I said yesterday:

If we can construe a concept with an object (via a schema), then we know that it is at least the concept of an ens imaginarium (not, like the concept diangle, that of a nihil negativum [A291/B348]; and not, of course, of an ens rationis or nihil privativum, either).

But I now think I was misunderstanding the relationship between ens imaginarium and nihil negativum. A nihil negativum is indeed, in a sense, less (more nothing) than is an ens imaginarium, but only because the concept of it is more fully objective. That is: an ens imaginarium cannot properly be called either objectively, that is, transcendentally possible or impossible. (It must be subjectively, that is, formally possible; even an ens rationis is that much.) An ens imaginarium is “without substance” (A291/B347), i.e. without relation, and so the issue of possibility, i.e. modality, does not arise.

This must then affect the suggested interpretation of konstruieren. Rather than saying that the Konstruktion promotes a concept to the level where it becomes the concept of an ens imaginarium, but that then some further step is needed to promote it to the concept of a possible being, I should have said that the concept of an ens imaginarium is a concept which lacks a Konstruktion. Such a concept is not fully objective in that it fails to posit its object as heterogeneous to a ground of possibility. In particular, according to the thesis of transcendental idealism: such a concept fails to posit its object as heterogeneous to consciousness (pure space and time, entia imaginaria, are “in us”). A “construed concept” (konstruierte Begriff, see A716/B744), on the other hand, is a concept taken as a (purported) determination of the general (transcendental) relation between consciousness and its external object. As such it will be the concept of a possible object if the general relation admits of being determined in that way and, if not, not.

Our intellect is discursive. That is: there is for us a pure form of intuition, which puts specific conditions, not derivable from the unity of apperception itself, on the manifold which is to be unified in our having an object. (We have a particular species, Art, of intuition.) It is thanks to such conditions that the general relation in question, in our case — i.e. the “formal conditions of experience” (again: A218/B265) — admit of some determinations (e.g., determination to perception of a triangle) and not others (e.g., determination to perception of a diangle).¹ And so, finally, what Kant actually says about the diangle (that is: about a non-Euclidean figure) in the proof of the First Postulate is that its impossibility

rests not on the concept [of the diangle] itself as such [an sich selbst], but rather on [the concept’s]² Konstruktion in space, i.e. on the conditions of space and the determination of it [desselben, = of space]; these, in turn, have their objective reality, i.e., they pertain to possible things, because they include in themselves the form of experience in general. (KdrV A221/B268)

Which I take to mean: the geometrical Konstruktion of the concept diangle is a construal in the above sense, that is a construal upon which the possibility or, in this case, impossibility of the concept’s object can rest, because the conditions of space are (among) the specific conditions of our experience in general.

Then this is the same as what he says a little later about the concept triangle (the passage I already quote in my previous post): that its object would remain “always only a product of the imagination” (i.e., an ens imaginarium) if it were not that

The very same [eben dieselbe] imaging synthesis by which we construe a triangle [with its concept] in the imagination is wholly the same as [mit … einerlei] that which we exercise in the apprehension of an appearance, in order to make from it an empirical concept. (A224/B271)

That is: the procedure of the imagination in schematizing the concept makes it more than just a product of the imagination (posits it as heterogeneous to the imagination itself) only because the imagination in that procedure is subject to the same conditions to which it would be subject in construing an empirical concept with an object: that is, in experiencing such an object.³ The latter conditions — the conditions on experiencing the object of an empirical concept — are the formal conditions of experience in general.

This apparatus is what allows Kant to say that the Euclideanness of space is a special case, while at the same time denying that we know the possibility of any other case. We know the formal possibility of the concepts (such as diangle) which might function is such other cases, but we don’t know the possibility of such alternate geometries as geometries. That is: we don’t know the possibility of alternate specific formal conditions of experience in general. Because pure space and time are themselves mere entia imaginaria, we don’t even know the possibility of our own geometry except insofar as it is actual.

