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Aboutness, objects, propositions

Another brain dump, continuing my ongoing effort to (a) make sense of Brian Cantwell Smith (b) be of some use to OBO Foundry, which in my opinion is in a crisis regarding information
(see IAO_0000136). Don’t take this too seriously – I’m a dilettante when it comes to philosophy. Take this as a homework exercise for someone who’s trying to figure it out. Please provide corrections. [edited 2014-07-04 to change ‘OBO’ to ‘OBO Foundry’]

Alan Ruttenberg once gave me the following definition of ‘about’: a sentence (or other utterance) X is about an object Y iff a [syntactic] part of X refers to Y.

At a gut level I don’t like this at all, but the following is the best alternative I’ve come with:

A proposition X is about an object Y if the truth of X depends on the state of Y.

This seems better because it is semantic instead of syntactic. It doesn’t depend on how the proposition is expressed / coded, or on any understanding of reference, which is almost as mysterious as aboutness.

My alternative relies on an understanding of ‘depends on’. To nail this you have to rule out any changes to the truth of X caused by factors other than changes to the state of Y. [Added: That’s badly said, what I mean is that to prove the change to Y is responsible for the change in the truth of X, one would want to come up with a situation where there’s nothing else to attribute it to. See next sentence.] That would lead to the following: The truth of X depends on the state of Y, if there are two possible world states w1 and w2 such that w1 and w2 differ only in the state of Y, but in which X has opposite truth values.

The above is independent of your choice of modal logic and world states, which could just be temporal (BFO is effectively a temporal theory).

(Maybe there are other ways than this to depend, but I don’t want to get distracted by causation.)

Both definitions of ‘about’ depend on ‘object’ (which I take to be akin to BFO ‘continuant’). I take an object to be a part of the world, so a state of an object is part of a state of the world, and the state space of the world (the space of possible world states) is some kind of product of the object’s state space and the state space of states of everything that’s not that object.

And all this relies on some understanding of the integrity or identity or continuity of an object, such that if you pick out an object in world state w1 and then try to pick out the same object in world state w2, you’ll have some way to decide whether you’ve done so correctly.

I have been reluctant to grant legitimacy to ‘objects’ (or ‘continuants’) – I’ve been wondering whether they are primarily syntactic or logical or social constructs, as opposed to something with some objective clout. Maybe the question here is: if you have two candidate identity criteria for an object that coincide in some world states but not in others, is there some principled way to choose between them? Maybe: the parts of an object are more closely coupled to one another, both spatially and temporally, than they are to parts of things that aren’t that object. This is a bit mushy but seems to have potential.

In this formulation entities (such as mathematical ones) aren’t objects unless they can be said to have variable state. Does the state of the number 7 change through time? Is 7 an object? Hard to say, but I think it would be a pretty unnatural world view that would say it does / is. (But you can have a book about the number pi… hmm… maybe this particular ‘about’ is a term of art.)

There is also the question of what a proposition is, but I don’t see that as hard; a proposition is a 0-ary predicate, which in nonmodal logic is true or false depending on your choice of model / interpretation, and in modal logic is true or false depending on which world state you’re in. I.e. a proposition is a predicate over, or set of, world states, like an ‘event’ in probability theory.

How propositions fit into BFO, I’m not sure. In some ways they resemble universals, while in others they resemble particulars (maybe they’re so-called ‘qualities’ of the world).

[Added: I admit the above account only handles particular kinds of propositions. To be complete I ought to provide ‘aboutness’ accounts of propositions about the past and future, whose truth doesn’t vary over time; and of universal and conditional propositions, such as “where there’s smoke there’s fire”.]

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