Archive for June, 2015

When does x refer to y?

I have been concerned about the situation where a claim of the form ‘x refers to y’ is to be tested, perhaps because it is a requirement of a specification and one wants to see whether an engineered artifact (specifically a language-using agent) conforms to the specification. Claims of reference appear, on the surface, to require introspection, which is not generally something you do in an engineering context. What experiments or analysis do you perform (on an agent) to see whether the claim might hold, or not? Recognizing of course that in engineering, as in science, there is no proof, only absence of disproof.

Knowledge representation naysayers and semantic web pooh-poohers are in effect saying that talk of meaning and reference is not objective – it does not belong in science or engineering. I wonder if the failings of KR and semweb are not because they are inherently ill-founded, feeble, or intractable, but rather are due to inadequate understanding of meaning and reference, and consequent poor execution.

The question – how do you tell whether x refers to y? – was central to my puzzlement over W3C TAG issue httpRange-14 when I was involved with the TAG. Any answer to the question would seem to put a requirement on whether and how a URI refers.

I’ve argued here and in other posts (I repeat a lot) that it is possible to test claims of the form ‘s means p’ where s is a sentence and p is a proposition. This is because, in contrast to referring phrases (x above), there is an observable connection between the sentence being said, and certain states of affairs in the world. (Imperatives such as ‘complying with s leads to p’ work the same way.) Put briefly, s means p, if {s might be said} if and only if p.

I tried saying that x can refer to any y that has the property that every sentence of the form k∙x means the proposition p(y), where p is the meaning of the predicate phrase k. This is ugly and creates a circularity, since it would seem that assaying the meaning of x would require assaying the meaning of various p’s, which would require assaying the meaning of various x’s, etc. One might use this formulation to look for relative meaning of referring phrases and predicate phrases, but not for any independent statement of meaning of phrases (of the sort one can make for sentences). I acknowledge that relative meaning is more or less what model theory advances, but it seems counterintuitive to me. We argue about what a word means; we don’t seem to argue about what one word means relative to others.

(I write k∙x to denote the sentence composed from predicate phrase k and referring phrase x.)

What I recently noticed is that to test reference you don’t need to know what predicate phrases mean, only what sentences that contain them mean. I propose the following:

   x refers to y, if every sentence k∙x means a proposition that is about only y.

This proposal has a gazillion qualifiers.

  • ‘k∙x is about only y’ means that the truth of k∙x is affected only by (the state of) y; a change to something else that doesn’t affect y can’t change the truth of k∙x.

  • Not all sentences mean, so I’d want to change “every sentence k∙x” to “every meaningful sentence k∙x”. I left the word out to avoid clutter.

  • If a sentence has two referring phrases x and x′, then the proposition that the sentence means is ‘about only’ a combination of the two things that x and x′ refer to.

  • Sentences can mean propositions whose truth value is affected by variables not referenced in the sentence. ‘Grue‘ is the classical example, but ‘highly rated’ is similar (it is not said who is doing the rating). As a patch I would say that the languages under analysis would have to forbid such predicates, or else would have to be translated into some second language lacking them.

  • It is possible that two distinct subjects / entities / referents change their state exactly in tandem, in which case looking for patterns of change would not be enough to tell them apart. One example might be the two propositions p and not p. I suspect there are others, but there enough cases where a subject is adequately determined by its state space that I don’t consider this a fatal flaw.

  • The proposal may fail to uniquely ‘identify’ some intended y as the referent, in that applying all possible predicate phrases k to x could yield propositions all of which are about only some y’ that has ‘fewer’ states than x (i.e. the state space of y, considered as a partition of the world state space, might be a refinement of that of y’). That is, distinctions between certain states of y cannot be expressed in the language under consideration. – If this is the case, ways out would include: to consider the language to be deficient; to consider y to be a pathological or disallowed subject; to take the proposal to be a definition of reference; or to argue that the distinction between x and x’ cannot make a difference to whether an agent meets any specification.

  • The proposal may also fail to uniquely determine y if candidate referents can differ in ways other than in what doesn’t matter to them, i.e. other than in how their state spaces partition the world state space. After Yablo, I find the idea that subjects (or subject matters) are iso-ontic with their world-state-space partitions to be appealing, and while there are a few things about it that I don’t completely get, I’m sticking with it for the time being.

  • Deciding whether any given change to the world constitutes a change to some given y is by no means a science. This would be a negotiation between what is meant (at the meta-level) by the world state space, and what is meant by y.

  • Indefinite reference will require additional machinery or handwaving.

  • To broaden applicability we can interpret ‘change’ (i.e., differences between points in the world-state-space) broadly: not just as change in the physical world through time, but ‘motion’ through any kind of state-like set, such as possible contents of a document, possible identities, possible worlds, and so on. Not that I suggest a free for all, but that I don’t want to lose the framework on account of it appearing to be too narrow or rigid.

  • Obviously all the richness of human language is being put aside.

With apologies to Leibniz, Yablo, and the usual cast of characters (you know who you are).

More to come, I hope – this idea will require testing and elaboration.

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That last post had a bug in it, so I withdrew it. Sorry. Email me if you want to see it. I don’t think the flaw is fatal, and I hope to have a revised version up later.

[Later that day: Reinstated under new title.]

Categories: Uncategorized