I’m interested in all of this, in part, because of a question I asked in a previous post, namely: what are the objects of mathematics? (That is: what should we say they are, taking that Kant must be at least partly wrong about that.) I want to suggest something like: that an object of mathematics is a kind of deconstrual of a concept, or of a type of concept. So, for example, one object of mathematics would be: the deconstrual of geometrical concepts which displays Euclidean geometry as a special case. Here “deconstrual” must be a form of determinate negation. What was the construal becomes absorbed into the formal content of the concept itself, and so abstraction from it becomes possible. (But, I’m suggesting, it’s the deconstrual itself, rather than the abstraction it subsequently allows, which is an object of mathematics.)

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Footnotes

¹In an intuitive intellect, so to speak, every representation which is not itself formally deficient is the representation of something possible. There is no other form with which it must be compared. But so to speak already displays how little we really understand the possibility of an intuitive intellect. I mean: that we do not know what are the formal conditions on such representations (their conditions qua determinations of the consciousness which is their subject). The law of noncontradiction is a formal restriction on discursive intellectual representations, i.e. universal concepts.

²This is the meaning according to the text of A and B. The 5th edition, apparently, reads derselben instead of desselben, so according to that we would have to understand “[the figure’s] Konstruktion.” As I pointed out in my previous post,
Kant speaks in both ways.

³Kant often, but I think not always, restricts Konstruktion to (what I am calling) the construal of a concept in the case where this can be done a priori (including, apparently, in the passage I’ve been discussing from A223–4/B271). I take it it is not too great a stretch to extend the term to the case of empirical concepts, simply by removing the qualification “a priori” in the definition “ihm gänzlich a priori einen Gegenstand geben” (A223/B271) or “die ihm korrespondierende Anschauung a priori darstellen” (A713/B741).

I’m in the midst of (yet again) trying to understand what Kant means by (to use the modern spelling) Konstruktion. I first had the thought, which no doubt I’ve had before, that it means “construal,” in the sense of “interpretation.”

That would fit a context such as KdrV A224/B271, where Kant equates “[den Begriff eines Triangels] konstruieren” (to construct/construe the concept of a triangle) with “to give [the concept] … an object,” i.e. to give it what he elsewhere calls “a reference [Beziehung] to objects, and hence a significance [Bedeutung]” (A145–6/B185), or, taking Bedeutung more broadly: to give it an “imagined significance [eingebildete Bedeutung]” (A84/B117), as opposed to a mere “logical significance” (A147/B186). To construe, that is, interpret, is to give significance.

Unfortunately, this appears not to be an accepted sense of the German verb (and moreover, according to the OED, is only a late and derivative sense of the English one). Moreover, we have to take into account another use of konstruieren in the exact same passage (from the proof of the First Postulate). Kant also talks there about the synthesis “wodurch wir in der Einbildungskraft einen Triangle konstruieren” (A224/B271). Whatever that means, it doesn’t mean “by which we construe (= interpret) a triangle in the imagination.”

Many would take it, instead, to mean something like: by which we construct (= build up) a triangle out of imaginary pieces, using an imaginary compass and an imaginary ruler, on a piece of imaginary paper. But that in itself makes little sense. Moreover, to the extent that it does make sense, it leads straight back to Descartes’s argument that we can’t do any such imaginary drawing in the case of a chiliagon (a point of which Kant is well aware: see A140/B179–80). Finally, such an understanding of konstruieren wouldn’t work at all in the first example, where Kant talks of constructing the concept of a triangle. A concept presumably can’t be drawn on any paper, no matter how imaginary.

So my new thought is this: that both of these ways of talking are short for: “einen Begriff mit einem Gegenstand konstruieren,” to construe a concept with an object (on the model of: to construe a verb with an object).

If we can construe a concept with an object (via a schema), then we know that it is at least the concept of an ens imaginarium (not, like the concept diangle, that of a nihil negativum [A291/B348]; and not, of course, of an ens rationis or nihil privativum, either). What he’s saying in the proof of the First Postulate (i.e., the proof that “what agrees with the formal conditions of experience (according to intuitions and concepts) is possible” [A218/B265]) is that to promote a concept from the concept of an ens imaginarium (which, although not impossible, is still a kind of nothing) to the concept of a possible being, we need to connect the procedure of the imagination in the schema of that concept to the synthesis of the imagination in perception.

