Do T-Theories Display Senses?{1}

Peter Ludlow

SUNY Stony Brook


[1] One of the central ideas in recent philosophy of language has been the notion that a semantic theory should take the form of a theory which delivers Tarskian truth conditions for sentences of the language under study. So for example, such a theory might deliver a theorem like the following, which gives the truth conditions of the object language expression "Snow is white".

(0) "Snow is white" is true iff snow is white
Much of the interest in such theories has stemmed from the suggestion, due to several authors, that T-theories can deliver more than the truth conditions of expressions, but that they can deliver the truth conditions in a way that "shows" or "displays" the sense of expressions.{2}

[2] To illustrate, it has been argued (since Frege) that while two expressions like "Cicero" and "Tully" have the same referent, they have distinct senses, for the expressions have different modes of presentation -- that is, they present the referent of Cicero/Tully in different ways. Accordingly, because "Cicero" and "Tully" have different senses, there is supposedly no contradiction in the beliefs of someone who believes both that Cicero was bald and that Tully was not bald. (The first belief is a belief about Cicero under a certain mode of presentation; the second belief is about the same individual under a different mode of presentation.) With respect to T-theories, the question naturally arises as to whether the theorems of such a theory deliver only the referents of expressions, or the senses as well. That is, does the right hand side of a T-sentence simply give the reference of the expression on the left, or does it also give the reference in a way that shows or displays its sense?

[3] This latter question turns out to have important consequences. Indeed, some recent authors have suggested that the ability of T- theories to display senses is central to whether a T-theory can serve as a meaning theory. For example, LePore and Loewer claim that there are certain adequacy conditions which a theory of truth must meet in order for it to function as a theory of meaning suitable for interpreting a language L. On their view, if a T-theory is to serve as a meaning theory, then it must be the sort of T-theory which can display senses.

[4] But can T-theories display senses? In this paper I will suggest that they cannot. It follows that one must either reject the adequacy condition advanced by LePore and Loewer, or give up the idea that T-theories can serve as a theory of meaning.

[5] According to LePore and Loewer (1987: 104) an adequate T-theory for an agent (call her "Arabella") will contain theorems (1)-(2) without containing theorems (3)-(4).

(1) "Cicero is bald" is true iff Cicero is bald

(2) "Tully is bald" is true iff Tully is bald

(3) "Cicero is bald" is true iff Tully is bald

(4) "Tully is bald" is true iff Cicero is bald

[6] The reasoning is that Arabella may believe that "Cicero is bald", but not not that "Tully is bald", so a T-theory which generates (3) as a theorem will not correctly characterize Arabella's semantic competence. The danger of introducing (3) into a semantic theory for Arabella appears to be that it leads to a false belief attribution in the following fashion.
(a) Arabella utters "Cicero is bald"

(b) Arabella believes "Cicero is bald" is true. (from (a) and certain assumptions about Arabella's truthfulness, etc.)

(c) Arabella believes "Cicero is bald" is true iff Tully is bald (by hypothesis)

(d) Arabella believes that Tully is bald (from (b), (c), + assumptions about closure)

[7] Step (c) is interesting, for it relies upon the assumption that Arabella actually believe a theorem of the T-theory. This assumption is interesting, since it suggests that Arabella (presumably not a semanticist) must have beliefs about theorems of a particular kind of T-theory. Since it is implausible to suppose that Arabella (unless trained in semantics) would have conscious knowledge of such matters, it appears to entail that Arabella must have some sort of "tacit" knowledge of (3). This is a point to which I will return shortly. (For now, it is worth noting that assumptions about closure of belief are highly controversial here -- particularly since it is applied to a tacit belief.)

[8] Granting, for the time being, the claim that the introduction of (3) will allow us to infer (d), there remains an important assumption at work in the above line of reasoning which stands in need of justification. Specifically, does theorem (3) attribute any more semantic knowledge to an agent than (1) does? LePore and Loewer assume an affirmative answer to this question, but the question is subtle, and the answer needs to be carefully argued. Not only does the assumption lack any explicit justification, but, I shall argue, it may well be false.

[9] One way to get a handle on this issue is to think of the axioms and theorems in a T-theory as akin to the laws in any other science. When we consider other sciences we never find that the manner of presentation of the laws is of importance. For example, it would be absurd to suppose that laws about the atomic elements are sensitive to the names we give those elements. Likewise, no economic laws are sensitive to what we name the unit of currency, and no geological laws are sensitive to the names that we give glaciers and minerals. Why should semantics be any different? That is, why should a semantic theory be sensitive to the name we give to a semantic value?

[10] It might be supposed that within a broadly Davidsonian program, T- theories are treated in a "deflationary" way, so that they do not refer to objects or states of affairs, etc. As LePore and Loewer argue the point: "If one thinks... that a truth theory assigns possible states of affairs or facts to indicative sentences then we can see why [certain] truth theories assign the same truth conditions to the two sentences 'Cicero is bald' and 'Tully is bald'. But it is not necessary to think of truth theories in this way. Davidson rejects the reification of truth conditions..." (LePore and Loewer 1987: 103).

[11] But contrary to this argument, even so-called deflationary theories cannot display senses. The fundamental problem is that because one is using (e.g.) English on the right hand side of a T-sentence, then what is stated on the right hand side can be no more nor less than what is stated by that English expression. The question then becomes whether one states something different when one says "Cicero is bald" vs. when one says "Tully is bald". The answer to this question is entwined with our intuitions about 'what is said.'

