Saturday 13 August 2011

Essence, Belief and Epistemic Modality (Part 2 of Sketch)

This is part 2 of a Sketch of a Way of Thinking about Modality. In this part we shall consider:

- Essences and the de re/de dicto distinction,
- The indefiniteness of necessity,
- Intentional contexts ("propositional attitudes"), and
- Epistemic modality.

The first topic is really the main one. What I say about the remaining topics will be very scant - a rough indication of how these issues are to be approached according to the way of thinking being sketched out here, rather than an attempt to really deal with them. (I hope to really deal with them in my book.) They fit quite naturally here, since intentional contexts come into the more substantial discussion of the first topic. If nothing else, the brief discussion here should prevent readers from thinking that I have given no consideration to such issues, or that my account of modality is straightforwardly unable to deal with them.

Three Interpretations of Modal Claims about Individuals

As a preliminary, it should be noted that epistemic modal claims are not counted in this taxonomy. Consider, to begin with, sentences of the form 'a is necessarily F'. I distinguish the following three interpretations of such statements:

(1) The contextual interpretation. The locus classicus for this interpretation is Lewis in On the Plurality of Worlds, who expresses it better than I can:
I suggest that those philosophers who preach that origins are essential are absolutely right - in the context of their own preaching. They make themselves right: their preaching constitutes a context in which de re modality is governed by a way of representing (as I think, by a counterpart relation) that requires match of origins. But if I ask how things would be if Saul Kripke had come from no sperm and egg but had been brought by a stork, that makes equally good sense. I create a context that makes my question make sense, and to do so it has to be a context that makes origins not be essential.' (p. 252)
There is one ruffle here: Lewis (who is notorious for playing fast and loose with ordinary modal language) talks of 'how things would be if Saul Kripke had...', rather than how things would have been. This might suggest a kind of epistemic reading, concerning what it would be like if it turned out that Saul Kripke actually had such-and-such an origin. But the range of possibilities in this sense - the things which could turn out to be true of an individual, for all we know (or all we know a priori) - is something quite different from what we are discussing here. In two-dimensional semantics, this corresponds roughly to the difference between A- and C-intensions.

(2) The "unrestricted" interpretation. In contrast to the above, we are now beginning to enter the realm of what could more legitimately be called 'essence'1, and are looking at proper metaphysical (or subjunctive) modality. On this interpretation, something like the following holds: 'a is necessarily F' is true iff 'a is F' is satisfied by all configurations of the host system of these propositions, and the concepts involved are adequate to their objects with respect to 'a is F'. (This form of account is introduced more generally in part 1.)

Thus, in this case, we might say that the necessity, as opposed to contingent truth, of 'a is F' stems from the nature of the individual concept of a, rather than any contextual restrictions placed on our representations. Why, then, are there scare-quotes around 'unrestricted'? This is because the present way of looking at things may over-dramatize the difference between the contextual restrictions of Lewis's account, and the constitution of concepts in the relevant fine-grained sense. We might think of the nature of these concepts as being at least partly determined by more-or-less invariant restrictions of some more general apparatus. This more general apparatus can be used to understand epistemic modality (and epistemic space).

On this interpretation, to say that a is necessarily F is to say something like: according to the way I think of a - and this way is adequate - it could not have failed to be F. (This isn't meant to be a proper analysis.) But we will probably want to recognize the possibility of slightly different concepts in other systems which have a as their object, and are adequate. Thus while we might think of John in such a way that we may say, intending the present "unrestricted" interpretation, that he is necessarily F, we might recognize that other people might legitimately think of John in such a way that they may say that he is contingently F. (This could be called 'adequacy pluralism about concepts'.)

(3) The generalized "unrestricted" interpretation. Clearly, we will want an interpretation of modal claims about individuals which does not tie their truth to one particular conceptualization (namely, that embodied in the host system of the modal claim). This interpretation gives us that. On this interpretation, something like the following holds: 'a is necessarily F' is true iff all configurations of all systems containing an adequate concept of a represent a as being F. (Another, less natural interpretation would be to substitute 'at least one system' for 'all systems'. This interpretation would be natural for 'a is possibly F'.)

A Simplification

I have simplified the above by concentrating on subject terms and ignoring different construals of the role of the predicate. One might distinguish interpretations analogous to (2) and (3) above, i.e. an evaluation involving a particular F-concept in a system, versus one involving all systems with some concept of the property F. An analogous simplification will be made below in the discussion of ascriptions of intentional content. 

The Indefiniteness of Necessity

The account of necessity given here, based on the notion of all configurations of a conceptual system, may give the impression that I think a sharp boundary can be drawn between necessary and contingent truths. It is important to realize that this is not the case. (I probably should have emphasized this already in part 1.)

