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I am wondering how much of the semantic of basic philosophical questions can be expressed by formal arguments in modal logic. Here is one argument I formalised myself:

P1 ◇ ∀a, ∃x // GNB(x, a) ∧ C(a) ≡ S(x)

P2 ◻ ∀b, ∃y // GNB(y, b) ∧ A(b) ≡ F(S(y))

C ◇ ∀c // A(c) ≡ F(C(c))

The original argument, in ordinary language, proved very difficult to understand for most people I have tested with it.

Is it possible to prove the validity of such an argument in a formal way, given its apparent complexity for most people? How complex proven arguments can be? Could you give a representative example of a complex argument?

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    Is GNB a single predicate symbol? – Gregory Nisbet Jan 16 at 21:55
  • I am unsure of the symbolism; it would be a great help if you explain them. – Bertrand Wittgenstein's Ghost Jan 17 at 7:29
  • I'm not sure that the argument is formally valid; forget about GNB... we instantiate the universal quantifiers of P1 and P2 with c, but the x of P1 and the y of P2 can be different. Thus, we have C(c)=S(x1) from P1 and A(c)=F(S(x2)) from P2 and we cannot perform the required substitution. – Mauro ALLEGRANZA Jan 17 at 7:41
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    @GregoryNisbet Yes, GNB(x, a) could be rewritten as G(x, a) for example. – Speakpigeon Jan 17 at 10:42
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    @BertrandWittgenstein'sGhost ◇ ∀a, ∃x // GNB(x, a) ∧ C(a) ≡ S(x) just mean: For all we know, it is possible that whatever a, there is at least one x such that the predicate GNB is true of the ordered pair (x, a) and that the predicate C being true of a is identical to the predicate S being true of x. Is that enough? – Speakpigeon Jan 17 at 10:47

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