Blackburn's Interpretation of Wittgenstein as a Proto Quasi Realist

In his 1993 'Review of Paul Johnston's Wittgenstein: Rethinking the Inner' (published in Ethics vol. 103 that year, pp. 588 - 590), Simon Blackburn tries to demonstrate that Wittgenstein has shown us the way to a fruitful theoretical perspective, while not going all the way himself. The view in question is Blackburn's quasi realism. According to the Oxford Dictionary of Philosophy (which Blackburn wrote!), quasi realism is the view that projectivism or expressivism about ethics can make legitimate sense of the 'realist-sounding' aspects of ethical discourse. This contrasts with error theory, on which these aspects are held to reflect a false 'realist metaphysics'. (End of quotation.) Though quasi realism is by default regarded as applying to ethical discourse, analogous claims can be made about other kinds of discourse with 'realist-sounding' aspects. Some 'realist-sounding' discourse - for example discourse describing the present location of observable objects - is fully realistic, and can be taken at "face value" - that is, as describing reality. Terms like 'truth', 'fact', 'correspondence' and 'description' primarily apply to this kind of discourse, but also find legitimate uses elsewhere, e.g. ethical discourse, which are less transparent but can be explained by the quasi realist. That is the view; problems may have suggested themselves to you already, but this is not the place to criticize quasi realism directly.

Blackburn begins by noting that Wittgenstein 'is constantly suggesting that underneath the superficial similarity of linguistic form there is deep difference of function'. He gives several examples: philosophical statements are treated as 'rules of grammar', mathematical statements 'do not have the use of statements but of rules', apparent self-descriptions are 'forms of self-expression', ethical, aesthetic and theological assertions are 'not what they appear', and more. Blackburn is very approving of all this, but then comes the question:

So can we continue to talk of truth, fact, knowledge and the rest in these nondescriptive areas without blushing? It seems a good question, and I do not think Wittgenstein ever confronted it squarely. His answer is going to be that we can, but it is not at all plain how he gets to it, for the difference of activity he harps on is introduced precisely by contrast with describing and representing how things are, and those are the activities that most obviously must conform to norms of truth and fact. Wittgenstein seems to leave unfinished business ... taken up by the character I call the quasi realist, with whom he should therefore be allied.

Against this, I think it can be demonstrated that while Wittgenstein may be an inspiration for quasi realism, he cannot truly be regarded as its ally. To begin with, is Blackburn right in saying that the question above was never squarely confronted by Wittgenstein? There doesn't appear to be any extended philosophical treatment of this question in his corpus, but it would be too quick to conclude from this that Wittgenstein has left unfinished business here, something he might have got around to. Let us try to get clearer about the question of whether we can 'continue to talk of truth, fact, knowledge and the rest in these nondescriptive areas without blushing', in order to see where Wittgenstein might stand in relation to it.

Blackburn is expressing himself figuratively; actual blushing is not in question. I didn't even take note of that when I read it, which is noteworthy in itself; one feels here that Blackburn is making things rhetorically easier for himself by expressing his question this way. Since he does after all have a definite agenda, namely to ally Wittgenstein with quasi realism, I think we are justified in asking: what did Blackburn really mean by this figure?

A simple answer would be that Blackburn means to ask whether can we truly speak of truth, fact and knowledge in what he calls 'nondescriptive areas'. This will not do, however, since it is possible to express truths in a way which is misleading and confused, and perhaps this could be cause enough for 'blushing' in Blackburn's sense. Hence it cannot be merely truth and bare meaningfulness which is in question, but also the appropriateness of certain forms of words in certain uses. And what kind(s) of uses are relevant here? There are very diverse cases of talk about truth, fact and knowledge in what Blackburn calls 'nondescriptive' areas. As a rough heuristic, we may divide this talk into two categories: everyday and philosophical (or, to put a different slant on the matter, practical and idle). Intermediate and other cases are no doubt common too, but let us consider some clear examples of practical uses and philosophical uses.

Practical:

- "There are four primes between 10 and 20." 'That's not true! ..oh, wait, yes it is.'

- "I have very little knowledge in topology."

- "I know it's a bad screenplay, in fact it's terrible, but the performances were somehow wonderful nonetheless."

- "At that point, he knew he had done the right thing."

- "...and that was when I first felt the pain. As a matter of fact, it's come back; I'm going to lie down."

- "She is basically a decent person." "I just can't believe that. If that were true, she wouldn't have..."

Philosophical:

- "The knowledge we possess about the realm of natural numbers is eternally valid, and more certain than any empirical knowledge."

- "There are ethical facts."

- "I know with certainty that I am conscious, but I can only hypothesize that others are."

- "There are many facts about the properties of my sense-data which I cannot express, for lack of a proper phenomenal language."

There is reason to think that Blackburn's question largely concerned with the practical uses. Firstly, quasi realism is inconsistent with full-blown Realist philosophical claims about the 'nondescriptive' areas, which can after all be made in terms of fact, truth and knowledge. Blackburn would not want to say we're entitled to make them. Secondly, Wittgenstein himself would probably take such utterances as symptomatic of philosophical confusion. This may not mean that all philosophers who say such things should in any sense blush, or be ashamed of themselves, but such assertions do seem like the sort of thing Wittgenstein would want to investigate critically. Therefore we shall focus on Blackburn's question as it applies to the practical uses.

On this understanding, it does seem Blackburn is right in saying that Wittgenstein's answer will be that we can speak in this way without blushing. But what of the next, quasi-realism-motivating claim, that it is 'not at all plain' how Wittgenstein 'gets to' this answer?

