A Counterexample to the Principal Principle

25 01 2008

In his paper ‘A Subjectivist’s Guide to Objective Chance’, Lewis proposes an intimate connection between subjective probabilities and objective chances: the Principal Principle. In Lewis’s eyes, this principle captures almost all there is to know about our conception of objective chances.

In a forthcoming paper entitled ‘Knowledge and Objective Chance’, Hawthorne and Lasonen mention in passing a counterexample to the Principal Principle (a draft of which you can find here). Essentially, they think that instances of the contingent a priori provide a source of potential counterexamples. This idea stands in an interesting relation to a recent paper of Williamson (‘Indicative versus Subjunctive, Congruential versus Non-Hyperintensional Contexts’), in which the modal status of statements involving objective and subjective probabilities is discussed (a draft of which you can find there). It seems to me that Williamson’s considerations may provide a deeper reason to explain why we should not expect something like the Principal Principle to hold. In the following note, I will present a structurally similar counterexample by way of relating it to Williamson’s claims about the modal nature of the two kinds of probability.

Posted by Moritz.

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New Journal: Semantics & Pragmatics

28 11 2007

The new journal Semantics & Pragmatics is now accepting submissions. The journal, editetd by Kai von Fintel and David Beaver, is peer-reviewed and open access and has managed to assemble a very impressive team. You can find the journal’s website here and the editors’ blog here. Good luck S&P!

Posted by Miguel.

Schlick’s Chair

27 11 2007

I just stumbled across the following passage from Moritz Schlick’s “Form and Content” (1932):

I might use a chair in my room, for instance, as a means of saying anything I like. All I need to do is to select a number of different positions of the chair in the room and agree that each one shall correspond to a letter of the alphabet. By this agreement I shall have constructed a new language which will consist in changing the position of the chair; and by moving it about in the room I shall be able to express all the plays of Shakespeare with the same perfection as the best of the printed editions. (p. 288)

It is quite amusing to picture Schlick wildly moving his chair around his office to “read”, say, a passage from Macbeth. I wonder whether Carnap would have stayed and “listened”. On a more serious note, though, Schlick seems to be quite wrong when he says that he has created a new language. But what has he done? In a way, I guess, he has created, not a new language, but merely a new set of letters. His chair’s standing in the relevant position stands to the letter A as, e.g., “A”, “A” and “A” stand to it.

Posted by Miguel.

Can Truth Conditional Semantics Explain Linguistic Competence?

24 11 2007

[The issue of this post has been discussed by Jeff Speaks in a recent paper here. Hence, even though I am setting things up in a different manner and with a different target, I am not claiming originality on the main point. Speaks’ point deserves reiteration since it raises a challenge that has not been sufficiently addressed by proponents of truth conditional semantics. Another sidenote: a more precise title for this post would be: “Can TCS explain *the possibility of* linguistic competence?”. But it just looked too awful with such a long heading…]

Natural languages are infinite. Human beings are finite. Yet humans are competent with natural languages. A finite being cannot learn, one by one, what each of the infinitely many expressions of a language means. How is it possible that a finite being acquires competence with an infinite language? The task of answering this question is one of the central themes that drive the truth conditional project. Hence, if it turned out that truth conditional semantics (TCS) cannot provide a satisfying answer that should be worrisome to the Davidsonian. This post is about whether the Davidsonian should be worried. In the end, I believe, she should. Read the rest of this entry »

Grades of Truth-functionality

21 11 2007

Truth-functionality is a notion at the heart of classic propositional logic. A standard explication of the notion runs roughly as follows:

An n-ary connective C is truth-functional iff it corresponds to a truth-function.

More precisely, C is truth-functional iff there is a mapping from the truth-values of any n sentences S1 … Sn to the truth-value of the concatenation of C with S1 … Sn.

According to that explication, the following operators are equally truth-functional:

T It is true that …

TF It is either true or false that …

EX It is expressible in English that …

The two latter operators are only special in corresponding to a constant truth-function, namely the function that maps both True and False unto True.

But one may sense an important difference between TF and EX: the former connective actually operates on the truth-values of the embedded sentence such that the truth-value of the complex sentence is a result of that operation. But the latter connective does not operate on the truth-value of the embedded sentence at all. That it corresponds to a constant truth-function is not the result of its being sensitive to the truth-value of the embedded sentence; in some sense, it does not depend on that truth-value.

