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Tusi wrote a compact treatise on establishing the existence of a being separate from matter that is the ground of the truth of our necessary judgments. Here’s my summary of his argument:

A necessary truth is one whose truth-value can’t change. Now, where p (= belief, judgment, proposition, statement) is necessarily true, concede this: p is true iff p corresponds to something.

This something then, call it x, to which p corresponds, either exists (1) outside the mind or (2) it doesn’t. If (2), it follows that p* (where p* is a false judgment, belief, proposition, statement) is true; for p* also has something corresponding to it in the mind. But that’s a contradiction. Therefore, x exists outside the mind.

As external to the mind, x is either (1.1) self-subsistent or (1.2) inheres in another being. If (1.1), x is either (1.1.1) spatio-temporally located or (1.1.2) not. If (1.1.1), p would not be, contra what was assumed, necessarily true. But that’s a contradiction. If (1.1.2), x would be a Platonic Form. But there are no such entities. Therefore, (1.2) x inheres in another being outside the mind.

This other being x inheres in is itself either (1.2.1) spatio-temporally located or (1.2.2) not. If (1.2.1), x would inherent its spatio-temporal condition; p would then, again, not be necessarily true –  a contradiction. Therefore, (1.2.1) x inheres in another being that is not spatio-temporally located.

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