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I have made an argument in another thread that a proposition must be provable or falsifiable to be valid. Are there any flaws in this definition of validity? What might be a potential counter-argument here?

Is there some other criteria that can be used to validate a proposition conclusively? Could such criteria be considered scientific?

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Chad
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"God exists" is similar to "an electron exists", because neither claim is completely falsifiable nor is its negation. For example, imagine the sum total of all scientific data that has ever been collected to support the existence of an electron. Now suppose every single experiment was affected by an improbably large (but still possible) amount of experimental error. So it is possible that all future replications of those experiments will fail to establish the electron's existence. But it is also possible that at some point the experiments will start working again, and it will then be believed instead that it was the experiments disproving the electron's existence that were affected by experimental error. Neither "an electron exists" nor "no electron exists" is truly falsifiable. The existence of the electron is ultimately dependent on shared intuition, experience, and belief. Likewise, so is the existence of God. If God came to Earth and demonstrated his existence to every person in a way that all persons could understand and communicate effectively, then there would be no difficulty accepting "God exists" as a scientific statement. And if God then left Earth, and many persons were no longer able to be convinced of his existence, then "God exists" would cease to be considered a scientific statement.

For a claim to be a valid scientific claim, it has to have precise and agreed-upon definitions, and there must be a convincing argument that it is extremely likely to be true.

Dan Brumleve
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  • So what you are saying is that if enough scientists believe that the world is flat, then a claim of the world being round is not a valid scientific claim? – Chad Jun 20 '11 at 13:17
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    The argument is that science is subjective, like democracy, so yes. I don't think this is a very useful (or scientific) point of view but I guess it is necessary for the question to be answerable. If nobody can agree about the definition of "God" then it is not science, and if nobody can agree about the definition of "round" then that is not science either. – Dan Brumleve Jun 20 '11 at 22:53
  • I am not certian that I agree with your premise that Science is subjective. http://en.wikipedia.org/wiki/Science **Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the world** This definition really encompasses how I have defined science in my mind. – Chad Jun 21 '11 at 13:15
  • How can I make this answer acceptable? Here http://dictionary.reference.com/browse/enterprise "enterprise" is defined primarily in terms of "energy", a word whose meaning is subject to whims. I am playing the devil's advocate now, but what does God mean to science, or to scientists? – Dan Brumleve Jun 22 '11 at 05:03
  • Well the existance of god could be used to rationalize some currently irrational behavior that seems to exists at the really big and really small ends of the scale. But please do not focus on the content of the question so much as that it could be used but it is not provable or falsifiable. Is there another way to validate the claim. – Chad Jun 22 '11 at 14:55
  • @Dan I think you would have to show how the general agreement of scientists makes the claim valid. Until recent times most of the scientists believed in god. While a claim may be accepted that is not provable it is generally because there are other claims about it that are provable or falsifiable. Most of those claims are not able to be proven not because they are not measurable but rather that we do not possess the ability to accurately measure it. – Chad Jun 22 '11 at 15:06
  • Chad, another angle on this is the concept of a zero-knowledge proof http://en.wikipedia.org/wiki/Zero-knowledge_proof, by which a claim can be justified in an essentially non-constructive manner. – Dan Brumleve Jun 23 '11 at 04:18
  • Also you make a good point that Newton, Cantor, etc. were theologians. So the argument is that in some sense theology really _was_ science. – Dan Brumleve Jun 23 '11 at 04:33
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In formal systems, axioms (e.g., the Axiom of Choice mentioned by Michael McGowan) are typically taken to be true and cannot be proven or disproven.

In the sciences, axioms are expected to reflect measured reality. So, while Euclidean geometry (although incomplete) has a well agreed upon, non-contradictory, set of axioms, the axiom requiring parallel lines to remain at a fixed distance from each other (a later rewording of his fifth postulate) does not agree with General Relativity, and my extension it does not agree with our interpretations of our measured reality (note a level of indirection here). That does not mean that Euclidean geometry has been disproven per se, but that it does not agree with reality.

I'm not sure how this applies to your question of God. It's a question of faith, which has similarities to axioms, but is not the same as.

Ben Hocking
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  • Part of the problem is that the boundaries of science are always being redrawn: was geometry part of mathematics or physics back then? – Dan Brumleve Jun 18 '11 at 01:56
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In short: No.

According to Gödel there will always be statements that are true, but that are unprovable.