The trick is to see that Wittgenstein doesn't get to it at all. The propriety of such talk is not something Wittgenstein establishes with philosophical considerations; it is his starting point. Wittgenstein's acceptance of our ordinary employment of language does not derive from philosophy but from life. In his philosophy, it is the given. As evidence for this, I offer the following remarks from the Philosophical Investigations:

§124:

Philosophy may in no way interfere with the actual use of language; it can in the end only describe it.

For it cannot give it any foundation either.

(...)

§126:

Philosophy simply puts everything before us, and neither explains nor deduces anything. (...)

§132:

(...) we shall constantly be giving prominence to distinctions which our ordinary forms of language make us easily overlook. This may make it look as if we saw it as our task to reform language.

Such a reform for particular purposes, an improvement in our terminology designed to precent misunderstandings in practise, is perfectly possible. But these are not the cases we have to do with. The confusions which occupy us arise when language is like an engine idling, not when it is doing work.

Blackburn pre-empts this exactly, by speaking of 'cluster of interpretations' of Wittgenstein on which there is no unfinished business. As Blackburn says, on this view:

The true Wittgensteinian reaction is just to find more motley. Talk of truth, knowledge, certainty is itself a patchwork. For these notions do not just arise in connection with descriptions and representations but with rules, ejaculations, and so on as well. Provided we have a correct "übersicht" of what we are doing, nothing needs explanation, nothing is hidden.

I think this is right, and that it is the truly Wittgensteinian reaction. (For the sake of simplicity, I will anticipate my conclusion by referring to it as such.) Blackburn's objection to this view gets us to the heart of the problem. I quote it in full, so that we may see in detail how it fails:

It is true to much in Wittgenstein, yet its problem is obvious: it denies Wittgenstein any words to say what he wanted about the differences that the position starts by celebrating. Maybe "description" and "representation" are a patchwork, or what might be called mottled themselves ("this is what we call describing ethical facts"). Drunk on clusters, we evade the problems that torment the quasi realist by reaching once more for the mottle. Of course ethical (mathematical logical, philosophical, psychological) statements are true, describe the facts, can be known, say how it is. No contrasts there! But they do not do so in the way that empirical statements do. Don't they? Find an interesting way in which they allegedly contrast and watch me mottle it!

The first claim, that the truly Wittgensteinian reaction denies Wittgenstein 'any words to say what he wanted' about the relevant differences, is simply false: all it says is that the propriety of 'realist-sounding' talk in (what Blackburn calls) 'nondescriptive' areas is part of the given, and not to be interfered with, and that such talk is variously used. This might deny Wittgenstein certain words to say what he wanted about the relevant differences, but he doesn't need them anyway. In fact, they can get in the way. There are many ways of talking about, and showing, relevant differences. Some basic examples:

- In Wittgenstein's simple language-games involving 'slab', 'there', etc., it is unnatural to regard the counting-words 'a', 'b', 'c', etc. as 'names of objects', and even if one does call them this, their completely different function is nonetheless manifest.

- It makes sense to say 'I doubt whether he is in pain', but not 'I doubt whether I am in pain'.

- Our method of verifying the proposition '25 x 25 = 625' is different in kind from our method of verifying the proposition 'It is raining'.

- It makes sense to talk about the destruction or disappearance of chairs, but not numbers.

This shows that Blackburn's first claim is wrong: there is plenty Wittgenstein can say about differences of function in language without employing the 'realist-sounding' words to do the distinguishing. The next claim which needs to be put right is: 'Drunk on clusters, we evade the problems that torment the quasi realist by reaching once more for the mottle.'

It is hard to know how to object to such a sentence. For a start, I think the quasi realist ought to be tormented by certain problems so long as they remain a quasi realist, since their view is not tenable. That the truly Wittgensteinian reaction avoids ('evades') these problems is a strength, not a weakness. However, it neither avoids nor evades the problem, shared with the quasi realist, of clarifying important differences in the working of language. Wittgenstein took that task very seriously. We 'reach once more for the mottle' only to show that Blackburn's particular approach, quasi realism, won't work. This is not to say: 'Find an interesting way in which ['nondescriptive' and 'empirical' statements] allegedly contrast and watch me mottle it!'. Here, Blackburn gives the impression that the quasi realist has proposed contrast after contrast, only to have each one mottled by the true Wittgensteinian. But not at all! He has only proposed one - that between quasi realistic and really realistic uses of language.

The examples given earlier, on the other hand, show some genuine contrasts which no Wittgensteinian would want to mottle. Unlike Blackburn's proposal, they are not distinctions which require extensive theoretical elaboration in order to have a chance of getting off the ground. Perhaps Blackburn finds them insufficiently 'interesting' or general, but this is a prejudice which Wittgenstein did not share, and which we need not share.

The Non-Indexical Core of Presentism is Monism

In recent discussions about temporal ontology, there has been interest in the question of the prospects for a non-indexical, or externalist, formulation of presentism. Some say there are no prospects. Thus Hinchliff (2000):

[A substantive distinction between presentism and eternalism] cannot be formulated in nonindexical terms. That is why I have formulated [presentism] with the aid of the indexical 'presently'.

Others have tried with elaborate means to formulate something which could reasonably be called a non-indexical version of presentism. Matthew Farr, for example, is currently exploring a strategy involving two temporal dimensions. (This note was inspired by a talk he gave at the University of Sydney on 25/3/13 called 'Supertemporal Ontology and the "Triviality" Problem'.)

