8. Truth and Meaning

This section seeks to briefly deal with and discuss the features of truth and meaning based mainly on David Wiggins.^[1]

In his Begriffsschrift^[2] Frege (1879) describes the matter for the artificial language as below:

It is determined through our stipulations [for the linguistic expressions and devices comprising the language of Begriffsschrift] under what conditions [any sentence of Begriffsschrift] stands for the True. The sense of this name [of a truth-value. i.e., the sense of this sentence], that is the thought, is the sense or thought that these conditions are fulfilled. The names [expressions], whether simple or composite, of which the [sentence or] name of a truth-value is constituted contribute to the expression of a thought, and this contribution [of each constituent] is its sense. If a name expression] is part of the name of a truth value [i.e., is part of a sentence], then the sense of the former, the name [expression], is part of the thought expressed by the latter [the sentence]. (Wiggins 2005: 4)

This statement is potentially perfectly general, and the stipulations of sense for the expressions of his invented language simulate what it is for the expressions of a natural language to have a given or actual (not merely stipulated) sense. The institution of the Begriffsschrift at once illuminates natural language, albeit only in microcosm, and extends it. It illuminates it by displaying clearly the workings of a distinct language abstracted from natural language, namely the concept-script in which Frege hoped to make newly perspicuous all questions of “inferential sequence.” The purposes this serves are akin to the practical and theoretical purposes that the construction of an artificial hand with a specialized function might have for a community of beings whose normal members had natural hands with less specialized functions.

Given Frege’s concern with “a formula-language for pure thought,” it is unsurprising that, as he said, he “confined [him]self for the time being to expressing [within it] relations that are independent of the particular characteristics of objects. Given the universality and generality of the insights that originate with Frege, what we now have to envisage is the final extension of Begriffsschrift, namely the extension which will even furnish it with the counterpart of such ordinary sentences as “the sun is behind cloud.” In the long run, the extended Begriffsschrift might itself be modified further, to approximate more and more closely to the state of some natural language. In the interim, however, in the transition from Frege’s to our own purposes, it stands as an illustrative model of something more complicated.

In such an extension as the one we are to imagine, a sentence like “the sun is behind cloud” will have a sense if and only if it expresses a thought. For the particular thought that the sun is behind cloud to attach to this English sentence will be for the sentence to be so placed in its total context that it stands [in some situation] for the True just in case [in that situation] the sun is behind cloud.

Once so much is said, what mystery remains about what a thought is? The thought expressed by a sentence is expressed by it in virtue of ordinary linguistic practices which expose the sentence to reality, and its author to the hazard of being wrong, in one way rather than another way.

The truth-conditional thesis can be detached from more questionable features of Frcgc’s semantical doctrine, such as the idea that a sentence is a complex sign standing for objects called the True or the False, or is a name of a truth-value.

Wittgenstein does detach it in Tractatus Logico-Philosophicus (TLP) (1921)^[3] as below:

TPL: 022. A sentence in use (Satz) shows how things stand if it is true. And it says that they do so stand.

TLP: 024. To understand a sentence in use means to know what is the case if it is true.

TLP: 061. A sentence in use is true if we use it to say that things stand in a certain way, and they do.

(Wiggins 2005: 5)

Suppose that the sentence “the sun is behind cloud” is now true. Then all sorts of other things have now to be the case. It is daytime, the sun has risen, it is not dark, more people are awake than asleep, and millions of automobiles are emitting smoke into the atmosphere, and so on -all this in addition to the sun’s being behind cloud. For these are the invariable consequences or accompaniments, in the world as it is, of its being daytime and the sun’s having actually risen. It is only to be expected, then, that, where s makes such a particular historical statement as it does, in a manner dependent upon some historical context, any of these extra things may in that context be added salva veritate to the right-hand side of the biconditional “s is true if and only if the sun is behind cloud and....” (It is certain that any necessary truth or natural law can be added so.) It is only by virtue of knowing already what s means that one would pick on the “sun is behind cloud” conjunct, from out of the mass of things that also hold when the “sun is behind cloud” is true, to be the clause to give the proper truth-condition for s. It follows that, to put down what a given utterance of a sentence s means and impart its meaning to someone, we need to be in a position to signal some ‘intended’ or ‘privileged’ or ‘designated’ condition on which its truth depends. Only where ‘s is true iff p’ signals on its right-hand side an intended, privileged or designated condition, can we conclude from this biconditional’s obtaining that the utterance of s means that p.

One way to try to put all this on the proper basis and lend a point to some particular condition’s being marked out as the semantically pertinent condition is to recast Frege’s and Wittgenstein’s thesis as follows:

Sentence s has as its use to say that p -or s means that p -just if whether s is true or not depends specifically upon whether or not p.

