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'.)

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.

Philosophers' Carnival #144 + Statement of New Direction

Welcome to the 144th edition of Philosophers' Carnival, the first edition since I took over organizational duties from Richard Yetter Chappell of Philosophy et cetera. The next edition will be hosted at Philosophical Pontifications on the 10th of November.

Those who have been following the Carnival lately will have noticed its decline. Brian Leiter recently decided to stop linking to it, due to declining quality. Last edition was a complete scandal. Depressed, I wrote to Richard Chappell offering to host the next edition, and to try to make it a better one. As an afterthought, I offered to take over the organization of the Carnival, and Richard accepted. 

I'm very excited about this opportunity to promote the free online dissemination of serious philosophy (something I believe in strongly), and I expect to give Brian Leiter reason to reverse his decision.

The two main things I think were wrong with the Carnival before are:

(1) It wasn't ambitious enough. It presented, and was regarded, too much as just a bit of fun.

(2) The work of highly visible and established bloggers, instead of being the backbone of the Carnival, was neglected.

Regarding (1): I see no reason why a significant amount of the serious, groundbreaking philosophy being produced now and in the future can't appear in the form of blog posts. Insofar as it can, the mandate of the Carnival should be to locate that stuff and help bring it to a wider readership.

Regarding (2): I suspect this is partly due to misguided attempts at fairness - people thinking 'Why should I link to Eric Schwitzgebel (or Berit Brogaard, or Brian Weatherson, or Richard Chappell etc.)? Those guys get tonnes of traffic already, and the Carnival is all about giving less visible writers a leg up'. Firstly, the Carnival isn't all about that - that's part of it, but it comes second to the main aim, which is to showcase the best philosophical writing of the blogosphere. Secondly, neglecting the best bloggers doesn't help anyone; there are surprisingly few people regularly posting serious philosophy on blogs - at least, blogs which aren't hidden away in dark parts of the web. Excluding the pillars of the online philosophy community, the central pool of talent, only reduces the Carnival's quality and interest. It doesn't make it any more open to new writers.

Look forward to a more serious Philosophers' Carnival, with higher aims and higher standards!

The Carnival Proper

Is Lewis's ontology qualitatively or ideologically parsimonious? - by Ross Cameron of Metaphysical Values. Highly recommended!

Impredicative Truth - by Abram Demski of In Search of Logic.

Whewell on Newton's Laws III: The First Law - by Brandon of Siris.

Bader against contingent and occasional identity - by Wolfgang Schwarz of wo's weblog.

Thoughts on evolutionary debunking arguments against religious belief - by Helen De Cruz of Prosblogion.

The Value Component of Plantinga's Free Will Defense - by Kenny Pearce of Prosblogion.

643 Words About Inferentialism, Disquotationalism, the Tonk Problem and the Liar Paradox - by Ben Burgis of Blog&~Blog.

Soames on the Abstract View - by Jeffrey Ketland of M-Phi.

When is true belief knowledge? - thoughts on Richard Foley's book of the same name, by Clayton Littlejohn of Think Tonk.

The Nature of Phenomenal Consciousness - by Richard Brown of Philosophy Sucks!

An arithmetico-temporal paradox - by Sam Alexander of xamuel.com.

Simmons' Paradox and the Barber - by Martin Cooke of enigMania.

What Experimental Philosophy Might Be - by Eric Schwitzgebel of The Splintered Mind.

Next edition at Philosophical Pontifications on November 10.

On the Problems of Reference and Intentionality

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

1. What determines reference?

2. Not, in general, descriptive or conceptual content associated with the name. Although the usual counterexamples to descriptivism do not apply to a range of names - for example, names of mathematical objects.

3. Not, in general, a causal connection between the object and the name. Both because the kind of connection in question is unclear, and because there is clearly no such thing in many cases - e.g. mathematical objects. But there is no clear counterexample in a range of cases: names of spatiotemporal individuals which someone in the linguistic community at some time has been perceptually acquainted with, for example.