The issue is obviously interesting, assuming that the question of the meaning of presentism is interesting. One special connection in which it is interesting is this: if there is no non-indexical core of presentism, then perhaps the metaphysical dispute between presentism and non-presentism can be dissolved, on the grounds that presentism is not a distinctive thesis about the structure of reality, but something else (a "view from inside", or something).

I am certainly sympathetic to the idea that the debate in temporal ontology (between presentism, eternalism, the growing block view etc.) is something which should be dissolved or transcended. I seriously doubt that this is a debate about some real subject matter, let alone that it is a debate about some real subject matter where one of the positions is right and the others wrong. I think the confusion here is deep, philosophically important, and deserves to be investigated carefully, not just dismissed. However, I do not think that the idea that the debate cannot be formulated non-indexically is a way to make progress on this, because I think that idea is wrong.

My suggestion here is that we can analyse presentism as the conjunction of two claims, one of which is non-indexical and incompatible with eternalism, growing blockism and shrinking blockism, the other of which is indexical but agreed to by all these parties.

(P) Only the present moment exists.

may be analysed as

(P-conj) Only one moment exists, and this moment exists (where 'this' indicates the present moment).

Call this the conjunction analysis. The non-indexical core of presentism, on this suggestion, is simply the first conjunct: monism about moments (or times, instants, timeslices or whatever).

This non-indexical core is, of course, compatible with strange propositions like:

(S) Only one moment exists, and it is the moment of Napoleon's birth.

But so what? No one believes that, and everyone (presentist, eternalist, growing blockist, shrinking blockist) believes that the present moment exists. Forget the label 'presentism' - look at the conjunction analysis, and it becomes clear that what is really distinctive about this view - i.e. what distinguishes it from other actual contenders - is its monism.

Reference

Hinchliff, M. 2000. 'A defense of presentism in a relativistic setting', Philosophy of Science 67, pp. S575-S586.

Philosophers' Carnival #150

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On the Truth-Functional Account of Indicative Conditionals

The "if/⊃"-question has an interesting history. It had evidently been considered (in essentials) by the Stoics, and by some mediaevals (Abelard especially). By the 19th century, many logicians endorsed the view that '⊃' (or whatever symbol was used) could be read as 'if...then'. This continued through the early years of the 20th century, but conscientious objectors came into view. This is socially and historically interesting, in that (as we shall see) the essential matter of the controversy had lain dormant in logic books for years beforehand, without being much discussed. It is as though logic had started to come to life again: gradually, more people were moved to think critically (but without complete dismissal) about what they read in logic books.

In the English-speaking world, MacColl was one of the earlier dissenters, though his criticisms were partly obscured by his own unpopular doctrines and procedures.

In 1908, in a short polemic against Russell, MacColl wrote: 'For nearly thirty years I have been vainly trying to convince [logicians] that this assumed invariable equivalence between a conditional (or an implication) and a disjunctive is an error'. (This is a reference to the Or-to-If Argument, which we will consider in a future post.) Russell's reply was made easy by the fact that MacColl had, in his objection, overlooked the former's distinction between propositions and propositional functions. After correcting this, Russell addressed the main issue swiftly, writing 'I say that p implies q if either p is false or q is true. This is not to be regarded as a proposition, but as a definition', and admitting happily that this definition does not give 'implies' its usual meaning. But this does not square well with the justification of the 'Definition of Implication' given in Principia.

More successful criticisms came later from Strawson. By the time of Quine's (1953) review of Strawson's Introduction to Logical Theory, the former was able to treat the semantic divergence between '⊃' and 'if...then' as rather old news:

The well-known failure of the ordinary statement operators 'or', 'if-then', 'and', and 'not' to confirm in all cases to the precepts of truth- functional logic is well expounded by Mr. Strawson. Because 'and' and 'not' deviate less radically than the others, I have found it pedagogically helpful (in Elementary Logic) to treat the translation of ordinary language into logical form, at the truth-functional level, as funnelled through 'and' and 'not'; and Mr. Strawson follows suit.

And later:

Mr. Strawson is good on '⊃' and 'if-then'. He rightly observes the divergences between the two, and stresses that 'p⊃q' is more accurately read as 'not (p and not q)' than 'if p then q'.

This state of affairs did not last. A series of post-1960 events has changed things irrevocably, so that Quine's comments above seem to come from a bygone era when things were much simpler. In my own view, the Quine-Strawson view was basically right, but one cannot make a respectable case for that today without discussing the post-1960 events. Therefore I shall now give a summary of the events, followed by a series of critical comments.

The resurgence of '⊃': a potted history

Phase 1: In his William James Lectures at Harvard in 1967, Grice makes public his theory of implicature and conversational maxims. People are impressed by this idea: 'John is poor but honest' has the same truth-conditions as 'John is poor and honest', but the former (in some contexts) strikes people as objectionable and unassertable, even when the latter may be both true and assertable, the difference being that the former can carry an implicature that poor people aren't honest. Secondly, the maxim of 'Assert the Stronger' is developed; if someone asks where John is, and I know he's at the library, it's not proper to respond that he is either in the library or at the pub. Similarly, Grice argues, sentences like 'if snow is green then I am king' are true (just because snow isn't green), but unassertable, since we should assert the stronger: that snow isn't green. (The work is published in Grice (1975).)

Phase 2: Meanwhile, other philosophers had been continuing to develop more sophisticated accounts of the truth-conditions of conditionals. Among these is the possible worlds account of Stalnaker (1968), who, following Adams (1965) (who himself wasn't interested in the question of truth-conditions), conjectured that the probability (in some sense) of a conditional 'If A then C' is the probability of 'C' given 'A'. That is: P(If A then C) = P(C/A) = P(C & A)/P(A) (where P(A) is positive).

