Reply to David Braun's comments on "Probability and Propositions"

Reply to David Braun's comments on "Probability and Propositions"

David J. Chalmers

Philosophy Program
Research School of Social Sciences
Australian National University
Canberra, ACT 0200, Australia.

chalmers at anu dot edu dot au

I would like to thank David Braun for his detailed and helpful commentary on my paper "Probability and Propositions".

Objects of belief

First, I think I need to clarify an important difference in the way that Braun and I approach the central issue. In the first two sentences of his commentary, Braun defines propositions as the referents of 'that'-clauses in propositional attitude ascriptions, and stipulates that he will understand the objects of belief to be propositions in this sense. Consequently, he spends the first half of the commentary reviewing relevant material in the philosophy of language, and his arguments against me are largely devoted to making the case that my observations about probability do not undermine a view on which the referents of 'that'-clauses are referential.

By contrast, I had intended to largely bypass issues in the philosophy of language about attitude ascriptions and 'that'-clauses. As I say at the start of my paper, the debate in that area has reached something of a stalemate in recent years, so I aim to approach objects of belief from a different starting point. I consider one of our most successful theories in which belief is associated with objects, namely Bayesian confirmation theory, and ask what sort of objects can play the role that this theory needs them to play. And I argue that if objects of belief are understood this way — that is, as the entities to which credences are assigned for the purposes of Bayesian analysis — then referentialism about objects of belief is false.

In effect, Braun agrees with the conditional. He accepts that for the purposes of probabilistic accounts of rational belief, credences are to be assigned to nonreferentially individuated entities: namely, ordered pairs of guises and Russellian propositions. So he agrees that if objects of belief are understood this way, referentialism about objects of belief is false. But he thinks that objects of belief should not be understood this way: objects of belief are by definition the referents of 'that'-clauses, and the point about Bayesianism just comes to the observation that credences are assigned to entities other than the objects of belief.

Now, I did not attempt to establish in the paper that the referents of 'that'-clauses are nonreferential. I discuss the issue only briefly (p. 19), acknowledging the possibility of a position like Braun's, offering a reason for finding it uncomfortable, without attempting to refute it. Setting aside the point about discomfort (which I discuss further below), I say there that my arguments do not rule out the possibility of pluralism about objects of belief, on which the objects of belief in one sense (say, the referent of 'that'-clauses) are referential, and the objects of belief in another sense (say, the entities to which credences are assigned) are nonreferential. In effect, the Braun-style view is regarded as a version of this sort of pluralism.

Of course Braun himself does not regard his view as pluralistic about objects of belief. But this difference stems largely from terminology: for Braun, it is a stipulation that "object of belief" is used for the referents of 'that'-clauses, while for me it is not. So it is not clear that this difference runs deep.

It may be that Braun is only concerned to defend referentialism about the referents of 'that'-clauses, and is not concerned with objects of belief in any other sense. If so, my paper was not primarily intended as an argument against the sort of referentialism that Braun is concerned to defend (although see the discussion below). As I tried to make clear in my paper (but probably did not make clear enough), I was not principally concerned with referentialism as a thesis in the philosophy of language, but with referentialism as a thesis in the philosophy of mind. As a consequence, I was not principally concerned with the semantics of propositional attitude ascriptions, but with the nature of thought itself. Of course there must be some connection between the two, but one cannot assume that the former is a perfect guide to the latter.

Where the analysis of thought is concerned, the substantial claim that matters to me is that nonreferentially individuated entities play certain key explanatory roles in normative theories of thought, roles that one might expect objects of thought to play. If so, it is natural to see thought as involving relations to nonreferentially individuated entities, entities that can reasonably be regarded as objects of thought. Again, this view is compatible with pluralism about the objects of thought: referentially individuated entities may also play an important role. But a full analysis of the objects of thought requires going beyond such entities.

