>> That last reaction incorporates one criticism of Times-er, namely that it is "illogical" or "irrational": X times more than Y MUST MEAN 'Y plus X-times-Y (that is, 'X+1 times Y'), not 'X times as many/great as Y' (that is, 'X times Y'). (In the most common variant of this reaction, X times more than Y is disparaged because it is said to be ambiguous, with both the 'X times Y' and 'X+1 times Y' interpretations.)
>> The appeal here is to the idea that ordinary-language expressions are simply realizations of logical (or arithmetical) formulas. This is just backwards. The formulas are there to represent the meanings of expressions; they are not the prior reality, merely cloaked in (those devilishly vague) words of actual languages.
>> That last reaction incorporates one criticism of Times-er, namely that it is "illogical" or "irrational": X times more than Y MUST MEAN 'Y plus X-times-Y (that is, 'X+1 times Y'), not 'X times as many/great as Y' (that is, 'X times Y'). (In the most common variant of this reaction, X times more than Y is disparaged because it is said to be ambiguous, with both the 'X times Y' and 'X+1 times Y' interpretations.)
>> The appeal here is to the idea that ordinary-language expressions are simply realizations of logical (or arithmetical) formulas. This is just backwards. The formulas are there to represent the meanings of expressions; they are not the prior reality, merely cloaked in (those devilishly vague) words of actual languages.