Chalmers' Modal Epistemology

 1. Concepts

1.1 Primary vs. secondary intensions

According to Chalmers’ two-dimensionalism (henceforth 2D), each concept has two components: a primary intension and a secondary intension.   The primary intension of a concept is a function from scenarios to extensions.  Very roughly, a scenario is a comprehensive, consistent hypothesis of a way the actual world could turn out to be that’s not ruled out by what you know a priori.   Thus, consider the hypothesis H that the actual world is one in which everything is the way I believe it to be, except that the stuff that plays the watery role is not H20, but rather XYZ. I can’t rule it out from what I know a priori that H accurately describes the world I live in; H is therefore a scenario.  Now with the notion of a scenario in mind, consider the concept, water.  The primary intension of water is a function from scenarios to extensions, and thus picks out the class of things that, for all I know a priori, can play the watery role (e.g., H20, XYZ, etc.).

By contrast, the secondary intension of a concept is a function from worlds to extensions relative to a world held fixed.  Thus, consider water again. The secondary intension of water is a function from worlds to the set of tokens that play the watery role relative to a world held fixed.  So if the actual world is held fixed, then the secondary intension of water yields the set of H20 tokens; if instead an XYZ-world is held fixed, then the secondary intension of water yields the set of XYZ tokens.

In light of the preceding, we see that primary intensions are more coarse-grained than secondary intensions.  Primary intensions track all epistemically possible occupants of a given role, without distinction.  But if so, then if it turns out that there is more than one possible occupant of a given role, then the primary intension is liable to track different referents at different worlds .  For they only capture what I shall call role information – the primary intension of being F means, roughly, ‘whatever plays the F-role’.   By contrast, secondary intensions capture a specific, perhaps smaller, subset of the possible occupants of a given role. And they can do this in a way that rigidly tracks the same individuals across different worlds. They thus capture what I shall call occupant information – the secondary intension of being F means, roughly, ‘the stuff that plays the F-role in W’, where ‘W’ denotes a particular world-held-fixed.  

1.2 Comparison: Kaplan, character, context and content

It’s helpful to think of Chalmers’ 2D framework in terms of an unrestricted version of David Kaplan’s treatment of indexicals : all expressions – not just indexicals – are amenable to the character/context treatment.  For one can use Kaplan’s basic two-component approach to zero in on just about any referents one likes by means of two semantic components: a primary intension – which functions, roughly, as a Kaplan-style character in the 2D framework – and a world – which functions, roughly, as a Kaplan-style context in Chalmers’ 2D framework.  Together, a primary intension and a world-held-fixed constitute a secondary intension, and thus capture a determinate referent, just as a character and a context together capture the content of an indexical, and thus capture a determinate referent.

2. Statements

2.1 Primary vs. Secondary Intensions

With Chalmers’ account of concepts in mind, we can now explain his account of the meaning of statements. Thus, statements are associated with a primary intension and a secondary intension, where these are composed of the sorts of concepts explained above.  Chalmers calls the primary intension of a statement its primary proposition, and he calls the secondary intension of a statement its secondary proposition.   The primary proposition of a sentence is composed of the primary intensions of the concepts associated with that sentence.  It is a function from scenarios to truth-values.  By contrast, the secondary proposition of a sentence is composed of the secondary intensions of the concepts associated with that sentence. It is a function from worlds to truth-values, relative to a given world held fixed. 

To illustrate the distinction between primary and secondary propositions, consider the following sentence:

S. The Morning Star is the Evening Star.

The primary proposition of S, Spp, captures the information of the primary intensions of ‘The Morning Star and ‘The Evening Star’ – i.e., information about the role played by the Morning Star and about the role played by the Evening Star in all scenarios. A rough approximation of Spp is thus:

Spp. The heavenly body visible in yonder region of the morning sky is the heavenly body visible in yonder region of the evening sky.

Thus, Spp is true in just those scenarios where the occupants of the two roles are identical.  But since there are scenarios in which distinct occupants play the roles, Spp is a contingent proposition.

By contrast, the secondary proposition of S, Ssp, captures the information of the secondary intensions of ‘The Morning Star’ and ‘The Evening Star’.  Thus, if we hold the actual world fixed, it asserts that the thing that plays the Morning Star role in the actual world is the thing that plays the Evening Star role in the actual world; in effect, then, it asserts that

Ssp. Venus is Venus.

Thus, Ssp is a necessary proposition (given the necessity of identity).

3. Evaluating Intensions

The truth-conditions for primary propositions differ from those of secondary propositions.  Accordingly, they differ in their evaluation-conditions.  To evaluate the truth-value of a primary proposition at a world, you consider that world as actual; to evaluate the truth-value of a secondary proposition at a world, you consider that world as counterfactual.   It will be helpful to explain the distinction by employing an example.  Thus consider the following sentence:

S. Water is XYZ.

Now consider an XYZ-world, WXYZ.  To consider WXYZ as actual, I suppose that in the actual world, it turns out that the scientists are wrong, and that the clear, potable liquid that falls from clouds, etc., is really composed of XYZ, and not H20. In other words, I consider a scenario of the sort described above. Doing so enables me to evaluate the following indicative conditional:

IC. If WXYZ is actual, then water is XYZ.

Now the primary intension of S is true at WXYZ iff IC is true.  In this way, considering WXYZ as actual can be used as a method of evaluating S’s primary intension.

On the other hand, if I consider WXYZ as counterfactual, I hold the actual world, WH20, fixed, and then consider WXYZ as counterfactual to WH20.  Doing so puts me in a position to evaluate the following subjunctive conditional:

SC. If WXYZ were actual, then water would have been XYZ.

