similarly the I Ching would have impressed the ignorant (who could not count to 64 in binary)
you’d throw your sticks and the gods of chance would determine the outcome- and then you could look it up in this BOOK! no matter what you threw – the book knew about it! you could turn right to it.
so many possible ways you couldn’t keep track of them- but the book knew.
to this day, ‘publication’ confers status. one infers a person has a formidable mind if he has erudition and loquacity and puts it in print.
‘speaking’ engagements are not unusual, still, and it’s the rare performer who gets through a speech or presentation without written words to channel.
so historically and to this day, printed matter is regarded as more credible and important than speech.
when you ‘sign the papers’, this somehow makes your ‘word’ into more of a committment than it was without ink. there is no such thing as ‘hearsay’ with something in print. there is a qualitative difference in the outcome if you try to cross a border with no documents (to prove who you are, no less…lol)
and so- you can think up the most irrational bullshit – then print it- and suddenly it acquires a new level of credibility or importance. magical.
‘defending the constitution which protects our rights’ < get literal on that. defend a piece of paper with ink on it? an inky parchment protects rights?
so there's a whole lot of magical thinking around anything printed. but being printed is not evidence of validity. a story of ganesh doesn't constitute evidence of ganesh; only that somebody can write a story.
statistics, aka 'odds' or 'probabilities' are magical routines to deal with what one does not know. cause and effect are undefined (or given some magical name).
'possibilities' are something one can know and define and do allow deduction. possibilities have a corrolary set of 'impossibilities'. that allows certain deductions.
http://www.reocities.com/Athens/Aegean/1835/kandide.html
my first webpage was a book. plz pirate relentlessly.
oh, so much work – i need to be granted a monopoly so i can send armed thugs to stop anybody from copying it! without that i would never have written it ! (one example to falsify, right?)
copyrot – cuz the written word has magic powers and you can't let everyone just run amok with it or there would b chaos!.
it would interfere with the immanentization of the eschaton! all hail the mighty narrative, Manifesto!
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“They sat down at the end of a long table in the non-farting section” 🙂 🙂
Can´t copy that into my work – gave me a good belly laugh though. D)
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“This is a work of fiction. Any resemblance to actual persons or incidents is real or imagined.”
I like that – fiction is a combination of real and imagined things. 🙂
Just like much of so-called peer-reviewed science these days!
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ah… i may as well throw this in now as it will form the basis of whatever you construct in the way of a ‘user’s manual for the mind’
SOME DEFINITIONS:
Philosophy: Love of understanding
Metaphysics: study of the nature of existence
Consciousness: identification
Understanding: Conception of an implication or set of implications
Sanity: a metaphysical view that corresponds one to one with reality
Reality: the largest possible context of existence
Science: the systematic discovery of truth
Truth: an idea that can not be contradicted by any other implications within its context
Logic: non-contradictory identification
Language: a system of words for communicating ideas
Thinking: manipulation of ideas
Idea: a concept or set of concepts
Concept: a set of implications
Implication: the relationship of a cause and its effect
Word: a symbol with a definition
Definition: The set of those properties or characteristics that distinguish a thing from all other
things, i.e. a distinct set of implications
Symbol: A perceptual unit designating a set of implications
Label: to define a symbol – or- the token for an idea or concept
Money: a commodity that has special utility as a token of wealth. the special characteristics of money are:
infinitely divisible, indestructible, uncounterfeitable, comparatively rare, easily identifiable/verifiable. these characteristics make it useful as a store of wealth and as a medium of exchange. nevertheless, it is a token- not the wealth itself.
Wealth: current values
Ownership: exclusive control of a property
Property: a characteristic of something- or- a thing that is owned
Right: a property acquired by some virtue
Humor: the art of assembling contradictory elements into an apparently consistent entity
Joke: an idea that appears self-consistent until enlargement of the context reveals a
contradiction
Virtue: the means used to gain or keep something of value
Value: synonym for “good” – something that is consistent with the nature of an organism
Sacrifice: the exchange of something of value for something of lesser value, i.e. the negation
of a value
Bad: contradictory to the nature of an organism
Love: the admiration and respect one feel for someone who possesses the virtues and
qualities one most admires in oneself
Art: the confection of symbols into a consistent concept
Beauty: The degree of consistency among observed implications
if these definitions are acceptable then the structure you are building can really begin. if not, then they need to be adjusted until they are made acceptable. it doesn’t matter whether one uses inches or centimeters- as long as the rule is universally applied, all the relationships will be the same.
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A great set of definitions – thanks, I sincerely hope that I won´t need them all within the scope of this work.
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you will need definitions, though. it’s the only way reasoning can be performed.
you’ll need them for every word you use. analogies are always incomplete and inaccurate. one can’t literally ‘see the point’ of an argument. That is, itself, a metaphor which are as good for making a point as they are for confusing one.
Imagery is not adequate for argumentation- a monkey can be taught to use sign language- a metaphor is defined as the use of imagery- it is therefore semiotic in nature- semiotics can never support the use of logic- observe that “I see” refers explicitly to the perceptual level of consciousness where logic can not be done.
That’s why we have words- they are the only tools that can serve for the purpose of deduction- as long as they ARE words- i.e. they have definitions- because otherwise, they can be credited with no more meaning than an animal grunt.
can’t “explain” without words, or “understand” without logic— example
Take two words: BRASS and GRASS
They LOOK very much alike… both black marks on a piece of paper… same shapes, mostly- but the difference between their meaning is great- furthermore, neither one looks like what it represents….
Monkeys can be taught sign language because the symbols involved have a resemblance to the referents- perceptual in nature – NOT suitable for logic because not to the necessary degree of abstraction
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I see your point 🙂
Wow – you write fast and think fast.
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rehearsal. practice.
and keeping copious notes – prosthetic substitute for genius
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LIFE:
anti-entropic system that replicates!
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How would you define “identification”?
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there are 2 ‘realms’ of consciousness i find useful to distinguish.
the automatic form of learning is accomplished by association- every multicelled animal learns this way.
in this context, identification is the formation of a unique set of associations for any particular entity and could very well be replaced by the term ‘recognition’
language is a meta layer of consciousness mediated thru concepts which are abstractions that have labels that have definitions.
in this context, identification is the act of definition.
logic can be performed on this meta level using words which allow associations to be validated or falsified.
identification is the act of labeling and defining an entity.
the premise of entity (which is an axiomatic notion as previously proven and discussed) has a couple corollaries:
a thing is itself (and not any other thing)
a thing is a kind of thing (a subset of a broader category)
the first corollary is where determinism dies but that’s not a rationale for the erroneous notion of ‘probability’.
the premise of probability is ignorance which is the basis of faith and of fear.
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Thanks a lot – that was very useful.
I searched through Ayn Rands introduction to objectivism, but couldn´t see that “identification” was properly defined.
The use of the term probability may also be recognition of the fact that that the value of most measurands cannot be determined exactly.
In an a posteriori quantification of uncertainty, by comparison of the measurement result with a reference of known uncertainty, I will have a pretty good basis for establishing a measure of probability.
A a priori estimation of uncertainty is a different animal.
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rules 8, 9 and 10 are about inductive ‘reasoning’, i.e. postulates without proofs.
i wish to pass on those – at least for now.
phlogiston ‘theory’ is supported by observation. one can see a flame. it’s real.
what was wrong about it was the cause and effect relationships were erroneous.
so induction by statistical observation is susceptible to that kind of error by its very nature.
in a way it’s like art – a way of groping toward a concept. it’s not gonna produce an identity but it may lead to one.
i’d put that all under rule 1 and leave it alone…lol
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That´s fine. I plan to redo 1 rule every 1 or 2 day´s and see where it brings me.
The problem of induction deserves some attention and probably an example in addition to the black swan example. I think I got an idea about it.
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k.
if you’re really gonna do it, i really wanna see it.
it looks like you’re more than half way- a few loops thru the refinement cycle might do it.
i’ll check back in a couple of days. you’ll want some quiet to think.
