PHILOSOPHICAL EGGS

Truth, for so many thinkers throughout history, has been seen as existing independent of human minds. But it seems far more sensible to embrace an anthropological account of truth which Robert Adams nicely describes as the view “that the truths of logic and mathematics are true in virtue of some feature of human thought, which might be ideas in our heads, our intentions regarding our use of language, or proofs we have actually constructed.” (see his book Leibniz: Determinist, Theist, Idealist, p. 182) But this view, while initially plausible, seems to have the following undesirable and counter-intuitive implications that, once understood, may make a commitment to an inhuman ground of truth more attractive: (1) there are no propositions whose truth or falsity we have not yet uncovered or will never uncover; (2) there are true propositions that have no contradictories which threatens the foundations of logic; (3) human communication about the same propositions would seem impossible; (4) truth, rather than our estimations of the truth, would change; (5) there would be no necessary truths, that is, truths that are true in all possible worlds; and (6) the impressive applicability of necessary truths to the physical world becomes unacceptably mysterious. Let me take each in turn.

(1) and (2) can be approached by considering a thought-experiment presented by Bradley and Swartz. Suppose someone is walking alone in the woods and encounters a birch tree which he correctly believes is a birch. Thus, according to the theory that propositions are human creations, we would maintain that the person has a true proposition in his mind or brain, a proposition that doesn’t exist independently of the man and which came into existence with his encounter and consideration of the tree.  Now, suppose further that the birch subsequently burns down in a forest fire and no one ever entertains the false proposition that the tree the man encountered was not a birch. This would mean, as Bradley and Swartz point out, “we would have to give up the claim that to every truth there corresponds a non-empty class of falsehoods each of which is a contradictory of that truth. Under this proposal, some truths and some falsehoods would be without contradictories. Not only would this make shambles of logic; it is thoroughly counterintuitive as well. We have a strong disposition to insist that even if no one were to believe of the birch tree that it is not a birch [believing here would be having an affirmative attitude towards the proposition ‘this tree is not a birch’], then were anyone to believe it, what he would believe is false” (see their book Possible Worlds, p. 70). So by agreeing that propositions are not human constructions we can do justice to logic and account for our intuition that there are propositions independent of us whose truth value we don’t know yet or will never know.

(3), that human communication about the same propositions would be impossible, seems to follow if we only share information about propositions that reside in our particular, changing, and unique minds. But if propositions are independent of human minds then perhaps we can think and talk about the same propositions (for example the Pythagorean Theorem). This seems to be required if we are going to have objective truth and avoid the pitfalls of relativism.

(4) In his dialogue On Free Choice of the Will (Macmillan, 1964) St. Augustine wrote: “If truth were equal to our minds, it would be subject to change. Our minds sometimes see more and sometimes less, and because of this we acknowledge that they are mutable. Truth, remaining in itself, does not gain anything when we see it, or lose anything when we do not see it” (p. 67). If so-called true propositions reside in our changing minds then truth would change which is absurd. To be sure, our estimations of the truth change. But not the truth itself.

(5) If all truth is a function of human beings then, since humans are contingent beings that at one time didn’t exist, we would have to accept that truth is as contingent as we are. But this seems unacceptable for at least three reasons.

First, axiom 5 of modal logic (logic that deals with contingency, necessity, possibility, or impossibility), an axiom included in the widely accepted system of modal logic S5, states that, as Raymond Bradley and Norman Swartz nicely put it in prose, “if a proposition P is possibly true, that is, if P is true in at least one possible world then the proposition that it is true in at least one possible world will be true in all possible worlds and thus necessary” (see their book Possible Worlds, pp. 223-224). For example, the sentence ‘Dwight Goodyear was born in 1970’ expresses a proposition that is contingently true (true in some worlds and false in others) and thus possible since something is possible if it is true in at least one world. But once we have this possibility in place then, according to S5, we can infer the following necessary truth that holds in all possible worlds:

‘The proposition ‘Dwight Goodyear was born in 1970′ is true in at least one world’.

So according to S5 all possibility claims entail necessary truths that exist in all possible worlds – even worlds without humans. And we should accept S5 since it comports so well with our modal intuitions and helps us make sense of modal logic.

A second reason for believing in necessarily true propositions is this: if we don’t postulate them then, as Alvin Plantinga points out, certain counterfactual claims (a counterfactual is a subjunctive conditional containing an if-clause which is contrary to fact) cannot be coherently described such as “if there had been no human beings, it would have been true that there are no human beings” (see Plantinga, Warrant and Proper Function, pp. 117-120). After all, if propositions aren’t necessary – if they are just contingently existing things that arose when humans began to entertain and express them – then there would be no propositions if there were no humans. And if there were no humans then the proposition ‘there are no human beings’ would not be true (since there would be no propositions at all to be true or false). But isn’t that absurd? Don’t we want to avoid being committed to, as Plantinga puts it, “possibly, (there are no people and it is not true that there are no people)”? (118)

Now it might be thought that we could get along with forms of relative necessity in which certain things necessarily follow once a set of contingent limitations is established. For example: (a) It is not physically possible to go faster than the speed of light given the laws of nature as we currently understand them. But these laws, we can easily imagine, could be different in a different possible world or indeed our own. (b) It is not biologically possible for me, given my genetic make up, to naturally sprout some wings and fly. But we can easily imagine a different genetic makeup for me in a different possible world. (c) It is not possible for someone living in New York to legally have many wives given the laws of the state. But we can easily imagine the laws being changed. In each of these cases there is a form of necessity in place which, upon consideration, is revealed to be relative or contingent: relative to certain conditions such as laws of nature, biology, and the state.

But it may be that an understanding of these forms of relative necessity requires a notion of absolute necessity. Joseph Melia explains in his book Modality: “There are indeed many forms of necessity. But many can be defined in terms of what is (absolutely) compatible with a certain set of facts, which we have arbitrarily decided to keep fixed. Throughout, a particular kind of necessity – absolute necessity – is needed to define these various relative modalities. Moreover, the mere notion of relative modality is not enough to capture a distinction we want to capture: a distinction in kind between the laws of logic and the laws of biology; a distinction in kind between the laws of mathematics and the laws of physics – a distinction between what is absolutely necessary and what is absolutely contingent” (pp. 17-18). But if we accept the anthropological account of truth then there will be no absolutely necessary truths and therefore, perhaps, no relatively necessary truths either. Thus we have a third reason to accept necessarily true propositions.

(6), the claim that the successful applicability of necessary truths to the physical world becomes unacceptably mysterious, is nicely presented in the form of a question by Bradley and Swartz: “[I]f these necessary truths are merely the result of arbitrary human conventions for the use of mathematical symbols, all this [successful application of necessary truths] becomes a seeming miracle. Why should the world conform so felicitously to the consequences of our linguistic stipulations?” They argue that it is precisely by embracing necessary truths as propositions which are true in all possible worlds, including worlds without humans, that we can provide an adequate explanation of their application in engineering, aeronautics, and so on: “Necessary truths, such as those of mathematics, apply to the world because they are true in all possible worlds; and since the actual world is a possible world it follows that they are true in (i.e., apply to) the actual world” (Possible Worlds, p. 61).

If this cumulative case against the anthropological view of truth succeeds then truth wouldn’t be a human construction. Rather, when we think true propositions we would be contacting entities independent of ourselves. But what would these entities be? Could they be, as Augustine argued, ideas in God’s mind? Could they be propositions in multiple non-human minds? Might they be abstract entities that exist outside of space and time independent of all minds as some Platonists believe? Or could true propositions be facts or states of affairs as Bertrand Russell once maintained? Are there some other plausible options? What are they?