Phase 3: David Lewis proves his triviality results in Lewis (1976), to the effect that 'there is no way to interpret a conditional connective so that, with sufficient generality, the probabilities [of truth] of conditionals will equal the appropriate conditional probabilities'. He considers the possibility of accommodating this with a theory on which conditionals do not have truth-values (i.e. are not truth-apt): 'Why not? We are surely free to institute a new sentence form, without truth conditions, to be used for making it known that certain of one's conditional subjective probabilities are close to 1. But then it should be no surprise if we turn out to have such a device already.' He writes: 'I have no conclusive objection to the hypothesis ... . I have an inconclusive objection, however: the hypothesis requires too much of a fresh start. ... [W]hat about compound sentences that have ... conditionals as constituents? We think we know how the truth conditions of compound sentences of various kinds are determined by the truth conditions of constituent sentences, but this knowledge would be useless if any of those subsentences lacked truth conditions.' This boosts Grice's proposal, which Lewis has come to endorse: 'It turns out that a quantitative hypothesis based on Grice's ideas gives us just what we want: the rule that assertability goes by conditional subjective probability.' And so the truth-conditions of indicative conditionals are identified with those of '⊃'-statements. And for sophisticated reasons.

(To complete the story, though this is less important for what follows: in a postscript to his (1973) in his Philosophical Papers, Volume II, Lewis admitted that in 'special cases', assertability and conditional probability diverge. Secondly, he abandoned the 'Assert the Stronger' explanation of apparent counterexamples to the '⊃'-analysis, due to apparent counterexamples to the 'Assert the Stronger' maxim itself, in favour of an ingenious alternative theory devised by Frank Jackson: one may assert 'if A then C', even when one is in a position to assert the stronger 'C', if one wants to give information which is robust with respect to 'A' (which could have low probability): information which, even if 'A' turned out true, would still hold. For more details on how this theory works, see Lewis's postscript and Jackson (1979).)

Thus the Grice-inspired Lewis-Jackson version of the '⊃' analysis is today regarded as a serious proposal, even if it is not widely accepted. Some other major accounts on the market deny truth-aptness, either completely (cf. Edgington 1991, 1995) or in certain cases, such as when the antecedent is false (cf. McDermott 1996). All these accounts have in common that they are error-theoretic with respect to many or most competent speakers: the '⊃' analysis implies that competent speakers often get a conditional's truth-value wrong, while accounts which partially or totally deny truth-aptness have it that competent speakers often mistakenly ascribe truth-values to sentences which have none.

Comments on the resurgence

Comment on Phase 1: Note a fundamental difference between the cases of 'but' and 'or' on the one hand, and the case of 'if' on the other: people do not generally judge it false to say that a poor and honest person is poor but honest, but rather wrong in some other sense. This is even more pronounced in the case of 'or'. In that case, we can see perfectly well that the misleading statement about John is true. By contrast, competent speakers will confidently classify a sentence like 'If grass is blue, it isn't blue' as not true. Thus it seems any view which says that for every '⊃' sentence, there is a corresponding 'if' sentence with the same truth-conditions, will inescapably be an error theory with respect to competent speakers.

Comment on Phase 2: The notion that assertability or probability of conditionals goes by conditional probability may seem initially appealing, but apparent counterexamples abound: sentences such as 'If 6 is greater than 5, then 7 is greater than 6' and 'If Gödel's proof really was valid, the sun will thankfully rise again' do not seem at all assertable or probable. They seem like bits of nonsense. Furthermore, the idea that assertability can be quantified, and that it equals any sort of probability, seems odd; if I attach a probability of only .5 to some proposition P, why would I assert it? Such a proposition seems not assertable at all in a normative sense - and therefore not 'half assertable' either, whatever that means. A common proposal in response to this is that assertability remains low until probability gets high, at which point it shoots up. This has been criticized by Dudman (1992), using lottery cases: someone who has a ticket in a lottery will usually not be prepared to assert that they won't win, even though they may realize that not winning is very highly probable indeed.

Comment on Phase 3: Lewis, wanting to maintain that assertability of conditionals goes by conditional probability ('A = CP' for short), uses his triviality results to argue in effect that, since we can't give any truth-conditional analysis of conditionals such that probability of truth will equal conditional probability, any truth-conditional account will (by A = CP) have to explain divergences between assertability and probability of truth, so why not at least start with something simple like the '⊃' analysis? The quite different course of denying truth-aptness remains open, but - says Lewis - that requires too much of a fresh start.

The first thing to note about this line of argument is that, for reasons given in the previous comment, A = CP is really not independently attractive, once you consider certain examples. So perhaps no 'divergences' need explaining at all, and philosophers can go on looking for a non-gappy truth-conditional account of conditionals which is more plausible than the '⊃' analysis.

The second thing to note is that the logical space between giving a truth-conditional analysis of conditionals and denying truth-aptness remains largely unexplored. Consider the case of subject-predicate statements about explanatorily basic things possessing explanatorily basic properties: this is a class of truth-apt statements for which no non-circular truth-conditional analysis can be given - what we might call an 'analytically basic' class of statements. A view on which conditionals are analytically basic - an antitheory of conditionals - can happily avoid the error-theoretic consequences of prevailing views, although it could be retorted that such a view is error-theoretic with respect to analytic philosophers. Surely the response to that is: when faced with a choice between a set of accounts which are error theoretic with respect to (almost) all competent speakers, and an error theory with respect to some philosophers, one of whom also believed in other universes inhabited by donkeys which speak, the latter should at least be examined properly. (This, of course, would go beyond the scope of the present inquiry.)

