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We cannot limit the evidences quantitatively or qualitatively. In some cases just one would be enough. But in some cases this wouldn't be enough. For example, we can put forward so many evidences for the existence/reality of this universe as we experience it now. But a time will come when one realizes the true knowledge about existence/reality. Then all the ...


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I know it’s a formal logic question with a mechanical proof, but maybe taking a semantic approach might help you see what’s going on. Firstly, we’re talking about a constant object C. (In practice C might be a parameter for any object, but let’s think of it in specific terms first) We have three premises about C to start with. Firstly, the last one is the ...


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Lines 6 and 7 should not be assumptions. They should be derived from Premise 1 by conjunction elimination; and thus do not raise contexts. The disjunction you should be eliminating is ~Mythical(c) v Mythical(c), derived by LEM. If you cannot use a TautCon to derive ~Mythical(c) v Mythical(c) you can use nested proof by contradiction. |_ : | |_ ~...


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I have a feeling that we need to use ∀Intro for the second conjunct of conclusion as well as ∀z (Cube(z) → (z = x v z = y)) part of premise. Yes, you need to apply Universal Elimination thrice, once to each arbitrary term. You can then derive three disjunctions through Conditional Eliminations. Up next is a nested disjunction elimination, where you ...


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Hint: Universal elimination can be to any term in the context, which includes the assumed witness for the existential. |_ Ex Ay (Cube(y)<->y=x) Premise | |_ [a] Ay (Cube(y)<->y=a) Assumption | | Cube(a)<->a=a Universal Elimination | | : | | : | | Ex (Cube(x) & Ay (Cube(y)->y=x)) ...


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I am not sure why I cannot assume the negation of B. You can assume it; it just will not do anything for you. You do not have the disjunction ~B v C derived anywhere to "eliminate". Disjunction elimination is the "Proof By Cases" structure. Building it requires a disjunction, and two subproofs. In each subproof you derive the same conclusion from the ...


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This is as close as I got: I think I'm stuck on the last step. Please update if you end up finding out how to do it. Cheers!


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Inside the subproof for B: Instead of doing a subproof with ~B, do one with A, so that you set up a v Elim on A v C Also: I note that the last line does not check out ... did you forget to select A v B as the statement on which to apply the v Elim? It's a common mistake to only point to the subproofs, and forget to point to the v statement that is actually ...


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If there was no way of proving that dinosaurs existed would it still be true that they did? Truth is truth regardless of who knows it, or whether nobody seems to know it. Can there be truths no evidence of which exists? In the sense of transient facts that are of no importance, maybe (such as instantaneous the position of every particle in the universe ...


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Let's use a concrete example. There exist supermassive black holes such that the tidal forces at the event horizon aren't strong enough to tear you apart. Suppose we were to throw an enthusiastic volunteer across the event horizon along with a red button. After 30 seconds (using their inertial reference frame), they either push the button or they don't. By ...


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Note that the first premise is a conjunction. So, you can just get the two conjuncts using Conjunction Elimination. You have the two conjuncts as the respective assumptions of the two subproofs you have, which would make sense if the conjunction was a disjunction ... but it is not. So again, you can get the two conjuncts at 'ground' level ... and hence you ...


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Yes .the proof of your truth ,which lacks evidence ,need only make sense i.e convince the mind of your companion with fact of your proposed proof


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Clearly there is scope for different views on this but it is largely a matter of your choice of terminology. I prefer to consider that exactly one of the two statements "Intelligent life exists on other planets" and "Intelligent life does not exist on other planets" must be true, but we have no evidence to tell us which of the two statements is true. But if ...


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Evidence requires a truth to be evidence of, but a truth does not require evidence to be true. We don't know everything. Thus we are missing evidence, thus there are truths we don't have the evidence for. But even if that evidence wouldn't exist, that wouldn't make the truths any less true. Dinosaurs existed. We know that because of the fossils, but even ...


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I would say they exist because of the definition of Knowledge as Justifiable True Belief. Now obviously the answer is that it's subjective, because we're going to have to define a lot of terms. However, the claim that knowledge is "justifiable true belief" is popular enough to be a meaningful anchor in the discussion. In particular, I point out that "...


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Evidence is an interpretation, connected points of view, or rather connected assumptions. Its definitive nature differs little from wittgenstein's very short statement about tautologies. At best evidence is a form, in a platonic sense, where empirical truth is a matter of memory due to the flow of time. You can prove that the dinosaurs existed, without ...


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The answer is a point of contention between realism and anti-realism. Truths that "do not have evidence" are termed verification-transcendent truths (coined by Dummett), and realists are committed to their existence. Anti-realists, on the other hand, hold that unverifiable in principle statements have no truth values. So if no trace of dinosaurs remains, ...


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