Given the discussion of parts I, II and III, I want to propose a way to understand intensions which may end up speaking to certain questions about modal semantics. As an introduction, let’s recall that Carnap engaged in a similar project in Meaning and Necessity. In that work, state-descriptions were to play the functional role of possible worlds, where a state-description is a “maximal” collection of atomic sentences. In other words, for every one-place predicate term
φ1 and every singular term
α, a state-description is such that it contains either ‘
α)’ or ‘~
α)’, for every two-place predicate term
φ2 and arbitrary singular terms
β, a state-description is such that it contains either ‘
β)’ or ‘~
β)’, and similarly for n-place predicate terms where n > 2.
A state description, for Carnap, is to represent a possible world: (somewhat metaphorically) a state-description contains the sentence ‘
β)’ just in case in the possible world this state-description is to represent
. To spell the notion out a bit more deliberately and to examine some of the presuppositions that make Carnap’s picture possible, we notice first that there must be an interpretation in mind for the terms of the sentences of the state-descriptions. If a state-description is to represent a possible world by describing in that possible world which individuals have what properties, then it seems reasonable (indeed required) that predicate terms have their usual “intended” meaning. For example, if the predicates ‘is blue’ and ‘is cold’ are to be among the predicates that feature in the atomic sentences of a state-description, then an individual should fall under the predicate ‘is blue’ just in case that individual is (or would be) blue, and an individual should fall under the predicate ‘is cold’ just in case that individual is (or would be) cold. Second, the class which was to give us a sketch of how to provide intensions (a semantic notion) was exactly that class which was to provide us with modal facts (a properly metaphysical notion). This is the conventionalist overtone that I spoke of in part II.
I’d like to take each of these assumptions (for convenience, call the first (A) and the second (B)) in turn and try to see if we can offer more justification and if we can offer an account of modal semantics based on what we’ve learned in our investigation.
First, (A) the implicit requirement that the predicate and singular terms of the sentences of a state-description are to be interpreted according to the usual (or at least an implicit) understanding of those terms. We can begin to address this requirement by making the general observation that part of what we have in mind when we speak of the meaning of a predicate term is the extension of the term; at least part of the meaning of the predicate ‘is red’ is captured by the fact that the predicate applies to all and to only red things. Of course, one doesn’t grasp the meaning of ‘is red’ if all one knows is that the predicate applies to all and to only actual red things, one must also know that the predicate ‘is red’ would apply to something were that thing red.
The important thing to see is that part of what is required for a predicate (or any other referring) term to have an implicit interpretation is for the term to denote some (most likely, non-linguistic) individual or set of (again, most likely, non-linguistic) individuals. For the terms of a language to have an implicit interpretation is for these terms to be about something “in the world” and to be able to make claims about those “worldly” things.
What might be called ‘meaning stability’ is another critical feature of referring terms if we are to able to speak of their intensions. Specifically, if a predicate term (for example) is to have an intension, then that term must be such that to be used correctly it must be used in a consistent manner in different, yet similar situations. In terms of the example predicate ‘is red’, for us to be able talk about its intension we must be guaranteed that ‘is red’ will be used in talk of actual and / or counterfactual situations to pick out red things.
From just this much we can see that much was packed in “under the surface” in the seemingly straightforward state-descriptions of Meaning and Necessity. Carnap’s state-descriptions are merely syntactic in nature, but because of the fact that the terms of the sentences of the state-descriptions are to be interpretable and that the interpretations of the terms are to be “stable” from state-description to state-description, we see that state-descriptions (or something very like them) are the right sort of things to provide us with semantic information about the referring terms occurring in the constituent sentences of state-descriptions. It’s a bit difficult to tease all this out of Carnap’s work because so much philosophical territory is covered in it. Specifically, it’s difficult to determine exactly how referring terms should be interpreted (in the sense of being about or picking out some non-linguistic individual or set of individuals); it seems likely that Carnap would shy away from admitting into his ontology the possible worlds themselves that his state-descriptions were to represent. But in the absence of such how are we to make sense of the semantics of the referring terms?
I have a suggestion for how to provide an interpretation for the referring terms. This suggestion may do some violence to Carnap’s view, but I hope such violence will be in the service of helping us get clear on the notion of intension of predicate terms (and an epistemology of those). My suggestion is to take a different methodological viewpoint with regards to our use of state-descriptions (or properly semantic “proxies” for state-descriptions) and in so doing put state-descriptions (or our semantic proxies for them) primarily to use in characterizing intensions of predicate terms in an epistemically responsible fashion.
The idea is to think about a state-description (call it ‘S’) as describing a merely conceived of counterfactual situation. We understand the sentences of S to describe, in appropriately nauseating detail, a conceived of or imagined universe. For example, if ‘
β)’ is an element of S, then the particular counterfactual situation S is to represent is such that, were it to be conceived of or imagined, in that situation,
β would be
φ1. So in S, all the individuals
, … which are such that ‘is
‘ applies are all those individuals which would be such that, were the counterfactual situation which S is to represent to be imagined, they would be
in this imaginary universe. On this way of thinking about things, the sentences of S can be thought of describing the way in which the terms of the language of the sentences of S are used to describe the imagined counterfactual situation given that those terms are used in the usual way.