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Draft for a new rule # 2:
Rule # 2:
«A scientific idea must consist of a well-defined concept having a well-defined capability of prediction within a well-defined context.»
Definitions for Rule # 2:
By concept is here meant: a set of measurands and their functional relationships
By definition is here meant: the set of essential properties or characteristics that distinguish a measurand or a functional relationship from all others
By capability is here meant: a measure of the closeness of agreement between a prediction and an observation
By prediction is here meant: an a priori quantification or characterization of a measurand for a particular set of conditions
By condition is here meant: a set of those things which have an influence on the capabilities of the concept
By observation is here meant: a quantification or characterization of the properties of a measurand
By context is here meant: a range of conditions within which the concept is claimed to perform within stated capabilities
Reason for rule # 2:
The purpose of definitions is to ensure that an idea is intersubjectively understandable and suitable for intersubjectively application or scrutiny. Without well-defined measurands and well-defined functional relationships, the scientific idea would not be objective – the concept will not be intersubjectively consistent and replicable.
Without well-defined capabilities, it will not be possible to judge whether the concept has the potential to be useful for a particular application or to judge whether the idea performs within it´s stated capabilities or not.
Most scientific ideas tend to be valid within a limited range of conditions – like e.g. temperature. Without some knowledge about influencing conditions and the range of conditions within which the scientific idea performs in accordance with its capabilities it will not be possible do judge whether the concept has the potential to be useful for a particular application or to judge whether the concept performs within it´s stated capabilities or not.
Vague definitions are the hallmark of pseudo-science as it opens up for ad-hoc changes of definitions to save flawed ideas.
—
Eventually, I will collect the new rules in a new article. However, I think I´ll just post the drafts here as long as it works.
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how is ‘measurand’ distinct from ‘parameter’ (if it is)?
how to distinguish between ‘prediction’ and ‘deduction’, if you are?
you’re parsing like a kendo master now
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Thank you, Gnomish Sensei
Good shot, I kind of sensed that the terms parameter and variable needed to be defined. I have already used the term parameter in the definition of measurand (stolen from the freely available standard, «Guide to the expression of uncertainty in measurement» by the way).
By parameter is here meant: a measurand which is regarded to have a fixed value in the context it is used
By variable is here meant: a measurand which can take on two or more values in the context it is used
Regarding deduction, I was about to say something like:
By a priori quantification is here meant: a quantification of a measurand which is deduced from the concept by mathematical rules and deductive logic, before the measurand is measured or observed by other means for comparison
but I think I will let it be for a while. If I define deduction as following strict mathematical rules or strict logic, I guess somebody will come dragging with fuzzy logic, artificial intelligence or something like that and claim that it isn´t strict deduction but it belongs to a new paradigm which most people won’t understand works perfectly fine.
I also guess that my black box analogy kind of opened up for complex models which cannot be fully comprehended or analysed in detail, but they can still be tested by comparing their prediction with observations.
I will have to let it rest and mature for a while, I guess it will pop up again rather soon.
Keep shooting 🙂
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don’t want to bog you down while you’re brainstorming this because you’re on a roll – you should go with it and not lose any momentum.
some mental exertions take a lot of time to get the disparate elements in play- like juggling – and it’s only when you get that going that you can make progress. time for editing can come afterwards.
i don’t know what your experience is for the empirical referents you are building on and i could use a little more concreteness to understand better – but i will be pleased to wait while you run your process until there is time to examine the results.
so far i’m seeing a strong thread of statistical induction in the theme. dealing with ‘black boxes’ is not a problem for me per se. but i have to admit a bias against it because idea: set of inter-related concepts, ‘concept: a set of implications, implication: relationship of cause to effect.
fuzzy logic isn’t… the fuzz is imposed. noise seldom makes music better, musically. ah- sorry for the metaphors…
that doesn’t mean a deterministic universe. ‘possibilities’ (which term i prefer to ‘probabilities’) are useful for a calculus, yes. but i digress…
Information theory was invented by a Bell Labs genius named Claude Shannon. He was studying signal to noise ratio and found it necessary to define ‘signal’ and ‘noise’. He invented the word “bit” to signify the “atom” of information.
you may have to invent a new word or two before you’re done…lol
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One particular reason why I hesitated about deduction was that I know that random number generator is used in MonteCarlo method .
Hang on, the most important thing to know about statistics, in this context, is that every measurement has an uncertainty and that the uncertainty estimate is a way of indicating the probability of finding the true value at a certain distance from this average value. The height of the curve in the diagram below (the height of the probability density function) is proportional to the probability of finding the true value at the corresponding distance from the measured value:
That is pretty much all there is to it – the blue curve indicates a high probability of finding the true value close to the measured value (low uncertainty). The yellow curve indicates a lower probability of finding the true value close to the measured value (higher uncertainty). (The green curve indicates that there is a systematic error in the measurement.)
I will not make it much more complicated than that.
And then to the clue. Computers can only use a single value for each input in each calculation cycle. It is generally impossible to feed directly into the computer the measured values together with their probability density function to see how the uncertainty in the input variables propagates through a computer model and causes uncertainty in the output value – uncertainty in the prediction. The Monte Carlo Method is a way around this, by using a random number generator in combination with a probability density function for each input variable and run thousands of computation cycles.
More on probability density functions here: Normal distribution
Anyhow, deduction is in! And I don´t think there will be any room for statistical induction.
Now to the fun part – yes I could use a new word. I need a word for the following definition:
By «new word» is here meant: a central estimate for a measurand, determined as the average of a number of measurements, together with a corresponding probability density function which provides the estimated probability of finding the true value at any distance from the central estimate
Yeah I know, I´m loosing momentum, but it was quite important for me to sort this out – if I did.
Anyhow – I will be cut off from writing until over the weekend. So long.
I´m very determined to work this through. I´m having fun 🙂
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i will have some comments on this bit (statistics) later on. now is not the time for that diversion, tho.
but i did find something that is fun- and maybe diverting in that sense…lol
http://www.worldwidewords.org/articles/exceedance.htm
i loved his objective analysis.
i love tools. some are atomic (made of atoms) and some not (words, for example)
words are yout tools of cognition (rerun, right?) so they fascinate me.
and i’ve noticed something i call ‘the pidgin effect’
a quick description of that is:
white man heap strange – speak well and he doesn’t listen. talk funny and him all ears
(cashiers would routinely hold up the line to keep my g/f talking in her british accent)
(henry kissinger lived in the usa since age 12 but he never gave up his heavy churmann accent – for a reason)
(examples abound)
so, besides tribal signaling, neologisms can be done just to get attention.
tho that can also backfire via what i call the ‘mascara moustache’ effect. that’s when a young man darkens his lip hairs to make himself look more mature but everyone sees what he did so it merely betrays his failed aspirations) (these days, 12 yr old boy wants boobs…)
i will return to the category of ‘non.atomic tools’ later to discuss statistics.
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Nice article on uncommon words. I look forward to your take on non.atomic tools.
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I got a new rule regarding uncertainty:
Rule # Uncertainty in observations
“All measurements are associated with some uncertainty. A proper presentation of a measurement result consists of:
– A value
– A well-defined non-standard unit or an international standard unit
– A corresponding probability curve
A proper measurement report also provides:
– Traceability for the measured value – when such traceability exists
– The information and arguments used to arrive at the probability curve”
By “probability curve” is here meant: a mathematical function defining the probability of finding the exact value of the measurand within any range of values near the reported measurement result.
By traceability is here meant: an unbroken chain of calibrations to the definition of the unit.
By calibration is here meant: a comparison of a measurement with a traceable reference having a known uncertainty.
By reference is here meant: a measurement having an unbroken chain of calibrations to the definition of the unit.
Reason for rule # 3:
“When reporting the result of a measurement of a physical quantity, it is obligatory that some quantitative indication of the quality of the result be given so that those who use it can assess its reliability. Without such an indication, measurement results cannot be compared, either among themselves or with reference values given in a specification or standard.