There is a different family of accounts, known as "support" theories, which are not strikingly error-theoretic. Such accounts are for the most part out of favour today, but a highly sophisticated one has been developed by my teacher Adrian Heathcote, in unpublished work. In my view, all such accounts - if they purport to be reductive - will face circularity problems. (A defence of this view is beyond our scope here.) However, even if they don't succeed as reductive analyses, the key ideas behind "support" theories seem important for understanding the logic and context-sensitivity of conditionals.

In a post coming soon, I will discuss the Or-to-If Argument. This is a simple, initially-compelling deductive argument-form which, if valid, would suggest that '⊃' can be read as 'if...then'.

Adams, Ernest W. 1965. 'The Logic of Conditionals', Inquiry 8, pp. 167-197. Adams, Ernest W. 1975. The Logic of Conditionals, Dordrecht, Reidel.

Dudman, V.H. 1992. ‘Probability and Assertion’, Analysis, 52:204-11.

Edgington, Dorothy. 1991. 'Do Conditionals Have Truth-Conditions?' in Jackson. ed. (1991, pp. 176-201).

Edgington, Dorothy. 1995. 'On Conditionals', Mind 104.414., (Apr. 1995), pp. 235-329.

Grice, Herbert Paul. 1975. ‘Logic and Conversation’, in The Logic of Grammar, D. Davidson and G. Harman (eds.), Encino, California, Dickenson, pp. 64-75. Reprinted in Grice (1989).

Grice, Herbert Paul. 1989. Studies in the Way of Words, Cambridge MA, Harvard University Press.

Jackson, Frank. 1979. 'On assertion and indicative conditionals.' in The Philosophical Review 88, 565-589. Reprinted in Jackson, ed. (1991, pp. 111-135). Lewis, David. 1976. 'Probabilities of conditionals and conditional probabilities.' in Philosophical Review, 85(3):297–315. Reprinted with Postscript in Philosophical Papers, Volume II, pp. 133-152.

Lewis, David. 1986. Philosophical Papers, Volume II. Oxford University Press, Oxford.

McDermott, Michael. 1996. 'On the truth conditions of certain “If”-sentences' in The Philosophical Review, Vol. 105, No. 1 (Jan., 1996), pp. 1-37.

Quine, W.V.O. 1953. 'Mr. Strawson on Logical Theory' in Mind, New Series, Vol. 62, No.248 (Oct., 1953), pp. 433-451.

Russell, Bertrand. 1908. '"If" and "Imply", A Reply to Mr. MacColl' in Mind, New Series, Vol. 17, No. 66 (Apr., 1908).

Stalnaker, Robert: 'A Theory of Conditionals', Studies in Logical Theory: American philosophical quarterly monograph, Oxford, Blackwell 1968, pp. 98-112.

Whitehead, Alfred North and Russell, Bertrand. 1910. Principia Mathematica, Vol. 1. Cambridge: Cambridge University Press. Second edition 1925.

A Modification to Lewis's Theory of Counterfactuals

I propose a modification to Lewis's (1973) theory of counterfactuals, which has come to be treated by many as the standard semantics for counterfactuals. Lewis's theory is that a counterfactual conditional with antecedent A and consequent C is true iff all the most similar A-worlds (worlds at which A is true) are C-worlds. Lewis admits that what matters for similarity varies a lot from sentence to sentence, and from context to context.

What I propose is that similarity sometimes plays no part at all, and that whether it does also varies with sentence and context. When it plays no part, the truth of the counterfactual in question requires that all A-worlds are C-worlds. (To state the modified theory elegantly, we could speak of 'all relevant A-worlds', defining 'relevant' using 'most similar' but adding that sometimes all A-worlds will be relevant.)

The argument for this modification involves what could be called categorical counterfactuals. Consider the following sentence, uttered in the context of teaching someone how to use the word 'bachelor':

(A) If I had spoken to a bachelor this morning, I would have spoken to an unmarried man this morning.

Intuitively, the truth of this hinges on the fact that bachelors are necessarily unmarried men. Lewis's analysis, without my proposed modification, although it gives the right truth-value, gives the wrong truth-condition and thus distorts the meaning of (A); it is false to say that the truth-condition for this sentence is that all the most similar A-worlds are C-worlds - on any understanding of similarity.

The modified theory handles (A) much better: this is one of those cases where similarity plays no part, and so (A) is true iff all worlds where I spoke to a bachelor this morning are worlds where I spoke to an unmarried man this morning. This seems right.

(A note on the structure of Lewis's theory as formally developed with systems of spheres: this can remain as is, but in the case of categorical counterfactual conditionals the “innermost” sphere will contain all worlds, and so it would be misleading to call the worlds in this sphere 'the most similar A-worlds'.)

Rachael Briggs has made me aware that the resulting theory bears a resemblance to Angelika Kratzer's “strict conditional” theory of counterfactuals, which has been taken up by others. (I haven't compared them.) Indeed, Lewis refers to his theory as a 'variable strict conditional' analysis.

Worries and replies

Worry 1 (thanks to Rachael Briggs):

It's not clear to me that Lewis does give the wrong truth condition for (A). Your account seems to yield the result that (A) is necessarily true, since at all worlds, all worlds where I speak to a bachelor are also worlds where I speak to an unmarried man. Lewis's account also yields the result that (A) is necessarily true, since at all worlds, there is either no world where I speak to a bachelor, or some world where I speak to an unmarried bachelor closer than any world where I speak to a married bachelor. So both readings of (A) appear to agree about its truth condition---i.e., the set of worlds where it is true. Perhaps your complaint is that Lewis's analysis somehow fails to pinpoint the facts that ground (A)'s truth?

