Matematické vety ako pravidlá I.

Róbert Maco
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Abstract

The main aim of this paper is to convince the reader that in philosophizing about mathematics, the least misleading and most productive way of understanding mathematics is the so called normative conception; i. e. the way of conceiving mathematical propositions as rules and not as descriptive sentences. This approach has been inspired by the works of later L. Wittgenstein. I attempt to reach the outlined objective in two steps. In the first step, I will focus on how mathematics actually becomes a philosophical problem. The second step will consist in introducing a normative understanding of mathematics, and in particular its core: the normative account of mathematical propositions. I will try to answer the question of what it means to understand mathematical propositions as rules and I will emphasize the naturalness and productivity of this understanding. The forthcoming second part of the paper will contain responses to several standard objections to the normative conception of mathematics.
本文的主要目的是使读者相信,在对数学进行哲学思考时,理解数学的最不容易引起误解和最有效的方法是所谓的规范概念;即把数学命题理解为规则而不是描述性句子的方法。这种方法受到后来维特根斯坦(L. Wittgenstein)作品的启发。我试图分两步达到概述的目标。在第一步,我将集中讨论数学实际上是如何成为一个哲学问题的。第二步将包括引入对数学的规范理解,特别是其核心:数学命题的规范说明。我将试着回答这个问题,将数学命题理解为规则意味着什么,我将强调这种理解的自然性和生产力。即将到来的论文的第二部分将包含对数学的规范概念的几个标准反对意见的回应。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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