Arithmetic and Future Fact

We are committed to the thesis that English has no way of encoding claims of future fact, because all English messages concerning future time are judgements (that is, tensed verdicts), and verdicts do not have truth-values and so cannot possibly depone fact.

Agent Comboni raises the question of arithmetic. In a nutshell, her worry is that

Two plus three will be five tomorrow

surely propounds a fact, albeit a mathematical one; and therefore something true or false. And yet on our account the form of the sentence indicates that the encoded message is a judgement, an item lacking a truth-value.

The problem (if it is a problem) is not just about ‘will’. It is about abstract thought in general. For we are in any case committed to the doctrine that the ‘is’ in

Two plus three is five

encodes a piece of temporal intelligence. Specifically, it locates the claim at the point of speech. And yet surely no temporal intelligence is either intended or conveyed when that sentence is uttered. How is this possible?

Simply because all parties know that time is not of the essence where arithmetic is concerned. English grammar requires a choice of verb form, so a speaker must select between (say) ‘is’ and ‘was’ and ‘had been’. But neither speaker nor hearer pay any attention to it, and the temporal information is not an ingredient of the message conveyed.

So if this is a problem for anybody, it is a problem for arithmeticians, and not a problem for the code, whose resources (nota very bene) remain unimpaired. After all, we can still say

2 plus 3 is 5 today, but things may have been different in the Old Stone Age.

And sometimes we will actually need to encode pieces of temporal intelligence:

Yes, Cretin-Mangler, two plus three will be five tomorrow. It is five, it always was five, and it always will be five.

If 2 was/had been odd, then all its powers would be/would have been odd.

So even though

2 plus 3 will be 5 tomorrow

technically encodes a judgement, all can appreciate that the arithmetical fact in question is not a future fact, because not a temporally located fact at all. It holds at any point in time purely because it holds simpliciter.

You can read a more detailed version of this point in Dudman, “Conditional Interpretations of If-Sentences” (1984).  Search for ‘arithmetic’, or just go to Section 48 on page 196.

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