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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 - 06:23 PM:
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#11
sqeecoo wrote:
Well, yes, I am a full-blooded Popperian :P
But again, I don't deny the messiness of science at all. I am just saying that falsification can be described validly in logical terms however messy it might be in practice, whereas verification cannot. What is impossible is conclusive falsification, which you seem to be expecting to get. Like verification, that's just something we can't get, unfortunately sticking out tongue

Inconclusive falsification, on the other hand, is perfectly possible, and is what scientific reasoning consists of. As long as you adopt Popper's methodological rule not to accept any auxiliary hypotheses that don't increase the testability of the theory in question, they are not a problem. And interpreting test results is of course hard. Again, you don't get conclusive or "probable" falsification, you get tentative falsification. But you have a rational, logically watertight method that you can use to inconclusively but perhaps successfully search for errors.


I am not familiar with the distinction of conclusive v. inconclusive falsificationism. Please explain.

"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 08/13/09 - 06:36 PM:
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I don't think any falsificationist (certainly not Popper) ever said conclusive falsification is possible, so only "inconclusive falsificationism" exists sticking out tongue

Conclusive falsification would be falsification where you prove (or have "sufficient evidence", whatever that is supposed to mean) that the theory in question is false. Inconclusive falsification is falsification where the test is as much a conjecture (i.e. guess) as the theory in question.

The latter can't be used to attain any level of rational certainty, obviously, but it can be used to avoid actual errors even if you don't "know" (in the sense of justified true belief) that you have avoided them. Unfortunately, that's the best we can do. But look how much we have achieved despite that!

EDIT: Someone (I forget who, and am too lazy to check) summed up Popper's theory of science as "Look before you leap!".
We always leap - guess - whether we tentatively accept or dismiss the theory being tested, but we look - test - first. This way, we hope to avoid some errors.
But just as our acceptance of theories is tentative (we might guess, perhaps correctly, that the theory is false later on in light of new tests), the falsification of theories is also tentative - they can be rehabilitated if we guess, perhaps correctly, that it was actually the tests that were wrong.

If falsification were conclusive, a falsified theory would be proven false, never to be rehabilitated.

Edited by sqeecoo on 08/13/09 - 06:49 PM
Arkady
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Posted 08/13/09 - 06:48 PM:
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sqeecoo wrote:
I don't think any falsificationist (certainly not Popper) ever said conclusive falsification is possible, so only "inconclusive falsificationism" exists sticking out tongue

Conclusive falsification would be falsification where you prove (or have "sufficient evidence", whatever that is supposed to mean) that the theory in question is false. Inconclusive falsification is falsification where the test is as much a conjecture (i.e. guess) as the theory in question.

The latter can't be used to attain any level of rational certainty, obviously, but it can be used to avoid actual errors even if you don't "know" (in the sense of justified true belief) that you have avoided them. Unfortunately, that's the best we can do. But look how much we have achieved despite that!


Honestly, I don't understand much of that. What happened to the crisp, either/or of logic? What's the difference between inconclusive falsificationism and just muddling by via abductive reasoning?

"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 08/13/09 - 07:03 PM:
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The logic is crisp - if the falsifying test is true, the theory is false. That's where the logic ends. Figuring out whether the test is correct is where it gets muddy.

The problem with abductive "reasoning" is twofold. First, it is not reasonable - the logic of falsification is abstract and simple, but there is NO logic to abduction. There is simply no logical connection between the theory "fitting the evidence" and the theory being true.

Second, there is always an infinite number of theories that fit the evidence. The evidence does not tell us which one to choose - it doesn't really do anything at all, actually. Falsificationism just says that accepting the evidence means we must reject the theory if it contradicts it.

Of course, abduction is correct in saying that we should fit the theory to the evidence in the sense that if the theory DOES NOT fit the evidence, either the evidence or the theory (usually the latter) must be rejected. This is what falsificationism is all about.
However, abduction usually claims that if the theory fits the evidence, that gives us some "degree of probability/confidence" that our theory is true. This is the main point of disagreement.
Falsificationism says that all our theories (and refutations) are purely conjectural.

If you accept that, and agree that the point of checking whether the evidence and the theory fit is in seeing whether there are any places where it DOES NOT fit (and not "verifying" or "proving" the theory), then our positions are identical.

EDIT: There is also a point of difference in method: falsificationism says we should actively look for places where the theory does not fit the evidence, where abduction makes no such emphasis. This may look minor, but may be pretty significant in practice, since most theories usually agree with some of the evidence.
Another difference is that abduction tends to take the evidence as "given", or not open to doubt. Falsificationism says that there is no pure evidence or observation - all observation is theory-laden. The tools and methods and techniques and lower-level theories we use to collect evidence are equally fallible and conjectural as the theories being tested. If we ever suspect that they, and not the theory, are in question, we can turn our attention to them by testing and criticizing them.

Edited by sqeecoo on 08/13/09 - 07:13 PM
Arkady
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Posted 08/13/09 - 07:08 PM:
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sqeecoo wrote:
The logic is crisp - if the falsifying test is true, the theory is false. That's where the logic ends. Figuring out whether the test is correct is where it gets muddy.

