The sentence [i] “snow is white” is true if, and only if, [ii] snow is white.
We are in a position to say what kind of logical and linguistic entity [i] is—it is a sentence in an object language L that conveys a proposition—but we have no idea what [ii] is. If it were a state of affairs (or a perceptive experience) we would be extremely embarrassed: a state of affairs is a state of affairs and a perceptive experience is a perceptive experience, not a sentence. If anything, a sentence is produced to express a state of affairs or a perceptive experience. But if what appears in [ii] is a sentence about a state of affairs or a perceptive experience, it cannot be a sentence expressed in L, since it must guarantee the truth of the proposition expressed in [i]. It must be, then, a sentence expressed in a metalanguage L2. But in that case Tarsky’s formula ought to be translated as follows:
[i] The proposition “snow is white,” conveyed by the sentence (in L) snow is white
is true if, and only if,
[ii] the proposition “snow is white” conveyed by the sentence (in L2) snow is white is true.
It is clear that this solution is destined to produce a sorites of infinite sentences, each one expressed in a new metalanguage. If we assume Tarsky’s example in a naïve fashion, we find ourselves in the same boat (or wagon) as the editors of De Saussure who represented the relationship between signifier and signified with an oval split into two superimposed halves, in which the word arbre is contained in the bottom half while the top half contains a drawing of a tree. Now, the signifier arbre is certainly a word, but the drawing of the tree is not intended to be and cannot be the signified or a mental image (because what it is, if anything, is another nonverbal signifier that interprets the word below it). Seeing that the design excogitated by De Saussure’s editors had no formal ambition, only a mnemonic function, we can forget about it. But the problem with Tarsky is different.
We could of course interpret the definition in a strictly behaviorist sense: snow is white if, when confronted by the stimulus snow, every speaker reacts by saying it is white. But, apart from the fact that we would find ourselves up to our necks in the difficulties of radical interpretation, I do not believe this was what Tarsky had in mind, and, even if this was his intention, this would not be a way to decide whether a proposition is true, because it would simply tell us that all speakers are guilty of the same error of perception, just as the fact that for thousands of years all speakers declared that the sun sinks into the sea in the evening does not prove that the proposition was true.
It seems more convincing to admit that, in Tarsky’s formulation, [ii] stands conventionally for the assignment of a truth value to [i]. The Tarskyan state of affairs is not something we can check in order to recognize the proposition that expresses it as true; on the contrary, it is what a true proposition, or indeed anything that is expressed by a true proposition, corresponds to (cf. McCawley 1981: 161), in other words its truth value. In this sense Tarsky’s notion does not tell us whether it is more true to say that a cat is a cat than it is to say that a cat is a mammal.
17.6. Meaning, Referent, Reference
This node, between truth-conditional semantics, reference semantics, semantics of the sentence, and textual semantics compels us to revise a few concepts, something I attempted to do in my Kant and the Platypus.
1. Meaning of a term like cat. It may contain categorial elements like mammal and feline, but it also contains instructions to define the referent. But the referent of cat is not some individual cat, but cats in general. In this sense, terms that denote nonexistent objects may contain reference instructions (for instance, “unicorn”). It is possible to transmit and understand instructions for identifying the referent without having had and without ever having the occasion of referring to something.
2. References to cats (My cat is in the kitchen). Reference as a linguistic act, to be negotiated. The reference, however, is completely unconnected either to the empirical truth of the proposition (if I am lying or mistaken, the cat is not there) or to any discussion of its truth value. To be sure, if there is a cat in the kitchen, there is a feline mammal in the kitchen (sense 4), I am certainly referring to a specific cat, mine (sense 3), but it might not be true that it is in the kitchen. Senses 1 and 2 are presupposed by semantics of the third type, and can be taken into consideration by semantics of the fourth, but the converse is not true. Let us not forget that Morris (1938) reminded us that semantics is concerned with the relationship between a sign and its designata, that a semantic rule establishes under what conditions a sign is applicable to an object, but that the notion of designatum has nothing to do with the existence of the object; the designatum of a sign is something the sign may denote—but establishing whether there really are objects of this kind goes beyond the competence of semiotics.
Let us now suppose that I were to visit a culture (with a language adequate to express it) in which only two animals are known: the cat, hairy, smaller than a human being, domesticated, and harmless, and the crocodile, usually bigger than a human being, and scaly. For the members of that culture, based on such an elementary system of oppositions, which constitutes the full extent of their classification of the animal kingdom (a cat is everything a crocodile is not, and vice versa), if a dog were to show up, given that it was hairy, domesticated, and friendly, it would be defined as a cat (however unusual its appearance) and certainly not as an unusual crocodile. Let us suppose again that I realize that there is a boa constrictor behind my native interlocutor’s back. I wouldn’t be able to tell him that it was a boa because there is no adequate term in his language, and I couldn’t describe the strange and unusual animal without wasting precious time. I would therefore have to tell him that there was a crocodile behind him, assuming that, since in that culture animals are divided into harmless and hostile, I would thus be informing him that he was in a dangerous situation. This example is not chosen at random because in some medieval encyclopedias, not knowing how to define a crocodile (since the author had probably never seen one), they were content to call it a serpens acquaticus.
If I succeed in causing my interlocutor to be concerned, as was my intention, and if I obtain his consent to my proposition (he turns around, gives a start and concedes that the animal, obviously not a cat, is indeed a crocodile), I will have behaved according to certain methodological principles of sense 2, to make a successful reference in the sense of sense 3, obtaining his consent in terms of sense 4.
But in fact all this is because I am basing myself on the principles of sense 5, according to which it is the text and the context that have the last word in defining the meaning of terms.
This whole discourse will no doubt lead someone to opine that there is no semantics that does not need to be backed up by a pragmatics. I can only agree, as indeed I always have, from my A Theory of Semiotics (1976) to Kant and the Platypus (2000).
Paper presented at the symposium “La semantica fin de siècle: Dalla fondazione di Michel Bréal all’attualità della ricerca” (“Fin de siècle semantics: From Michel Bréal’s foundation to contemporary research”), held at the Center for Semiotic and Cognitive Studies of the University of San Marino in November 1997. It was later published with the title “Cinque sensi di ‘semantica’ ” [“Five Meanings of ‘Semantics’ ”] (Eco 2001).