The following international standard provides a guideline to the expression of uncertainty in measurement:Guide to the expression of uncertainty in measurement.“
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And here is a draft of a rule which is closely related to uncertainty in observation:
Rule # Uncertainty of predictions
“Quantitative predictions are associated with some uncertainty. A proper presentation of a prediction consist of:
* A well-defined context within which the prediction is valid
* A well-defined set of anticipated capabilities for the prediction
* A well-defined non-standard unit – or an international standard (SI) – unit for the prediction
* Predicted values for the measurand
* A corresponding probability curve for the measurand
A proper prediction also provides:
* A proper presentation of input variables and constants
* The sensitivity of the predicted values to input variables and constants
* A presentation of model uncertainty – when significant
* Traceability for input variables and constants – when such traceability exists
* Information, assumptions and a well-defined method used to arrive at the probability curve for the predicted measurand”
Definitions for rule #4
(See previous rules for definition of terms which has been used before)
By constant is here meant: a measurand which has an essentially fixed value in the context it is used
By parameter is here meant: an essentially fixed value used in the definition of functional relationships
By variable is here meant: a measurand which can take on two or more values in the context it is used
By “input variable” is here meant: a measurand which is used as an input in a model used for the prediction
By model is here meant: constants, input variables, parameters, mathematical and logical functions to predict the value of a measurand
By “model uncertainty” is here meant: the probability curve for the dependent variable when assuming no uncertainty in input variables and parameters
By dependent variable is here meant: a measurand deduced from a model
Reason for Rule # 4
“A concept is not nature per se, but an attempt to represent relations in nature by a model.
When reporting the result of an attempt to predict a measurand, it is obligatory that some quantitative indication of the quality of the prediction be given so that those who use it or consider it can assess its reliability.
Without such an indication, predictions cannot be compared, either among themselves or with reference values, observations or measurements. The validity of the concept cannot be judged.”
———————-
Estimated uncertainty of an observation and estimated uncertainty of a prediction are important when it comes to comparison of the prediction with observations.
My plan is to let the next rule be about comparing predictions with observations.
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i really like the comprehensively rational approach with every single thing defined – that pretty much eliminates any ambiguity and semantic quibbling if it’s done well.
i note you have an emphasis on measurement, uncertainty and probability with which i hope to contend – later.
for now i would simply note that definitions have zero uncertainty- just limits
and that deduction by logic is strictly binary with no uncertainty.
and finally that if i am dealt a hand consisting of any 5 cards, the hand i get is just as ‘improbable’ as getting a royal flush and so is every other hand ever dealt.
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I think I´ll have two rules about uncertainty. Uncertainty in observation and uncertainty in prediction.
I´ll get to logic, fallacies, deduction, and testing in a moment.
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Rule # Curve fit
“By curve fitting, a complex model can fit any data set – and still have no predictive capabilities whatsoever. ”
Reason for rule:
“Don´t confuse an ability to explain the past with an ability to predict the future.
By Fourier analysis, it will be possible to satisfactorily approximate literally any time series, like a series of stock prices. However, the Fourier synthesis will have no predictive capabilities. If Fourier analysis had any predictive powers, we would all be rich from stock marked speculation.
A famous example of the capabilities of curve fitting is demonstrated in the following post by John D. Cook; How to fit an elephant:
“John von Neumann famously said:
“With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.”
By this, he meant that one should not be impressed when a complex model fits a data set well. With enough parameters, you can fit any data set.
It turns out you can literally fit an elephant with four parameters if you allow the parameters to be complex numbers.
…..
“Drawing an elephant with four complex parameters” by Jurgen Mayer, Khaled Khairy, and Jonathon Howard, Am. J. Phys. 78, 648 (2010), DOI:10.1119/1.3254017.”
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Gnomish!
It took me some time to establish the following two rules. However, I´m ready to spend whatever it takes to get it right. I´ll throw it all away and start over again if I have to. This really has to be flawless. I guess this is right up your alley – shoot:
Rule # 3 Scientific ideas are logically valid constructs
“A scientific idea must consist of statements which are logically valid conclusions deduced from premises which are themselves logically valid conclusions or axioms.”
By statement is here meant: a well-defined sentence which can be either true or false within the defined context
By conclusion is here meant: a statement deduced from the premises
By logically valid is here meant: the truth of the premises guarantees the truth of the conclusion – it will be impossible for the premises to be true and the conclusion nevertheless be false.
By true is here meant: a statement which cannot be contradicted by a logically valid statement
By false is here meant: not true
By deduced is here meant: mathematically or logically valid combination of premises into a conclusion
By premise is here meant: a statement used in a deduction
Reason for rule # A scientific idea must be a logically valid construct
If a scientific idea is based on at least one logically invalid conclusion – or deduced from at least one logically invalid, or false, premise – there must be something wrong with the idea – or the presentation of it.
The further judgement of such idea should be suspended until the source of the invalidity has been found and rectified. To avoid that previous false statements are maintained on false premises, new judgement should encompass all consequences of a rectification.
Rule # 4 About hypothesis
“A concept which depends on a least one premise, which has not yet been validated, should be referred to as a hypothesis.”
By validated is here meant: provided data or a precise reference which supports the truth of a premise
By “precise reference” is here meant: an identification of the source and a quote of the statements which is regarded as a sufficient support for the premise
Reason for rule # About Hypothesis
“To communicate clearly about the status of a scientific idea and avoid a premature use of an idea, it is wise to communicate clearly that an idea is resting on premises which have not yet been validated.”
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😀 hi!
i’m reading the stuff you mentioned in your previous post but i have some things i have to do immediately that prevent me finishing it.
what you just did- it’s entirely cohesive and rigid like a spine. that makes it absolutely harmonious and beautiful – bulletproof, if you will.
you just topped rand and popper is way back in the dust.
you just gazed into the crystalline heart of that which has no greater whichness.
heh- not so difficult, is it? it’s not yet ready for printing on a bumper sticker- but you just stepped past objectivism.
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Thanks! 🙂 🙂
You have no idea how much that feedback meant to me. You have no idea how much of this due to your input and inspiration. This would never have happened without your guidance.
I´m starting to believe that we can ride this through.
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u can if u want to. don’t need me any more. i just showed you some zippo tricks.
one more, tho-
with proper words, you find it is axiomatic that ‘if it is true, it can be proven.
then there is the occulted corollary…lol
http://www.dictionary.com/browse/mystery
“Word Origin and History for mystery Expand
n.
early 14c., in a theological sense, “religious truth via divine revelation, hidden spiritual significance, mystical truth,” from Anglo-French *misterie, Old French mistere “secret, mystery, hidden meaning” (Modern French mystère), from Latin mysterium “secret rite, secret worship; a secret thing,” from Greek mysterion (usually in plural mysteria) “secret rite or doctrine,” from mystes “one who has been initiated,” from myein “to close, shut” (see mute (adj.)); perhaps referring to the lips (in secrecy) or to the eyes (only initiates were allowed to see the sacred rites). ”
now what makes a mystery a mystery is that you can’t prove it. otherwise it wouldn’t be mysterious.
silly, eh? and yet here we are…
and when yu find the truth of the mystery of mysteries, you are said to be ‘illuminated’.
how nice to see the ineffable get effed.
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I think I need to work a bit more on “truth”. I guess truth is something many people will have an opinion about. To put forward a proper argument I should also address probable counter-arguments.
Regarding:
“one more, tho-
with proper words, you find it is axiomatic that ‘if it is true, it can be proven.”
I imagine that this axiom might be challenged. One thing is to say that if a statement cannot be contradicted it is true.
In that lies that a statement can be regarded true until someone suddenly discovers a way to contradict that statement. Then suddenly, it isn´t true any more?
I don´t immediately see that the axiom ‘if it is true, it can be proven.” is self-evidently true?
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“‘if it is true, it can be proven.”
I imagine that this axiom might be challenged. One thing is to say that if a statement cannot be contradicted it is true.
