I want to know if proving the existence of something by using only logic is possible.

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    By only logic do you mean only formal logic but not math? Or do you mean proving something exists without direct experience or observation? For example mathematical objects have mathematical but not physical existence, and we can use logic plus some math axioms to prove their mathematical existence. Is that what you mean? – user4894 Jan 24 '19 at 23:32
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    Nothing can be proved by logic only. Logic connects premises to conclusions, it can not generate premises out of nothing. To prove something, one has to assume something. – Conifold Jan 24 '19 at 23:49
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    The only way in which you might be able to get an affirmative answer is from the fact that it is a theorem of standard predicate logic that something exists. This is a very weak proposition however, amounting to nothing more than the assumption that the domain is non-empty. – Bumble Jan 25 '19 at 1:56
  • You can logically prove that logical arguments exists, and that something that can use logical arguments exists, and all that that implies. – Ask About Monica Jan 25 '19 at 17:56

No, it general it can’t.

To show that something exists one has to either find it, like Mount Everest or to construct it, like an aeroplane.

Some people make an exception for mathematics arguing that anything that can be defined consistently neccesarily exists, this is the formalist programme. This misses the point that often things are found or constructed first without their being a consistent way of defining them. An important example of this is Feynmans Path Integral. Another important example is the calculus which is at the root of the modern effloresence of the sciences.

The other important concern missed by the formalist programme is of relevance. Far too much mathematics is shown to ‘exist’ whose relevance is dubious at best, and misleading at worst.

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No, this is the lesson of Goedel's incompleteness theorem: no self-consistent system is sufficient. We also get this sense from Decartes: without some superfact such as "I exist", we can't even know anything.

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    This has absolutely nothing to do with the Goedel incompleteness theorem – Jishin Noben Jan 24 '19 at 23:21
  • @JishinNoben, I saw the parallel that logic is kind of like arithmetic, and "proving something exists" is equivalent to the consistent system of axioms (logic, in this case) being true. – elliot svensson Jan 24 '19 at 23:40
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    "Proving something exists" is not equivalent to a set of consistent axioms; not in the least. Philosophical argumentation calls for correct use of words and theories. Goedels theorem has been misused enough, so much that a book was written about it. – Jishin Noben Jan 24 '19 at 23:50
  • I think the answer is still no though. Without axioms nothing can be deduced. Descartes managed to narrow existence down to thought.. but went on to misuse logic to arrive at dualism. (Leibniz’s law.. doubt is a mental phenomenon etc.) – Richard Jan 25 '19 at 0:21
  • That theorem only states that some mathematical frameworks can have no proofs. Regardless of assumptions. There are weaker frameworks where proofs are possible, but all frameworks themselves are based on assumptions. – rus9384 Jan 25 '19 at 9:31

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