(Wiggins 2005: 6)

But this, according to Wiggsins, is not really the end of the difficulty. For one of the things that the truth of “the sun is behind cloud” depends specifically upon, in one ordinary and standard sense of “depend,” might perhaps (at that time and place) be low atmospheric pressure plus the obtaining of other meteorological conditions. None of this, however, is what the sentence actually says. And for the same reason we cannot improve the formulation just given by ruling that the truth of the sentence has to depend only upon the designated condition. It cannot depend “only” on that condition, in the ordinary sense of “depend.” For it will have to depend (in that ordinary sense) on everything that the satisfaction of the intended condition itself depends upon.

Consider now what Frege might have said in reply to this difficulty. Let us suppose that the language of his Begriffsschrift has been formally expanded to enable one to say “the sun is behind cloud” and all sorts of similar empirical things. Each new primitive expression (‘sun’, ‘cloud’. etc.) will have had a reference stipulated for it in accordance with an empiricized extension of Frege’s canon for definitions. In each case, the sense of the new primitive expression will consist in the fact that its reference is stipulated thus or so. By virtue of this, it will have been contrived that the sense of any complex expression can be determined from its structure and from the referential stipulations governing each constituent expression. But now, in the light of all this, Frege is entitled to insist that. if we stick scrupulously to what actually flows from the full and appointed referential stipulations for all the individual expressions and devices of the extended Begriffsschrifft let us call the set that consists of them Θ(Bg+) -then we shall never be able to arrive at an unwanted biconditional like ‘the sentence “the sun is behind cloud on 25 June 1993” is true if and only if on 25 June 1993 the sun is behind cloud and the sun has risen and there is low pressure and more people are awake than asleep and...’ (or its counterpart in Bg +). For the stipulations for the extended Begriffsschrift furnish no way to derive such a biconditional: and the intended condition will be the condition that the appointed stipulations do suffice to deliver. Not only that. In concert, these stipulations, which license nothing about low pressure as part of the truthcondition for s, will spell out the specific particular dependence that had to be at issue in the restatement of the Frege-Wittgenstein thesis.

No wonder that we can hear ‘“the sun is behind cloud” is true if and only if the sun is behind cloud’ as more or less equivalent to ‘The truth of “the sun is behind cloud” semantically depends upon whether or not the sun is behind cloud. For we hear “The sun is behind cloud” is true if and only if the sun is behind cloud’ as something delivered to us by whatever plays the part for English that the Fregean stipulations Θ(Bg +) will play for the extended Begriffsschrift.

What we are saying is in effect, this:

[s means in Bg+ that p] is equivalent to ˫_Θ(Bg+) [True s if and only if p].

(Wiggins 2005: 7)

There is nothing strange or scandalous in the suggestion that we hear the conditional as nested in this way within an operator “˫” whose presence has to be understood. Countless conditionals we utter are intended by us to be understood as presupposing some norm or tendency that we could roughly identify but do not attempt to describe in the form of an explicit eneralization. In so far as some residue of a philosophical problem still persists, the place to which it escapes is the characterization of “˫” and the idea of a set of referential specifications Θ(Bg +) that imply this or that equivalence in the form [True s if and only if p]. The point that is left over, which we shall have to attend to in due course, is that, although Θ(Bg +) would exemplify such a set, Θ(Bg +) could scarcely stand in for a general characterization of what a referential specification is. We need ˫_Θ(L) for variable L.

It will consolidate the position now arrived at to pause here to show -if not in Fregc’s symbolism or even in exact accordance with every particular of Fregess own view of predication -how, more exactly and in more detail. the claim might be made good that Frege can pick out the particular sort of dependence that he needs to secure between the obtaining of the condition that p and s’ s truth. Let us do so by giving the referential specification of the semantics of a tiny sublanguage L(1) of English that might be the counterpart of some small fragment of the extended Begriffsschrift (or Bg +).

Suppose the constituent strings of L(1) are simply the following:

(1)^[4] The sun is behind cloud

(2) Not (the sun is behind cloud), [which is said aloud as follows: the sun is not behind cloud]

(3) The moon is behind cloud

(4) Not (the moon is behind cloud), [which is said aloud as follows: the moon is not behind cloud],

together with all possible conjunctions of (1), (2), (3) and (4).