4. What determines reference? - What gives this question its power?

5. The question seems to be: given that someone is referring to a particular object, what determines which particular object that is?

6. This is to be distinguished from: What is it which characterizes all cases of representation of, or reference to, an object? I.e. what do they all have in common which distinguishes them from other phenomena, apart from 'involving representation of an object'? But it is close to: Given some particular object O, what characterizes all cases of representation of, or reference to, O?

7. The thing we just can't accept is that we have nothing definitive to say in answer to the question: what determines reference?

8. It is extremely remarkable and important that people have tried hard to say something definitive here. It not a matter of course that anyone is moved in this way by that question. (Many people innocent of philosophy would find the whole thing quite unnatural and meaningless.)

9. I would like to talk about the feeling that, when the investigation goes empirical and scientific, we have left the realm of essence, so to speak. Is that right, anyway? Could one not maintain that by increasing our knowledge of the contingent facts - how reference actually gets going - we may be better able to penetrate to the essence? I.e. to what it takes in principle for reference to get going?

10. Well, historical development itself cannot be part of the essence. It is clear enough that there is no logical impossibility in a whole lot of organisms being spontaneously generated out of nowhere and beginning to speak of things.

11. When we think of the representation of external, physical objects, some kind of correspondence or covariance theory seems attractive. One thinks of primitive representation (or proto-representation) which is of this kind.

12. However, the merest thought of arithmetic, and Wittgenstein's builders, at once makes all this look inessential.

13. There is no reason why one cannot erect a concept which applies, for example, only to the representation of physical phenomena. But if one is inclined to say that we refer also to abstracta, and to wonder how reference in general is possible, then an investigation of the first concept alone will never satisfy.

14. It is clear enough that the idea of referring, which is primitively connected with the ideas of looking-at and pointing - the picture of representation and represented - is widely useful, and widely used.

15. Now, it looks very much as though one might, having noticed this, ask for an explanation of why it is. I.e., what makes the picture of representation and represented apply in this wide range of cases. Or better: what is it about all these cases which makes the picture of representation and represented apply to them?

16. This traces the problem down quite deeply. At this point we see that none of the common 'theories of reference' is going to help us here.

17. No answer comes to this question. This seems to have something to do with the fact that, once you are talking about a potential object of reference, you have already prejudged, so to speak, that the picture of representation and represented applies. Wherever we think of an object, there already we have the material for a higher-order thought about our representation of that object.

18. 'The problem of the essence of the representation of things leads, in a certain sense, to the problem of the essence of things.' The problem of the essence of things is obviously no ordinary one! 

19. To explain this tracing again: whenever we find ourselves in conditions where we can refer to an object, we thereby find ourselves in conditions where we can apply the picture of reference.

20. But, this is not the same as saying: wherever the conditions for objecthood are fulfilled, thereby are the conditions for a representation. For this is refuted by imagining a world in which there is just one object and nothing else. (This sort of distinction is important all through logical philosophy. It appears to be neglected, for instance, when people try to analyze existence and identity statements as designation and codesignation statements respectively.)

21. Two senses of truth conditions, two conceptions of what I will call fulfilment worlds for representations:

(1) All conditions/worlds in which what the representation actually represents to be the case is the case.

(2) The narrower set of all conditions/worlds in which the representation exists, represents what it actually represents, and where what it represents is the case.

22. What I was saying above now comes to: all the fulfilment worlds in the second sense for 'x exists' are automatically fulfilment worlds in the first sense for '"x" refers to x'. Or: once 'x exists' is fulfilled in the second sense, '"x" refers to x' is fulfilled in the first. (This holds not just for 'x exists' but for any proposition which contains 'x' in an extensional context.)

22. By dwelling on this we can start to see that reference is no ordinary relation.

23. As long as one is prepared to ignore the distinction between (1) and (2), or to openly switch from one to the other mid-analysis, then one can analyze existence and identity both in terms of reference. (Early Frege, Geach.)

Part II.