Is Number Subjective? Essay

620 words - 2 pages

Is Number Subjective? In section twenty-two of The Foundations of Arithmetic, while in a discussion of whether or not number is a property of external things such as a pile of playing cards, Gottlob Frege writes "The Number 1, on the other hand, or 100 or any other Number, cannot be said to belong to the pile of playing cards in its own right, but at most to belong to it in view of the way in which we have chosen to regard it." Reading this passage alone, Frege may seem to be implying that number is something subjective, something that depends on a decision on our part. Yet in section forty-seven Frege writes "That a statement of number should express something factual independent of our way of regarding things can surprise only those who think a concept is something subjective like an idea. But this is a mistaken view." What is Frege's meaning in the first passage, since its apparent implications seem to be contrary to the passage in section forty-seven? With further investigation, it becomes apparent that he is not saying that statements of number are subjective, but that statements of number are really statements of concept, and therefore are objective. The way which we choose to regard it an object is another way of saying the objective concept which we choose to apply to an object, which may be subjective. But number is never subjective.In the first passage cited above, where Frege writes that the number that belongs to the pile of playing cards depends on "the way in which we have chosen to regard it," he is not claiming that the number belonging to the pile of playing cards is a subjective decision on our part. In fact, Frege insists repeatedly throughout the book that number is something objective. Rather, he is saying that the number...

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