Logic Pt.2

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Thus, as I have pointed out, he illustrates the use of the word function in his first paragraph in three different ways which are sym- bolised as follows : '« is hurt,' 'x is hurt,' and '^ is hurt' The last application of the word function is that which he wishes to be finally adopted; but, in spite of this, he continually uses the word in both of the two other ap- plications. It is still more surprising that, on page 6 of his Introduction, where he gives a preliminary account of the ideas and ...notations of logical symbolism, he uses the word function without any explanation of its meaning, and in deliberate defiance of his own later definition.
Thus he speaks of the fundamental functions of pro- positions in these words : 'an aggregation of propositions considered as wholes, not necessarily unambiguously determined, into a single proposition more complex than its constituents, is a function with propositions as argu- ments.' This account appears clearly to suggest that un- ambiguously determined constituents are allowable as arguments for a function, which contradicts his explicit definition.


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