One way of responding to this would be to try to modify our picture of modality - instead of picturing a conceptual system as being like a mechanical apparatus which can be put into a definite set of configurations, one might imagine a device with an indefinite set of configurations; one might, for example, imagine growing resistance as one manipulates the apparatus into further out configurations (i.e. further from what we think is actually the case).

This sort of response has its place, but we needn't respond like that. We can also hold on to our simpler, more definite picture, but with due regard to the indefiniteness of its application.

Either way, it is important to note that there are clear cases. Some propositions are clearly necessary, and some are clearly contingent, and the distinction between them is of fundamental importance.

The following analogies from Wittgenstein are very helpful in connection with this theme:
The use of the words 'proposition', 'language', etc. has the haziness of the normal use of concept-words in our language. To think this makes them unusable, or ill-adapted to their purpose, would be like wanting to say 'the warmth this stove gives is no use, because you can't feel where it begins and where it ends'.
from Philosophical Grammar, Part 1. p. 120.
It is essential to logic to draw boundaries, but no such boundaries are drawn in the language we speak. But this doesn’t mean that logic represents language incorrectly, or that it represents an ideal language. Its task is to portray a colourful, blurred reality as a pen-and-ink drawing.
from The Big Typescript, p. 144.

The De Re/De Dicto Distinction(s)

This is widely acknowledged to be a confusing topic. The pair of terms 'de re' and 'de dicto' appear to get employed in philosophy to mark several important distinctions (or sorts of distinction). Complete clarification of this will have to wait for another time, but for now I want to characterize two basic sorts of distinction for which these terms can be used:

(1) De re: Generalization (universal or existential) over dicta involving a particular object vs. De dicto: specification of a particular dictum. (Dicta here are contents, propositions - something like that.) The distinction above between the "unrestricted" and generalized "unrestricted" interpretations of modal claims about individuals is an instance of this. It echoes, at least in part, Quine's distinction between believes-notional and believes relational.

In intentional contexts (for example, belief-reports), the distinction appears in the following way. The name 'Hesperus' in a belief report like:

(A) Ralph believes that Hesperus is F.

can be read as doing two things at once. (1) specifying the object of Ralph's belief, and (2) specifying the concept (or mode of presentation) via which he has it. On such a reading, (1) could be expanded to:

(B) Ralph believes, of Hesperus, via his Hesperus-concept, that it is F.

(A similar thing could be done for the 'F'.) Some belief reports, on the other hand - purely de re belief-reports - may be read as only specifying the object. (A) read this way could be expanded to:

(C) Ralph believes, of Hesperus, via some concept(s), that it is F.

(Cases such as 'John believes that Santa Claus exists' suggest that there are also readings where the name just functions to indicate an individual concept or intension involved in the propositional attitude, i.e. does not specify any real extension.)

Substitution of co-referring terms salva veritate (i.e. without change in truth-value) will fail in modal and intentional contexts which are de dicto in this sense.

(2) De re: Involvement of a dictum featuring a rigid (or rigidified) designator vs. De dicto: Involvement of a dictum featuring a non-rigid, unrigidified designator. This distinction most clearly makes its appearance with definite descriptions.

To illustrate: as a result of these two distinctions together, a sentence like 'The winner could have been shot' - once we rule out salient epistemic readings and Lewis-style contextually restricted readings - still has three readings left:

De dicto in both senses (1) and (2): true iff the non-rigid dictum 'The winner was shot' is satisfied by at least one configuration of the host system. (In this configuration (so to speak), the winner might be someone else.)

De dicto in sense (1) and de re in sense (2): using 'The winner' to indicate an individual concept - the concept of the actual winner, that very person - i.e. as a rigidified description, and true iff that dictum is satisfied by at least one configuration of its host system.

De re in sense (1) and therefore neither de re nor de dicto in sense (2): using 'The winner' purely to indicate a particular object, and then making a claim about all dicta which are rigidly about that object and which fulfil certain conditions (in this case: saying that the object was shot, or saying that the object was shot using some particular concept of being shot). It is only on this sort of reading, I submit, that substitution of co-referring terms salva veritate will be valid.

