When faced with a paradox, we say: well this can't be because it doesn't make sense.

p = "x doesn't make sense"
q = "x doesn't exist"

The contrapositive preserves validity:

p implies q
(not q) implies (not p)

So, if x exists, then x makes sense.

Maybe the objective universe is a proper subset, or equal to the universe of what makes sense. But if this is a sound argument, then we'd know that it's at least a subset of that universe.

I know this is awkward and not perfectly clear, but what are your thoughts on this?

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    The problem with your argument is that there is no reason to accept the assumption that if something doesn't make sense then it doesn't exist. To take a simple counter-example, words written on a piece of paper may not make sense but still exist. – Eliran Jul 15 '19 at 22:25
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    @Eliran But you'd be hard-pressed to defend the idea that saying something, makes it so. – QWERTY_dw Jul 15 '19 at 23:13
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    "Makes sense" is just a generic sign of approval, it does not mean anything in particular, and so "universe of what makes sense" is an empty phrase that lets us "know" nothing. Not to mention that different things, including mutually exclusive ones, "make sense" to different people. – Conifold Jul 15 '19 at 23:19
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    I think you don't understand what I'm saying so let me try again. You said that if x doesn't make sense then x doesn't exist. In my example, x = the words. The words don't make sense, but the words nevertheless exist. – Eliran Jul 15 '19 at 23:47
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    @Eliran I understand what you're saying. But if we make the distinction between, things and representation of nonthings then this is a nonproblem. – QWERTY_dw Jul 15 '19 at 23:50

I find the question a little awkward but important.

In metaphysics 'making sense' would mean being logically coherent. So, where the existence of a thing would not be logically coherent we would assume its non-existence. The usual measure is contradiction, such that if the existence of a thing would cause a formal contradiction then we would assume it does not exist.

The complication is that our usual idea of Existence doesn't make sense, suggesting that nothing exists as we usually think it does. So, we have a choice. We can believe things exist as we usually think they do despite the incoherence of their existence, or we can assume that things do not exist as we usually think they do.

These two views coincided roughly with 'Western' thought, which is stereotypically naively-realistic, and 'mysticism' or the Perennial philosophy, for which Existence would not be what we usually think it is.

It is an odd philosophical fact that the latter is more in accord with reason and logic than the latter. Thus Russell, having rejected the latter view, must dismiss metaphysics as useless, while the 'mystical' view he works so hard to avoid makes full use of it.

Your p and q argument is fairly meaningless unless you carefully define what you mean by 'make sense' and 'existence', but it might work with the right definitions.

Perhaps you could ask yourself whether you can make sense of Existence. Your argument suggests that if you cannot do so then nothing exists. This seems a rather strange argument. I would rather say that if you cannot make sense of existence within a metaphysical theory, its origin and nature, then things do not exist in the way the theory states.

Thus rather than say a thing cannot exist if its existence would be logically incoherent, (such that its existence would be a 'true contradiction'), it would be better to say either it does not exist or our idea of 'things' and their existence is incoherent. Which it is would be for us to figure out as a separate issue.

If your idea of existence is incoherent then your argument will force you to deny the existence of everything. If your idea of existence is coherent then I think it might work, but you'd have to clarify what you mean by 'make sense'.

EDIT: The question title seems to have changed, or maybe I misread it. So, I'll just add that there is no evidence to suggest the world does not make sense, but plenty to suggest it is not easy to make sense of it.

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The formalist mathematician David Hilbert wrote: (page 185)

I myself have always supposed that only statements, and hypotheses insofar as they lead through deductions to statements, could contradict one another. The view that facts and events could themselves be in contradiction seems to me to be a prime example of careless thinking.

What Hilbert is saying about contradictions may apply to paradox and even validity. The paradox, contradiction and validity is in our language.

The OP notes the following:

Maybe the objective universe is a proper subset, or equal to the universe of what makes sense. But if this is a sound argument, then we'd know that it's at least a subset of that universe.

Although our languages are part of the universe, properties such as contradiction, paradox and validity apply to the domain of "statements, and hypotheses insofar as they lead through deductions to statements". They are properties of certain statements in our languages and not to the universe as a whole.

Hilbert, D. On the infinite. Reprinted in Benacerraf, P & Putnam, H. Philosophy of mathematics: selected readings Second Edition. 1983. Cambridge.

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