So the object of the concept triangle would remain “always only a product of the imagination” if it were not that

The very same [eben dieselbe] imaging synthesis by which we construe a triangle [with its concept] in the imagination is wholly the same as [mit … einerlei] that which we exercise in the apprehension of an appearance, in order to make from it an empirical concept. (again, A224/B271)

The concept triangle passes this test, but the concepts of pure time and pure space as such, “die zwar Etwas sind, als Formen anzuschauen, aber selbst keine Gegenstände sind, die angeschaut werden” [A291/B347], do not. The synthesis by which the pure imagination produces time and space as pure images of the categories is not the same as any synthesis of the empirical imagination in perception (but is rather a condition of possibility of all such empirical synthesis). Hence the concepts of time and space are concepts of entia imaginaria.¹

However, I’m not sure yet if this will work in other places or whether Kant anywhere actually uses the locution “to construe a concept with an object.”

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Footnotes

¹ The ursprünglich pure intuitions of time and space, I take it, do not have objects: intuitions without concepts are blind.

Here are two ways to think about mathematics (among possibly others). (1) As a discipline: an institution with some degree of political organization, a history, etc. (2) As an intellectual virtue: a habit of the cognitive faculty which consists in the enhanced potential to carry out certain cognitive acts. (I say “enhanced potential” because a faculty in itself is already a potential.)

It is in sense (2) that mathematics can be said to have objects. A cognitive act in general is a representation, and a representation, if at all successful (if not, e.g., self-contradictory) has some at least possible being as its object. If there is such a thing as mathematics at all in sense (2), then there must be something which characterizes the objects of just those acts for which it is the enhanced potential.

(Note I’m using “object” in the correct, relative sense: an object is the object of something. According to idealists of various stripes, every being, or at least every contingent being, must be the potential object of some cognitive faculty. But for just that reason it’s a bad idea, especially if, like me, you’re an idealist of some stripe or other, to use “object” as a synonym for “being.”)

It would be wrong to define the intellectual virtue (2) solely in terms of the institution (1). We should want to say that every normal human, past some fairly young age, possesses (knows) at least some mathematics. On the other hand, the people who play the leading role in institution (1) — that is, professional mathematicians — owe their position, on the whole, to being very good at something. There may be some disciplines where success depends, not on any cognitive ability, but rather, for example, on political or social skills. But if you know any even moderately good mathematicians you will know for sure that their skills don’t mostly lie in that direction. We should want the intellectual virtue (2), which we all share to some extent, to be the one successful mathematicians must have to an unusual extent.

But this puts constraints on the objects of mathematics. For example: although some may think that mathematicians are particularly good at counting to very high numbers, that is not actually the case. Hence, the cognitive act of representing a given (high) finite cardinality is not as such an act of the virtue (2). It follows that a given natural number simply as such (unless perhaps it is very small) is not an object of mathematics.

A story about recent trends in philosophy of science:

A bunch of people are sitting in a room discussing the question, whether you can step into the same river twice. Some deny that you can, either because the river is never the same or because motion is impossible. Some say that you can, but only because the river has a defective mode of being. Or that you can, because the form of the river remains while the matter changes; or because being is nothing; or because temporality is ecstasis; or because a river is a set-theoretic construct or a mereological sum of time slices or both; or because that’s the way we use the words “river” and “step,” and if you use them differently you no longer speak for us; etc.

Suddenly someone runs in and says: “Hey guys! Believe me (and you should, because I once spent five years trying and failing to become a fisherman): you’ve all been working with a really simplistic and impoverished version of what a river is. A real river is shallow on the edge and deep in the middle. Sometimes the water is green, sometimes brown, sometimes blue. And there are fish! Not once in all of your discussion do you so much as mention fish.”

Not news, and not helpful.

Here is something about the relationship between David Lewis and Stanley Cavell. I can’t tie it all up nicely, and I’m not confident that I’ve found the right way of approaching the subject at all. But, for what it’s worth:

One thing they have in common is that many philosophers find it easy to dismiss one or both of them. I think they are both suspected of, as critics of Cavell often call it, “self-indulgence.” People feel: well, I could do that, too, if I gave in to temptation and allowed myself to talk or think so outrageously. Once the suspicion is voiced, however, it seems silly. Which one of us is capable of talking or thinking the way either of them do? What is to be resisted is rather the temptation to reach for an easy way of dismissing thinkers, our own contemporaries, of such terrifying power.