Clarifying and separating these distinctions helps to clarify Quine's skepticism about de re modality, and Kripke's famous arguments against Quine's attitude, as well as making it clearer why this debate is so confusing. Below is a lengthy quote of an important passage of Naming and Necessity. The above discussion can help us disambiguate the ensuing talk of particulars having modal properties independently of how they are described: this may be indicating de re-ness of the second kind (involvement of an individual concept rather than a non-rigid, unrigidified designator), or the first (generalizing over concepts of a particular object, rather than fixing on a particular concept).
Some philosophers have distinguished between essentialism, the belief in modality de re, and a mere advocacy of necessity, the belief in modality de dicto. Now, some people say: Let's give you the concept of necessity. A much worse thing, something creating great additional problems, is whether we can say of any particular that it has necessary or contingent properties, even make the distinction between necessary and contingent properties. Look, it's only a statement or a state of affairs that can be either necessary or contingent! Whether a particular necessarily or contingently has a certain property depends on the way it's described. This is perhaps closely related to the view that the way we refer to particular things is by a description. What is Quine's famous example? If we consider the number 9, does it have the property of necessary oddness? Has that number got to be odd in all possible worlds? Certainly it's true in all possible worlds, let's say, it couldn't have been otherwise, that nine is odd. Of course, 9 could also be equally well picked out as the number of planets. It is not necessary, not true in all possible worlds, that the number of planets is odd. For example if there had been eight planets, the number of planets would not have been odd. And so it's thought: Was it necessary or contingent that Nixon won the election? (It might seem contingent, unless one has some view of some inexorable processes....) But this is a contingent property of Nixon only relative to our referring to him as 'Nixon' (assuming 'Nixon' doesn't mean 'the man who won the election at such and such a time'). But if we designate Nixon as 'the man who won the election in 1968', then it will be a necessary truth, of course, that the man who won the election in 1968, won the election in 1968. Similarly, whether an object has the same property in all possible worlds depends not just on the object itself, but on how it is described. So it's argued.

It is even suggested in the literature, that though a notion of necessity may have some sort of intuition behind it (we do think some things could have been otherwise; other things we don't think could have been otherwise), this notion [of a distinction between necessary and contingent properties] is just a doctrine made up by some bad philosopher, who (I guess) didn't realize that there are several ways of referring to the same thing. I don't know if some philosophers have not realized this; but at any rate it is very far from being true that this idea [that a property can meaningfully be held to be essential or accidental to an object independently of its description] is a notion which has no intuitive content, which means nothing to the ordinary man. Suppose that someone said, pointing to Nixon, 'That's the guy who might have lost'. Someone else says 'Oh no, if you describe him as "Nixon", then he might have lost; but, of course, describing him as the winner, then it is not true that he might have lost'. Now which one is being the philosopher, here, the unintuitive man? It seems to me obviously to be the second. The second man has a philosophical theory. The first man would say, and with great conviction 'Well, of course, the winner of the election might have been someone else. The actual winner, had the course of the campaigner been different, might have been the loser, and someone else the winner; or there might have been no election at all. So such terms as "the winner" and "the loser" don't designate the same objects in all possible worlds. On the other hand, the term "Nixon" is just a name of this man. When you ask whether it is necessary or contingent that Nixon won the election, you are asking the intuitive question whether in some counterfactual situation, this man would in fact have lost the election. (Kripke, Naming and Necessity, first lecture.)
Epistemic Modality and Ascriptions of Intentional Content

For the purposes of understanding metaphysical or subjunctive modality, I have been talking about conceptual systems in a fine-grained sense such that changing one's mind about an empirical identity statement involving individual concepts, for example, constitutes a change in the system itself. Since we believe that Hesperus is Phosphorus, there is no configuration of our fine-grained system which satisfies 'Hesperus is not Phosphorus'. And yet we can truly say things like 'It could turn out that Hesperus is not Phosphorus after all', and even (despite worries of Kripke's) 'It could have turned out that Hesperus was not Phosphorus'.

This is connected with the idea of 'two spaces of possible worlds' in other approaches. (Cf. Chalmers' 'The Nature of Epistemic Space'.) When we say that it could be that Hesperus isn't Phosphorus, we are not considering a configuration of our existing system in the sense we have been talking about, but are rather considering a change in our system. But in another sense, of course, making this change would constitute a reconfiguration of some "wider" system - the system relevant to epistemic modality. Making various abstractions and idealizations, we can imagine a space of possible ways things could be for all we know a priori - epistemic space. Moving from that to the space of ways things could have been involves getting rid of epistemic possibilities which are not metaphysically possible (the lesson of the necessary a posteriori), but also adding epistemic impossibilities which are metaphysically possible (the lesson of the contingent a priori), i.e. things which couldn't be the case, but could have been, such as this room being bigger than it is. (This latter thing will occupy us in part 3.)

