Frege on Arithmetic
1. Frege characte
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1. Frege characterizes a posteriori truth in terms of the basis on which a judgment of truth is made, or the "justification for making the judgement" (3). Why something is true, on this view, appears to be just as important as whether or not it is true. Frege implies that if the logical justifications for the truth are valid, then the truth is valid as well. And of the justifications are invalid, or if they do not follow logically one from the other, then the truth may be valid, but its proof is not so. An important component of justification in a posteriori truth is the "appeal to facts, i.e., to truths which cannot be proved and are not general" (4). In other words, the generalization of truth will have been derived from observation of particular instances of a case. A priori truth does not require observation, according to Frege, but "can be derived exclusively from general laws, which themselves neither need nor admit of proof" (4). General laws in this context refers to whatever is obviously, reasonably the case no matter what particular instance presents itself.Because Frege is concerned exclusively with mathematical proof, he is not concerned with the metaphysical structure of philosophical reality, as are other philosophers. Indeed, he specifically removes his discussion "from the sphere of psychology," although when he says that the more completely one attempts to determine why something is true, "the fewer become the primitive truths to which we reduce eve
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dge of general principles. Frege's position is that Kant formulation of a priori knowledge cannot be the basis for the general laws of arithmetic because such laws cannot emerge with reference to sense experience. The moment a general arithmetical law has reference to empirical mathematical fact it becomes specific and symbolic and loses its general property. For Frege, arithmetical law is general because it encases all attributes of number and because if one conceives a contrary case in which attributes of number cannot be conceived, "complete confusion ensues" (21). That is, one is really conceiving not merely random rational activity but chaos, wherein, logically, no intuition is possible. This is in the background of the statement that arithmetic is "the widest domain of all; for to it belongs not only the actual, not only the intuitable, but everything thinkable . . . connected very intimately with the laws of thought" (21).
If, however, P is a priori according to Frege and according to Kant, then it is the case that the two components of Kantian rational activity are operating, but prior to (or independent of) the mediation of empirical truth. That is, they are existing in the realm (domain) of pure logic and not in conjunc
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Approximate Word count = 1927
Approximate Pages = 8 (250 words per page)
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