This might seem formally possible, but, so far, we have no idea how to ground, in a non-circular way, these counterfactual situations which are described by predicate and singular terms used in the usual way so that we are guaranteed epistemic access. I believe there is a non-circular ground for this sort of way of thinking about Carnap’s state-descriptions. Recall that long ago, I claimed that to possess a concept of the sort that is expressed by a predicate term that might occur in a state-description is to have the ability to sort individuals into two classes — those to which the concept rightly applies and those to which is doesn’t rightly apply. In order to provide a “backing” for the properly semantic way I’ve suggested to understand Carnap’s state-descriptions, we need only consider that a cognizer conceives of an entire universe and in that universe, as its conceived, describes that universe in terms of whether every individual, pair of individuals, triple of individuals, … , n-tuple of individuals in that universe falls or does not fall respectively under every one-place predicate, two-place predicate, three-place predicate, … n-place predicate corresponding to the respective concept that is expressed by those terms.
An ideal cognizer, given infinite time and resources, could generate an infinite set of atomic sentences and negations of atomic sentences which would accurately describe, in appropriately nauseating detail, an entire imaginary, or merely conceived of universe in terms of n-place predicates (for n > 0) and “tag” names (names with no associated senses) for individuals. Such conceived of universes so described would be just the sort of thing to characterize intensions of predicate terms in an epistemically responsible fashion because the collection of all such conceived of universes would completely exhaust the meaning of predicate terms by providing each and every circumstance in which it would be appropriate to use these terms to describe any particular counterfactual situation.
An immediate objection to this approach concerns why we need entirely imagined universes to exhaust the meaning of predicate terms. An opponent might wonder why we need to traffic in the entire collection of imagined universes just to exhaust the meaning of ‘is red’. Why not just consider a few red things (perhaps actual things that are red), generalize by saying that ‘is red’ applies to all and only things that are, in the relevant ways, similar to those individuals and be done with it?
There are two responses.
First, for complete generality in treating and n-place predicates for arbitrary n, we need to consider arbitrarily large “swaths” of an imagined universe. There’s no principled place to draw the line in how much of the imagined universe to consider when we try to imagine a situation in which an arbitrary n-place predicate holds of an n-tuple of individuals. We can follow the commonsense advice of the last paragraph and take ‘is red’ to apply to all and only things that are similar to actual red things, and at the same time consider the whole imagined universe in which we “situate” conceived of red things. At first blush, it doesn’t seem that anything is lost (in terms of the commonsense way of understanding the intension of ‘is red’) or made inconsistent by situating the red things that make up the class of all actual or imagined red things in respective imagined counterfactual situations.
The second response is related to the first. By using just the technique of imagined complete universes, we can get something very much like a class of possible worlds but the members of which are such that they are epistemically accessible — they are after all conceived of. This response is not so much a justification for our use of entire conceived of counterfactual universes as much as it is a reason for seeing how the use of counterfactual universes as conceived would be extremely useful in an account of modal semantics.
Finally we can return to (B) and evaluate reasons for believing that the class of semantic proxies are of the right sort to be able to provide us with modal information.
First, the class of semantic proxies for state-descriptions gives us the right result for de dicto modal claims such as ‘necessarily, if x is three sided planar figure with straight lines, then x is a triangle.’ If we have the concepts expressed by the predicates ‘is three sided’, ‘is a planar figure’ and ‘has straight lines’ and ‘is a triangle’, we see that the sentence is true.
Second, we can reiterate what we offered as justification for the use of entire conceived of counterfactual universes. Under the assumption that possible worlds are the sort of things that could give us modal information it seems that the semantic proxies for state-descriptions must also be of the right sort to give us this information.
Finally, we can return to the objections raised by Shalkowski against reductive accounts of alethic modality that I mentioned in part I. Strangely enough, I think one of the very grounds on which Shalkowski criticizes a class of possible worlds as the reductive base for an account of modality is a ground for a criticism against his suggestion for where to begin to give an (albeit non-reductive) epistemically responsible account of modality. Whereas the use of completely conceived of counterfactual universes to explain necessity does give us an at least theoretically plausibly coherent way to understand an epistemology of modality, Shalkowski’s own hints that modality may be a primitive feature of the world don’t seem to give us an even at least theoretically plausible way to understand our intuitions that certain modal claims are true or false. If the modal aspect of objects, properties or propositions is primitive, then to have epistemic access to the truth or falsity of modal claims, it seems we’d have to be somehow in epistemic contact with that primitive modality. We may very well be, but to say so would require the postulation of a special(?) faculty with which we apprehend the primitively modal.