Beyond that, two points stand out immediately, one about rational disagreement and one about ordinary language. The two can’t really be separated, but I don’t know how to develop them together, either, so I’m going to start here with the first and hopefully get to the second in another post.

Both Lewis and Cavell are concerned to explain how a form of argument can be fully rational even though it doesn’t (even ideally, in the long run, etc.) embody any guarantee that the parties will eventually agree.

This doesn’t mean that they think agreement is wholly irrelevant as an aim in such cases. Cavell says that “without the hope of agreement, argument would be pointless” (Cavell, Claim of Reason, 254, my emphasis). Lewis, similarly, describes the general point of argument, or at least debate, as follows: “each of two debaters tries to get his opponent to grant him — to join him in presupposing — parts of his case, and to give away parts of the contrary case” (“Scorekeeping in a Language Game,” Phil. Papers 1:239). But the argument has been worthwhile even if the hope is frustrated, and so the lack of definite procedures for reaching an agreement is no defect in the rationality of the method. (Both think there are such procedures in at least some other cases.)

The target form of argument is not the same: for Cavell, it is moral argument; for Lewis, philosophical argument — in general, one may gather, but the only examples he ever discusses in detail are “debates over ontic parsimony” (“Holes,” Phil. Papers 1:9). (Although “Holes” is co-authored with Stephanie Lewis, I assume that everything in it speaks for both authors.)

Cavell emphasizes that the failure of agreement in moral argument has been used to impugn its rationality, based in part on the premise that “the rationality of an argument depends upon its leading from premisses all parties accept, in steps all can follow, to an agreement upon a conclusion which all must accept” (CoR, loc. cit.). Lewis doesn’t emphasize the corresponding fact about ontic debates, but he might and he knows that he might. What Cavell quotes Stevenson as saying, namely that disagreements in science are “disagreements in belief,” whereas disagreements in ethics are “disagreements in attitude” (CoR 259, citing Stevenson, Foundations of Ethics, 7), was said first by Carnap, and, at first, only about ontology, rather than about ethics.

What does an argument accomplish when it doesn’t, and wouldn’t even when all was said and done, result in agreement? “Argle has said what we accomplish in philosophical argument: we measure the price” (Lewis, Introduction to Phil. Papers 1, p. x). That is either the same as, or very similar to, what Cavell says about the process of “questioning a claim to moral rightness” in the course of a moral argument.

assessing the claim is, as we might now say, to determine what your position is, and to challenge the position itself, to question whether the position you take is adequate to the claim you have entered.… The point of the assessment is not to determine whether it is adequate, … the point is to determine what position you are taking, that is to say, what position you are taking responsibility for — and whether it is one I can respect. (CoR, 268)

The last clause strikes a note which is not mostly heard in Lewis, namely the possibility that the argument will leave us no longer on speaking terms. I want to say more about this in my next post on this topic, on ordinary language (it has to do with the “tragic” outcome that we find we cannot speak for one another). But Lewis does consider the stakes in ontic debate to be that high, at least among academics (note that “academic” is normally a term of disparagement for Cavell, but not for Lewis). This is clear, for one thing, from the elaborate care which Argle and Bargle take, in “Holes,” to avoid such an outcome, and for another thing from the care which Lewis himself takes to remain in conversation with a wide array of competing philosophers (Armstrong, Plantinga, Van Inwagen, Lycan, Reutley, etc.), while at the same time tacitly excluding others. (After a single response, in Convention, to “Must We Mean What We Say?”, Cavell is among the excluded.) More explicitly: Lewis holds that the main or, at least, only fully sufficient reason that debate is allowed to continue in academic philosophy is the “tacit treaty” by which various schools of thought agree not to prefer one over the other in hiring. But the treaty clearly doesn’t extend to any school whatsoever: “Maybe,” Lewis suggests, “the treaty is limited to ‘respectable’ schools of thought, as opposed to ratbag notions” (“Academic appointments: Why ignore the advantage of being right?”, Papers in Ethics and Social Philosophy, 199 n. 7). Lewis says there that I don’t come to respect your position by coming to give some credence to it (he respects Graham Priest’s “hard-line paraconsistency” even though he considers it “certainly and necessarily false”). He doesn’t say exactly how I might come to respect it. But how else, if not by the methods of Argle and Bargle?