In that lies that a statement can be regarded true until someone suddenly discovers a way to contradict that statement. Then suddenly, it isn´t true any more?”
can not != did not or has not.
can not means impossible and if it were possible then it wasn’t true.
a contradiction is a proof to the contrary – falsification requires a proof of some contradictory postulate.
not finding one is very different from ‘impossible that there be one’
there is nothing that exists without context. existence is an axiom because nothing else is possible but that.
non-existence does not exist. there is no such thing as ‘nothing’. games with words like ‘i’ll fill you full of holes’ notwithstanding,
in fact, you can make a lot of jokes with words – a new one i found recently is ‘reddish green’.
there is no such thing and there can be no such thing – do you understand why? well, only if you examine the context which was not given.
just watch for when you have to enlarge context to avoid the goedelian incompleteness. word are the tools and label – they are not the entities they label. (except when we talk about words, themselves…lol)
it something exists, then it is true that it exists. if it is true that it exists, then nothing can falsify its existence (nothing = not a single thing – and that means that a contradiction is nonexistent.)
the only ‘thing’ that doesn’t exist is ‘nothing’ (and this is where we must watch our use of words).
to assert that there is a truth which CAN NOT be proven is to say something exists which has no existence
the only ‘thing’ that can not be proven is ‘nothing’ because it is the definition of falseness.
existence is true. the negation of it is nonexistence and that is false.
anything true exists; if it doesn’t exist it isn’t true.
nothing is not something. something is not nothing. (the only case where a = -a is when a = 0, get it?)
there is no truth that is nonexistent.
the law of identity is A=A, a thing is itself. this is where the weak implication (if/then) works both forward and backward: a->b AND b->a.
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well, let me know if i was able to communicate that concept some people struggle with the mystery of mysteries their whole lives and give themselves into slavery in pursuit of some understanding…lol
people stumble over ‘everything i say is a lie’ when the correct and easy way to handle it is to label it as a self contradictory statement
but it’s a little more than that – it’s a statement that can not be proven because it can be neither true nor false on the face of it. IT IS AN UNPROVABLE STATEMENT and therefore IT IS A SELF CONTRADICTION (not the other way around)
so yeah- we get around it by enlarging the context and then we recognize a class of conceptual entities (to which goedel referred) that are unprovable within a certain context.
the class of entites which can not be proven are not true and therefore they are false.
so that’s how you know that the statement: “there are true things that can not be proven, such as this one”
belongs to a class of conceptual entities you have previously encountered which are not true; can not be true.
having falsified the proposition that ‘there are true things that are unprovable’, the contrapositive is proven because it can not be otherwise.
therefore ‘anything true can be proven’ is true (and, actually, self evident unless you’re infected with the relativist’s existential doubt). and ‘that which can not be proven ‘ is false.
though it go by the name of ‘mystic revelation’ it is not, now, a mystery to you.
mysteries are lies.
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I think you have communicated this very clearly. Thank, you for elaborating on this. I´will go through our comments a few times more to ensure that I got it under my skin.
I hope I don´t screw up that statement by demonstrating that I didn´t really understand it by the following:
A statement must be regarded false until it has been proven. (Or to explain my alias – fiction until proven science.) Else, we would become slaves of mysteries, slaves of ideas on the form: “I can assure you that this statement is true but it cannot be proven”. We would have a chaos where contradictory ideas are termed true. Within science the common term for an idea which has not been proven is a hypothesis – an idea proposed for testing.
The consequences of this is that good science is characterized by an ability to create tests which the idea can not pass if it isn´t true. Good scientists deduce a necessary consequence of the idea an check if that consequence is materialized. If the test got the potential to positively confirm that the concept fulfill claimed capabilities within stated context, and the idea passes the test – then it is true.
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http://www.merriam-webster.com/dictionary/hypothesis
Origin and Etymology of hypothesis
Greek, from hypotithenai to put under
sub + pose (suppose)
the short form of this thesis:
things which are true CAN (somehow) be proven because they exist.
(there is some cause for their existence and there is some effect as a result)
there are statements which can not be proven
(the goedelian incompleteness theorem, of which a prime example is the statement ‘everything i say is a lie’)
statements which CAN NOT be proven are false.
some common statements that can not be proven:
death is life everlasting [-A = A]
there is a ‘first cause’ (prior to which there was nothing) [nothing caused something and it has a holy name]
there are truths that can not be proven. [something has no cause or effect and it has a holy name, too]
mysteries can only be divinely revealed. [which is itself a mystery and i told you first so pay up]
everything i say is a lie. [and while you puzzle over that, let me just check what’s under your skirt…]
these are parlor tricks with the language that baffle the unsophisticated.
they are aka ‘mysteries’ and they have been collected and used by gurus to paralyze the critical faculties of their prey.
anything true can be proven to be true
if it can not be proven true it is a lie
somehow this most recent generation seems to have lost the distinction between ‘may’ and ‘can’…
‘can’ refers to an existential possibility, not to permission by somebody
‘may’ has nothing to do with what’s possible; only with what somebody wishes.
(it’s also vestigial subjunctive tense in english – which is used for discussing that which is not.)
it is an ordered universe. contradictions do not exist. they couldn’t possibly.
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Regarding truth, I would like to expose my ideas before I eventually elaborate on the reasons for this rule:
Rule # About truth
«A scientific statement can be written in the form of a functional relationship between A and B:
– If A is taking place, together with a set of conditions C, then prediction B will be the result. –
It might have been tested if the statement is logically consistent and valid
It might have been tested if a corresponding set of measurements could be observed or measured.
It might have been tested if necessary deductions of the statement could be observed or measured.
If the statement failed one of those tests, then there is something wrong with the statement – or the test of it.
If the statement has been exposed to a series of tests and passed all of these tests, then it is true that the statement has passed those tests – if no errors were made during testing.
Nothing more is necessarily true about that scientific statement.»
Definitions for Rule # About truth
By functional relationship is here meant: a quantifiable change in measurand A is followed by a quantifiable change in measurand B
By conditions is here meant: a set of parameters and variables which might affect the value of the measurand
By result is here meant: observable or measurable event
By test is here meant: comparison of a prediction with an observation
By necessarily is here meant: can not be anything else in a logically valid and consistent framework
By deduction is here meant: an a priori characterization or quantification of a measurand by application of non-contradictory logic and mathematical rules on the scientific statement
By mathematical is here meant: a consistent and logically valid system of symbols and operations on these symbols
By failed is here meant: the prediction or deduction did not correspond to what was observed or measured
By wrong is here meant: not corresponding with observations or measurements
By passed is here meant: the predictions or deductions corresponded with observations or measurements
By true is here meant: has not been contradicted by the tests which have so far been conducted
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“«A scientific statement can be written in the form of a functional relationship between A and B:”
means ‘logical proposition’
“– If A is taking place, together with a set of conditions C, then prediction B will be the result. –”
if A then B subsumes the C in the set A
“If the statement has been exposed to a series of tests and passed all of these tests, then it is true that the statement has passed those tests – if no errors were made during testing.”
then it has identity and we give it a name…
“By functional relationship is here meant: a quantifiable change in measurand A is followed by a quantifiable change in measurand B”
‘functional’ better replaced with ‘causal’? because that’s the nature of implication in the real world and it posesses the inviolable temporal relationship we use to abstract it from natural observation based on the arrow of time.
“By wrong is here meant: not corresponding with observations or measurements”
definition of insanity…
“By mathematical is here meant: a consistent and logically valid system of symbols and operations on these symbols”
this aka ‘grammar’
“By true is here meant: has not been contradicted by the tests which have so far been conducted”
‘has not’ leaves undefined ambiguity… there’s nothing ‘iffy’ about truth. it just is or is not.
“If the statement has been exposed to a series of tests and passed all of these tests, then it is true that the statement has passed those tests”
then you have identified an entity at the intersection of all those sets. you defined it.
you said to go ahead and feed back, so there you go.
notice how verging.on.trivial is my difference in perspective? that means i find nothing seriously asking to be challenged. it’s almost picking lint off a tux.
bravo. i like watching this develop.
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Thank you for valuable feedback – you are all too kind.
I´m still working on this one, I can not have undefined ambiguity in the definition of true. 🙂
I just need some more time to work through it all.