Then we can determine the sense of an arbitrary string of L(1) by the following provisions:

Terms: — T(1) “The sun” is a term and stands for the sun.
                T(2) “The moon” is a term and stands for the moon.
Predicates P(1) — “Behind cloud” is a predicate and stands for behind cloud.
Connectives: C(1) — “Not” is a unary connective: where A is a string of L, “not” + A is true if and only if A is not true.

Syncategorematic Expressions — “Is” is a syncategorematic expression, whose role is to signal the fundamental mode of combination exemplified in R(1) below.

Rule of Truth (R(1) — A sentence that is of the form [t + “is” + Φ], i.e., a sentence consisting of a term t. such as “the sun” or “the moon,” followed by the syncategorematic expression, “is,” followed by a predicate expression, Φ, such as “behind cloud,” is true if and only if what t stands for is what Φ stands for [i.e., the reference of t has the property that Φ stands for].

Now let us put these rules together and note their effect. Given the sentence [“the moon” + “is” + “behind cloud”] = [The moon is behind cloud], we can agree, by R(1), that the sentence is true if and only if what “the moon” stands for is what “behind cloud” stands for, which last we can show to be true (see T(2) and P(1)) if and only if the moon is behind cloud. That does not make news -no more than news is made when, having multiplied 13 by 25 and got 325, you then divide 325 by 13 and get 25. But it verifies something. Similarly, as Davidson (see Wiggins 2005: 9) would point out here on Frege’s behalf, our semantic derivation helps verify something, namely that, so far as they go, T(1), T(2), P(1), C(1), C(2) and R(l) represent a correct reckoning of the semantic resources of L(1).

What is achieved would have looked more impressive, no doubt, if L(1) had been a fragment of French and our referential specification had been done in English. Such a specification is something we can more easily imagine someone’s failing to get right. There is no question, however, of a specification of this sort’s looking impressive (or its needing to do so) -unless it solves neatly and correctly a known grammatical difficulty or casts some light, however indirect, on a real obscurity in the workings of a given language. Note too that for purposes of these derivations from T(1), T(2), P(1) and R(l), nothing at all depends on the meaning of “stand for.”

This completes the referential specification or semantic theory Θ^L(1) for a language L(l), which is a specimen sublanguage of Bg +. (More strictly speaking L(l) is the natural language counterpart of a sublanguage of Bg+). It leaves nothing to chance in the idea that, where s is an L(1) sentence, s means in L(1) that p if and only if the biconditional [True s if and only if p] flows from Θ^L(1). In the context of Frege’s own particular purposes in the Grundgesetze der Arithmetik, let this serve as a model for the complete defence of what Frege wanted to say there about sentence sense. For all he needed to be able to do in that work was to illustrate there his complete grasp of and control over the sense of a Begriffsschrift sentence. There is no relevant doubt, either theoretical or practical, of that grasp.

In Tractatus (see TLP 024) Wittengenstein is heir to Frege’s idea of sentence sense, and he tries to present from the particularities of Begriffsschrift in order to make a general claim. Then in TLP 061 he attempts to bring real, live speakers into the picture. Once we take their presence seriously, however, we shall notice a new kind of difficulty. For the proper response to this problem is to concede something.

Giggins (2005) has adjusted the Frege-Wittgenstein thesis to read as follows:

Sentence s has as its use in L(i) to say literally (to say in the thinnest possible acceptation of ‘say’) that p -thus s means that p in the narrowest strictest sense of ‘means’ -if and only if the referential specifications specific to the language L(i) rule that whether s is true or not depends upon whether or not p. (pp.10)

In his own account,^[5] Tarski turned to his his teacher Tadeusz Kotarbinski’s book Elementy Teorji Poznania, where we find the following passage (itself reminiscent of Tractatus 061):

Let us pass to the classical doctrine and ask what is [to be] understood by “[a sentence’s or thought’s] accordance with reality.” The point is not that a true thought should be a good copy or [fac]simile of the thing of which we are thinking, as a printed copy or photograph is. Brief reflection suffices to recognize the metaphorical nature of such a comparison. A different interpretation of 'accordance with reality’ is required. We shall confine ourselves to the following explanation: “John judges truly if and only if things are thus and so: and things are in fact thus and so. (Wiggins 2005: 15)

Spelling out this explanation for the case of some particular sentence, we have John judges truly in saying “snow is white” if and only if

(19) John is right in saying “snow is white” if and only if snow is white
(20) snow is indeed white.

But then it seems we can have, more simply “Snow is white” is true if and only if snow is white.

The chief thing that it seems a definition of “true in L(i)” must do in order to conform to Kotarbinski’s requirements is to imply one such equivalence in respect of each sentence of L(i).

