Saturday, September 16, 2006

Concepts and Propositions - I

Sorry, folks, about being absent from my blog for so long. I'm currently under a crunch-time of sorts regarding several different projects. Blogging for me is a spare-time thing, not an obsession, so when things get too hectic I have to take a break. And with this year's philosophy job search fast approaching, posting will continue to be sparse for the next several weeks.

Anyway, I am, yet again, rethinking my views on propositions. I have already written four posts on this topic (I, II, III, and IV). After the last post I thought I had everything settled in my mind, but recent reflections on tense logic (which I'll discuss in a later post) have brought a new issue to my attention: the distinction between concepts and propositions.

First, I take it to be a definitional truth that a proposition is a unit of meaning that is capable of bearing a truth value. One issue that arises concerning this is how to tell when we have such a unit of meaning. In particular, what I'd like is a test that will enable us to distinguish sharply between concepts and propositions. As I see it, (a) both concepts and propositions are units of meaning, and (b) necessarily, every proposition contains at least two concepts - a subject and a predicate. But then is a proposition merely a type of compound or complex concept? If so, then how can a proposition meaningfully be said to possess a truth value? If not, then what is the extra ingredient required to transform a complex concept into a proposition?

It seems to me that for a unit of meaning to qualify as a proposition it must be something that can intelligibly be either asserted or denied. This requirement can be understood in two different ways, depends on what we mean by "assert" and "deny". In the weaker sense, to "assert" or "deny" 'p' is just to utter a phrase like "'p' is true" or "'p' is false". In other words, take any putative proposition-expressing phrase, prefix it with "It is true that ..." or "It is false that ..." and you should get a verbally meaningful result. I'll call this the grammatical assertibility-deniability test (GAD test, for short). To illustrate, here are a few examples. In each case, the italicized phrase is the one being tested for propositionality.
  • It is true/false that dog. (Nonsensible. Not a proposition, but a concept.)
  • It is true/false that red roses and a bluejay. (Nonsensible. Not a proposition, but a compound concept.)
  • It is true/false that being about to sing the national anthem. (Nonsensible. Not a proposition, but a complex concept.)
  • It is true/false that 2+2=4. (Makes sense. A necessarily true proposition.)
  • It is true/false that a cat is on the mat. (Makes sense. A contingently true proposition.)
  • It is true/false that square circles exist. (Makes sense. A necessarily false proposition.)
I regard the GAD test as a necessary condition for propositionality, but I doubt that it is a sufficient condition. The reason is that there are various expressions that satisfy the test but that also are, in some sense, "pathological". For example:
  • It is true/false that this sentence is false.
  • It is true/false that I am lying right now.
Both of these are grammatically well-formed sentences, but they are also problematic.

The first is problematic because it is self-referential in a way that makes it impossible to assign a fully determinate meaning. I'll try to spell this out more in a follow-up post, but it suffices for now to point out that sentences aren't true or false in themselves but only by virtue of expressing a true or false proposition. So to say "this sentence is false" is to say that this sentence expresses a false proposition. But we are left no way to specify which proposition is false other than the proposition expressed by "this sentence is false", which brings us right back to where we started. The lack of any independent means of expressing the proposition in question indicates that the sentence is cognitively incomplete.

The reason why the second is problematic is that the proposition that I am lying right now creates a performative contradiction when it is genuinely (as opposed to merely verbally) asserted. After all, a genuine assertion is a sincere reflection of one's beliefs. A lie, however, is a deliberate misrepresentation of one's belief. Hence, a lie is by definition insincere, and thus not a genuine assertion.

What I want to suggest, then, is that the sort of assertibility and deniability that is relevant to propositionality is stronger than what the GAD test gives us. In the stronger sense, to "assert" or to "deny" are partially epistemic (or better, doxastic) notions. To "assert" p in this sense is not essentially to utter a phrase like "'p' is true", but rather to cognitively assent to p. Thus, a assertion or denial (in the verbal sense) is only a genuine assertion or denial if it is a sincere expression of a person's beliefs. For a unit of meaning to be assertible or deniable in this stronger sense it must be potentially believable. In other words, there must be some possible being in some possible world that could be in a position to give it either cognitive assent or dissent. I call this the cognitive assertibility-deniability test (CAD, for short).

CAD rules out as propositions anything that is either cognitively incomplete (as is the case with the self-referential example) or that is in principle unassertible in the cognitive sense (as is the case with the liar example). It is important to note that CAD does not require that a proposition be both cognitively assertible and cognitively deniable. It only has to satisfy one of those disjuncts to quality. The reason for this stipulation is that even if a necessarily false proposition like I am a married bachelor is not cognitively assertible in any possible world, it most certainly is cognitively deniable. Likewise, even if a necessarily true proposition like all triangles have three sides is not cognitively deniable in any possible world, it most certainly is cognitively assertible.

I believe that both the GAD and CAD tests for propositionality are useful, but the stronger CAD test may also be able to help resolving various sematic paradoxes, such as those stemming from self-reference and liar-type paradoxes. In short, if CAD is right, then such paradoxes arise from falsely supposing that all grammatically well-formed declarative sentence-tokens express propositions. Rather, such sentence-tokens express propositions if and only if they reflect the actual beliefs of the speaker.

To be continued ...


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