1.In a recent paper, Hartley Slater points out that the Tarski T-scheme
T `p’ if and only if p
Does not hold (nor was it intended to hold) of sentences that are ambiguous or indexical. It holds only when the sentence substituting for `p’ has a determinate, unqualified truth-value (H. Slater, `Tarski’s Hidden Assumption’, Ratio 17 (2004), pp.84-89. We must therefore modify the T-scheme accordingly, and the result is:
If T`p’ or F`p’ then T `p’ if and only if p
2.
With this restriction in place, if we substitute for
`p’ any of the problematic, paradoxical sentences, we simply derive the result
that it is neither true nor false. There
are three problems for Slater: First, a proof is not a rationale – we might
accept the proof that the paradoxical sentences cannot be true or false, and
yet still seek an independent reason for accepting that this surprising result
is plausible. Second, notoriously, the
suggestion that paradoxical sentences are neither true
nor false only leads to `strengthened’ versions. Third, clearly the restriction is needed for
sentences that are ambiguous or indexical, but is there any reason for holding
that the paradoxical sentences fall into either of these categories? All of
these problems would evaporate if we could give a convincing demonstration that
these paradoxical sentences fail to make statements.
3.Hilary Putnam begins his book Reason, Truth and History (Cambridge University Press, 1982) with the following question: `An ant is crawling on a patch of sand. As it crawls, it traces a line in the sand. By pure chance the line that it traces curves and recrosses itself in such a way that it ends up looking like a recognizable caricature of Winston Churchill. Has the ant traced a picture of Winston Churchill, a picture that depicts Churchill?’
4.Most people need little persuading
that the correct answer to this question is `No’. As Putnam goes on to point out, ` the line is not 'in itself' a representation
of anything rather than anything else’.
By a series of steps, Putnam establishes the more surprising, but no
less correct result that it is `an important conceptual truth that even a large
and complex system of representations, both verbal and visual, still does not
have an intrinsic, built-in, magical connection with what it
represents — a connection independent of how it was caused and what the
dispositions of the speaker or thinker are. And this is true whether the system
of representations [e.g., words or images]….. is
physically realized — the words are written or spoken, and the pictures are
physical pictures — or only realized in the mind. Thought words and mental
pictures do not intrinsically represent what they are about.’
5.Thus, think of a footpath, made of pebbles that each day get squished
and squirted and scattered by the feet of innumerable walkers. Suppose that, at the end of one day, some
pebbles, quite by chance, have ended up looking like a string of letters
forming the sentence `My brother is a doctor’.
It would obviously be lunacy to ask `Which brother are they talking
about?’ or `By “doctor” do they mean a physician or
someone who has earned a Ph.D.?’ By
contrast, when I say to you `My brother is a doctor’, I am talking about my brother
Hugh, and by `doctor’ I mean, on this occasion `physician’ and by the sound
`is’ I mean the present tense of the verb `to be’ and by `a’ the indefinite
article. As Putnam remarks, the words in
a sentence do not intrinsically possess semantical
properties, but there may be occasions on which those words are used, and the
statement so made does have semantical properties.
6.Consider, for example, the sentence `The next statement is true’. Obviously, this acquires a truth-value only when the next statement is made. It would be ridiculous, before that time, to declare that the sentence is true. Or that it is false. In the case of the Yablo sequence, the first sentence refers to all the following sentences. And, since the sequence is infinite, the determination of the truth-value of the first sentence is infinitely postponed. Therefore, again, it would be ridiculous to say either that the first sentence in the Yablo sequence is true or that it is false (Compare the danger of premature commitment in the case of the `Infallible Seducer’ paradox.)