The difference between moral argument and ontic debate must be important, but it is difficult to assess just how. Cavell says a lot about the contrasts and similarities between ethics and epistemology, but he remains enough of a good logical positivist to hold that “To say a dispute is about a matter of fact is exactly to say that there are certain ways of settling it” (CoR, 259). Lewis disagrees:

If you say flatly that there is no god, and I say that there are countless gods but none of them are our worldmates, then it may be that neither of us is making any mistake of method. We may each be bringing our opinions to equilibrium in the most careful possible way, taking account of all the arguments, distinctions, and counterexamples. But one of us, at least, is making a mistake of fact. Which one is wrong depends on what there is. (Introduction to
Phil. Papers 1, p. xi)

The result is that, as far as I know, Cavell never discusses at all the type of argument which for Lewis (after Convention) is always paradigmatic of philosophy.

Lewis, on the other hand, does discuss moral argument, as well as other types of philosophical argument, including epistemological argument, semantic argument, and (obviously, from the above quotes) argument about the methodology of philosophy itself. But it is unclear whether or how these other types of argument are supposed to resemble ontic debate. In “Scorekeeping,” Lewis imagines a discussion which looks a lot like one of the sample moral arguments from The Claim of Reason. To put it in Cavell’s form:

A (a corrupt politician): You see, I must either destroy the evidence or else claim that I did it to stop Communism. What else can I do?

B (rudely): There is one other possibility — you can put the public interest first for once!

A: I can’t do that. (cf. “Scorekeeping,” 247)

Lewis says about this, first, that A’s initial statement may be true while his final one is mistaken, because B’s “rude” reply (the term “rude” is Lewis’s, repeated several times) shifts the boundary between relevant and ignored possibilities, “and the boundary, once shifted outward, stays shifted” (ibid.). He then goes on to compare this to the case of a “commonsensical epistemologist” who claims, truly, to have infallible knowledge that the cat is in the carton, but then must concede defeat when the skeptic replies, “You might be the victim of a deceiving demon.” Again, the skeptic succeeds in shifting a boundary which the commonsensical epistemologist cannot then move back. Then Lewis adds:

We get the impression that the sceptic, or the rude critic of the elected official, has the last word. Again this is because the rule of accommodation is not fully reversible. For some reason, I know not what, the boundary readily shifts outward if what is said requires it, but does not so readily shift inward if what is said requires that. Because of this asymmetry, we may think that what is true with respect to the outward-shifted boundary must be somehow more true than what is true with respect to the original boundary. I see no reason to respect this impression. Let us hope, by all means, that the advance toward truth is irreversible. That is no reason to think that just any change that resists reversal is an advance toward truth.

This sounds vaguely related to Cavell, especially in the concern about “reversibility.”¹ It also sounds quite un-Cavellian, especially in its confidence that the skeptic has succeeded in establishing a context which justifies the objection.

It’s hard to know what more to say without understanding exactly what Lewis thinks has gone wrong, in both cases, such that we must (by the rules of ordinary language!) have the impression of a last word, but an impression which nevertheless is not respectable. Toward the truth about what do we hope to advance in such cases? Not toward the truth about what is strictly, absolutely possible: Lewis has an answer to that, and an answer according to which the politician and the commonsensical epistemologist are wrong (there is a possible world at which a counterpart of the politician puts the public good first, and a possible world at which a demon deceives a counterpart of the epistemologist into believing that the cat is in the carton, or rather into having a corresponding belief). Rather, toward the truth about what is morally or epistemically possible for us. And is it still true, in such cases, that, although neither of us makes a mistake of method, and although we continue then to disagree, “what there is” will make at least one of us wrong? But isn’t the question here precisely one of method: a question of which “arguments, distinctions, and counterexamples” need to be considered, and which can or should be ignored? And so won’t “what there is,” if it makes us wrong, eo ipso make us mistaken in method? Or, to put it the other way around: what is the standard by which Lewis calls the critic “rude” and the skeptic (p. 245) “a player of language games”? Suppose — as I believe most of us, including Lewis, would want to suppose — that the rude critic does force an advance towards truth, whereas the skeptic does not. By what standard is Lewis nevertheless implicating them in a common error (or worse)?