But now, having come this far, we shall be moved to ask: how otherwise can the definition of truth in L(i) furnish the thing Kotarbinski required, or ensure the complete eliminability of “true sentence of L(i)” that is required for the explicit definition of “true sentence of L(i)” that Tarski desired, than by doing first the sort of thing we have seen that Θ^L(i) did? This is how Tarski’s path comes to cross the path that we have seen Frege’ sand Wittgenstein’s thoughts as marking out. The parties go in different directions, but at the intersection there is one common thing each party needs in order to arrive where it is headed. Each party needs to be involved, for any language that comes into consideration, in something like (15-18) above.

In the light of this, how is the problem to be solved of saying what a referential specification is? Well, if there is this convergence, then Tarski must have the same problem under a different name if he is to say what a definition of truth is. Tarski has to say what such a definition must be like in order to be adequate.

The problem is solved as follows:

A formally correct definition Θ^L(i) of the predicate “true” as applied to L(i) sentences is materially adequate if and only if, for every sentence sentence s of L(i), Θ implies a biconditional (or so-called T-sentence) in the form [True s if and only if p], where ‘p’ holds a place for a translation of s into the metalanguage ML(i). (Wiggins 2005: 16)

Tarski calls this provision -which is evidently not itself statable at any level lower that the meta-metalanguage -Convention T. It is simply the generalization of Kotarbinski’s desideratum. Similarly, then, a referential specification for L(i) assigns a value to every expression in L(i): and a set of such assignments is materially adequate under the very same condition as Tarski gives. It must yield a T sentence for each sentence of L(i). And each T-sentence must in the same way be translational, which is to say that, in each case, ‘p’ must hold a place for a translation of s into the metalanguage.

To understand Donald Davidson’s revival of the general idea of meaning as given by truth-conditions, and the distinctive advance that this made possible, it helps to appreciate the immediate background of his speculations. This was not any concern on Davidson’s part with the theory common to early Wittgenstein and Frege. The background was more topical. namely Davidson’s doubts about Carnap’s methods of extension and intension. What Davidson wanted was to retain Quine’s naturalistic approach to such questions, to align himself with Quine’s objection to all “museum myths” of meaning, but to do so without commitment to Quine’s talk of ocular irradiation, neural impacts upon subjects and the rest. According to Davidson, the thing that impinges on subjects had better be the world itself, the world that is common to both interpreter and subjects.

Seeking for some framework within which to give a systematic account of the information (or putative information) that an interpreter would need to amass and draw upon in order to interpret others, and to frame his hypotheses about the meanings of his subjects’ uttered sentences, and seeking at the same time to sweep away the supposed obscurity of ‘s means that p’, the construction Davidson found himself reaching for was in effect none other than Tarski’s:

Let us try treating the position occupied by ‘p’ [in’s means that p] extensionally: to implement this, sweep away the obscure ‘means that’, provide the sentence that replaces ‘p’ with a proper sentential connective, and supply the description that replaces s with its own predicate. The plausible result is

(T) s is T if and only if p.

It is worth emphasizing that the concept of truth played no ostensible role in stating our original problem [the problem of a theory of meaning for a given language]. That problem upon refinement led to the view that an adequate theory of meaning [for the language spoken by the interpreter's subjects] must characterize a predicate meeting certain conditions. It was in the nature of a discovery that such a predicate would apply exactly to the true sentences.... A Tarski-type truth definition supplies all we have asked so far of a theory of meaning. (Wiggins 2005: 17)

The discovery is of course a rediscovery, the rediscovery of the thing that Frege and Wittgenstein had articulated and that Davidson failed to credit to Frege. If Frege’s original insight had not been correct, there could have been no such discovery. Working within Quine’s framework, however, the attitude Davidson had towards Tarski was as follows. Taking translation for granted, Tarski had defined “true sentence of L(i).” Conversely, then, why should not Davidson take truth in L(i) for granted, in order to define “means in L(i)?” The only residual problem was to dispense with Turski’s use of the word “translation.”

Davidson’s first thought about the problem seems to have been that he could secure everything he needed if he were simply to omit the requirement that the T-sentences generated by Θ^L(i) in the form [s is true if and only if p] should provide translations on the right-hand side of the L(i) sentence s mentioned on the left. Could he not stipulate instead that absolutely all the T-sentences that Θ^L(i) generated should be true? But it is now pretty clear that the condition is not sufficient.

From the beginning of all Davidson’s speculations, however, shaped as they were by Quine’s Word and Object, the correct solution to this problem was always at hand. Perhaps Davidson’s best account of this solution is the one given in his “Radical Interpretation” (1973).