See here for more: Gödel's incompleteness theorems

vonjd
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    Some care is needed here. The question does not ask whether truth should be equated to provability. It asks whether provability or falsifiability are the only criteria that can give us good reasons to *assert* a 'claim of truth' (i.e. a proposition). Even if we take Godel to have proved that there are true unprovable statements, that says nothing about the existence or not of alternative **assertability** criteria/conditions. – Chuck Jun 17 '11 at 15:17
  • @Chuck: I find this a little bit unfair because the title of the question is "Does a claim of truth need to be either Provable or Falsifiable to be Valid?" - and I answer just that. So the answer in itself is not wrong albeit the formulation of the question seems to be inconclusive. – vonjd Jun 17 '11 at 15:42
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    It only addresses the provablity not the falsifiablity though. I read the piece and even his examples seemed to be falsifiable. It is a good link just doesnt answer the question. – Chad Jun 17 '11 at 16:17
  • @Chuck Let me make sure I understand you correctly. Take a theorem relevant to the Goedel discussion that can neither be proven true nor false under (under standard axioms)...say the Axiom of Choice. Although we can't prove it, it might very well be true. Are you saying that, even if it is the case that it is true, it would not be valid for me to assert it as true (since I have no proof)? – Michael McGowan Jun 17 '11 at 16:57
  • @Michael @vonjd What I am saying is that it seems to me that the question is asking whether there are any alternative *criteria* (other than provability of falsifiability) that would determine the *truth-value* (whether it is true or false) of a given proposition. I am saying that to show that Truth≠Provability although interesting in itself does not answer THAT question. An answer to the question would be e.g. "In my opinion if a person I consider holy tells me that God exists then I will assert that God exists" - i.e. an assertability condition involving authority/expertise. – Chuck Jun 17 '11 at 17:08
  • (cont.) I am not saying that these assertability conditions are right, but Chad, the way I understand him, is asking whether there are any worthy of consideration. Godel may have proved that provability is not an adequate assertability criterion because arithmetical truth cannot be recursively enumerable, but that in no way 'proves' that provability was ever the only criterion worth considering. Do you understand me now? (I may have misread Chad, in which case Chad please say so.) – Chuck Jun 17 '11 at 17:12
  • @vonjd This is still early days for this site, so we are consciously trying to be quite strict with answers, but to downvote is in no way a personal affront and please don't take it as one - it is merely an indication of the compatibility of the answer to the question, not the worth of the answer itself – Chuck Jun 17 '11 at 17:16
  • @Chuck: It is good that you said that - (I indeed have the unfortunate tendency to take these matters personally ;-) So thank you. – vonjd Jun 17 '11 at 18:19
  • Argh...how do you know 'it' is true? By a proof. Things that are true but not provable...they're not provable __in a particular system__. The 'it' is true in the system but just needs principles outside the system to be proven true. Just remember that one thing and Goedel's theorem won't be so misapplied. – Mitch Sep 24 '11 at 22:49
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I don't know what you mean by "valid" here. That said, there exist plenty of claims which can't get proven nor refuted which come as necessary for inference in logical or mathematical systems. This no doubt extends to reasoning in science, since mathematical and logic theories do often get used there in one way or another. Each axiom of a correct set of axioms for group theory, ring theory, lattice theory, semigroup theory, field theory, Boolean Algebra, etc. for instance can't get refuted or proven. Each axiom comes as contingent upon the domain of discourse in question, and so qualifies as contingent in the context of the entire predicate calculus. Even in propositional logic, many, many statement forms can't get proven nor refuted. The truth values of those statement forms comes as contingent upon on what truth values the atomic variables take on. As a very simple example, suppose you have a natural deductive system and no axioms. Suppose you want to show that CApqAqp, where "C" denotes the material conditional and "A" disjunction. Though there do exist many ways to prove this in this context, at least most of them, rely on working with a contingent statement form like "Apq".

So, if mean by "valid" you mean "meaningful", then since in logic and mathematics there exist meaningful or valid claims which are not provable or refutable, it stands to reason that there exist valid scientific claims which are not provable or refutable. That said, the scope of a claim needs to get kept in mind. No axiom of say lattice theory can get proven or refuted, and if you lose track of the scope of an axiom, then you might get lead astray and think it can get proven or refuted.

Doug Spoonwood
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  • A valid claim can be validated. I do not understand where the problem with the definition is. So can you validate a claim where there is no way to show it is true or false. – Chad Sep 23 '11 at 16:28
  • @Chad Consider "tomorrow it will rain." If you agree to that as a valid claim, there exists no way to show it true or false today. It could get validated by pointing out certain weather conditions which seem to increase the likelihood that it will rain tomorrow. Consider a "duck-rabbit" figure. Any claim like "this looks like a duck" can't get proven true or false. But, it could get validated by pointing out how it might look like a duck to someone. – Doug Spoonwood Sep 24 '11 at 03:48
  • It "Looks" like a duck would not be a scientific claim. It will rain tomorrow both provable and falsifiable by simply waiting a day. You could even define a true and false state for the it looks like a duck. This question really involves more complex structures like immortality, general existance, and supernatrual beings. As wewll as vague scientific claims about causation and future effects. – Chad Sep 26 '11 at 13:42