So, we can configure our systems in the wide sense to represent ways things might be, and the way we think things are. But, speaking roughly, such a configuration of the wide system yields a system in the fine-grained sense, of ways things could have been. Sometimes, when we change our beliefs, this can be understood as simply moving to another configuration in the fine-grained system (and thus not directly changing any of our metaphysical modal judgements), whereas other times this must be regarded as involving change of the fine-grained system itself (e.g. going from believing that Hesperus is not Phosphorus to believing that it is).

(Note that I am not saying that the ways things really could be all have corresponding configurations in some system of ours, nor that the ways things really could have been all have corresponding configurations in our fine-grained system - not only may we be wrong, there will be possibilities we haven't dreamt of. Clearly much more needs saying here about these notions of 'the ways'. Some speculations can be found here.)

The Metaphysical Possibility of Metaphysically Impossible Thoughts

Hesperus could be distinct from Phosphorus after all, if we're radically deceived, but given that it is Phosphorus, it could not have been distinct from Phosphorus. So 'Hesperus is not Phosphorus' is not satisfied by any configurations of our fine-grained system. And yet 'John believes that Hesperus is not Phosphorus' is metaphysically possible, is satisfied by configurations of our fine-grained system.

This may be quite puzzling given a certain way of visualizing the fine-grained system and its relation to the wider epistemic system which gives rise to it. For a while it seemed like a real problem to me, and I called it 'the containment problem'. The bothersome thing is the way in which epistemic modal space seems to be contained in metaphysical modal space via our machinery for ascribing intentional states and propositional attitudes - our machinery for representing the thoughts and representations of others - despite epistemic modal space outrunning the metaphysical in the well-known Kripkean way.

It is very tempting to try to "fix" this "problem" by going metalinguistic. I.e. saying something like: 'When we say that John believes that Hesperus is not Phosphorus, we aren't really simulating, constructing, or dealing directly with a thought that Hesperus is not Phosphorus. Rather, we are simply employing our concepts of Hesperus, the Hesperus-concept and the Phosphorus-concept, and forming an idea of a proposition in another system which has the relevant properties.' That may be a good view of what we do sometimes (especially with very foreign thoughts), but it seems wrong - gratuitous, even - to suppose that this is always how we do it. After all, we naturally and frequently envisage epistemic possibilities which fall outside our current fine-grained system. We step outside it all the time. So, when we think something like 'John believes that Hesperus is not Phosphorus', we can think of this as employing - in tandem - our fine-grained system together with a configuration of our wider system which falls outside it, but which is "pointed to": to give ourselves the thing John believes, we step outside our fine-grained system and construct the thought directly, so to speak - and all of this in a sense just constitutes a configuration of our fine-grained system, but of a special kind.

Compare Russell's treatment in the Logical Atomism lectures of 'propositions with more than one verb', and his remark about Wittgenstein's 'discovery' that propositions like 'A believes that p' are 'a new beast for our zoo' (p. 226, Logic and Knowledge).

A Desultory Postscript about Water

Contrary to plan, I haven't included a proper section on 'Water is H20' and related examples (or apparent examples) of the necessary a posteriori. I don't have much to say about such examples for now, except that it is very difficult to avoid dogmatism when treating them; specifically, in the move from the fact that water is H20 - something we've all learned - to a particular interpretation and logical explication of 'Water is H20'.

One might regard this sentence as expressing a 'theoretical identity' as in Kripke. Scott Soames critically examines this way of going in detail in his book Beyond Rigidity. Alternatively, one might regard the 'is' here as being "the 'is' of constitution", and this in turn might be construed as a (non-symmetric) relation. Or one might simply interpret 'is H20' as a predicate. On the 'water' side, one may construe this as being tied to a concept of water in the Kripke-Putnam way (i.e. such that 'Water is H20' is necessary), or it may be construed functionally or phenomenologically, such that 'Water is H20' is contingent.

All these contents seem to exist, so to speak, and all seem like natural ways of interpreting 'Water is H20'. So we must be wary not to fall into holding views which might implicitly suggest otherwise; we can and should develop simplified, systematic, abstract views of logic and language, but we hinder and discredit this very development if we neglect the underlying variety of language use. Among other things, this may give the false appearance that the whole logico-philosophical enterprise depends on there not being this variety.

(Part 1, recently edited, is here.) 

(See this paper for a newer presentation of the basic ideas of part 1.)

1. For present purposes, I pass over Kit Fine's contention that not all necessary properties are essential in an intuitive sense (roughly because they are not all intrinsic to the thing in question). The classic example of a necessary property which is arguably not an essential property is Socrates' membership in his singleton set {Socrates}. There may be something important which distinguishes the essential properties from the merely necessary ones, but they will still be necessary properties, and hence will be amenable to my view.

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