Saturday, January 14, 2006

Tarksi's T-Schema, Truth-Conditions, and Senses

On a tip from hammsbear, I took a look at Peter Ludlow's article, "Do T-Theories Display Senses". Here are some of my thoughts on that article.

Tarksi's T-schema ("p" is true iff p) is often used to spell out the truth conditions for sentences. Thus, "snow is white" is true iff snow is white. ('iff' is short for 'if and only if')

By "senses" Ludlow means the ways in which something may be referred to. For example, "the Evening Star" and "the Morning Star" both have the same referent, namely, the planet Venus, but they pick out Venus in different ways, by appealing to different properties. Similarly, the names "Cicero" and "Tully" both refer to the same individual, Marcus Tullius Cicero. So they have the same referent. But they have a different sense because they pick out that individual in a different manner.

The question Ludlow raises is whether or not the expression on the right-hand side (RHS) of the T-schema can give information about the various "senses" of the expression on the LHS,. On the one hand, it seems that "Cicero is bald" and "Tully is bald" should have the same truth-conditions because they refer to the same individual. Thus,

(1) "Cicero is bald" iff Cicero is bald.
(2) "Tully is bald" iff Tully is bald.
(3) "Cicero is bald" iff Tully is bald.
(4) "Tully is bald" iff Cicero is bald.

On the other hand, suppose there is a person S who knows that Cicero is bald but does not know that Cicero=Tully. Such a person would affirm (1) and (2) but would not affirm either (3) or (4), in which case, (1)-(4) do not properly characterize S's semantic competence.

Here's how I understand this (and, mind you, I'm not a specialist in the philosophy of language):

Sentence tokens like "Cicero is bald" and "Tully is bald" have the same truth-conditions iff they express the same proposition. They express the same proposition iff they reflect the same belief on the part of the speaker. If, therefore, S believes that Cicero is bald and has no belief about whether Cicero=Tully or whether Tully is bald, then S's token "Cicero is bald" has the truth-conditions given in (1). If, however, S not only believes that "Cicero is bald" but also believes that Cicero=Tully, then the truth-conditions of S's token "Cicero is bald" may be given by either (1) or (3) or, more fully, by

(5) "Cicero is bald" iff Cicero/Tully is bald.

In (5) information about the senses is given in the RHS of the T-schema (by the '/' notation) and (5) does properly reflect S's semantic competence.

So I'm inclined to think, contra Ludlow, that information about senses can be supplied on the RHS of a T-schema expression when it does reflect the semantic competence of the speaker. The same state of affairs is being referred to in (1) and in (5), but (5) reflects a more extensive knowledge on the part of the speaker as to what that state of affairs is.


At 1/21/2006 4:32 AM, Blogger Ocham said...

David Braun (I'll locate the paper if you are interested, in why the meaning of names like 'Cicero' do not and cannot reflect the beliefs of the speaker.

He says (I just found the paper) "these [belief] theories say that speakers routinely think about other people's mental representations, and intend to talk about those representations when they utter belief sentences. But I seriously doubt that ordinary speakers have such sophisticated thoughts and intentions about mental representations when they utter belief sentences. In any case, I believe that a theory that does not attribute such thoughts and intentions to ordinary speakers is preferable to one that does, other things being equal."

Understanding Belief Reports - appeared in Philosophical Review, don't have exact reference.

At 1/21/2006 11:50 PM, Blogger Alan Rhoda said...

Maybe I'm misunderstanding what's at issue here, but it seems to me that Braun's setting up a straw man. Beliefs need not be conscious to be real. Freud taught us that much. Consequently, the proponent of a belief theory of semantics need not hold that ordinary speakers have "sophisticated thoughts and intentions about mental representations" when they speak. All such a semanticist needs to hold is that the meaning of a person's utterances expresses their beliefs whether conscious or not.

At 1/22/2006 4:16 AM, Blogger Ocham said...

Brauns' point would be that the semantic function of a proper name is to tell us which thing is the subject of the proposition in which it occurs. 'Socrates is bald' tells us which individual is said to be bald. How could it do that if its semantic value were subjective or psychological?

At 1/22/2006 4:57 PM, Blogger Alan Rhoda said...

Ocham, I think either you or Braun or both are confusing propositions with sentences. Braun's quote talks about what people mean when they utter "belief sentences". You're talking about the semantic function of a proper name in the "proposition" in which it occurs.