[12] By the usual standards of 'what is said' in scientific discourse there can be no doubt that "Cicero is bald" and "Tully is bald" say the same thing. But even in day-to-day discourse, there is a strong pull to suppose that the mode of presentation of a claim is of little importance in our intuitions of what was said. So, for example, if I say "Tully is a crook" I have said that Cicero is a crook, and it will do no good for me to plead that I did not know Tully is Cicero.

[13] So the problem is not one unique to certain kinds of T-theories in which it is stipulated that the right hand side of the T-sentences refers to a state of affairs. Rather the problem stems from the fact that natural language is used to state the truth conditions, and thus that the T-theory can "display" no more than what is said by the natural language expression used to give the truth conditions.

[14] One might think it would be advantageous if T-theories did deliver senses, for then it would be much more clear that a T-theory could serve as a theory of meaning. But wishing something to be so, does not make it so, and it is certainly not enough to stipulate that T- theories will deliver senses, for the question is whether T-theories can deliver senses.

[15] One possible rejoinder for LePore and Loewer is to follow a thread emphasized by Larson and Segal (forthcoming) and argue that if the theorems of a T-theory are part of the speaker's knowledge of language, then the way in which that knowledge is expressed does become relevant. If the theorems are part of the agent's knowledge, then the theorems can be thought of as embedded in a context like 'the agent knows that ....' Since knows-that environments are opaque, then the use of (1) to characterize the agent's semantic knowledge may be appropriate, but the use of (3) may not. Crucially, in such an environment, (1) and (3) will express different things.

[16] For expository purposes, we can put this point in Fregean terminology. Since the knows-that environment is opaque, then (1) and (3) (and their constituents) will not have their customary referents, but will rather refer to senses. Since the senses of (1) and (3) will be distinct, (1) and (3) will, in such a context, express different things.

[17] The difficulty with this move is that while the environments invoked by ordinary uses of "knows that" are opaque -- and hence occurrences of (1) and (3) may be distinguished, the knows-that relation used in a semantic theory like Larson and Segal's is not the ordinary relation, but rather a technical relation in a scientific theory of meaning. It differs from the ordinary knows-that relation in a number of respects, among them the fact that it allows for "tacit knowledge" -- knowledge which the agent may not be aware of or admit to. Unless trained in semantics, the agent will no doubt dissent from most of the axioms and theorems of the semantic theory, yet according to such theories, the agent will still "know" these axioms and theorems. Importantly, given such a radically different notion of knows-that, one cannot trade on intuitions about what is expressed in the ordinary knows-that environment. It cannot be assumed that in the environment invoked by the technical relation, (3) expresses something different from (1). In particular, it can be argued that an agent who tacitly knows (1) must thereby tacitly know (3).

[18] Suppose, however, that one gives up the notion of tacit semantic knowledge and utilizes the ordinary knows-that relation to characterize semantic competence. This might allow one to hold that (3) expresses something different from (1), but by giving up tacit knowledge one gives up too much. Since an agent untrained in semantics may dissent from virtually any expression containing semantic terminology, the prohibition on tacit knowledge would rule out even expressions like "x refers to y" or "x satisfies P". Clearly the prospects for constructing an interesting semantic theory with such constraints is dim.

[19] There is a general way to put this dilemma. Semantic theories which are theories of an agent's knowledge of meaning can come in two forms. Theories which utilize the ordinary notion of knows-that will allow the possibility that (3) expresses something more than (1), but they will be inadequate for providing interesting semantic theories. Theories which introduce a technical notion of knows-that in order to admit tacit knowledge may provide interesting semantic theories, but it is unclear that (3) will express something more than (1) in such theories.

[20] Finally, one might suggest that we can have a theory which displays the sense of an expression if we adopt a theory consisting of the theorems delivered by the T-theory in conjunction with a theory about the expressions used in stating the T-theorems. This strategy may well work, but such a higher order theory is not a T-theory. It is rather a T-theory combined with a theory providing the way in which the agent represents the truth conditions of the sentence. In such a case it is important to note that it is not the semantic theory which is displaying the sense of the natural language expression. Rather, the work is being done by the attendant higher order theory.{3} There may well be theories which can display senses, and T-theories may play important roles in such theories, but it is far from clear that T-theories by themselves can display senses.


Bilgrami, Akeel (1987) "An Externalist Account of Psychological Content." Philosophical Topics 15, 191-226.

Dummett, Michael (1973) Frege: Philosophy of Language. Harvard: Harvard University Press.

---- (1975) "What is a Theory of Meaning?" In Mind and Language, Guttenplan (ed.). Oxford: Oxford University Press.

Evans,Gareth (1982) The Varieties of Reference. Oxford: Oxford University Press.

Larson, Richard and Gabriel Segal (forthcoming) Knowledge of Meaning. Cambridge: MIT Press.

LePore, Ernest and Barry Loewer (1987) "Dual Aspect Semantics." In New Directions in Semantics, E. LePore (ed.), 83-112. London: Academic Press.

McDowell, John (1980) "On the Sense and Reference of a Proper Name." In Truth, Reference, and Reality, M. Platts (ed.), 111-30. London: Routledge and Keegan Paul.


{1} I am indebted to Richard Larson and Ernie LePore for comments on an earlier draft, and to an anonymous EJAP reader for a number of helpful suggestions. Return

{2} See, for example, (McDowell 1980), (Evans 1982), (Bilgrami 1987), and (LePore and Loewer 1987). These authors are influenced by remarks in (Dummett 1973) and (Dummett 1975). Return

{3} I am indebted here to discussions with Martin Davies. Return

Peter Ludlow
SUNY Stony Brook

The Electronic Journal of Analytic Philosophy 1:5 (1993)
ISSN 1071-5800
Copyright 1993