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Evidence and Theory
What is the logical relation between theory and evidence?

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Evidence and Theory

Arkady
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Posted 08/13/09 - 08:08 PM:	#21
sqeecoo wrote: That's a good point too. You ask great questions my friend. It's a pleasure to talk to you - I'll come out knowing more about the things I tried to explain. It's time for me to go to bed now, but I'll get back to you as soon as I can. I look forward to it. Have a good one.
"Sit down before fact like a little child, and be prepared to give up every preconceived notion. Follow humbly wherever and to whatever abyss Nature leads, or you shall learn nothing." -T.H. Huxley

sqeecoo
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Posted 08/15/09 - 07:21 AM:	#22
Arkady wrote: Ok, thanks for breaking it down. How would you deal with a statement (theory) such as "not all swans are white?" Isn't this provable (by a single observation, in fact), and not merely falsifiable? EDIT: by "provable" I mean "verifiable." Ok, I'm back! Had a busy day yesterday, so I couldn't reply earlier. On the other hand, I am well rested now, and less confused Things get a bit complex here, but I'll try to keep it simple as best I can. Or if not simple, then at least clear. The universal statement "all swans are white" is logically equivalent to the singular statement "there does not exists a non-white swan". Since this applies to all points in time and space - a virtually infinite number of cases - it is not verifiable, but it is falsifiable by the acceptance of the singular statement "here is a white swan". This is Popper's point, and the reason why we should test, not verify theories. Scientific theories, in as much as they are statements of natural laws - the stuff science tries do discover - have this universal, non-verifiable-but-falsifiable form (which is not to say that they are the ONLY content of science, just the main content and goal). The negation of above universal statement 'NOT "all swans are white"', is logically equivalent to the singular statement "there exists a non-white swan". This statement is thus verifiable, but not falsifiable. Accepting the truth of the singular statement "here is a non-white swan" mandates the rejection of the universal statement "all swans are white", and, conversely, the acceptance of its negation, 'NOT "all swans are white"'. Thus, statements of natural laws can't be verified by statements describing observations, but they can be falsified - i.e. their negations can be verified. However, this is purely logical "verification" and "falsification", which holds only in the sense that IF we accept the singular statement "here is a white swan", logic mandates that we reject the universal statement "all swans are white", and accept its negation. What does not happen is that this rejection is in any way justified - our acceptance of the falsifying singular statement is conjectural and unjustified. Hence I said that falsification is not conclusive, and is as conjectural and tentative and the acceptance of a theory that has passed all tests. This is in contrast to verification in the sense of abduction and induction, where "verifying" our hypotheses is supposed to offer some justification or reason to believe they are true. To sum up: so, a universal statement can be falsified by singular statements, and its negation verified, in the sense that logic mandates this if we accept the singular statement as true. However, the acceptance of the singular statement is not justified; it is a guess, a conjecture, but it can itself be further criticized and tested (or rather, the lower level theories that and tools that led to it). As opposed to induction and abduction, however, the LOGIC of this process is watertight, and no dogmatism is involved. Thus, the process is rational in the sense of USING REASON AND LOGIC to try to find the truth. It is basically rationally controlled guesswork. It is, however, NOT rational in the sense of giving reasons/justification that we are right about our choices. Arkady wrote: I'm not sure I agree. To say, for instance, "there exists (or existed) at least one dinosaur with feathers" does contain interesting (i.e. scientifically relevant) information. Perhaps you could clarify exactly what you mean by "logically universal" in the context of scientific theories? You are right, I made too strong a claim. The above singular statement is informative, but primarily in the context of either falsifying some scientific theory about dinosaurs, or in inspiring new theories. It is indeed informative, but the point I should have made is that science explains the world by trying to figure out natural laws - i.e. universal rules - by advancing hypotheses that consist of logically universal statements (statements that claim something to be true in every place in space and time). Singular statements are of course both informative and relevant, primarily because they can contradict theories, but there is no way to construct something that can be recognized as a scientific hypothesis purely out of singular statements. (of course, since every universal statement is logically equivalent to a negation of a singular statement, you can state a theory using negations of singular statements - i.e. by stating what the theory forbids, and, incidentally, what would falsify it were it true) There, I hope that's clear enough. If you have questions or criticism, I'd be glad to hear them. However, I'll be away for the next day or three, so after tonight I'll not be able to answer right away. Cheers! Edited by sqeecoo on 08/15/09 - 07:26 AM

ragus
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Posted 08/15/09 - 07:45 AM:	#23
sqeecoo wrote This is Popper's point, and the reason why we should test, not verify theories. Scientific theories, in as much as they are statements of natural laws - the stuff science tries do discover - have this universal, non-verifiable-but-falsifiable form (which is not to say that they are the ONLY content of science, just the main content and goal). It seems to me that Popper has conceptualised an asymmetry underlying how some forms of knowledge are derived. A kind of logical ratchet? Am I close?
"A word in your ear is like an untethered goat in a field" Wittigenstein