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truth is axiomatic, meaning it can not be otherwise (not ‘hasn’t been shown to be – but CAN NOT BE)
therefore, to falsify a proposition, it is only required that for a statement if A then B there is some case where if A then -B.
if a statement is true then there CAN BE no contradiction (if A then B)
if there is a contradiction then the statement CAN NOT BE true. (if -B then -A)
it’s absolute.
(not circular, but recursive)
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Which I guess bring us pretty much in line with Popper and Feynman.
If a proposition has been contradicted we know it´s wrong. But what will be sufficient to know that a proposition is true – that it can not be contradicted?
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as defined, truth is that which can not be contradicted in the specified context.
reductio ad absurdum is the technique used to establish the truth of a proposition by showing that any contradiction of the proposition can not be true.
note that ‘truth’ is a word which is part of a grammar – a set of productions or rules or definitions.
truth, therefore, is a logical abstraction, an idea.
we can sense things to be aware of their existence, but to ‘know’ is to validate a concept by means of logic.
the context of ‘truth’ is ‘conceptual representation’ (it’s not even constrained by reality. for instance we can speak of unicorns. if it’s a unicorn, it has one horn. the statement is true regardless of whether unicorns have any concrete existence. if it has no horn, it can not be a unicorn. logic is an abstraction of the relationship of entities. think of math- associative, transitive, commutative properties are grammatical entities.
so what is both necessary and sufficient is ‘the definition’.
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A scientific idea is true if it can not be contradicted that the predictions of the idea will correspond with observations.
Within science, there are things we can know for sure and there are things we can not know for sure.
If the predictions of the idea is contradicted by a test, we know for sure that there is something wrong with the idea – or the test of if.
One of the things which makes it so hard to be sure that an idea is true is the phrase can not
To know for sure that an idea can not be contradicted we must know for sure that every prediction of the idea will correspond with observations. And we must know this for every set of conditions in the room spanned out by the range of conditions for which the idea is claimed to be valid. It takes a vast amount of testing to be sure about the truth of an idea.
That is why real scientists are so sure when something is wrong and still doubtful when something is right.
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when you’re making something, you subject it to the great simulator of infinite precision and infinite dimensions. it’s never wrong.
in this universe, anything that can happen has, does or will do.
but whatever can not happen never will.
i like to anthropomorphize it if only for poetic acknowledgement of great classical art- which is enjoyable for a reason!
anway- mother nature never tells a lie. if you ask her the right way, she’ll tell you wtf, exactly.
science is how to ask her the right way.
there is NO THING you CAN NOT KNOW. anything that is true, you certainly can. just ask politely.
(i hope we will be testing a new controller board tonight. submitting my work to gaia for grading i hope i listened right when i asked the last time….lol anyway- we have a deal – when i asked to be born she agreed i can have anything i want as long as i make it and if i don’t do something right, i get to do it again and again and again until i do. fair deal.)
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the main loop of your consciousness is asking a question. what is the question.
consciousness is identification. identification is definition. definition is limits.
your mind is continuously asking ‘what is it?’
so you label an entity and define it. (delimit the context)
to know if something is ‘that’ or not is a binary alternative – same as it ever was- to be or not to be
if it is within limits it bears the label because the definition fits. otherwise not.
the question about whether it is ‘that’ or not is a binary alternative, true or false.
we are finite. we can only ingest the universe it bytes. we digitize to binary decisions.
any subset of the infinite must do the same; larger or smaller bites, but DEFINITE bytes.
phrase your science questions such that they have yes/no answers and you will get true/false responses.
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A perfect introduction to the problem of induction – when we induce something about nature but haven´t really asked nature a proper question about it.
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I have not been able to produce anything I´m happy with the last few days. Think I tried to chew through a too big chunk about testing, problem of induction, extrapolation etc. at once. I might need to rephrase my science questions. 🙂
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have you considered the possibility that ‘inductive logic’ is simply numerical conjuring?
http://plato.stanford.edu/entries/logic-inductive/
the indeterminate is not called ‘knowledge’ for a very good reason – have i failed to prove how this can be?
tacking the word ‘science’ on to a superstition does not make it a science.
tacking the word ‘democratic’ onto a tyranny does not make it egalitarian.
‘probability’ is a mystical notion. it is predicated on NOT KNOWING.
so, really, what can one expect? magic?
statistical populations and whatnots are a means of groping for a clue- not a way to establish a fact.
one can’t properly impute to ‘induction’ that which it manifestly lacks by its nature.
everything i say is probable…lol
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Thanks. That helped a lot.
I think there are to types of probability.
Probabilities determined a posteriori by repeated observations and pure mathematics, objectively determined from data. And a priori estimation of probability, in which the judgement of the scientist is involved in the quantification.
Induction is a kind of a priori probability estimation which is at least in part a measure of the confidence of the scientist, at least in part subjective.
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“Probabilities determined a posteriori …”
what has been determined is no longer indeterminate, of course, and therefore ‘probability’ is not its category.
” a priori estimation of probability”
but a guess is a guess…
how about a proper definition of ‘probability’ – one that has had its wave function collapsed by shrewd observation…lol
despite the joking, i don’t think it’s trivial.
to hearken back to the popperian view- is a statement of probability provable? is it falsifiable?
if so, how? if not – what must it be?
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Good points. 🙂
Probability is not a proper category for what has been observed. Frequency distribution is a more appropriate terminology.
However I think a statement of probability is provable, I think it is falsifiable.
One example is radioactivity.
Lets say I have 1 g of radioactive material, and measure that it is sending out 10 000 gamma particles during 1000 seconds.
Let us say that I have an idea that this material will send out in average 10 particles per second.
Let me also predict that the probability curve for number of particles measured during a 1 second period will follow a Poisson distribution.
I can then do a million measurements of the number of particles emitted during 1 second periods and plot the number of times the material emitted 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19or 20 particles during a 1 second period.
If the observed average value of gamma particles per second is anything else than 10 or if the plot differs from a Poisson distribution curve. There is something wrong with my idea, or the test of it.
To put is this way, if the observed frequency distribution differs from the predicted frequency distribution (here the poisson distribution) there is something wrong.
Hence, a predicted probability distribution is falsifiable by repeated observations.
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yes, you can made a logical proposition and validate it.
“if the observed frequency distribution differs from the predicted frequency distribution… there is something wrong.”
you are falsifying a statement which means the abstraction does not bear a 1:1 correspondence with reality.
reality is never false – not once (that is the epistemological root of the construct ‘logical falsification’)
‘sometimes’ falsifies. ‘probability’ implies ‘sometimes’.
“Hence, a predicted probability distribution is falsifiable by repeated observations.”
recall the definition of ‘definition’.
it is not a list of observations. it is the set of distinguishing characteristics that separate the set from all other entities.
a list of all green things is not a definition of ‘green’.
a book full of empirical samples is not a definition, either.
my thesis is that the concept of ‘probability’ is, effectively, the negation of an absolute (which is not specified for this argument)
similar concepts are ‘hole’ which is not a thing but the absence of something that one expects to exist
or ‘darkness’ which is the absence of electromagnetic radiation – not a ‘thing’
the concept of ‘probability’ is used in only one context – when you don’t know anything for certain
i assert that the concept of ‘probability’ is nearly synonymous with ‘uncertainty’
and how can uncertainty be used to validate anything?
any attempt to measure uncertainty is logically impossible – or it would not be uncertain.
and that’s why i conclude that ‘probability’ is a superstition.
frequency distribution might properly identify a valid concept in some context.
if there is any element of truth in another context, the term ‘probability’ will not be used in defining that truth because it can’t, by its nature.
i predict you will probably find truth requires the use a different word (cognitive tool) that does correspond with whatever aspect of reality is being treated.
do you want to define ‘probability’?
if i do it… you can tell how that will go because i mostly have done, already…
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how about a concrete example to play with-
a circle is defined as ‘the points on a plane equidistant from an origin’
those 2 parameters completely and correctly define the points on a circle (even though they happen to be infinite)
if you sample a thousand points and carefully record the coordinates you find you will not have a definition of a circle – not even of the circle you sample.
any list of coordinates will be incomplete and there are correct coordinates that you will be unable to represent. you can’t even completely and correctly specify some of the individual points on a circle.
your list of coordinate may give you a clue that you are dealing with a circle – but they can not prove it because they fail to abstract a principle or truth that defines the entity.
but you can completely and correctly define a circle very easily and with absolute certainty.
