Ch. 1 – Introduction
A discussion of the intuitive basis for thinking that there are modal truths as well as possible objections or suspicions regarding such truths.
Arguments/considerations for the existence of modal truths/facts include:
- Modal facts are needed to makes sense of the essence/accident
distinction (this is de re modality)
- Modal facts are needed to distinguish contingent from necessary
truths (e.g. all bachelors are unmarried from all emeralds are green) (de dicto modality).
Natural Language usage/practice supports the belief in modal facts.
The distinction between categorical and dispositional properties
appeals to modal facts (e.g. the glass would break if shattered).
- Acknowledging the special nature of physical law requires admitting a
form of necessity.
- The concept of logical validity utilizes modal notions (impossibility
of a false conclusion following from true premises).
- Modal concepts are also useful/utilized in physics, geometry and mathematics.
Problems and Deflationary Moves
- Modal facts and concepts do not seem compatible with Empiricism
concerning either concept acquisition or justification.
- Modal Concepts are susceptible to paraphrase into a non-modal
language. Melia seems to dispute the possibility of this. Moreover, he seems perfectly open to the idea that fundamental Reality is not categorical in structure but rather consists of dispositionally defined entities (13).
- Anti-Realism – perhaps modal concepts are response dependent.
The suggestion (now orthodoxy) that conceiving of modality within a framework of possible worlds (complete ways that reality might have been) offers the best means of utilizing modal concepts and understanding modal facts.
- Possible world semantics avoids introducing primitive modal operators.
Modal concepts are just understood as quantifiers.
Objection that possible world talk is merely heuristic.
Reply that possible world semantics does not commit one to the ontological and ontic theses that there are possible worlds with individuals existing in them.
Ch. 2 – Modal Logic
This section is largely over my head – or at least not clearly worth trying to get at the basis for every logical move that is made. So, from a reader’s perspective, I think the section suffers from being neither sufficiently in-depth for the logically adept nor sufficiently introductory for the logical novice. Melia seemed to lose what audience he was aiming at here.
The basic ideas though are fairly straightforward. We can construct a quantified modal logic (QML) out of the 1st order predicate calculus by the addition of the two modal operators (Box and Diamond) as well as one new one-place predicate letter E (existence). Though this language is a coherent one it displays many problems of translation of natural language sentences containing modals. In short, QML seems severely limited in its expressive power.
- There might be a distinction to be made between ‘there is some x such that necessarily x is F’ and ‘x is necessarily F’. QML does not recognize the latter sentence as grammatical.
- There are scope ambiguities in natural language but QML cannot handle sentences where there is a feature necessarily connected to some object but we are non-committal as to whether that object exists. Basically, the worry is that QML requires that if any properties are essential then any putative object which would have such a property must necessarily exist.
- QML can generate horribly long and complex sentences with many nested modal operators. While such sentences may be grammatical it is not at all clear how they might relate to our pre-theoretic practices with modal concepts.
- QML does not allow for numerical quantification (e.g. counting ways in which something is possible)
- QML does not allow for quantification over non-actual entities.
- QML cannot express natural language sentences using modalized comparatives (e.g. it’s possible your car could have been the same color as my car actually is).
The suggested solution to problems (4) – (6) is to allow quantification over possibilia – i.e. possible worlds and possible individuals ‘within’ those worlds.
(4) is resolved by identifying possible ways (partial possibilities) with sets of possible worlds (i.e. the set of worlds where those ways occur).
(5) is resolved by allowing for statements concerning the possible existence of non-actual things.
(6) understands modalized comparatives as making crossworld comparisons (e.g. your car at some merely possible world vs. my car at the actual world).
Melia then goes on to construct a model theory for modal languages where the notion of ‘truth-in-a-model’ is well defined for all modal languages based on the model – it gives us a basis for providing an interpretation of any language based on the model.
Besides getting into the nitty-gritty of some of the technical machinery (in a not entirely successful way) Melia’s main point is that commitment to model theory which uses possibilia is not yet commitment to the actual existence of possible worlds and possible individuals. Before thinking that we have gotten a working modal theory on the ontological cheap, Melia cautions that it is not clear that one can avoid the robust metaphysical commitments to possibilia.