Kwalish Kid
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Posted 08/15/09 - 09:40 AM:	#24
[quote=sqeecoo]You are right, I made too strong a claim. The above singular statement is informative, but primarily in the context of either falsifying some scientific theory about dinosaurs, or in inspiring new theories. /quote] But this is how any scientific claim is used. And how are we to judge what claims are strong enough to be used to falsify some scientific theory?
"Scientific truth is always paradox, if judged by everyday experience, which catches only the delusive nature of things." - KM, V, P and P Can you pass Religion 101?

Cadrache
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Posted 08/15/09 - 10:33 AM:	#25
I've always been somewhat interested in this relationship when you look at 'new' theories. It seems to me that a large proponent of the first examination is to determine whether or not somebody else has already stated a similar idea in their book. Or a variant of disproof by higher authority. Now; I expect large disagreement on the next part. Well, maybe. To me; theory is not much more then 'story' or 'narrative'. Instead of Einstein's equation being about relativity as it is currently known as - his evidence could be nothing more then the ratio at which two objects can interact with each other.
"...There was a writer who asked why it was that when we find positive experiences we say that only the physical facts are real, but in negative experiences we believe that reality is subjective. He made an example of those who say that in birth only the pain is real, the joy a subjective point of view, but that in death it is the emotional loss that is the reality." - Tony Ballantyne, Recursion. _____________________________________________ Truth is want. - The internal state of matters. Truth is Need. - The external state of affairs.

Arkady
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Posted 08/15/09 - 01:51 PM:	#26
Sqeecoo, welcome back. sqeecoo wrote: Scientific theories, in as much as they are statements of natural laws - the stuff science tries do discover - have this universal, non-verifiable-but-falsifiable form (which is not to say that they are the ONLY content of science, just the main content and goal). Not all scientific theories deal in universal truths. Biology, for instance is totally, or nearly totally devoid of any laws whatsoever. There may be "laws of physics" (even if they're only provisional conjectures awaiting falsification), but there really are no unique "laws of biology." Any putative law of biology one could think of (e.g. all organisms must take in sustenance to survive) ultimately reduces to physics. It is simply not the "main content and goal" of biology to discover universal truths. More and more I'm beginning to think one problem (or at least limitation) with falsificationism is that it was tailored almost exclusively to the physical sciences (mostly physics), and is a poor fit for some of the softer sciences, e.g. biology. This is unsurprising, as philosophy of science was preoccupied almost exclusively with physics for the first half of the 20th century. Philosophy of biology, for instance, is a relative newcomer, and not as much work has been done on it. Popper's own forays into the philosophy of biology did not seem to pan out all that well, e.g. when he referred to natural selection (and thus the entire theory of evolution) as tautologous. sqeecoo wrote: ...our acceptance of the falsifying singular statement is conjectural and unjustified. Hence I said that falsification is not conclusive, and is as conjectural and tentative and the acceptance of a theory that has passed all tests... ...To sum up: so, a universal statement can be falsified by singular statements, and its negation verified, in the sense that logic mandates this if we accept the singular statement as true. However, the acceptance of the singular statement is not justified; it is a guess, a conjecture... How is our acceptance of a falsifying singular statement "unjustified?" For instance, if we observe a non-white swan, thereby falsifying the universal statement "all swans are white", on what grounds should we doubt the veracity of this observation? It may actually be a white swan that someone has painted black? The field biologist could be very myopic? The observer has dropped LSD and is only hallucinating a black swan? It seems that you are making an epistemological argument about the reliability of perception, not a logical point about falsificationism. Would you agree with the statement: "GIVEN that our perceptions are reliable, falsifying singular statements can be justified?"
"Sit down before fact like a little child, and be prepared to give up every preconceived notion. Follow humbly wherever and to whatever abyss Nature leads, or you shall learn nothing." -T.H. Huxley