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How can we ever know that an idea is a true representation of nature?
Rule # About validation of an idea
“Nature is true.
An idea is tested by comparison of the predictions of that idea and necessary consequences of that idea with observations or measurements.
If the predictions differs from observations, there is something wrong with the idea – or the observations.
If the predictions differ from the measurements, by more than the combined uncertainty of the measurements and the claimed uncertainty of the prediction, there is something wrong with the prediction – or the measurement.
If the average value of the predictions differs significantly from the average value of the measurements – there is a systematic error with the prediction – or the measurements.
A validated idea has passed all conceivable tests.
However, we can never know if:
– A more accurate idea can be found
– An idea valid for a broader range of conditions can be found; or
– If someone comes up with a test which proves something with the idea wrong”
By nature is here meant: anything existing or happening in the universe
By comparison is here meant: establish if it is true or false that A is equal to B
By necessary is here meant: can not be anything else
By consequence is here meant: happen as a result of
By differ is here meant: is not equal to
By wrong with is here meant: not true
By claimed is here meant: stated capability
By average value is here meant: the sum of values divided by the number of values
By significantly is here meant: larger than the combined uncertainty of the two values
By systematic error is here meant: difference between the average of an infinite number of predictions, or measurements, and the exact value of the measurand
By conceivable is here meant: logically valid statement about
By more accurate is here meant: lower uncertainty
By prove is here meant: provide a set of true statements by which another statement is necessarily true
Reason for Rule # About validation of an idea
“There are all kinds of ideas about truth. This rule is based on the tradition famously established by scientists and philosophers like Albert Einstein, Karl Popper and Richard Feynman as evident by the following quotes:
” The only source of knowledge is experience.”
“A man should look for what is, and not for what he thinks should be.”
“Truth is what stands the test of experience.”
“Whoever undertakes to set himself up as a judge of Truth and Knowledge is shipwrecked by the laughter of the gods.”
– Albert Einstein
“According to my proposal, what characterizes the empirical method is its manner of exposing to falsification, in every conceivable way, the system to be tested. Its aim is not to save the lives of untenable systems but, on the contrary, to select the one which is by comparison the fittest, by exposing them all to the fiercest struggle for survival.”
– Karl Popper
“In general we look for a new law by the following process. First we guess it. Then we compute the consequences of the guess to see what would be implied if this law that we guessed is right. Then we compare the result of the computation to nature, with experiment or experience, compare it directly with observation, to see if it works. If it disagrees with experiment it is wrong. In that simple statement is the key to science. It does not make any difference how beautiful your guess is. It does not make any difference how smart you are, who made the guess, or what his name is – if it disagrees with experiment it is wrong. That is all there is to it.”
– Richard Feynman
—-
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A circle is a perfectly defined abstract idea.
However, we will never find an exact circle in nature. And even if we did we would not be able to measure that it is an exact circle.
That is where uncertainty or probability distribution may be to help. We cannot measure all things exactly and we cannot predict all things exactly. By defining an uncertainty we kind of say that the exact value will be within a range around the prediction. And we kind of say that the exact value will be within a range around the measurement. If these two ranges does not overlap there is something wrong.
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“A circle is a perfectly defined abstract idea.
However, we will never find an exact circle in nature. And even if we did we would not be able to measure that it is an exact circle.”
it was rather the point that perfect definition is what it is.
to be able to tell if a thing is a circle or not, you have to first know what a circle is, right?
and once you have this perfect definition, you can tell is it or not with absolute certainty.
without a definition you can only really say you have a feeling about it; not that you know.
having a feeling is not knowledge. not that the SJW would have it that way…lol
“That is where uncertainty or probability distribution may be to help. We cannot measure all things exactly and we cannot predict all things exactly. By defining an uncertainty we kind of say that the exact value will be within a range around the prediction. And we kind of say that the exact value will be within a range around the measurement. If these two ranges does not overlap there is something wrong.”
still no definition of ‘probability’. without it, we end up in the clouds.
if you give that a shot, can you distinguish probability from uncertainty, plz?
do you have to measure all things exactly (and what means ‘exact’ in this context?) for any reason ever? if you can’t does that mean you can’t measure anything? isn’t that the goedel fallacy, there?
i have 5 fingers on my left hand. perfectly counted. zero error.. i don’t have to count the stars in the sky to count my fingers. what you can measure that doesn’t have countable units? units that are perfect abstractions by definition and also necessary and sufficient. where else does ‘exact’ come from?
if you have an abiding concern with tolerances, those can be specified to suit the occasion.
and we can tell perfectly well if a peg fits in a hole or not. tolerance is definition. and that’s what exact really means in this context. it means within specified tolerances. in bounds. part of the set of things that fit.
do you distinguish between tolerance and uncertainty? because i don’t see what is uncertain about specifying tolerance. https://en.wikipedia.org/wiki/Go/no_go_gauge
if i predict that the sun will be shining in the next 3 seconds i will be 100% accurate, right?
i might say something like ‘the sun will be shining sometime between 2 and 4 seconds from now, too.
specifying the boundaries or limits is the very act of defining and by doing that and only by doing that can you tell is something in or out of bounds, part of the set or not – absolutely.
if you don’t like sunshine for an example, how about gravity? it never fails. or if that’s too abstract ‘the universe will exist tomorrow’ is a perfect prediction. nobody will ever falsify that one…lol
so what idea are you trying to capture in your set? it feels like a unicorn. nothing wrong with unicorns, of course, but you can’t ride them anywhere because there are none in the real world (that’s actually part of the definition)
so please:
define probability and maybe remark on the distinction between probability and uncertainty.
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” We cannot measure all things exactly and we cannot predict all things exactly.”
whatever that means…
the universe is analog. infinities are literally everywhere.
a brain takes bites of it- thinking is digital. that is not a bug, it’s a feature.
we define whatever we want to whatever arbitrary precision we care to and specify that precision if warranted.
that does not invalidate the very concept of knowledge – it’s what makes it possible in the first place.
definitions are the outlines of the cognitive entities used for logic.
you can make them as rococo or as simple as you wish – to any arbitrary precision warranted by the occasion. there are smooth ones, fuzzy ones, fat ones, thin ones. all they have to do is enclose space.
oh- here’s a nice joke:
a mathematician is tasked with fencing in a flock of cattle.
he stands in the field and puts a fence around himself and declares himself outside the fence.
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i think i understand what you are trying to express but perhaps i may be wrong.
if it’s amusing, can you pick some concrete example and walk me thru that?
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You are just great 🙂 🙂
Thanks
and spot on weaknesses
e.g. I wondered if “exact” would pass, being undefined – I should know better by now.
I´ll work out an example.
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Imagine that I have a digital scale. The resolution of the scale is 0,01 g. However, It is not a perfect scale. It has both mechanical and electrical imperfections which cause a variation in the measurement result when I measure the same object several times in a row.
I decide to do an experiment.
First, I get an object – a reference mass – of 10.00 g (gram) from a laboratory. The reference mass is traceable to the definition of the kg. So I know that the weight is 10.00 g. Not 10.01 or more – not 9.99 or less – but 10.00 g.
I decide to perform 10 000 measurements of this reference mass. I then plot, at a resolution of 0.01 g the number of times i get each measurement result. The plot have a shape like the red curve in the following figure:
The center of the curve is at 10.00 g. the X axis is the measurement result minus 10.00 g. The area under the red curve is 1. The area under the curve for a range, is equal to the number of times I got a measurement in this range divided by the total number of measurements. The height of the curve at a value is proportional to the number of times I got that value as my measurement result.
For example: The area on the negative side of X = 0 is 0.5; That is equal to 5 000 out of the 10 000 measurements showing 10.00 g or less.
I then decide to do 1 additional measurement:
Together with the reference mass I also received another object having the same size, but I do not know the weight of it.