Now the secondary intension of S is true at WXYZ iff SC is true. But since, on our assumption, the reference of ‘water’ has been fixed at WH20, ‘water’ rigidly refers to H20.  Since this is so, the stuff with the water-stereotype at WXYZ – i.e., XYZ -- is not water, and thus SC is false.  In this way, considering a world as counterfactual can be used as a method of evaluating S’s secondary intension.

At this point, we’ve sketched enough of Chalmers’ 2D framework to put us in a position to understand his account of the epistemology of possibility. We will therefore move on to discuss the basic contours of the latter.

4. 2D, conceivability, and possibility

4.1 1-possibility vs. 2-possibility

Chalmers uses his 2D framework to distinguish between two sorts of possibility-statements.  Thus, a statement S is 1-possible iff its primary proposition is true at some possible world, i.e., if it’s true at some world considered-as-actual.  These are statements about what’s metaphysically possible irrespective of what occurs at a world held fixed. Thus, the statement that, possibly, there is XYZ-stuff that plays the watery role is a 1-possibility statement. 

By contrast, a statement S is 2-possible iff its secondary proposition is true at some possible world, i.e., if it’s true at some world considered-as-counterfactual.  These are the more familiar sorts of possibility statements, viz., those about counterfactual possibilities. Thus, unlike 1-possibility statements, 2-possibility statements are those about what’s possible relative to a world held fixed. So, for example, the statement that, possibly, there is XYZ water is a (presumably false) 2-possibility statement.

4.2 Primary vs. secondary conceivability

Relatedly, Chalmers also uses his 2D framework as a basis for distinguishing between two sorts of conceivability. Thus, Chalmers calls a statement S primarily conceivable if it’s conceivable that S is actually the case.  This is the sort of conceivability involved in evaluating primary intensions via considering a world as actual. Thus, we can use the evaluation-conditions for primary intensions when engaging in primary conceiving: we imagine a world considered as actual, and then see if it verifies the relevant indicative conditional of the form, “If W is the case, then S is the case.” If it does, then one is prima facie justified in believing that S’s primary proposition is possibly true.

By contrast, Chalmers calls a statement S secondarily conceivable if it is conceivable that S might have been the case.  This is the sort of conceivability involved in evaluating secondary intensions via considering a world as counterfactual. Thus, we can use the evaluation-conditions for secondary intensions when engaging in secondary conceiving: we objectually imagine a scenario considered as counterfactual, and then see if it verifies the relevant subjunctive conditional of the form, “If W were the case, then S would have been the case.” If it does, then one is prima facie justified in believing that S’s secondary proposition is possibly true.

4.3 The resultant modal epistemology: a first pass

With Chalmers’ distinctions between primary and secondary conceivability, and between 1- and 2-possibility, we’re in a position to grasp the fundamental contours of his 2D account of the epistemology of possibility. Thus, on Chalmers’ account, primary conceivability provides prima facie justification for claims about 1-possibility, and secondary conceivability provides prima facie justification for claims about 2-possibility.  However, primary conceivability is a dubious guide to 2-possibility. For it is liable to lead to modal error, due to the a posteriori necessities pointed out by Kripke and Putnam.

4.4 Positive vs. negative conceivability

So far, we’ve seen that Chalmers distinguishes between two sorts of possibility claims and the two corresponding methods of evaluating those claims. We’ve also seen that evaluating these differing sorts of claims involves conceiving scenarios of certain sorts. However, one is no doubt concerned about what conceiving such scenarios amounts to. For as we’ve seen, one’s account of conceiving can make or break one’s modal epistemology. 

Of course, Chalmers is well aware of this concern, and finds promise in the basic contours of Yablo’s imaginability account of conceiving. He thus advances a version of imaginability that’s similar to Yablo’s in at least two key respects.  First, he accepts Yablo’s distinction between propositional and objectual imagining, and requires the latter as epistemic backing for the former. Thus, he labels the mere failure to find incoherence within a statement, or its implications, negative conceivability, and the act of objectually imagining a scenario that appears to make the target modal claim true positive conceivability. And when it comes to justifying possibility-claims, positive conceivability is the sort of conceivability that’s relevant.   

Second, he accepts the key elements of Yablo’s notion of verifying a possibility claim. Thus, he requires that a primary or secondary intension of a statement S be backed not only by an objectual imagining, but also that such an imagining verify the relevant conditional -- indicative for primary intensions; subjunctive for secondary intensions -- if it is to be prima facie justified for one as possibly true.  

4.5 Prima face vs. ideal conceivability

However, Chalmers’ version of imaginability is a bit more nuanced than that of Yablo’s.  For beyond his two-dimensionalist innovations of the primary/secondary conceivability distinction and the 1-possibility/2-possibility distinction, he makes the further distinction between prima facie and ideal conceivability.  Thus, P is prima facie conceivable if an initial fleshing out of an objectually imagined scenario seems to verify P.  And P is ideally conceivable if, roughly, (i) it is prima facie conceivable, and (ii) no amount of further fleshing out of the scenario would undercut this seeming verification of P.   He gives an account of the latter notion because he thinks a good case can be made for the thesis that conceivability entails possibility, given his 2D account.  Thus, he thinks other contemporary philosophers who have worked in the sub-field of modal epistemology, such as James Van Cleve and Stephen Yablo, have construed the link between conceivability and possibility a bit too weakly, viz., as a relation of fallible prima facie justification, as opposed to one of entailment. For (thinks Chalmers) they worry too much about cases of misdescribing worlds, such as occurs in, most saliently, the a posteriori necessity cases.   However, given his careful separation of primary and secondary conceivability, of 1- and 2-possibility, and given his prescription against using primary conceivability as a guide to 2-possibility, he thinks he can avoid such cases.