Reply to Worry 1:

Admittedly, if a truth-condition is considered as a set of worlds, then I cannot say Lewis gives the wrong truth-condition. But it seems pretty clear to me that:

(i) Lewis is trying to give the meaning of counterfactuals with his "truth-conditions" - with the RHSs of instances of his analysis. (Recall his remark at the beginning of Counterfactuals about what the kangaroo conditional seems to him to mean.)

(ii) A set of worlds by itself does not fully characterise the semantics of a sentence in use; necessary truths don't all mean the same thing. Perhaps a set of worlds specified in a particular way can do this in a sense, but then the way is doing important work that the set alone doesn't do.

In light of this, I guess I should either say more about what I mean by 'truth-conditions', or drop the term and talk about 'meaning-giving clauses' or something instead, as well as making it clear that I am assuming (ii) (plausibly, I hope). What do you reckon?

Reply to reply to Worry 1 (thanks to Rachael Briggs):

You're right that that there's a lot to meaning that isn't captured by functions from worlds to truth values, and that Lewis seems to be after it. I think what I said was really more of a quibble than a substantive criticism. People usually use "truth conditions" for intensions - functions from possible worlds to truth values, and "hyperintensions" for anything finer-grained than intensions. Saying you're trying to capture their meanings makes good sense, and saying that there's something hyperintensional about their meanings also makes good sense.

Worry 2 (thanks to Michael McDermott):

Are you saying that the ‘if’ construction means different things in (A) and (B)?

(B) If I had spoken to a bachelor this morning, I would have learnt something interesting.

That does not seem plausible. It would be like saying that ‘=’ means different things in (C) and (D) because (C) is a necessary truth.

(C) The number of boys = the number of boys.
(D) The number of boys = the number of girls.

Reply to Worry 2:

I don't want to claim that here, no. My own background view about meaning is that we can carve up meanings at different levels of granularity, so that while a meaning distinction could be made here, we can also be less fine-grained and say that the 'if' construction means the same thing in (A) and (B), which we can gloss as 'All relevant A-worlds are C-worlds'.

Analogously, a quantifier like 'all' can be used in an unrestricted sense, or with implicit restrictions. We can say that 'all' means different things depending on this, but we don't have to.

Reference

Lewis, D. 1973. Counterfactuals. Basil Blackwell: Oxford.

Notes on Identity (and the idea of a 'law of metaphysics' concerning it)

(I) Everything is identical with itself and with no other thing.

Consider what results when we try to express (I) in first-order logic:

(FOL I) (x) x = x  ~ (y)(y = x  ~ y = x)

For a closer articulation, let us introduce a function SelfOf() - the identity function – and a distinctness relation D, yielding

(FOL I 2) (x){ x = SelfOf(x)  ~ (y)(y = x  y D x)}

This shows what we are doing in the case where we use something like (I) to introduce 'identity' and cognates, e.g. making sure it's not taken qualitatively. We are presupposing, using, the notions of self and distinctness/otherness, and showing how identity connects with them; if we had fixed interpretations for 'D' and 'SelfOf', we could use (FOL I 2) to define '='. And we could of course reverse this, presupposing '='. (In the first use, we would naturally emphasise 'self' and 'no other thing', or just 'other', in pronunciation. In the second, we would emphasise the word 'identical'.) We can also presuppose nothing, and take these propositions as just specifying how these notions are to relate to each other.

All these construals can be called grammatical in Wittgenstein's sense. But now, is there some other way of taking (I)? It can certainly look that way in philosophy. ('Law of Metaphysics'.)

It can look as though (I) is ruling out worlds where the identity relation looks like this:

 

or like this:

and ruling in this sort of picture:

 

But no one wants to say that these worlds are real, or even possible. So then can't we – mustn't we - take this ruling in and out as grammatical too?

Somehow, instead of seeing it that way, philosophical thinkers try to give it another, impossible sort of application – or so I want to say. But what is this other application, and how am I to describe it without falling prey to the sort of confused thinking I am trying to correct?

What makes these mistakes, or confusions, hard to correct is their slippery, elusive character. (This no doubt has to do with the way so many of our key terms slip and slide so naturally between slightly different uses.)

It is not as if my opponent thinks their Law of Metaphysics is empirical, or anything like that. Rather, they have a spurious category for it, I want to say – or, at the very least, they spuriously categorize it.

They fail to make a category at the right level, so to speak – fail to regard identity statements as being sufficiently special in their fundamental workings. Instead, they are assimilated to other relational statements, giving rise to the conception of a special sort of fact (which we have some kind of special access to, perhaps).

A purported picturing of the world as being one way rather than another. A purported division in some space of representations. Also, perhaps some vague conception of an analogue of empirical verification – as it were, rational perception (cf. Plato, Goedel, the notion of an “eye of Reason”). The sort of thing no one would ever feel like positing for 'Bachelors are unmarried' (except perhaps in a heroic effort to be consistent).

How is it that this comes about here, and not, say, with 'Bachelors are unmarried'? I believe it arises from the mixture of two modes of representation. This should become clear in a moment.

* * *

It is odd the way (I) can inspire phrases like 'Law of Metaphysics' while 'Everything exists' is much less likely to. Of course, for the latter to be false, there would have to be things which do not exist, which is obviously contradictory. OK, but isn't that also true of the following natural description of “what it would take for (I) to be false”?: there would have to be things which do not bear the identity relation to themselves, or distinct objects between which it holds.