I think we would have to answer such questions before deciding whether the clear success of Lewis’s skeptic is inconsistent with the unclear failure of Cavell’s, and also whether Cavell’s worries over the difference between the epistemological case and the moral one could find any echo in Lewis.

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Footnotes

¹ Lewis does not touch, here, on another Cavellian theme, the stability of the conclusion. Elsewhere he makes equilibrium — apparently, stable equilibrium — the prime goal of philosophical thought: “If our official theories disagree with what we cannot help thinking outside the philosophy room, then no real equilibrium has been reached. Unless we are doubleplusgood doublethinkers, it will not last” (Introduction, x).

Here’s new, improved version of my previous question (on FB) about David Lewis’s motives for eliminating the worldmate relation, along with a possible answer.

In “Counterpart Theory and Quantified Modal Logic,” Lewis sets out his counterpart theory using four primitive predicates:

Wx (x is a possible world)
Ixy (x is in a possible world y)
Ax (x is actual)
Cxy (x is a counterpart of y)

A series of postulates then guarantees, among other things, that every possible thing (everything in the range or domain of C) is in exactly one possible world, and not (in the relevant sense of “in”) in anything else (see Philosophical Papers, vol. 1, pp. 26–7).

In On the Plurality of Worlds, he goes to work eliminating all of these primitives. For our purposes the important two are W and I, which he eliminates in two steps. First, he defines both in terms of two other relations: the part–whole relation and the worldmate relation. To be in a possible world is taken to be nothing more or less than to be a part of it, in the (supposedly) ordinary mereological sense, and a world is defined as a maximal whole of parts which are worldmates. Then he tries to eliminate the worldmate relation, in turn, in favor of something like spatiotemporal relations. My question is about the motivation for that second step.

The second step lands Lewis in some difficulty, as he is well aware. The rough idea is to say that two things are worldmates if and only if they are spatiotemporally related. But this would have a consequence Lewis regards as unwelcome: it would become a necessary truth that all non-simple worlds are internally related by what we call spatiotemporal relations; that is, by the ones we actually have at this world; that is (we think) by relativistic spatiotemporal relations. Lewis wants to allow that at some worlds (e.g., a Newtonian world), the relations might be different (p. 74). So instead he proposes that any relation counts as spatiotemporal if it satisfies certain criteria, including at least: naturalness, pervasiveness, discriminativeness, and externality (pp. 75–6).

But this has a further consequence which strikes me as odd.

It will still be a necessary truth that something like our geometry (in a very general sense) holds at every non-simple world. That is: if a possible thing is not simple, then all of its parts must be related by something like our spatiotemporal relations.

Technically this becomes an analytic truth (it follows from the counterpart-theoretic definition of “possible [thing]”). But in effect it becomes synthetic a priori, insofar as it is an independent source of what Lewis calls the “obscurity” of our modal language (“Counterpart Theory,” Phil. Papers 1:29). Since the first three criteria are vague, it will be vague (therefore obscure) whether some things are possible, not because we are uncertain if we are describing them consistently, nor because we are uncertain what to count as a counterpart of what, but because we are uncertain whether to count all their parts as belonging to the same world.

Here is what Lewis could have done instead. First, define the part–whole relation in terms of the worldmate relation and the relation of exact duplication: say that x is part of y just in case every exact duplicate of y has as a worldmate some exact duplicate of x. This makes Lewis’s principle of recombination (On the Plurality of Worlds, pp. 87–91) come out true by definition. Then, if a broad definition of quasi-spatiotemporality seems desirable, it could go this way: spatiotemporal relations are relations that hold between things just in virtue of the fact that they are parts of the same whole. This would be similar to what Leibniz and followers mean by defining space as the order of simultaneous possibles.

Quasi-spatiotemporal relations would still have to be external (because of the “just in virtue of” provision), but the other criteria would be eliminated. There would be no obscure rule against any kind of geometry, no matter how exotic.

