本文關(guān)鍵詞：弗雷格關(guān)于數(shù)的本體論研究　出處：《河北大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

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【摘要】：德國(guó)數(shù)學(xué)家弗雷格于1879年創(chuàng)立了一階邏輯系統(tǒng),并借助該系統(tǒng)進(jìn)行了數(shù)學(xué)基礎(chǔ)的研究。他關(guān)于數(shù)的本體論研究包括兩個(gè)方面:一是反駁傳統(tǒng)的關(guān)于數(shù)的本體論觀點(diǎn),二是從一階邏輯的角度出發(fā)揭示數(shù)的本質(zhì)。弗雷格的批判主要在于:反對(duì)把數(shù)看做一種物理現(xiàn)象,反對(duì)把數(shù)看做心理活動(dòng)的產(chǎn)物,以及反對(duì)把數(shù)看做客觀對(duì)象的一種性質(zhì)。弗雷格對(duì)于數(shù)概念的分析方式,是運(yùn)用一階邏輯的方法進(jìn)行語(yǔ)言分析。他通過對(duì)數(shù)詞在語(yǔ)句中的使用進(jìn)行討論,明確了“數(shù)的給出包含著對(duì)一個(gè)概念的表達(dá)”。通過概念和對(duì)象層面的討論,弗雷格確定了每一個(gè)個(gè)別的數(shù)都是一個(gè)對(duì)象。在明確了數(shù)的性質(zhì)后,弗雷格將屬于“與自身不相等”這一概念的數(shù)定義為0,從而確定了自然數(shù)序列的起點(diǎn)。他隨后定義了“緊跟”,作為自然數(shù)數(shù)列的后繼規(guī)則。借助這樣的起點(diǎn)和后繼規(guī)則,弗雷格推出了整個(gè)自然數(shù)序列。弗雷格的這些工作最終因遭遇羅素悖論而陷入困境。晚年弗雷格對(duì)自己早年關(guān)于數(shù)的本體論的觀點(diǎn)進(jìn)行反思,試圖重新建立一個(gè)算術(shù)基礎(chǔ)的研究體系,但最終沒有成功。弗雷格關(guān)于數(shù)的本體論研究對(duì)于一階邏輯和數(shù)學(xué)基礎(chǔ),都產(chǎn)生了重大的影響。
[Abstract]:German mathematician Frege founded the first order logic system in 1879, and carried out the research on the basis of the system with the aid of the system. His ontological research on numbers includes two aspects: one is to refute the traditional view of number ontology, and the two is to reveal the essence of numbers from the perspective of first-order logic. Frege's criticism mainly lies in his opposition to counting as a physical phenomenon, opposing the number as a product of mental activities, and opposing the nature of number as a guest object. Frege's analysis of the number of concepts is to use the method of first order logic to carry out the language analysis. By discussing the use of logarithmic words in statements, he made it clear that "the given number is contained in the expression of a concept." Through the discussion of conceptual and object levels, Frege determined that each individual number is an object. After defining the nature of the number, Frege defines the number of the concept of "unequal to itself" as 0, thus determining the starting point of the sequence of natural numbers. He then defines "heel" as the successor rule of the number of natural numbers. With the help of such starting points and following rules, Frege introduced the whole sequence of natural numbers. Frege's work was in the end because of the Russell paradox. In his late years, Frege reconsidered his early views on the ontology of numbers, trying to reestablish an arithmetic basis, but eventually failed. Frege's research on the ontology of numbers has a great influence on the first - order logic and the mathematical basis.
【學(xué)位授予單位】：河北大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：O156

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本文編號(hào)：1341075