In part I of this series, I promised to outline what I felt were shortcomings of the view according to which we could provide a genuine modal semantics (semantics for a language with modal operators) under the presupposition that this language was “antecedently meaningful” — which I take to mean at a minimum that at least some predicate terms are meaningful, or have an intension that might be grasped. In this post, I’ll consider an example of this sort of approach (I’ll call it the ‘antecedently meaningful language as a prerequisite (for genuine modal semantics)’ approach or ‘AMLAP’ for convenience.), and try to point why I believe it to be problematic, or at least not as helpful as an approach to modal semantics might be.
As an example of the AMLAP view, Professor Greg Ray builds on a work of Christopher Menzel aimed at bridging the gap between modal model theory and a genuine modal semantics by showing how an intended interpretation of a language with modal operators can be given with no commitment to an ontology including mere possibilia. Briefly, the strategy is the following.
The process is two-stage. Step one: we consider the possible worlds-style model structure suitable for (providing the formal semantics of) a particular antecedently meaningful formal language with modal operators. Variables, singular terms and predicate terms are “valuated” over abstract sets (given values as members of, or subsets of those sets); the members of these sets are elements of what is called the ‘domain of discourse’. Step two: we define an embedding, relative to a particular model structure, as an assignment of (1) the individuals in the domain of discourse (that is, the elements of the models of the model structure over which the language is valuated) to actual individuals “in the world” and (2) set of individuals in the domain of discourse to actual sets of individuals “in the world”. An embedding for a particular valuation can be restricted in such a way that the antecedent meanings of the predicates and singular terms of the language for which we provide the semantics are correctly presented and held constant in each of the “counterfactual situations” that were to be represented by the possible worlds (technically speaking just indices) of a particular model. Specifically, we can produce an intended interpretation of a particular language relative to a particular model structure if that model structure is the one intended for language and if the embedding is such that it restricts in certain ways how terms can be correctly used relative to how those terms are used in ordinary discourse about the actual world. We can show what this requirement is by way of example: if ‘Billy’ is a meaningful term — a proper name — of the antecedently meaningful language, then the valuation of ‘Billy’ is to an individual of the domain of discourse which is, in turn, mapped by the embedding to the actual Billy, and the valuation of ‘is red’ is to a set of individuals in the domain of interpretation which is mapped by the embedding to the set of all actual red things.
As much as Ray’s work accomplishes, I believe the extent to which this approach can bear philosophical fruit is limited at the outset by the seemingly innocuous assumption that in order to provide a semantics for the sort of languages he’s considering, we must begin our endeavor with an antecedently meaningful language as the basis for the semantics we’ll provide. To put the claim in some context, let’s consider what we don’t get by considering a completely artificial and formal language with modal operators and giving its semantics.
If we begin with or are provided such a language, then obviously the terms of that language have no antecedent meaning (to show this with an example, the predicates might be something such as ‘is F1,229 ‘ and ‘is F65, 221 ‘). Now we can give the semantics for this language simply by providing formally the model-theoretic interpretation(s) of the languages terms, formulas and sentences at a set of indices (possible worlds). In the sense of a completely artificial formal language, the “meaning” or “intension” of terms can be entirely explained in terms of extensional interpretations of these terms in a model of a certain kind of model-structure which includes certain indices (or “possible worlds”) to provide the semantics for modal operators. So, if we want to give the semantics for some idealized version of a natural language like (a subset of) English (perhaps regimented so as to admit the use of formal semantical methods), we can’t simply pick the assignments of terms to objects in the domain of discourse or the world as we could do in the case of an artifical and formal language, we must start with some idea of what the terms mean before we give the “genuine modal semantics”.
An AMLAP approach to doing this is fine as far as it goes. That is, fine so far as we’re prepared to accept the result that the genuine modal semantics we’re trying to provide are (and indeed must be) moot on “genuine” questions of modality — questions over whether certain modal claims are in fact true or not. Put another way, the assumption that the modal language for which we provide a genuine semantics is antecedently meaningful ensures that this semantics will only be (and I assert, can only be) descriptive with regard to the truth or falsity of modal claims. Such a semantics can at best accurately endorse as true all the modal claims we’ve argued are true and as false all the modal claims we’ve argued are false; an AMLAP approach can’t give any pointers at all to where we might look to find an answer to a certain question about the truth or falsity of a modal claim. This is so because it is the antecedent meaning of the terms of the language we’re giving the semantics for that places the restrictions of the embedding of Step two above. This embedding in turn is (partly) that which ensures that the interpretation we produce is the intended one. The intended interpretation for the modal language we’re concerned with can’t tell us anything more than we would know by knowing the antecedent meaning of the terms of that language and how to use those terms to create sentences in some compositional fashion or other.
I think one reason for this limitation is that, as I’ve hinted before, there is a modal element involved in explaining what it is for a predicate term to be have the meaning or intension that it does (or at least for someone to understand the meaning of a predicate term). Why take a detour through the (as it stands with the AMLAP approach) mysterious region of an antecedently meaningful language to arrive at an understanding of modal semantics with which we can make no progress in explaining why the modal claims we think are true are true, when all we need to do is to advert to how to understand the modal nature of meaning in the first place? Strangely enough, to do this I believe we need to make use of a notion which bears eerie similarities to a class of possible worlds… More about this in part IV.
By way of preview, I think Carnap and the other positivists were on to this point. In Meaning and Necessity, a class of state-descriptions (maximal sets of atomic sentences an negations of atomic sentences) was put to both the task of explaining intension (for singular and predicate terms) and accounting for the truth of modal claims. I think there were two background assumptions in Carnap’s work. First, that there was an antecedent interpretation for both the predicate and singular terms which were constituents of the sentences of a state-description. And second, that modality was to be explained in something like conventionalist fashion (that is, there was to be a coincidence of necessity and analyticity; a sentence is analytic iff it expresses a necessary truth). These two unquestioned assumptions weaken the force of Carnap’s work. In part IV, I’ll argue that by examining these assumptions that we can give a model-theoretic reworking of Carnap’s state-descriptions to get clearer on the notion of intension and perhaps shed some new light on how to understand the truth or falsity of modal claims.