Possible world semantics needs some sorty of explanation or justification for its adoption as a semantics for modeling a modal natural language. So we can’t deny metaphysical commitments of the former without denying metaphysical commitments of the latter (or denying that we have any sort of genuine modeling relation going on).
Ch. 3 - Quine’s Objections
This chapter is basically a whirlwind tour of Quinean objections to the coherence of modal concepts as well as replies on the behalf of the modal realist (though not necessarily restricted to the possible worlds theorist).
There are three basic objections:
Modal logic is intensional rather than extensional
Modal operators render the sentences/thoughts in which they occur
- Quantifying into modal contexts commits one to nonsense or to an
untenable ‘Aristotelian’ essentialism.
Melia’s reply to (1) is to ask after the motivation for a purely extensional language. He ties such a motive to a commitment to explanation of the compositional character of language and thought (the feature of being able to endlessly generate new sentences/thoughts out of basic elements and have the menaing of those thoughts be governed by the meanings of their elements).
Melia rightly points out that there is no reason why the intensionalist should limit themselves to the resources provided by a purely extensional language whose ontology consists purely of individuals, extensions of predicates, and truth-values. So there is no immediate reason to think that the intensionalist cannot account for the compositional features of linguistic meaning. Furhter, Melia adds that PWS can account for compositionality via an appeal to the inductive definition of truth-in-a-model. The truth-value of any modal sentence in the model will depend upon the semantic values of the simpler components of the modal sentence, just as compositionality demands.
So Melia thinks the debate really turns on worries concerning the modal theorist’s bloated ontology, with the worry about compositionality better stated as a worry about the cost of giving a compositional semantics by appealing to the notion of possible worlds.
Melia’s defense hinges on there being no other significant general objections to an intensional language. I don’t know enough about the debate to competently assess this.
The problem of (2) referential opacity hinges on the worry that referentially opaque contexts violate the indiscernibility of identicals. They do this because substitutions of different names for the same objects in some sentences will result in a change in truth-value. Hence this objection is really a special case of the general worry about intensionality.
Melia’s reply consists in noting that we can avoid any worry about violating the indiscernibility of identicals by simply reltivizing the assignment of an object to a name to a particular world.
Problem (3) is generated, Quine thinks, in cases where a variable occurring within the scope of a modal operator is bound by a quantifier (e.g. there is some x, such that, necessarily x is F.) But Quine thinks that what means we use to specify the object to be substituted for ‘x’ will determine the truth of the sentence, even if the object is the same in both cases (e.g. ‘9’ vs. ‘the number of planets’) – again, we have here a special case of a general worry concerning the features of an intensional language.
Melia appeal to the de re//de dicto/ distinction to dissolve the worry. We don’t get into problems so long as it is possible to treat at least one of the sentences as expressing merely a de dicto truth (e.g. necessarily 9 is greater than 7) and also see that acceptence of the de dicto truth does not entail thinking that there is an object which has the specified property, and so deny that there must be a de re truth entailed by the de dicto one.
I find this solution less convincing. It is not at all clear that, in the mathematical cases that Melia uses, we can simply regard the mathematical statements as de dicto. Certainly Frege didn’t think so. It seems to me then that Melia’s solution is much more controversial than he lets on.
Since Melia tries to avoid the essentialism charge (whatever exactly it is – I wasn’t clear on this) in basically the same way, the same objection applies here as well.
The final objection Melia raises is one concerning transworld identity. This is, I think, a major problem but its statement and resolution must wait for an evaluation of specific theories of Possible worlds.
Ch. 4 – Modalism (Modal realism without PSM)
Not much to say here other than a need to read Peacocke’s discussion of necessity in Being Known. Peacocke is someone trying to characterize modality without being committed to an ontology of possible worlds. However it is not clear to me that Peacocke is thereby to be understood as a ‘modalist’ in Melia’s terms.
Melia’s main point is that Modalism cannot be nearly as expressive as PWS, nor is it clear that the logical language it utilizes is interpretable once the appeal to possible worlds (even as a heuristic) is given up. Melia seems to think that we cannot grasp the meanings of the modal operators reuired in the modalist’s language without appealing to possible worlds. This renders modalism nothing other than a notational variant of PWS.