Can Brown Save Platonism This Time?

1678 words - 7 pages

From the book "Philosophy of Mathematics", the author James Brown addresses many problems involving Platonism's view in mathematics; such as how other mathematicians and philosophers debunk Platonism's view. Brown, however, saves Platonism by attacking the intruders first. Before reaching the stage where Brown fights the intruders, it is necessary to understand the following: (1) the Platonism's claim in mathematics, which is described in the second paragraph; (2) its two main fundamentals problems, which appears in paragraph three; (3) how Conventionalism, Empiricism, and Nominalism rejects Platonism, as described in the fourth paragraph. In the fifth paragraph, Brown will defend Platonism by attacking the intruders. Finally in the sixth paragraph, I will give my opinion on how well Brown defends Platonism and whether he's objective.First, Platonists claim that "mathematical objects are perfectly real and exist independently of us" (Brown, p11). They are perfectly real in the sense that they do have a unique form like any ordinary object. Since they have a unique form, we should be able to describe them. Thus, Platonists came up with the idea that using standard semantics, which is the theory of how truth is assigned to sentences, we are able to describe these mathematical entities. For instance, if the statement 'Jerry has one hat' is assumed to be true, then a person named Jerry must exist. Similarly, '1 x 2 = 2' and '1 > 0' are true statements if and only if the number 1 exists. By showing that objects exist in these true statements, Platonists claim that mathematical objects exist as well. Second, they claim that all mathematical objects are abstract. Abstract doesn't mean universal, but it means "outside of space and time, and they are neither concrete nor physical" (Brown, p12). For example, when we describe a red apple, the redness of the apple is universal, but the 'red-apple' itself is a particular because the apple has an instance color of red. Consequently, a mathematical object such as 7 is a particular, but also abstract-it exists outside of space and time. Third, they claim that men are born with limited mathematical perceptions, which is similar to the fact that men have limited perceptual access to the physical realm. In the mathematical realm, all men are intuited of simple addition such as '1 + 1 = 2', but not the Fundamental Theorem of Calculus. Similarly, within in the physical realm, men can only see ordinary objects like trees, but not the exotic entities of science-electrons. Fourth, they claim that "mathematic is a priori, not empirical" (Brown, p13). Unlike in empirical knowledge, which is dependent upon the five physical senses, priori is independent from them. Priori, according to Platonist, is a physical-sense-independent mechanism that allows a person to experience mathematical objects through the "mind's eye" (Brown, p13). Fifth, they claim that although mathematics is a priori, it's not necessary certain. The...

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