It is as though the two conflicting things here are less similar, a bit further apart in language, than in the existence case.

What if I had said 'there would have to be things which aren't themselves, or things which are other things'? That sounds more flatly contradictory; no one, unless doubly perverse, would formulate a “Law of Metaphysics” running 'Things are themselves'. (Butler's Dictum is not generally presented as a Law of Metaphysics.) The flavour changes markedly when we bring in 'identical', talk of 'bearing the identity relation' etc. That is where we begin to get the mixture of modes of representation.

A natural picture to illustrate, or put by, 'Everything is what it is' would be:

Things are represented as dots and are shown “just being themselves”. Whereas the natural picture to put by (I) is: 

 

And here we get the feeling of a contrast, of substance, of something being ruled out. Namely stuff like:

 

The mixture of two modes of representation here consists in the fact that each dot in the picture is taken to represent a different object, and yet lines are drawn indicating the identity relation – lines which could only be of use if two dots sometimes represented one object.

* * *

With identity statements, merely specifying the relation in question (identity) and the pair of objects involved in the ascription (assuming the names involved refer) fails to specify 'what is said' in any natural sense, however minimal. This problem cannot be avoided either by expelling repetitive identities from language – there can be multiple different non-repetitive identities concerning one and the same object.

If you find this strange or unacceptable, I suggest you have in the back of your mind a conception of relations which identity does not really fall under. Perhaps you are picturing something like the dots above, and imagining relations as encoding further information on top of that structure. This may be a good conception, in which case you should stop classifying identity as a relation, stop classifying identity statements along with propositions like 'John loves Mary'. This, rather than, e.g., moving to an unnatural conception of 'what is said' – which is, I think, what hard-line Millians such as Scott Soames do.

This move in semantics to an unnatural conception of what is said, then, may have an origin related to that of the conception of a Law of Metaphysics discussed critically above. Also, they can be made to support each other: if it's a 'substantial metaphysical fact' that everything is identical to itself, then a repetitive identity is an instance of this, and so perhaps it inherits some metaphysical substantiality for itself, in which case perhaps there is an informative, substantive extensional core to extensionally equivalent identity statements – something which they all say. Conversely, if we take this last thing for granted: what sort of thing does a repetitive identity say which an empirically informative counterpart also says? It had better not be something trivial, since the latter doesn't seem to say anything trivial, in any sense of 'say'. And so what sort of thing is this non-trivial thing which repetitive identities say? Perhaps we could call it 'an instance of a Law of Metaphysics'!

On the Problems of Reference and Intentionality II

The following remarks were written when I was wrestling with these problems over an extended period. They might act as a stimulus to someone. Part I is here.

Part II

24. What do I mean when I say 'reference is no ordinary relation' in (22)? Perhaps the point would be better put in terms of reference-ascribing propositions.

25. I have long had the feeling that the desire for a classical analysis of reference ('x refers to y iff ...') comes from within a way of looking at things which involves something which might be called a 'transcendental illusion'.

26. For some reason I want to say: remember, in reference-talk, we are, as always, presupposing a connection between our concepts and their objects. But what this means, if anything, is very unclear.

27. There is the urge to say something like: 'Remember, you can't get outside your own mind'. But what the hell kind of reminder is that?! Who would ever think otherwise? (Satisfaction with such remarks belongs to a relatively low level of philosophizing.)

28. I can imagine someone proposing a two-component theory of reference which makes use of a "disquotational base" together with "equivalence criteria". So when I say 'my concept of John is of John' this comes from the base, and so is similar to 'I have a concept of John, who exists'. But I can also say, for example, this name 'X' seems to be refer to John, this being similar to: This word is used in the same way as my 'John'.

29. We might say: Reference is that relation which is presupposed when anything is spoken of.

30. This ignores some complications (e.g. fiction) but is more appropriate, I think, than:

(1) Existence is that property which is presupposed. and

(2) Identity is that relation which is presupposed

because that distorts the logical form of existence and identity propositions. Reference is more properly a relation (i.e. more properly a property-or-relation, i.e. thing which can be ascribed to things).

31. What do I mean by 'more properly a relation' here? Here is one way to explicate this. Imagine a form of representation where objects are represented with dots or boxes, which are then labelled with names (or otherwise made intrinsically unique). Properties can be indicated by labelled lines which have one point of contact with dots or boxes, two-place relations with labelled directed lines which have two points of contact, etc.

With such a technique, an existence property-representation and an identity relation-representation would serve no purpose. Every object would have exactly one point of contact with an existence line, and exactly two points of contact with a single reflexive identity line.

32. This is, of course, a consequence of the way I am imagining this mode of representation to work. There are of course more sophisticated possibilities, where one uses dots and boxes at a higher semantic level, so to speak - as representations of ideas of objects rather than objects themselves. In that case, one can meaningfully use something like existence and identity lines - but then aren't they more properly seen as ascriptions of the property of designating something and the relation of codesignating respectively?

33. Now, what about reference? Here we can start to see that we can sort reference propositions into classes, depending on how they work and get verified. One distinction we can make is between reference propositions which concern expressions belonging to the same language-system, and those which talk about expressions from another language-system. Let us call the former 'intrasystematic' and the latter 'extrasystematic'.

34. Now we may make a further distinction between disquotational intrasystematic reference propositions, and non-disquotational. (Some of the latter can be used to give all kinds of information, e.g. '”The winner of the race” refers to John' can inform someone that John won the race.)