Referentialism about language and Bayesian explanation

All that said, I am inclined to reject referentialism about language, as well as referentialism about thought, and I think that 'that'-clauses behave nonreferentially. In particular, I think that 'that'-clauses refer to nonreferentially individuated entities very much akin to those I discussed at the end of the paper: enriched propositions. I did not argue for that claim here, however. (I argue for it in a separate paper, "Propositions and Attitude Ascriptions: A Fregean Account".)

In the paper under discussion, I briefly suggested reasons (in sections 3 and 7) for rejecting referentialism about language. In essence, these came to the point that apparently successful Bayesian analyses involve claims such as p(Tinasky = Hawkins) = 0.5. If claims of this sort are true, referentialism about language is false. A referentialist about language must hold either (i) that these claims are strictly speaking false (raising questions about how analyses involving them can be successful), or (ii) that although these claims can be true, referentialism is false only of the associated slice of technical language, while it remains true of natural language (raising questions about the continuity between technical claims such as the above and natural language claims such as 'My confidence that Tinasky is Hawkins is low').

Braun does not directly address the semantic analysis of technical claims such as 'p(Tinasky is Hawkins)=0.5'. He addresses the analogous natural language claims, saying not only that they are false, but that they do not even convey any truths. My guess is that he would say the same about the technical claims. This raises the serious issue of how Bayesian analyses involving these claims can be as successful as they are. Braun does not address this point directly.

At one point, Braun suggests that Bayesianism and subjectivism are both false. I think it would be fairly remarkable to reject such successful theories based on somewhat arcane grounds from the philosophy of language. In fact, it turns out that Braun means only that certain specific versions of Bayesianism and subjectivism are false, versions where credences are assigned to propositions as Braun understands them. He allows that other versions, where credences are assigned to guise-proposition pairs, could be correct. But there then remains the question about how subjectivist and Bayesian claims couched in language such as the above, presumably involving propositions, relate to correct analyses in terms of guise-proposition pairs.

In the paper, I suggested that a referentialist could hold that claims such as 'p(Tinasky = Hawkins)=0.5' and 'My confidence that Tinasky is Hawkins is low' are strictly speaking false but convey truths about credences in nonreferential surrogates. On the current proposal, they might convey the true propositions that p(G, Tinasky = Hawkins)=0.5, and that the subject's confidence under guise G in the proposition that Tinasky is Hawkins is low, where G is a guise associated with the sentence 'Tinasky is Hawkins'. (Note that this differs from the line that Braun [p. 24] takes me to be suggesting on behalf of the referentialist, in that the nonreferential surrogate need not itself be a proposition.) This would raise questions about the wholesale falsity of claims involved in such a successful piece of analysis, analogous to questions that come up for views on which other successful analyses in science or mathematics turn on false claims. But the pragmatic story might offer the beginning of an answer, if a somewhat uncomfortable one.

Braun rejects the pragmatic analysis here, without offering anything in its place. His view appears to be that the relevant claims are false, and do not convey any truths. This view renders the challenge more pressing than ever: how is it that analyses involving these claims are so successful, if the claims neither express nor convey any truths?

Incidentally, I think it is in these issues about the success of Bayesian analyses that the appeal to Bayesianism goes beyond familiar appeals to attitude ascriptions, or indeed beyond a simple appeal to subjectivism about belief. Bayesianism is a powerful formal normative theory of belief, one that involves elaborate and succesful formal explanations and analyses of rational belief in many different circumstances. As such, it is much harder to simply reject Bayesian analyses than it is to simply reject ordinary intuitions about attitude ascriptions, or about degrees of belief. The success of this theoretical apparatus is intended to play a key role in the arguments of my paper. As far as I can tell, Braun does not address this aspect of the arguments.

Guise-proposition pairs as objects of credence

I'll now set aside issues about the referents of 'that'-clauses, and concentrate on probabilistic matters. Here, Braun's view and mine are closely related. Braun holds that for the purposes of the normative analysis of rational belief, credences are to be associated with pairs of guises and Russellian propositions. I hold that credences are associated with enriched propositions, which are themselves equivalent to pairs of guises and Russellian propositions. Our only difference here concerns the nature of the guises. I hold that they are best understood in terms of certain structures involving functions over centered worlds. Braun does not commit himself to a specific view of guises, but he expresses sympathy with a view where guises are something akin to sentences in a language of thought.

