关于任何话语的虚构主义的独特性质是(a)对该话语的一些有价值的目的的承认,以及(b)即使在该话语的语境中说出的句子不是真实的,也可以服务于该目的的主张。关于(b),如果所讨论的话语涉及数学,无论是纯粹的还是应用的,数学虚构主义者关于这种话语的观点的核心是,即使在上下文中产生的数学话语,也可以服务于参与该话语的目的。那种话语不是真的(或者,在诸如“没有平方素数”之类的负存在的情况下,只是简单地说是真的)。关于(a),在发展数学虚构主义时,数学虚构主义者必须至少在这个核心观点中加入数学探究的价值,并解释为什么如果我们不假设这个价值可以被服务的原因数学的字面值或面值真值。“虚构主义”这个标签暗示了数学与文学小说的比较,尽管虚构主义者可能只希望得出数学和小说都不是真实的最小比较,但虚构主义者也可能希望在更进一步的维度上发展这种类比,例如,通过讨论小说的语义,或小说如何表示。然而,在讨论这些问题之前,本文将考虑在数学探究的背景下所说的句子的字面真实性,以便理解虚构主义者希望拒绝的立场。

英国谢菲尔德大学数学Essay代写:数学哲学中的虚构主义

The distinctive character of fictionalism about any discourse is (a) recognition of some valuable purpose to that discourse, and (b) the claim that that purpose can be served even if sentences uttered in the context of that discourse are not literally true. Regarding (b), if the discourse in question involves mathematics, either pure or applied, the core of the mathematical fictionalist’s view about such discourse is that the purpose of engaging in that discourse can be served even if the mathematical utterances one makes in the context of that discourse are not true (or, in the case of negative existentials such as ‘There are no square prime numbers’, are only trivially true). Regarding (a), in developing mathematical fictionalism, then, mathematical fictionalists must add to this core view at the very least an account of the value of mathematical inquiry and an explanation of why this value can be expected to be served if we do not assume the literal or face-value truth of mathematics. The label ‘fictionalism’ suggests a comparison of mathematics with literary fiction, and although the fictionalist may wish to draw only the minimal comparison that both mathematics and fiction can be good without being true, fictionalists may also wish to develop this analogy in further dimensions, for example by drawing on discussions of the semantics of fiction, or on how fiction can represent. Before turning to these issues, though, this article considers what the literal truth of a sentence uttered in the context of mathematical inquiry would amount to, so as to understand the position that fictionalists wish to reject.

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