全面解析the paradox of the liarfrom the different components of modern logic to the ancient greek philosophical thinking
very complex and abstract reply, too complex and abstract for us to give it much
consideration now.6 However, we can at least consider how difficult it is to make sense of the possibility that a sentence expresses something coherent about the way things are and, yet, it is neither true nor false, i.e., things neither are that way nor not that way. Which way, then are things supposed to be?
It seems, then, that the Liar, unlike the Barber or the Law Court, is a genuine paradox.
IV. What the Liar Paradox Shows
Like questions about Russell s barber shaving himself, the Liar reveals the surprising paradoxicality that self-reference sometimes produces. Now, self-reference clearly is not paradoxical in general, for most instances of it are perfectly coherent. Consider some examples.
1. Sax self-referentially asserts that he is bald. His statement is simply false, but it isn t paradoxical. (Indeed, a statement must be coherent even to be false.)
2. (i)-(iv) of the following self-referential sentences are just true; (v)-(vi) are just false:7
i. This sentence contains five words.
ii. This sentence contains thirty-six letters.
iii. There are fourteen vowels in this sentence.
iv. This sentence is written in English.
v. This sentence contains precisely fifty characters.
vi. Deis ist kein Deutscher Satz. [Translation: This sentence is not in German.]
3. Epimenides can self-referentially assert the self-referential sentence, “The sentence I am now uttering contains nine words,” and his remark will be unproblematically true.
Still, the Liar shows that those instances of self-reference in which a statement directly or indirectly predicates falsehood of itself are logically pathological in the worst, most mind-boggling way: they generate ineliminable, unresolvable contradiction. And, the Liar also shows that a liar sentence can be constructed in any language with the resources to:
A. refer to its own sentences, and
B. predicate truth or falsity of those sentences.
Unhappily, all natural languages (like Gujarati, Magyar, Frisian, etc.) satisfy (A) and
(B). That is very bad, for, as we ve seen, liar sentences generate unpreventable contradiction, and, as we ve learned, every statement validly follows and is derivable from a contradiction. In such a language, therefore, the entire practice of deductive reasoning as part of the search for truth is hopelessly corrupt. So, deductive rationality carried on in English (Basque, Korean, etc.) is a farce and a delusion…unless we can escape from the Liar.
6
7 But, see the handout “Deviant Logic, No. 3: Bo var s 3-Valued Logic.” A sentence like these that describes its own content or construction is called an autogram.
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