rigelrover
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Posted 08/15/09 - 02:22 PM:	#27
Arkady wrote: This thread pertains to scientific evidence, but could legitimately be asked of any sort of evidence To set the grounds, what exactly IS evidence? I would hold that it must be something PHYSICAL, and not merely logical or mathematical in nature... So, some people who think about evidence ("E") hold that it has a DEDUCTIVE relation to theory ("T"). That is, if E obtains, then T necessarily follows from it. 1) It is rather still debatable among some if numbers do exist as objectively real. I do not debate this at this point (I happen to think they are), but if they are then why could we not posit a theory T that pertains to the existence of numbers as evidence of T? 2) It seems that it is an intrinsic property of the human mind to allow T to follow from the necessary E. And this intrinsic property as either a derivative of human logic (or universal logic if there is such a thing), or as the source itself. Formal logic (the kind that can be represented typographically) has been shown to be isomorphic to number-theory, so the existence of human logic as such could interestingly be taken as obtained E of the T "Number-like relations (ie number-theoretical relations) exist". (separate question): Could it be the case that some T that is deduced might reflexively necessitate that the required evidence E exists? This seems counter-intuitive, but would seem to be the case if 1) and 2) are true. If 1) and 2) are not, then how might you formally show that the answer to the above question is no?
I am more interested in questions than answers; dialog than dictation. If we can reasonably believe that there is not just a breach, but a fundamentally unclosable gap between the individual mind and the ultimate nature of the reality; the primordial thing in itself, then 'true' mystery does exist.

sqeecoo
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Posted 08/15/09 - 03:19 PM:	#28
ragus wrote: It seems to me that Popper has conceptualised an asymmetry underlying how some forms of knowledge are derived. A kind of logical ratchet? Am I close? Popper does call the fact that singular statements can falsify but not verify universal statements an "asymmetry" between falsification and verification. But I am not sure what you mean by saying that he "conceptualized" this and that this is a "logical ratchet" (I know what a ratchet is, I'm just not sure I get the metaphor). ------------------------- Kwalish Kid wrote: [quote=sqeecoo]You are right, I made too strong a claim. The above singular statement is informative, but primarily in the context of either falsifying some scientific theory about dinosaurs, or in inspiring new theories. /quote] But this is how any scientific claim is used. And how are we to judge what claims are strong enough to be used to falsify some scientific theory? I'm not sure what you mean by your first sentence, but it's fairly easy to judge what claims are strong enough to falsify a theory. That is pure deductive logic - the statement "here is a non-white swan" contradicts the statement "all swans are white". Whether there is actually a non-white swan here is a different, non-logical question that is much harder to decide on. ------------------------ Arkady wrote: Sqeecoo, welcome back. Not all scientific theories deal in universal truths. Biology, for instance is totally, or nearly totally devoid of any laws whatsoever. There may be "laws of physics" (even if they're only provisional conjectures awaiting falsification), but there really are no unique "laws of biology." Any putative law of biology one could think of (e.g. all organisms must take in sustenance to survive) ultimately reduces to physics. It is simply not the "main content and goal" of biology to discover universal truths. Hi! Actually, I disagree with this . We are talking about the logical form of the theories. The logical form of the statements "all swans are white" and "all terrestrial organisms must take in sustenance in order to survive" is universal. In this sense, biological theories are logically universal, even if they don't necessarily try to apply to all life forms anywhere in the universe or even on earth. If you like, give an example of a non-logically-universal biological theory and we'll try to clear this up. Arkady wrote: More and more I'm beginning to think one problem (or at least limitation) with falsificationism is that it was tailored almost exclusively to the physical sciences (mostly physics), and is a poor fit for some of the softer sciences, e.g. biology. This is unsurprising, as philosophy of science was preoccupied almost exclusively with physics for the first half of the 20th century. Philosophy of biology, for instance, is a relative newcomer, and not as much work has been done on it. Popper's own forays into the philosophy of biology did not seem to pan out all that well, e.g. when he referred to natural selection (and thus the entire theory of evolution) as tautologous. Well, Popper was actually quite anxious to point out that all sciences, even social sciences, share the same methodology of trial and error. If you can elaborate on why you think his theory is a poor fit in some branches of science, we can discuss this if you like. In general, I'd also be interested in hearing what you think about my description of abduction vs. falsification, and what method would you apply in "softer" sciences and how. Incidentally, Popper retracted his criticism that the theory of evolution was tautologous - although he maintained it was only weakly testable and more of a research program, with which I tend to agree. http://atheism.about.com/b/2006/06...y-based-on-a-tautology.htm One of the things I like about Popper is that he wasn't afraid to admit he was wrong. And just because I linked to an atheistic webpage, let me just note that to my knowledge he was an agnostic. Arkady wrote: How is our acceptance of a falsifying singular statement "unjustified?" For instance, if we observe a non-white swan, thereby falsifying the universal statement "all swans are white", on what grounds should we doubt the veracity of this observation? It may actually be a white swan that someone has painted black? The field biologist could be very myopic? The observer has dropped LSD and is only hallucinating a black swan? It seems that you are making an epistemological argument about the reliability of perception, not a logical point about falsificationism. Would you agree with the statement: "GIVEN that our perceptions are reliable, falsifying singular statements can be justified?" Nicely spotted! I am making an epistemological argument about the reliability of perception IN ADDITION to a logical point about falsification. However, the logical point about singular statements not being able to verify universal ones holds even if observations are self-justifying and fully reliable. Of course, IF our perceptions are reliable (and we know that they are such), falsifying singular statements can be justified. However, I don't think that this is "given". In fact, our perceptions, while being a great tool, are often wrong. What's more important, there are no "pure" perceptions. All perceptions depend on (unconscious) theories, for instance theories of how to recognize things (as an "animal", "swan", "piece of meat", "beautiful animal", "aggressive and dangerous animal", etc.). Furthermore, all reports of observations (like "here is a white swan") contain general concepts like "swan" and "white" which are themselves not reducible to particular observations. Anyway, the question of justifying statements about perceptions is, as you noted, different from the question of their ability to justify scientific theories. Popper's primary point is about the latter, but we can also discuss the former (and Popper agrees with me there too - one of his basic points is that falsification is inconclusive and unjustifiable, which it wouldn't be, or at least not fully, were singular statements based on perceptions justifiable). Cheers! Edited by sqeecoo on 08/15/09 - 03:24 PM