A sentence is a set of physical signs that is used to communicate a complete thought. A proposition is an assertoric unit of meaning. Sentences of the declarative sort are the typical vehicles for expressing propositions, but they are not the same thing. As for sentences, their semantic value is (quite obviously, I think) dependent on the speaker's belief states, as is evident from the fact that the same sentence can be used to express different propositions. For example, one might utter "Sammy Sosa is safe at home" and mean that SS just scored a run in baseball. Or one might utter the same string of words and mean that SS is safely ensconced in his house. Which proposition is expressed is determined by the speaker's intentions. The semantic value of a proposition, however, is not dependent on the speaker's intentions or beliefs because a proposition is its meaning.

At 1/24/2006 12:18 AM, Blogger Ocham said...

The standard meaning of 'proposition' is the verbal expression of a judgment or thought, rather than the judgment or thought so expressed, though it also can mean the latter (a usage introduced by Russell). If the latter, it is standard to assume the constituent of the proposition that corresponds to the singular term 'Cicero' is Cicero himself. Thus if John believes (Cicero, philosopher), he also believes (Tully, philosopher), for they are the same proposition.

Thus the standard theory of the proposition requires that coreferring terms be substituted salva veritate. That does not appear to be your view. What, then, is your theory of the proposition?

PS I tried to write angle brackets for the propositions but the editor thought it was html!

At 1/24/2006 2:58 PM, Blogger Alan Rhoda said...

Hmmm. I haven't gotten the impression from anything I've read yet that propositions are 'standardly' taken to be the verbal expressions of a thought. Perhaps that was the standard use at one time. I doubt it is so nowadays. Seems to me that most philosophers refer to the verbal expressions of a thought as 'sentences' and then refer to the judgment or thought expressed as either a 'statement' or a 'proposition'. I use 'proposition' because I like to reserve 'statement' to denote to declarative sentences.

At any rate, I take a 'proposition' to be the judgment or assertoric content expressed by a declarative sentence. But I wouldn't say that a proposition that contains a singular term contains the referent of that term as a constituent; rather, I think the referent of the singular term is a constituent of the state of affairs posited by the proposition. For example, the proposition expressed by "Caesar crossed the Rubicon" posits the state of affairs Caesar's having crossed the Rubicon. Caesar is a constituent of that state of affairs because it cannot obtain without Caesar himself. But Caesar himself is not, on my view, a constituent of the proposition. Instead the proposition contains an index (a "rigid designator" in Kripke's terminology) that points to Caesar.

I do agree that coreferring terms can be substituted salva veritate, but not salva significatione. In my view (Caesar, philosopher) and (Tully, philosopher) are different propositions because they differ in sense. While they both point to the same individual, they do so in different ways and John could believe one without believing the other.

At 1/26/2006 4:34 AM, Blogger Ocham said...

"John could believe one without believing the other. "

But then you can't substitute salva veritate. "John believes that Cicero was a philosopher" is true. But stick "Tully" in place of "Cicero", and it is false (for example).

At 1/26/2006 5:10 PM, Blogger Alan Rhoda said...

But then you can't substitute salva veritate. "John believes that Cicero was a philosopher" is true. But stick "Tully" in place of "Cicero", and it is false."

Now you're talking about substituting into an intentional context (John believes ...). Ok, in such cases I don't think coreferring singular terms in propositions can be substituted salva veritate. It is only when the singular term is not embedded in an intentional context that one can substitute salva veritate.

At 1/27/2006 12:22 AM, Blogger Ocham said...

But what is an 'intentional context'. Or do you mean, any context in which co-referring terms cannot be substituted salva veritate?

At 1/27/2006 9:48 PM, Blogger Alan Rhoda said...

I don't have a general description of 'intentional context' to offer. Obvious cases would be "believes that ...", "desires that ...", "supposes that ...", etc. I'd bet someone's come up with a general criterion, but I just don't know.

At 1/29/2006 4:43 AM, Blogger Ocham said...

Er, that was my point. Note that the substitution problem applies even to 'agentless' that-clauses. For example, suppose that Shakespeare really was Bacon. Then surely we can speak of the discovery that Bacon was Shakespeare (which is surely different from the discovery that Shakespeare = Shakespeare). Or of there being evidence that Bacon was Shakespeare, or probable that &c.


Post a Comment

Links to this post:

Create a Link

<< Home