If the interpreter of the utterance of a sentence is to say what it means, then he has to find out under what conditions the sentence, being the sentence it is, counts as true. To say so much is to say little more than Frege said. The next thought one will have, however, is less Fregean. It is that linguistic behaviour is a proper part of behaviour. But, if so, there ought to be some other than purely semantic way of specifying what it is for a radical interpreter to succeed in interpreting alien people. Surely the interpreter’s linguistic efforts are part of the larger effort to interact successfully with others, to coordinate one’s efforts with theirs, to make sense of them and so on.

But, if we can enlarge a little in such terms, namely terms that are not specifically semantical, upon what such an interpreter must then be attempting to achieve, and if the interpretation of speech is simply one proper part of the larger thing the interpreter seeks to understand, then here at last we shall find the substantive non-semantic constraint upon Θ^L(i) we have been looking for.

A definition of truth in L(i) will be materially adequate if it generates a T-sentence for each sentence s of L(i) and collectively the T-sentences that the definition implies, when experimentally applied to individual utterance by the speakers of L(i), advance unimprovably the effort to make total sense of the speakers of L(i). (Wiggins 2005: 18)

The notion of total sense is not a semantic notion, but it subsumes one. One person’s making sense of another is a matter of their participative interaction in a shareable form of life of their homing upon the same objects, of their being in a position to succeed in joint enterprises, and so on. In so far as we make sense of others, we deploy a mode of understanding that can be redescribed, however artificially, as follows. There is a store of everyday predicates of human subjects, of features of the environments that impinge on subjects, and of the events that are counted as the actions or conduct of such subjects. When we deploy this mode of understanding, we seek in response to circumstances, including the speech or conduct of subjects, to distribute predicates of these and other kinds across features of reality, mental states and actions in such a way that: (i) the propositional attitudes we ascribe to subjects, specifying the content of these attitudes, are intelligible singly and jointly in the light of the reality to which we take subjects (or their informants, or their informants’ informants...) to have been exposed; and (ii) the actions (and actions of speaking) that we ascribe to subjects are intelligible in the light of the propositional attitudes we ascribe to them.

In the form in which we now have it, the new elucidation of meaning finally bridges the gap between Frege’s doctrine and Wittgenstein’s. Of course it inherits all the well-known difficulties of the ideas of understandding, explaining, making intelligible, imaginative projection or dentification. But these difficulties are there any way. The proposal not only depends upon these ideas. It assists us by helping to trace their interrelations.

The conclusion is that what it is for a sentence to mean that the sun is behind cloud and to be available to say that the sun is behind cloud, is as complicated as this. It involves a biconditional. ‘“The sun is behind cloud” is true if and only if the sun is behind cloud’, which is imbedded within the scope of an operator whose presence indicates that this biconditional is derivable from the whole system by which we make sense to one another and make sense of one another. What we have here is the idea of a signifycant language as a system that correlates strings of repeatable expressions with the states of affairs that the strings can draw attention to or get across, this system itself being a subsystem of the larger system by which social beings participate in their shared life. There is nothing abstruse in that. It is because we grasp it so readily, both in philosophy and before philosophy, that we can hear a T-sentence given in the form “s is true if and only if p” as the output of such a system. When we grasp that, it is tantamount to our grasping something intuitively similar to the “˫” that played the part we described in the Fregean elucidation of the meaning of Begriffsschrift sentences.

Footnotes and references:

[1]:

David Wiggins. [1997] 2005. Meaning and Truth Conditions: From Frege’s Grand Design to Davidson’s. In A Companion to The Philosophy of Language. ed. Bob Hale & Cripspin Wright, 3-28. UK/USA: Blackwell Publishing.

[2]:

G. Frege.(1879). Begriffsschrift, eine der aritlmetischen nachgelbideten Formelsrache des reinen Denkens. Halle: Trans. in Terrel Ward Bynum. Conceptual Notation and Related Articles. 1992. Oxford: Charendon Press.

[3]:

L. Wittgenstein. 1921. Logisch-philosophische Abhandlung. In annalen der Naturphilosophie. Repr. and trans. as Tractatus Logico-Philosophicus, 1922.

[4]:

In this case, due to the continuity of number uses, functional structures, metrical grids, and so forth, in sequent numbers with other numbers, these, on the rule, continue the sequent numbers as its linguistic representations. Thus, in this subsection, (1) stands for style="text-align:center">(15)-(as its consequent data numbers of the chapter), (2) for (16), (3) for (17), and (4) for (18).

[5]:

A. Tarski. 1956. The Concept of Truth in Formalised Languages. In Logic, Semantics and Mathematics. Oxford: Clarendon Press, pp. 152-278.