This would not get back Lewis’s unrestricted mereology. It would eliminate so-called trans-world individuals, but Lewis doesn’t much like those, anyway. It would also mean that wholes composed of sets (and other non-individuals) would not be wholes in the usual sense, which might be more serious for Lewis (in view of Parts of Classes), although it accords well with common sense. Still, this way of proceeding seems sufficiently attractive that Lewis ought at least to have considered it.

My rough guess as to why he doesn’t is as follows. Although the principle of recombination, going this way, would be an analytic truth, there would be no guarantee that what can be recombined is (at least) spatiotemporal parts. It would be formally OK with this theory if our world were simple, for example, in which case there might be no other possible worlds (call this Spinozan Supervenience).

Against this, Lewis would need to appeal to common sense, pre-philosophical notions of compossibility. He needs to appeal to these on his way of going, as well: his non-analytic principle of recombination ultimately gets accepted on the same basis. But on the suggested alternative route, he would no longer be able to say this:

Never mind what makes our modal opinions count as knowledge; how do we come by the modal opinions that we do in fact hold? … In the mathematical case, the answer is that we come by our opinions largely by reasoning from general principles that we already accept; sometimes in a precise and rigorous way, sometimes in a more informal fashion, as when we reject arbitrary-seeming limits on the plenitude of the mathematical universe. Suppose the answer in the modal case is similar. I think our everyday modal opinions are, in large measure, consequences of a principle of recombination. (On the Plurality of Worlds, p. 113)

So what we learn from this exercise, maybe, is that the above, seemingly casual, argument is more important to Lewis than one might have thought.

He needs to isolate a non-analytic general principle behind many of our common sense modal opinions; otherwise, the business of unifying and systematizing them will not get very far.

A philosopher walks into a bar and says to the
bartender, “I’ll just have a coke” (perhaps because she agrees with
Thoreau: “I would fain keep sober always; and there are infinite
degrees of drunkenness”).

Let’s assume she does want a coke, and that she knows she wants a
coke. (It is strange to say “X knows she’s in pain,” but “X knows
what she wants” sounds normal to me.) By saying this, she brings it
about that the bartender also believes she wants a coke. At least,
that presumably is the immediate point of saying this.

However, she does not thereby make it possible for him to know, by the
same method she has followed, that she wants a coke. That is: she
doesn’t prove to him that she wants a coke. Rather, she gets him to
accept this belief by virtue of her (apparent) authority (in this
case, the apparent authority vested in her by the legal system as
apparent owner of the money he assumes she will use to pay her tab).

Question: is this permissible for a philosopher?

Here’s a more precise version of what I’ve been saying for years about
Carnap, Quine and David Lewis. It’s based on the following:

Our knowledge can be divided into two quite different parts. As best
we can, I think by seeking a theory that will be systematic and devoid
of arbitrariness, we arrive at a conception of what there is
altogether.… This conception, to the extent that it is true,
comprises our modal and mathematical knowledge. But a conception of
the entire space of possibilities leaves it entirely open where in
that space we ourselves are situated. To know that, it is necessary to
observe ourselves and our surroundings. And observation of any sort
… is a matter of causal dependence of one contingent matter of
fact upon another. (Lewis On the Plurality of Worlds, §2.4,
pp. 111–12)

1. Carnap agrees about the second type of knowledge: we find out
contingent truths, if at all, empirically. But he holds that the first
type of knowledge is knowledge of truths by convention: that is, more
or less, that the real questions in this area are practical, rather
than theoretical.

(The “more or less” is necessary because of complications about the
difference between internal and external questions. Once natural
numbers, e.g., are admitted to the language by practical decision,
there are theoretical questions about what natural numbers exist.)

2. According to Quine, this position is incoherent, because, if
conventions are supposed to do this, then empirical facts are not
sufficient to determine which convention we have chosen.

3. Lewis responds with the above doctrine. In the case of necessary
truths, we form our knowledge, to the extent that we have any, in the
way a conventionalist would suggest (seeking unity and simplicity,
etc.). But we are not choosing a convention; rather, we are choosing
what we should believe. Even if we follow the correct method, we might
be wrong.