Token-Omniscience?

It was in an article written by Stephen Torre which I read very recently that I was introduced to a very intriguing idea; namely, that tokens, and not propositions, are the fundamental bearers of truth-values. The usual view, of course, is that propositions (whatever one thinks of them) are those things to which the categories/properties ‘true’ and ‘false’ exclusively apply. Tokens, then, merely express truths insofar as (and just in case) they express propositions which are true. On the alternative story, which Torre refers to as the “Token View,” it is tokens which are the fundamental truth-bearers. This alternative story is as indifferent to different theories of truth (eg. correspondence, coherence, pragmatist) as the usual story. Turning to Torre, we read:

“There are different views regarding what the fundamental bearers of truth are. One view is that truth applies fundamentally to tokens. On this view, the predicate ‘is true’ is properly applied only to tokens. Such a view is committed to denying that there are token-independent truths. I will refer to this view as the ‘Token View’. A rival view takes truth to apply fundamentally to propositions. On this view, tokens are true or false only derivatively: tokens express propositions and a token is true iff it expresses a true proposition. This view does allow for the existence of token-independent truths.”[1]

I think it is worth having a bit of fun thinking about what the consequences of this prima facie absurd view would be. As it turns out, the view might have some theologically welcome consequences. For instance, it seems clear that the alleged set-theoretic problems for the doctrine of omniscience are evaporated of significance; even if there is no such thing as the set of all (true) propositions, there is clearly[2] such a thing as the set of all (true) tokens, at least if tokens are created by finitely many minds with finite capacities/abilities.

Tokens, like propositions, may require facts (i.e., extra-mental and extra-linguistic truth-makers), but God could be omniscient either factually (i.e., by having direct unmediated acquaintance with the facts, rather than their representations to the discursive intellect in the form of tokens or propositions), or else God can be token-omniscient. What is it, precisely, to be token-omniscient? Let us stipulate a definition:

G is token-omniscient =def. G knows all true tokens, and believes no false tokens.

Suppose that this view is correct quarum gratia argumentum, and suppose that God’s mental activity produces tokens. In this case it looks as though an old adage of Christian theology is more literally true than it seemed at first glance: to think truly is to think God’s thoughts after Him.

Objection 1: Surely quantification over tokens isn’t problematic unless there are indefinitely many of them. However, it is difficult to imagine a finite mind tokening a truth as of yet not tokened by God, even in any logically possible world. It seems plausible to say, then, that if God tokens any truths then he tokens all truths, but the set of all truths is indefinitely large. Set-theorists have no problem quantifying over infinite sets; the problem was always with quantifying over ‘indefinite’ sets, which are not sets at all. If the set of all true tokens is indefinitely large then the problem recurs.

Response 1: Perhaps we should make a distinction analogous to the distinction between first-order propositions (propositions about the world) and second-order propositions (propositions about propositions about the world), and restrict God’s knowledge to first-order tokens.

G is first-order token-omniscient =def. G knows all true first-order tokens, and believes no false tokens.

God would, of course, still know all first-order tokens about second/third/quadruple/etc-order tokens which occur to finite minds, and that seems sufficient for omniscience.

Objection 2: suppose that (logically/explanatorily) prior to God’s creating anything, He realizes that there are no tokens, and, in realizing this (and being always first-order token omniscient), mentally produces the first-order token T1: “there are no tokens.” This is false, and (being a token), is necessarily false. God would not only not be Token-Omniscient, but wouldn’t even have (all and) only true beliefs.

Response 2: It might not be logically possible for God to token T1, but perhaps it is possible, and inevitable (given the assumptions upon which we are now working in this thought experiment), that God token T2: “There are no (other) tokens” or, rephrased more elaborately, T2’:“there are no tokens other than this one.” Perhaps to avoid self-reference paradoxes we should say of tokens, as I am inclined to say of propositions, that (unless they pick out a universal quality, such as the disjunctive property of being true or false or meaningless) they all come with a caveat de aliis implicite (i.e., with an implicit caveat that they are ‘about’ others). Such stand-alone sentences as “the set of all things I say in this sentence is imponderable” are not true, they are entirely bereft of truth-apt content! Pseudo-meaningful sentence constructions. So also, it seems to me, “this sentence is true” is meaningless, and “there are no sentences” is meaningless. [I am not sure I’m right about this; this is just a knee-jerk reaction on my part to self-reference paradoxes].

What are the downsides of this view (other, of course, than that it seems crazy)? I’m not sure I can think of any unanswerable objections to it, and that alone may make it worth pondering, at least for fun.

 

Edit: Ok, here’s an obvious objection to Token-Omniscience which I, for whatever reason, didn’t think of previously: suppose I token the following: “I am Tyler.” The token’s content is irreducibly bound up with the sense of the indexical ‘I’ in such a way that nobody distinct from me could recognize that token as true, even if they could have recognized the propositional content to be true. The token, per se, is unknowable to any being distinct from me. Therefore, if tokens are the fundamental truth-bearers, and any more than one being ever uses a personal pronoun to index themselves in tokening a truth, no being can be (first-order) token-omniscient. That seems like a pretty definitive defeater to token-omniscience to me.

 

[1] Torre, Stephan. “Truth-conditions, truth-bearers and the new B-theory of time.” Philosophical Studies 142, no. 3 (2009): 325-344.

[2] I assume that it is logically impossible to have an actually infinite set of tokens created by finitely many finite minds. This can be challenged, of course, by either insisting that there is no absurdity, contra apparentiam, in positing actual infinities, or else that the absurdities do not arise for tokens. If such suggestions are to be taken seriously, then I would have to weaken my claim here from ‘clearly’ to ‘plausibly,’ but all else would remain the same.

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One thought on “Token-Omniscience?

  1. In the book Paul Gould edited “Beyond the Control of God”, Graham Oppy says:
    On the view that I favor, tokenings are the base-level truthbearers, and—perhaps—tokens and propositions are derivative truthbearers. … If there are propositions, then tokenings involve both tokens and propositions—”vehicles” and “contents”—but the base-level truthbearers are the tokenings, and not either the tokens or the propositions. … Tokenings are intentional—tokenings are about things. So, for example, thought tokenings are intentional—thought tokenings are about things. … Given the distinction between tokenings, tokens, and propositions, it is, I think, quite clear that, while tokenings are mind-dependent objects, tokens and propositions need not be. Certainly, once produced, written and verbal tokens are not mind-dependent; but, if there are mental tokens then, of course, they are mind-dependent. However, crucially, if there are propositions, then there is simply no reason at all to suppose that propositions are mind-dependent. If there are propositions, then propositions are the contents of tokens involved in particular tokenings-but, as just noted, it is the tokenings that are the clearly mind-dependent entities.

    Paul Gould and Richard Brian Davis describe Oppy’s view:
    Oppy isn’t inclined to think that propositions are truthbearers; nor are they to be identified with thoughts. Rather, on his favored view, there are tokens (e.g. the inscription “Quine is wise”), propositions (e.g. the content of “Quine is wise”), and tokenings (e.g. my producing the token “Quine is wise”). Oppy’s claim is that only tokenings are truthbearers, since only tokenings are intentional.

    I don’t recall Oppy rigorously arguing for his tokening view, but I think it’s similar to Wittgenstein when he says, “a proposition is true if we USE it to say that things stand in a certain way, and they do.”

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