On the Existence of Abstract Propositions and a Corresponding "Abstractese"

In the question of the ontological status of propositions, the realist claims that propositions are actually existing abstract entities to which our that-clauses refer. But if this is the case, then they must be in some sort of language -- for if they are not expressed linguistically in abstract-land, then it is hard to imagine how that-clauses could refer to them. That-clauses refer to concepts which seem to be expressed entirely through language. Indeed, what is an expression if not some sentence in some language? So which languageis it? Is it English? Surely not, because then English would be the perfect language: the language of thought. No, surely it is not any language that we now speak because if such a pure and natural language existed it surely would have revealed itself by now.

I am aware that a scientist might, here, complain that the language of nature is mathematics. But, I would respond, mathematics cannot explain itself in its own terms, and this has been proven by Gödel. The basic gist of Gödel's theorem is that no mathematical system can proven from a finite set of axioms, which means that no set of axioms can develop a system in which those axioms themselves are all provable. There is always a further axiom that must be added. And if a mathematical system is not provably true, then, in the multitude of mathematical systems, no one system can be a more appropriate language for absractese than any other.

But, you might say, what about a logical system? For because mathematical systems can be derived from symbolic logic, the natural language must be logic, which is more fundamental than mathematics. But the problem here is that logical language cannot support itself, as Quine, Putnam and Kripke's Wittgenstein have all independently shown. Language cannot explain itself in its own terms -- it cannot account for the experience of meaning that we all seem to have. Nothing like Frege's concept of a "sense" of a word, which is a meaning that is independent from the group of things to which we apply the word, has yet been found within language itself.

Therefore, abstractese must be some language that none of us speak. Let us call this language abstractese. So who speaks the perfect language out of which all propositions are formulated? Who has complete access to proposition-land where abstractese is the language of omniscience? Everyone should know the answer by now: It is God. The semantic realist has found a way to sneak God in through the backdoor. "God must exist," such a realist might claim, "because without him, there is nothing we could mean when we speak!"

It seems appropriate that we call mathematical realism "Platonism." For it was Plato that suggested to us that it wasn't enough for us to believe in an ontology of two substances: mind and matter (though Heraclitus did believe this, to his credit). Rather, he wanted us to believe in a third: the Good, where Forms and Mathematicals and other strange abstracta float freely. This one mistake has sent philosophy reeling for millennia. Plato was the first systematic philosopher who had a system worth mentioning, but it was a system that assumed an unprovable monism. Plato ignored the mind altogether and contrasted the physical world to the abstract. Out of respect for the more mysterious force, Plato decided that the abstract was the primary realm, and the physical was the derived realm. Of course, Christianity found a way to borrow this concept as well, which has provided years upon years of highly nuanced philosophy, otherwise known as "theology". Indeed, it was not until Descartes that we finally remembered that the mind creates its own realm. What Descartes should have mentioned was what Kant ultimately did mention: it is the mental and the physical which represent the real dichotomy. Those who ask what is outside the mind or outside the world are trying to posit things without sufficient cause.

The problem of the reference of words, phrases and entire clauses is the standard point of attack for realists against anti-realists. In this instance, the realist proposes these putatuve abstractese propositions as the objects to which that-clauses refer. But my question is this: if there is only the world and the mind that thinks the world, then why should our thoughts refer to anything but themselves? A thought can only be had mentally, so if the reference of the thought itself is mental, then the thought simply refers to itself. So if we adopt a mental ontology stance for propositions, that-clauses just refer to thoughts. How utterly intuitive!

But is this proof that some object or event named "mind" is the source of meaning? Well, the only proof that mind exists is the experience that a particular mind has. But because the specific content of this experience can only be explained after the fact, its existence is not provable deductively. Thus, the only evidence we have for the existence of the mind is inductive. But this essentially means that the act of inductive reasoning can only be supported inductively.

And here we have our answer. Symbolic logic and mathematics lacked the capability to prove their own premises. That is, deductive reasoning cannot be proven uniquely. But inductive reasoning can. If it is assumed that inductive reasoning leads us closer to the truth, then inductive reasoning can prove that it leads us closer to the truth, without the assistance of any other premise. So we have good reason to believe that abstractese is really the same as mentalese.

-Priam's Pride