I perform 1 measurement of that object. And get a result of 10.00 g.
I may now ask a series of questions:
Is the weight of that object 10.00 g? Probably not!
What is the weight of that object? I do not know!
What can I then say about the measurement:
The answer to that is that I should present the measurement result together with the curve illustrating the imperfection of my digital scale.
From that curve showing the imperfection of my digital scale I might expect that there is a 68 % probability that the weight of the object is between 9 and 11 g
95 % probability that the weight of the object is between 8 and 12 g
99.7 % probability the the weight of the object is between 7 and 13 g
Ref. 68-95-99.7
But I don´t know. The curve showing the imperfection of my scale illustrates the uncertainty of my measurement.
In reality the uncertainty within practical measurement is often much worse than in this example – with lots of unknown factors.
(The costs of reducing uncertainty are typically increasing dramatically with the reduction in uncertainty. My profession is to design systems with a reasonable balance between uncertainty and costs.)
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when you have a deck of cards and you deal out 5 – all possibilities are known.
what kind of predictive ability is there and where does it originate?
when you graph the outcome of a million trials, will the predictive power of that graph be less than, equal to or more than a graph of only 100 trials? (trick questions – why?)
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I´m not sure I understand the question – regarding a million trials – are we still talking about cards?
If we are not talking about cards but a measurand which can have any value within a range, the central limit theorem proposes that the probability curve will develop as the number of measurements increases.
The so-called Student´s t-distribution proposes that the probability curve – the uncertainty will be significantly wider if it is established by only a few measurements.
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yah- cards- just for an example
all possible hands are known completely (whether enumerated or not)
it doesn’t matter what you deal-
the ‘probability’ of dealing any hand is exactly the same as for any other hand. the only ‘predictive’ power is in saying what you can or what you can not possibly deal- 5 aces, for instance – because there are no 5 aces in the set of all possibilities.
sample size has absolutely no effect on the predictive power or lack of it. none at all.
this is the nature of ‘random’ data (which really means that no cause/effect relationships are known among the measurands (did i use the term correctly?)
by ‘random’, it is usually meant that the information entropy is high which means the predictability of a datum, based on what came before, is very low.
interestingly, when data is compressed to remove all redundancy and achieve minimum entropy, that compressed data is indistinguishable from random data of high info entropy.
(this was the joke behind the infinite improbability drive of doug adams’ hitchhiker’s guide)
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If the value of a measurand is truly random within a range there is nothing we can do to increase the probability of predicting the exact value of it at any particular moment.
“this is the nature of ‘random’ data (which really means that no cause/effect relationships are known among the measurands (did i use the term correctly?)”
Yes, you did – it makes perfect sense to me at least. (The term measurand isn´t my invention – the term is used in the standard – Guide to the expression of uncertainty in measurement.)
Regarding randomness in measurement of an essentially constant value I find the following sections useful:
“3.2.1 In general, a measurement has imperfections that give rise to an error in the measurement result. Traditionally, an error is viewed as having two components, namely, a random component and a systematic component.
3.2.2 Random error presumably arises from unpredictable or stochastic temporal and spatial variations of influence quantities. The effects of such variations, hereafter termed random effects, give rise to variations in repeated observations of the measurand. Although it is not possible to compensate for the random error of a measurement result, it can usually be reduced by increasing the number of observations; its expectation or expected value is zero.”
I guess this deserves an explanation. If we let a measurement result be the average of a number n of measurements, it is generally assumed that the uncertainty of the average value will be reduced by 1/(square root of n). Hence, if the exact value of the measurand is constant. The random variation of the measurement result is reduced as the number of measurements of this measurand is increased. However, we cannot remove systematic errors by increasing the number of measurements.
If you like Ayn Rand, I think you will also like section “3 Basic concepts” in Guide to the expression of uncertainty
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Correction – regarding the following statement:
“If we are not talking about cards but a measurand which can have any value within a range,”
It should have been:
“If we are not talking about cards but a measurand which has an exact value within a range,”
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completely off topic:
do you have any interest in 3d printing?
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No, not yet. I don´t know much about it, and have not spent much thinking about it. 🙂
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(starting a new thread cuz the other one is very long now)
k- while i might quibble about the assertion of uncertainty an order of magnitude greater than the resolution for this example-
my main confusion is what is probability?
there may be a distribution of your measurements, but there is no distribution of the mass of the entity being measured (in this example) it weighs what it weighs – not stochastically weight-shifting. it’s not a matter of collapsing its wave function by observation to make it suddenly magically determinate…lol
is it, in fact, a valid concept? does it actually correspond to any reality (better than does a notion like ‘phlogiston’, for example, which has an indisputable physical referent ‘flame’)?
i’m not trying to dispute the nature of measurement and tolerancing- just trying to get this notion of probablilty tied to anything real and that is not better done by some other cognitive tool.
uncertainty seems to be descriptive of a distribution but as you stated above, your inclusion of the boundaries is definitive rather than uncertain and the fact that there is a variation in results of measurements seems to lack bearing on that definition.
next time i may define it just because it needs to be done for clear understanding.
i’m really not clear on because when i parse your statements i can’t distinguish it from ‘uncertainty’ or even ‘tolerance’
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Ok – time to try to get productive again.
I know I will have to reconsider what I have already written about probability and uncertainty.
I will do that, but right now I was more tempted to put up a new rule.
Rule # About proper arguments
«A proper argument for a scientific idea must be a logically valid combination of well-defined terms and traceable facts into a conclusion.
A proper argument for a scientific idea must also be free from logical fallacies, vague terms and opinions.”
By term is here meant: a word or phrase used to identify a thing or a functional relationship between things
By traceable is here meant: precisely identified source
By source is here meant: document which contains facts
By document is here meant: any identified and available collection of words and symbols
By fact is here meant: a true statement about a value, property or characteristic of a thing or a relationship between things.
By logical fallacies is here meant: any conclusion which does not necessarily follow from the premises
By vague is here meant: does not distinguish a thing from all other things
By opinion is here meant: a statement which does not necessarily follow from observation, measurement or test.
Reason for rule # About proper arguments
“All kinds of errors and misconceptions are made within science. Common sources for such errors are all kinds of arguments where the conclusion does not necessarily follow from facts. Either because the premises are wrong, the terminology is too vague to be able to judge the validity of a statement or the conclusion does not necessarily follow from the premises.
Proper arguments will be a barrier against making many of these errors. Proper arguments will also help proponents and opponents of an argument to reveal errors and misconceptions about an idea.
Even though it is not necessarily the case, the strive for truth should characterise all scientific endeavour. The purpose of this rule is to promote precision in argument and facilitate scrutiny.”
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splendid!
approaching metaphase.
next comes anaphase and telophase.
i can’t help it, i see the same pattern…lol
that’s not even meant to be logical. but it is fascinating, your conquest of entropy.
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Thanks a lot for your feedback – I think I am almost through now.
( And then I will read your essay that you linked to 🙂 I look forward to that. )
I think I have a little handful left: Scrutiny / review, verification (maybe), proper citations, the problem of induction and a revisit on probability.
I am glad I did not know how much effort this would take. And I am very glad you have stood by me.
Rule # About openness
“A reliable scientist provides all data which are relevant and significant to the idea he propounds, together with precise information about how that data has been measured or obtained.
If data has been disregarded or corrected, then both the original data and the corrected data must be provided together with a proper argument for the correction.”
Definitions for rule about openness:
By provides is here meant: identifies the data and the documents containing that data and makes sure these documents are readily available
By data is here meant: measured or predicted value or property of a thing or relationship between things
By readily available is here meant: available, without further request, by anyone having access to the document in which the idea is propounded
By relevant is here meant: a premise or part of a premise for the propounded conclusion
By significant: the value or property has been considered to have an effect on the conclusion
By propounded is here meant: put forward for consideration
By precise information is here meant: sufficient for replication by scientists having the same or equal tools and equipment available to them
By disregarded is here meant: removed from a set of data
By corrected is here meant: an observed or measured value or property has been replaced with another value or property
By “original data” is here meant: observed or predicted value or property, or the output from a measuring device
Reason for # Rule about openness:
All kinds of errors can be made when evaluating or analysing data. To facilitate the investigation by other scientists, all relevant and significant data should be readily available for anyone who might like to verify that the propounded ideas are supported by the data or to analyse the data in alternative ways.