Arkady
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Posted 08/15/09 - 05:42 PM:	#29
sqeecoo wrote: Hi! Actually, I disagree with this . We are talking about the logical form of the theories. The logical form of the statements "all swans are white" and "all terrestrial organisms must take in sustenance in order to survive" is universal. In this sense, biological theories are logically universal, even if they don't necessarily try to apply to all life forms anywhere in the universe or even on earth. If you like, give an example of a non-logically-universal biological theory and we'll try to clear this up. Well, Popper was actually quite anxious to point out that all sciences, even social sciences, share the same methodology of trial and error. If you can elaborate on why you think his theory is a poor fit in some branches of science, we can discuss this if you like. These points are similar, so I'll address them together. When I said biological theories are non-lawlike and non-universal, I meant that biology deals in statistical trends, not in absolutes. I am hard-pressed to think of a uniquely biological theory that is universal in scope (i.e. applying to all members of some set). For instance, statements such as "mammals give birth to live young" are not without exceptions. The only such statement I could think of would be tautologous, such as "no invertebrate has a backbone." The reason I think falsificationism is a poorer fit for fields such as biology is precisely for the reason I gave in the previous paragraph, namely that biological theories are non-lawlike. Physicists, for instance, make a set of token measurements, and infer universals from this set of measurements. No scientist would ever speak of "THE mass of the elephant" because it's accepted that individual elephants differ in mass to some degree. But physicists speak of having measured "THE mass of the proton", and expect that all protons everywhere share this property even though such measurements have been performed only on an infinitesimal fraction of the total number of protons in the universe. Such reasoning is the core of induction: inferring general truths from token instances. Theories such as "ALL protons have mass M" are far more amenable to falsification than theories such as "SOME viruses use RNA as their genetic material." (Though I concede that a statement such as "ALL MEMBERS of virus species X use RNA as their genetic material" is precisely as falsifiable as the statement "all protons have mass M".) sqeecoo wrote: In general, I'd also be interested in hearing what you think about my description of abduction vs. falsification... I found it concise and non-problematic. I don't really take issue with your description of abduction (though I would possibly disagree on its validity, and in any event I am no expert on abduction). sqeecoo wrote: ...and what method would you apply in "softer" sciences and how. It's not that I think the methodologies of the "hard" and "soft sciences" are all that different (they are all empirical in nature, they all try to build explanatory models from sets of data, etc), it's just that I don't think the doctrine of falsificationism applies equally well to them. For instance, if we are cultural anthropologists, and we observe and state the fact that "tribe X has been known to perform human sacrifices" I don't even know how this would be falsified (recall we are accepting perception as reliable for the moment).
"Sit down before fact like a little child, and be prepared to give up every preconceived notion. Follow humbly wherever and to whatever abyss Nature leads, or you shall learn nothing." -T.H. Huxley

ragus
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Posted 08/15/09 - 10:07 PM:	#30
sqeecoo wrote Popper does call the fact that singular statements can falsify but not verify universal statements an "asymmetry" between falsification and verification. But I am not sure what you mean by saying that he "conceptualized" this and that this is a "logical ratchet" (I know what a ratchet is, I'm just not sure I get the metaphor). What I meant was that Popper had used the asymmetry of the logic - one counter-example can (logically) scupper a theory whereas support for the theory can be (logically) never-ending - to show how we can remove certain false theories. Thus scientific knowledge can advance in one direction (the ratchet metaphor - it was the best I could do) leaving a trail of failed theories in its wake. Echoes of natural selection?
"A word in your ear is like an untethered goat in a field" Wittigenstein

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