The problem with abductive "reasoning" is twofold. First, it is not reasonable - the logic of falsification is abstract and simple, but there is NO logic to abduction. There is simply no logical connection between the theory "fitting the evidence" and the theory being true.

Second, there is always an infinite number of theories that fit the evidence. The evidence does not tell us which one to choose - it doesn't really do anything at all, actually. With falsification, accepting the evidence means we must reject the theory.

Of course, abduction is correct in saying that we should fit the theory to the evidence in the sense that if the theory DOES NOT fit the evidence, either the evidence or the theory must be rejected. This is what falsificationism is all about.
However, abduction usually claims that if the theory fits the evidence, that gives us some "degree of probability/confidence" that our theory is true. Falsificationism disagrees, and is sincere about all our theories being purely conjectural. If you accept that, and agree that the point of checking whether the evidence and the theory fit is in seeing whether there are any places where it DOES NOT fit, that our positions are identical.


Falsificationism relies exclusively upon logical deduction, correct? This means there is some logically necessary connection between theory and evidence?

Could you run me through an example of a hypothesis (or "conjecture", if you like), and a test that would falsify it?

"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 08/13/09 - 07:25 PM:
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Arkady wrote:


Falsificationism relies exclusively upon logical deduction, correct? This means there is some logically necessary connection between theory and evidence?

Could you run me through an example of a hypothesis (or "conjecture", if you like), and a test that would falsify it?


The logically necessary connection is that if the evidence (or rather, the statements about the world, about the "evidence") that contradict the theory are true, the theory is false. In other words, if a logical consequence of the theory is not true, the theory is false. Formally:

A->B
~B
____
~A

This is modus tollens.

For instance, we have the theory "All swans are white". Let's see how falsificationism and abduction handle it:

ABDUCTION:

CASE1: Check all swans we see. All these swans are white. The theory fits the evidence, and is "probably true", "proven", "reasonable to believe" or whatnot.

CASE2. Check all swans we see. Not all these swans are white. The theory does not fit the evidence, and is disproven.


FALSIFICATIONISM:

CASE1: Check whether the theory is falsifiable (i.e. whether it contradicts any conceivable physical events). If yes, accept it as a scientific theory. Actively look for a non-white swan. We find none. The theory is tentatively retained until further notice - but it is as conjectural and unproven as before the testing. Additionally, someone might immediately come up with another test - for instance check whether some of the swans have been painted white.

CASE2: Check whether the theory is falsifiable (i.e. whether it contradicts any conceivable physical events). If yes, accept it as a scientific theory. Actively look for a non-white swan. We find one. The theory is tentatively considered falsified until further notice - but this is as conjectural and unproven as in CASE1. Additionally, someone might not accept the truth of the test, and immediately test the test - for instance check whether the swan in question has been painted non-white.
Arkady
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Posted 08/13/09 - 07:29 PM:
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sqeecoo wrote:


The logically necessary connection is that if the evidence (or rather, the statements about the world, about the "evidence") that contradict the theory are true, the theory is false. In other words, if a logical consequence of the theory is not true, the theory is false. Formally:

A->B
~B
____
~A

This is modus tollens.

For instance, we have the theory "All swans are white". Let's see how falsificationism and abduction handle it:

ABDUCTION:

CASE1: Check all swans we see. All these swans are white. The theory fits the evidence, and is "probably true", "proven", "reasonable to believe" or whatnot.

CASE2. Check all swans we see. Not all these swans are white. The theory does not fit the evidence, and is disproven.


FALSIFICATIONISM:

CASE1: Check whether the theory is falsifiable (i.e. whether it contradicts any conceivable physical events). If yes, accept it as a scientific theory. Actively look for a non-white swan. We find none. The theory is tentatively retained until further notice - but it is as conjectural and unproven as before the testing.

CASE2: Check whether the theory is falsifiable (i.e. whether it contradicts any conceivable physical events). If yes, accept it as a scientific theory. Actively look for a non-white swan. We find one. The theory is tentatively considered falsified until further notice - but this is as conjectural and unproven as in CASE1. Additionally, someone might not accept the truth of the test, and test the test - for instance check whether the swan in question has been painted non-white.


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."

"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 08/13/09 - 07:42 PM:
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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?



Ok. Right, so I guess that by falsifying a logically universal statement ("all swans are white"), you verify its negation ("not all swans are white"). Hmmm. That's a common objection to falsificationism, and I know I read Popper's answer and was satisfied with it, but I can't for the life of me remember what it was :P
I probably have the book at home, but it's like 4 AM and I'm too tired to look. I'll have to get back to you on this one tomorrow mate, sorry wink

Cheers!

Edited by sqeecoo on 08/13/09 - 08:03 PM
Arkady
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Posted 08/13/09 - 08:00 PM:
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sqeecoo wrote:
All scientific theories are logically universal however, since that's the only way they can have any explanatory power and contain interesting information.


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?

"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 08/13/09 - 08:07 PM:
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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.
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