35. Consider what happens when we use the graphical mode of representation described above, and a new (extralinguistic) object comes to our attention. We draw in a new box or dot (let us say "node" from now on).

But in so doing, we bring into existence a new object - one which stands in the reference relation to the original object. We can represent this fact now too. One way of going would be simply to draw in another node, which represents the last node drawn, and then to connect it to that node with a line indicating the reference relation. But of course this procedure can then be repeated for the new node. This procedure corresponds roughly to giving a name its own name in word language.

36. Another way of going, which corresponds roughly to quotation in word language, would be to introduce a kind of operator on points of contact. An unmarked point of contact is the ordinary case, a marked point of contact indicates that the contacted node is representing itself.

37. Consider the first technique, where we start at the bottom level, and then construct nodes to represent those nodes, etc., as required. This process thus "automatically generates" reference propositions. These automatically generated ones are the disquotational intrasystematic ones.

38. Also, among extrasystematic reference propositions, two kinds of verification criteria can be distinguished. Direct comparison with our systems (looking at arithmetic talk for instance), vs. coordination which "involves the object" more. (The field-linguist would be doing both of these things.)

39. There is a close connection here to the Twin-Earthable/Non-Twin-Earthable distinction. (Perhaps it is that the direct comparison verifications yield propositions about the referents of non-Twin-Earthable expressions, and the “object-involving” ones yield propositions about the referents of Twin-Earthable expressions, but that may be an oversimplification.)

40. Consider Idealism here. On Idealism, perhaps all extrasystematic reference criteria can be reduced to system-coordination. A kind of collapse of Twin-Earthability.

41. For example: I see a man point at a rock and say 'N', and I form the hypothesis that 'N' is a name (which is not part of my system) representing the rock I see in front of me. This is a paradigm case, it might seem, of acting on criteria for extrasystematic reference which cannot be reduced to system coordination. I coordinate a part of his system directly with its object, not with a part of my system.

42. An Idealist may insist that this is not so. Rather (they may say), I am correlating my perceptual representation of the rock with something. But it would seem that if we are to be consistent, we can't really say that the perceptual representation of the rock is correlated by us with the name 'N', since 'N' is not part of our system. Mustn't we now say that we correlate our perceptual representation with our representation of the extrasystematic name 'N'?

43. But still, this does not give the Idealist the distinction I want to have between external-object-involving verifications of extrasystematic reference-propositions and verifications of extrasystematic reference propositions which involve "merely internal" comparison of systems. For in the internal case they also have to talk about our representations of some extrasystematic expression.

44. Why is this interesting? Not 'in case Idealism is true'!

45. When '”A” refers to B' is not disquotational, it seems that for practical purposes it means the same as the statement that 'A' and 'B' codesignate, and can therefore be understood as being verified by correlation of (aspects of) the role of two signs.

46. x refers to y iff x codesignates with 'y' iff x's referent = y.

47. But not all reference propositions which look like disquotational ones are such. For example: '”N” refers to N in German too'. Or when setting up a new language, as in formal Peano arithmetic: '"0" refers to 0'.

48. We should take note of the singularity of a truly disquotational reference-thought.

49. In philosophy, we think: 'N' refers to N. Then we think: how?

50. Now, that first thought is a thought to the effect that a certain symbol stands in the reference relation to a certain object. That much is clearly true to say.

51. Compare the thought, as had by an English speaker, that 'Deutschland' refers to Germany. This too can be truly said to be a thought to the effect that a certain symbol stands in the reference relation to a certain object. Likewise the thought that 'John' refers to the man I met yesterday.

52. But clearly the first, disquotational thought is a very different beast from the latter ones. What worries me is the effect of their assimilation under the rubric: reporting a reference relation between symbol and object. Reference propositions are propositions which report such relations (connections), reference thoughts are thoughts that such relations hold.

53. We might want to say that the disquotational reference propositions and thoughts are a subset of all reference propositions and thoughts, characterized by the fact that the symbol which the thought is about is also used to represent the related object. And now we may ignore this subset and concentrate instead on the non-disquotational subset.

54. There is a problem with this formulation, however. For example, suppose we are told that someone used a certain expression which itself is named E, but one does not know which expression E is. One may learn something about E, namely that it refers to Venus. Suppose E is actually 'Venus', the same word used in the same sort of language system. In that case, on my formulation above, the thought that E refers to Venus would be classed as disquotational, even when the thinker doesn't know that E is the name 'Venus'.

53. So it seems what we really wanted is: the disquotational subset is characterized by the fact that the same symbol is used twice over – to specify the referer, and the referent. But even this doesn't quite work, for '”The bearer of 'N'” refers to N' fulfills that condition.

54. The difference between disquotational and other reference statements is reminsicent of the difference between trivial (repetitive) and informative identities. However, the problem is in a sense inverted: the naive relational view of identity statements makes all instances look trivial, including the nontrivial ones, whereas the naive relational view of reference statements makes all instances look nontrivial, including the trivial ones. (This use of 'trivial' may not be fully warranted, but suffices for making the point.)

55. It is instructive to compare ' "N" refers to N ' with 'The word "N" has reference, and it is used in the way it is used.' Or even just: 'The word "N" has reference, and it refers to the object which does in fact refer to'.

56. What looks like (and in some sense is) a tautologous appendage changes the modal profile radically.

57. It certainly seems that having purely disquotational reference propositions in the mix can blind us to how the rest work, owing to the special direct way the former are verified. But would it be right to discount these as degenerate?

58. 'London' refers to London. This fact could have an interesting historical explanation. (Contrast 'London is London'.)

Part III coming soon.