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carnap.philosophy.ubc.ca/book/3

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This chapter introduces a way of evaluating sentences and arguments of SL. The truth table method is a purely mechanical procedure that requires no intuition or special insight. Given the (albeit imprecise) translatability between SL and natural languages, this also amounts to a formal way of evaluating some natural language arguments. Any non-atomic sentence of SL is composed of atomic sentences with sentential connectives. In Ch. 2, we offered characteristic truth tables for each connective. Although we didn't emphasize it at the time, the fact that it is possible to give truth tables like this is very significant. It means that our connectives are truth-functional. That is to say, the only thing that matters for determining the truth value of a given sentence of SL is the truth values of its constituent parts. To determine the truth value of a sentence ¬Φ, the only thing that matters is the truth value of Φ. You don't have to know what Φ means, or where it came from, or what evidenc

Truth tables This chapter introduces a way of evaluating sentences and arguments of SL. The truth table method is a purely mechanical procedure that requires no intuition or special insight. Given the (albeit imprecise) translatability between SL and natural languages, this also amounts to a formal way of evaluating some natural language arguments. 3.1 Truth-functional connectives Any non-atomic sentence of SL is composed of atomic sentences with sentential connectives. In Ch. 2, we offered characteristic truth tables for each connective. Although we didn't emphasize it at the time, the fact t

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