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Is it a truism that, except for that which is proven impossible, everything is or must be considered possible? If so, why? It seems to me to be an argument from ignorance to say that just because we don't know whether something is impossible, we should therefore conclude it is possible.

  • It is a 'truism', in the sense of a useful platitude. It is obviously completely impossible and thus not true: unresolved questions where proof exists on neither side obviously cannot be considered both true and false at the same time, only alternately. It retains currency because it enforces the notion that you can't pointlessly shut down arguments you don't like without a counterargument. An open question 'must' be open to further consideration. That doesn't mean we won't eventually determine that it was never actually possible for it to be true. That 'must' is about manners, not facts. – jobermark Mar 9 at 0:04
  • On standard interpretations of modal logic this is false. Just because it is not proven yet that it is impossible for perfect numbers to be odd does not mean that it is possible (and most mathematicians believe it isn't). The error comes from confusing two different senses of possibility: epistemic (possible-as-far-as-we-know) and substantive (logical, physical, etc., depending on the context). We simply do not know whether something is (substantively) possible or not until it is proven so one way or the other, otherwise we get a logic where propositions true today will become false tomorrow. – Conifold Mar 9 at 5:04
  • proofs lie in the assertion, not in the negation. You can prove possibilities, you cannot prove impossibilities. Argumentation proofs are for showing possibilities, not impossibilities. – Swami Vishwananda Mar 10 at 9:22
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If the argument is: "there's no proof that X is impossible, therefore X is possible" then it is a fallacy of argument from ignorance, which takes the following form:

There's no proof that X is true.

Therefore, X is false.

So, for example, it is fallacious to argue that there are unicorns on mars just because there's no proof that there aren't.

It's also a strange thing to say "we don't know whether X, therefore not-X", because "we don't know whether X" just means "we don't know whether X or not-X" which implies both that we don't know that X and that we don't know that not-X.

  • I think you swapped true and false with your argument from ignorance form. – Cell Mar 8 at 19:44
  • @Cell It doesn't matter as the fallacy works both ways (true->false and false->true). – Eliran Mar 8 at 19:55
  • @Eliran Thank you for explaining! Would it make a difference if the word "possible" was referring to "logically possible"? I'm trying to explain to someone in a debate I'm currently having, that their claim "except for that which is proven impossible, everything must be considered possible" is not a truism, but an argument from ignorance, and they're now going on about how it's talking about logically possibility, which I find confusing. – John Weston Mar 8 at 20:07
  • @JohnWeston It makes no difference, if the argument is "it's not proven to be logically impossible, so it's logically possible". That's still in the form of argument from ignorance (not proven that X, therefore not-X). Also it's worth keeping in mind that "logically possible" doesn't say much. It's logically possible that the world will end tomorrow at exactly 3:14 pm. All kinds of things are logically possible but that doesn't mean we have any reason to think they are true or even likely to be true. – Eliran Mar 8 at 20:58
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The proposition "Everything must be considered possible" is an example of the kind of proposition that Plato's peritrope argument is designed to refute.

The peritrope or table-turning argument appears in Theaetetus as Socrates' coup de grace against Protagorean relativism. Its confutational sting lies in the fact that any assertion of the general proposition containing the relativism in question entails a contradiction and is, therefore, incoherent or false.

Socrates argues that Protagoras' pronouncement of "Man is the measure" entails that all opinions are true for the people holding them. So, someone who believes that Protagoras is correct would assert the proposition "Protagoras' claim that "man is the measure" is true."

However, someone who believes that Protagoras' is incorrect would assert the proposition "Protagoras' claim that "man is the measure" is false.

According to Protagoras' dictum, both propositions are true for those who assert them, so the proposition "Protagoras' claim that 'man is the measure' is true and false" must be true. But this is a manifest absurdity and must be false according to Socrates.

It seems that the proposition "Everything must be considered possible" entails a contradiction. If everything must be considered possible, then it must be considered possible for something to be impossible.

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I don't think there is much to ponder over.

Is anything not proven impossible therefore possible?

'Not proven impossible' means, it is yet to be proven. In other words nothing is proven (in this case). I am saying so because, you can't ask this question hiding the truth if possibility has been already proven. We all have a tendency to consider many things as understood. Here also 'not proven impossible' implies it is 'not proven possible'. Otherwise it is hiding a truth. We can't expect correct answer to a wrong question. See this:Does hiding a truth constitute lying?

So, if you change that part this way--'Not proven possible', the answer must be the same. Now see what happens to this question: Is anything not proven possible therefore possible? To this question, we can only say, 'sometimes'.

So your question also deserves the same reply--'sometimes'. Not, 'Not proven impossible therefore possible.' We can conclude it this way: 'Not proven impossible is sometimes possible.' This is the same answer we get without going through all these stuffs. That was why I said, 'there is not much to ponder over.'

Without asking any counter-question, this would be the most suitable answer even though the truth is hidden; I think.

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