A definition of truth-functionality that captures the described difference between TF and EX can be given in terms of the explanatory connective ‘because of’:

An n-ary connective C is truth-functional iff the concatenation of C with any sentences S1 … Sn has the truth-value it has because of the truth-values of S1 … Sn.

This definition will classify the standard connectices of propositional logic as truth-functional (a true negation, for instance, is true because the negated sentence is false, and a false negation is false because the negated sentence is true). And it also classifies TF as truth-functional (‘It is either true or false that snow is white’ is true because ‘Snow is white’ is true; had the latter been false, then the former had been true because of that.)

But EX does not count as truth-functional in the defined sense (‘It is expressible in English that snow is white’ is true, but not because ‘Snow is white’ is true).

While I do not think that these considerations show that the standard definition of truth-functionality is in any way flawed (it is a technical notion after all), the alternative definition captures differences between operators that might as well be associated with the term ‘truth-functional’.

(See the papers-section for a more detailed exposition of my proposal.)

Posted by Benjamin.

Really-Really-On-Topic Theories of Truth

7 11 2007

A T-equivalence for a sentence x is an instance of ‘S is true iff p’ in which ‘S’ is replaced with a quotational designator of x and ‘p’ with a sentence synonymous with x. A truth theory for L is a theory that has, for every sentence of L, a T-equivalence as a theorem. A theory of meaning for L is a finite theory knowledge of which could suffice for knowing the meaning of every sentence of L.

Theories of truth are not theories of meaning (this is widely acknowledged, though Davidson seems to go back and forth). Proof: Let L be a toy language comprising only the sentence ‘Snow is white’. Let T be a theory comprising the axiom ‘“Snow is white” is true iff snow is white’. T is a truth theory for L. But knowing that ‘Snow is white’ is true iff snow is white cannot suffice for knowing that ‘Snow is white’ means that snow is white, since a sentence can be true iff snow is white without meaning that snow is white. ‘Blood is red’ is such a sentence. In general, the information that a sentence S is true iff p is not sufficient to infer that S means that p, since every sentence that has the same truth value as ‘p’ will be true iff p, regardless of whether it means that p. Call this the Very Simple Coextensionality Problem (VSCP). A theory suffers from VSCP if the knowledge that it provides about a sentence S could be had about any sentence that is coextensional with S. No theory suffering from VSCP can be a theory of meaning.

Proper truth theories will not have axioms for whole sentences, but axioms for sub-sentential expressions. Such theories do not suffer from VSCP. Since they provide information about what, say, the predicate of an atomic sentence S is true of, they provide knowledge about S that one cannot have about every sentence that is coextensional with S. But these theories Read the rest of this entry »

Listen to Philosophy

12 10 2007

As most of you probably know, this years John Locke Lecture by Bob Stalnaker has been made available as mp3 on the Oxford philosophy page here. I found this to be a great thing, and I really hope it will set a new trend. It not only gives you the chance to listen to one of todays pre-eminent philosophers while, say, cleaning the kitchen; you can actually pause him or make him repeat those bits that you didn’t get straight away. Wouldn’t it be great to be able to rewind and replay some of the talks you have heard at conferences over the years? Well, the good ones, anyway…

So here is some more philosophical stuff that can be listened to on the World Wide Web. Of course, there is Philosophy Talk, a weekly show run by John Perry and Ken Taylor with well over 100 episodes by now, all available from their archives. And there’s Philosophy-Bites, where Nigel Warburton and David Edmonds present ‘pod casts of top philosophers interviewed on bite-sized topics’. Their latest episode, ‘aired’ on October 8, features Anthony Kenny on his New History of Philosophy, and past episodes include Tim Williamson on vagueness, Simon Blackburn on moral relativism, and Tim Crane on mind and body, to name but three. But there’s more. On Learnoutloud, you can listen to the whole of Plato’s Republic (or download it, well over half a gigabyte). They also showcase a 7 minute piece of Wittgenstein’s Tractatus, and a whole lecture series on Heidegger’s Being and Time (personal favourite: The One, part II).

So to all those setting up conferences with great philosophers: record and post!

Posted by Miguel.