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Sunday, October 13, 2013

Truth-making and Reference-making: Part 1

Part 1: Introducing the Idea

In this post I introduce the idea of reference-making, which I take to be more-or-less undefined, and use it to account for the idea of truth-making for subject-predicate sentences. I take a truth-maker to be a reference-maker for a sentence. In Part 2 I'll give a quasi-formal account of how it can be applied to truth-functional compounds and quantified sentences, and in Part 3 I'll discuss some of its philosophical implications.

Let us say that the reference-maker for a noun or a noun-phrase is just what is ordinarily called its referent,  the thing that it "corresponds to" or '"picks out" in the world. Nothing interesting so far. For predicates, however, the idea is different: Just as sentences can  have many truth-makers--"Planets exist" being made true by each planet--on this view a predicate can have many reference-makers, without thereby becoming ambiguous (as nouns/noun-phrases would become if they had many reference-makers). This is a key difference between predicates and nouns/noun-phrases. We will therefore say that predicates have reference, but not that they have referents. We could say that every reference-maker for F is a referent of F, but that would be misleading in that it would suggest that F was ambiguous. (This is a terminological point introduced to prevent confusion. Nothing beyond that hangs on our choice of terms.) A reference-maker for a predicate is something that it is true of, or that satisfies it. Any red thing is a reference-maker for the predicate 'red' or 'is red'. In this 'red' and 'is red' differ from 'redness', whose reference maker, if any, is redness; i.e., the property of being red.

Since I take the relation of predicates to reality to be, in general, one-many, I think it would be a mistake to take the "referent" or the semantic value of a predicate to be its extension, the set of things of which it is true. On my view, any reference-maker for a predicate can be said to be a semantic value of the predicate. Still, most predicates of  a given language will have but one meaning.

What of relational predicates? Their reference-makers can indeed be taken to be sets, namely ordered n-tuples. Still, we will not identify "the" semantic value of a predicate with its extension (nor with the property, if any, that it expresses): A reference-maker for an n-ary predicate is any ordered n-tuple of which that predicate is true, not the set of all such n-tuples--unless that set is one of the things of which the predicate is true; but still it would only be only one reference maker among many.

We can now say what a truth-maker, which is a reference maker for a sentence, is for subject-predicate sentences. An object x ('object' being broadly construed as anything that exists) is a truth-maker for a subject-predicate sentence p iff x is a reference-maker for p's subject term and is also a reference-maker for p's predicate term. Similarly, for relational sentences: An ordered n-tuple o is a truth-maker for an n-ary relational sentence p iff the objects ordered in o are each reference makers for one of p's subject terms, and o is a reference-maker for p's predicate term. In Part 2, I'll extend this account to define truth-makers for truth-functional compounds and quantified sentences.


Tristan Haze said...

This is a really interesting series of posts and I'm only just beginning to digest your main ideas here. They strike me as quite original. Do you know anything about the existence of similar or related stuff, and/or can you say anything about what inspired you?

As I say, I'm still digesting this (and flat out on a piece of work of my own at the moment), so I have no substantive comments yet, but here are a couple of minor points to help with the presentation:

From part two: 'We say that x false-maker' - missing 'is a'.

Also, there's a slight failure of parity between 'truth-maker' and 'false-maker' - 'truth' goes with 'falsity', 'false' goes with 'true'. (Perhaps you've noticed this but feel the ring and shortness of it outweighs the slight irregularity.)

From the appendix: 'will unhappy with this result' - missing 'be'.

From the appendix: 'as it stands, bivalence will fail for empty nouns or noun-phrases'. I'm not sure I understand this, but don't you mean 'bivalece will fail for sentences containing empty nouns or noun-phrases'?

Tristan Haze said...

Actually, one possibly substantive question comes to mind already - what are your thoughts on the following?:

An important part of theoretical role that people want truthmakers to play, as I understand it, is something like: the existence of a truth-maker (together perhaps with its internal or essential nature) for a proposition explains the truth of that proposition.

But the things which get called 'truthmakers' are on your account don't seem to fulfil that role. As I understand your account, John himself, if he's tall, is a truthmaker for 'John is tall'. But the mere existence of John, together, even, with his having the essential properties he has, doesn't seem to explain why 'John is tall' is true. (And that seems connected with the fact that your account makes no appeal to properties.)

My initial reaction is: your notion of 'truthmaker' is very interesting, and I'd like to get a better sense of what it can do, but in virtue of the above point, 'truthmaker' might not be a good choice of terminology. Or perhaps you need to emphasize a special story about what the truthmaker role really is.

Jason Zarri said...

Hi Tristan,

Hope you don't mind if I reply to your second comment first.

My initial response would be that what I call truth-makers *do* explain the truth of their corresponding truth-bearers, but that whether some particular truth-maker explains why some particular truth-bearer is a contingent fact. I reject accounts of truth-making in terms of any prior notion of necessitation (as those are currently understood)--instead, I define necessitation in terms of truth-making. If John is tall, John himself really does explain why "John is tall" is true--being tall, after all, *is a way that John is*, albeit a way that he contingently is--it's just that if John had been different, he would not have explained why it is true. John, as he is, is a truth-maker for "John is tall" because he is also a reference-maker for 'tall'. Why is John a reference maker for 'tall'? In part because of of the way John is, and in part because of the meaning of 'tall'. Had he not been a reference-maker for 'tall' (holding the meaning of 'tall' fixed), he would have to have been different. If'ways' talk requires genuine properties, then my account is committed to properties; if it doesn't, then my account does not. If the first holds, I would simply say that what properties--whether they are universals or tropes--help do is *explain why something is a truth-maker for a truth-bearer*--they are meta-explainers, they explain why something explain some truth-bearer's truth. If the second holds, then perhaps we would (given meaning) have to take reference-making to be brute, or posit reference-making as the sole genuine (contingent) relation. In any case, the main moral would be that necessitaion is a sufficient condition for a truth-maker's explaining a truth-bear's truth, but not a necessary condition for its explaining it.

Jason Zarri said...

R.e. your first comment:

Thanks, I'm glad you find it interesting.

As far as I'm aware the ideas are original to me. What motivated me was my desire to develop an account of the truth-making relation which would deliver the result that, insofar as possible, truths should be made true only by what they are intuitively "about". I also had the idea of reference-making, which I regard as an evident analogue of truth-making, floating around in my head for a while. It was only recently that I realized that I could account for truth-making in terms of reference-making and achieve the goal of providing relevant truth-makers for truth-bearers. The rest kind of flowed from that. Being aware of issues surrounding logical atomism and logical constants, I wanted to account for the connectives and quantifiers. At first I thought it would be fairly simple; I could define truth-makers for subject-predicate sentences and then give analogues of the usual clauses for the connectives. I realized that there was a problem if one wanted to preserve truth-maker maximalism; one would have to say what the truth-makers for truth-functional compounds were. Now, one can't say in general that some object x makes both p and q true, if p is not equivalent to q, so I hit on the idea of taking both sets *and* other object's as truth makers: a set can be a truth-maker for p and q if some member of it is a truth-maker for p and some other member of it is a truth-maker for q; and so on.

Thanks for pointing out the typos. And you're right about that sentence from the Appendix. Also, 'false-maker' despite the asymmetry, is already standard usage.

Tristan Haze said...

Thanks, that'll all very helpful.

Jason Zarri said...

No problem. Please let me know if you have any further thoughts--I'm still working through these ideas, and any comments/criticisms will be appreciated!