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i think you are almost through, yes.
now it must simmer a while, be stirred gently and condensed.
when you have prepared a formal treatise, then go through it and remove half the verbiage.
then do it again.
when you reach ‘teh elegant’, you will know because it will shine so brightly your eyes will water.
bah… i hope my stupid metaphors don’t get me kicked out of the kitchen… i want to encourage without interfering. and i like to watch.
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A good plan – and I know I have to go through that.
It´s quite amazing actually, given the time I have invested in every word, I still know that it will feel good to get rid of all the superfluous ones. I like to get to the core of things, even though it takes blood, sweat and tears.
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I look forward to the simmering phase now.
Rule # About scrutiny
“A scientist encourages all kinds of scrutiny of his work, and responds in a proper way to counterarguments or requests for clarification.”
By scrutiny is here meant: any attempt to prove true or false a premise or a conclusion
Reason for Rule # About scrutiny
“An idea is corroborated by the scrutiny an idea has been exposed to and survived. If an idea does not survive scrutiny that is a good thing too, because then we can avoid unfortunate consequences of any design or act based on a flawed idea.
“Review” is one kind of scrutiny which may be performed on some aspects of an idea. However, a successful review is no guarantee for truth.”
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‘By scrutiny is here meant: any attempt to prove true or false a premise or a conclusion.’
scrutiny = test (to restore emphasis on the objective result and deprecate the connotation of anybody’s approval) because it is irrelevant what anybody thinks about it.
In my yoot, there were 2 ‘sins’ of scientific writing: anthropomorphism and teleology.
these 2 errors have become firmly implanted in daily discourse today.
objectivity requires the notions to be uprooted and killed with fire!
proper scientific writing is done in third person passive in order to remove personal pronouns.
facts are impersonal. if the story is about the person AT ALL, then to that extent it is anecdote rather than reportage.
http://guides.lib.purdue.edu/c.php?g=352816&p=2377936
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Agree !
And noted, I will fix it in the simmering phase. It might be that the rule is superfluous as a separate rule.
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Last one:
Rule # About inductive reasoning
“Inductive reasoning is any conclusion which can not be deduced from a test.
A conclusion arrived at by inductive reasoning is invalid.”
Reason for Rule # About inductive reasoning:
Inductive reasoning is widespread within religion, politics and science.
A prediction arrived at by inductive reasoning might happen by luck.
However:
Science is not about luck – science is about reliable prediction.
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No definitions this time.
(Not perfect yet, but you will have noticed that I try to define terms the first time the term is essential , and also that I try to not redefine the terms which have already been defined.)
I will put it all together now – and start the distillation.
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the end is implied by the means and inseparable from it.
transparently clear, quality construction must produce a quality product.
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OK – cut in half. I felt ready to publish a cleaned up draft for further scrutiny, so here it is:
https://dhf66.wordpress.com/2016/11/26/the-rules-of-science/
Let me know if you miss something. 🙂
It is still a draft, I need a rest right now, but I will be ready to continue the journey very soon.
Thanks so far, for an invaluable and enjoyable journey. 🙂
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Regarding probability.
Imagine the following experiment:
A balloon is dropped from a height of 10 m.
I have a perfect mechanism for measuring the time it takes before it reaches the ground.
The timing mechanism has more than enough number of decimals.
(Time can actually be measured very accurately)
Due to turbulence, the time it actually takes for that balloon to reach the ground will show some variation.
If I do that experiment 10 000 times, my guess is that I will get a curve of a form similar to the normal distribution. (No I cannot prove it, and no I have not done that experiment).
For simplicity let us say that the red curve above shows the frequency distribution of my measurements.
Let us also say that the average time it takes for the balloon to reach the ground is 10 seconds.
This time, the distribution is not related to imperfections in my measurements. The distribution is related to natural variations.
Having determined the characteristic frequency distribution for the measurand, the probability that the next measurement will fall within a defined range of values can be quantified.
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quantity of what, exactly?
is it not self contradictory to say you’ve quantified something you don’t know?
it is fair to say you have defined limits.
but gambler’s fallacy with more decimal places is still fallacy.
ok- if you wanted to define probablitly nobody could stop you so you don’t .
so i will:
probability is a method of divination used by sorcerers in the 20th and 21st century.
Numbers are used as the magical means of prophecy instead of tarot cards or bamboo sticks or chicken entrails.
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Probability is an essential characteristic of a dice. Still, I have no idea if the next value, will be 1,2,3,4,5 or 6.
If I through a 6, I do not know if the the dice works as it should. If I through a 6, 50 times in a row, I got reason to believe that there is something is wrong.
It is hard to know something for sure from a probability, but it is useful.
The problem with the term tolerance, within measurement or prediction, is that tolerances does not seem to allow rare events far from the central estimate. The tolerance need to be really wide to make room for such events which seem to happen from time to time.
The term uncertainty seem to be a more appropriate word or terminology. Uncertainty is the term selected in Guide to the expression of uncertainty in measurement.
When the uncertainty becomes significant relative to the level of precision we need for an evaluation of truth, it is hard to make certain conclusions.
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through should have been “throw”
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I was a bit quick on the trigger. Sorry for being exceptionally slow to realize that probability has not been defined.
However, I think it is essential to distinguish clearly between what is observed, and what is predicted.
A probability can not be observed.
If it has been observed it is no probability, it has already happened.
A probability must be some kind of expectation.
Maybe, the following definitions is appropriate:
By observed frequency is here meant: the observed number of occurences of a particular event, value or values within a defined range, divided by the total number of events or values
By probability is here meant: the predicted number of occurences of a particular event, value or values within a defined range divided by the total number of trials for a defined number of trials
By trial is here meant: a test which will produce 1 event or 1 value
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And the following statement is crap:
“Probabilities determined a posteriori by repeated observations and pure mathematics, objectively determined from data.”
The mix up between what has been observed and what is expected – by chicken entrails – or whatever – even infects the guide to the expression of uncertainty in measurement:
“4.3 Type B evaluation of standard uncertainty
4.3.1 For an estimate xi of an input quantity Xi that has not been obtained from repeated observations, the associated estimated variance u2(xi) or the standard uncertainty u(xi) is evaluated by scientific judgement based on all of the available information on the possible variability of Xi . The pool of information may include
⎯ previous measurement data;
⎯ experience with or general knowledge of the behaviour and properties of relevant materials and instruments;
⎯ manufacturer’s specifications;
⎯ data provided in calibration and other certificates;
⎯ uncertainties assigned to reference data taken from handbooks.”
What I have started to realise in my profession is that “scientific judgements” quite often turn out to be just beliefs.
“In God we trust; all others must bring data.”
– W. Edwards Deming
And I don´t trust in any God – bring data.
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that was really quite something. may your powers increase. banish the shadows!
*salutes*
if a test doesn’t prove anything, then how was it a test?
if the test doesn’t have a yes or no answer, how could it prove anything?
anything that is true can be proven.
nobody can prove that there is any truth that can’t be proven.
‘truth that can not be proven’ is titled mysticism
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we’ve already noted the distinctions separating the concepts of the sensory, perceptual and conceptual realms.
statistics falls squarely and entirely in the realm of pattern matching, or perception.
for that reason it is not possible to perform conceptual calculus with statistics.
the meme that proof is impossible while falsification is not applies exclusively to the realm of pattern recognition and not to the realm of logic.
feelings count for nothing, basically.
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Thanks for calling in. 🙂
I have been a bit distracted lately.
One of the distractions has been the election in USA. Anyhow, I´m now determined to work this through now.
I think it will be possible to prove that a distribution of values around an average value is an essential characteristic of a measurand, and that it can be free from subjective judgements.
But first, I need to get some sleep, I really should not be awake now.
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