I think there is good reason to hold that guises have more structure than that of a mere sentence. The reason is that for the purposes of probabilistic analysis, it is highly desirable to be able to associate probabilities with sets of events or outcomes or possibilities. The same goes for the credences invoked by Bayesian probabilistic analyses. But there is no natural way to associate sentence-proposition pairs with sets of outcomes, except perhaps with the sets of possible worlds where the proposition is true, but on Braun's proposal these sets will behave referentially, so that assignments of probabilities to these sets cannot mirror assignment of credences to the associated guise-proposition pairs.

By contrast, on my proposal about the nature of guises, guises are naturally associated with sets of centered worlds (or scienarios), and credences in enriched propositions mirror credences associated with these sets. This allows one to bring to bear the full set-theoretic power of the probabilistic apparatus in the analysis of rational belief. This is not a knockdown argument for my view of guises, as a probability assignments can coherently be defined in the absence of the associated set-theoretic apparatus. But doing so loses some important explanatory structure. So if other things are equal, a view that allows set-theoretic analysis is preferable.

The two-dimensional analysis

Braun raises a few problems for my analysis of the objects of credence in two-dimensional terms. In 8.1, he says that a problem I raised for Braun's view — that objects of credence and belief come apart — arises equally for my view. But this seems incorrect: here, our views are disanalogous. On my ultimate view, the objects of credence and belief are the same: they are enriched propositions. The worry for Braun arises in virtue of his explicit rejection of the parallel claim, grounded in his rejection of the claim that guise-proposition pairs are objects of belief.

In 8.2, Braun objects that my association of credences with assertions is problematic: there are not enough assertions to serve as the domain of an agent's credence function. But I did not suggest that assertions serve as this domain. On my view, the domain of an agent's credence function involves enriched propositions. Credences in enriched propositions will exist even in cases where there is no assertion, and in cases where there is an assertion, its associated credence will be equivalent to the credence in an associated enriched proposition. I claimed only that in cases where an agent makes an assertion, that assertion can be associated with a credence, in a manner I discuss. Nothing here undermines the coherence of this association, or its usefulness in placing constraints on a theory of credence.

In 8.3, Braun worries that I have not defined the credence associated with a primary intension (or an enriched proposition). Fair enough: in the paper I only explicitly define the credence of an assertion, and the primary intension of an assertion. But it is easy enough to extend the analysis. One could do this by invoking credences in (counterfactual) assertions with the relevant primary intension. Or better, one can associate thoughts (occurrent mental states) with both credences and primary intensions, along similar lines, and then say that a subject's credence in a given primary intension is the credence associated with a thought with that primary intension. One can make the case along lines suggested in the paper that any two thoughts (of a subject at a time) with the same primary intension will have the same credence, so this credence function will be well-defined.

In 8.4, Braun expresses skepticism about the determinacy of primary intensions as I define them. This skepticism arises from doubts about the determinacy of conditional probabilities of the form pr(A|S(W)), where A is an assertion and S(W) is a specification of a scenario W. These doubts are themselves associated with doubts about what I call the scrutability thesis. I did not argue for the scrutability thesis in this paper, but as I note in the paper, a version of the thesis is argued for in Chalmers and Jackson (2001). Braun acknowledges these arguments but does not address them. It is also worth noting that the vocabulary involved in S(W) need not be nearly as restricted as the vocabulary discussed by Chalmers and Jackson, so the claim required for the current framework is correspondingly weaker.

In 8.5, Braun worries that primary intensions are not the sort of thing that are necessarily true or false, and says that it is correspondingly odd to say that they are objects of belief or credence. I take it that this is another instance of a worry I raise in the last section of the paper, about primary intensions not being able to play all the roles of objects of belief. For reasons of this sort, I hold the objects of belief are not primary intensions but enriched propositions. Enriched propositions are certainly the sort of thing that can be necessarily true or false, so the issue does not arise for them.

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