• Journal of Educational Research in Mathematics
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• v.25 no.1
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• pp.59-74
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• 2015

It is an increasing research area to explore mathematics learning from discursive perspectives. However, there have been little studies conducted on why and how discursive perspectives in mathematics learning were adopted and developed. Especially, not much discussion has been done on the later Wittgenstein's philosophical stance in terms of the relationship between language and thought as a background of discursive approach to learning mathematics. This study aims to explore the later Wittgenstein on language to get better understanding about discursive approaches to mathematics learning. For the attainment of this aim, first the later philosophy is compared with the former philosophy in depth. Then the later philosophy is discussed focusing on how his point of view on the world and the language have been changed. After providing an account of his later philosophy, it is clarified that what is discursive approaches to learning mathematics and how this philosophy brace the approaches. This research concludes with implications and limitations, as well as suggestions for future researches.

• Korean Journal of Logic
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• v.19 no.1
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• pp.49-82
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• 2016

In this paper, I argue that it is Kripke's Tractarian notion of rule-following that prevents him from giving a non-skeptical (straight) solution to Wittgenstein's paradox. I characterize the Tractarian notion of rule-following as the 'determinate/infinistic' notion of rule-following. The later Wittgenstein, however, advocates an opposite notion of rule-following: the 'indeterminate/finistic' notion. Considering the later Wittgenstein's context-sensitive, pragmatics-oriented approach to meaning and rule-following, the later Wittgenstein could not have endorsed the determinate/infinistic notion of rule-following. To the contrary, a motive behind Wittgenstein's skeptical paradox was to blame the Tractarian notion of rule-following as the major culprit giving rise to the paradox. At the end, I argue that Kripke's adherence to the Tractarian-correspondence theory of truth also contributes to his failure to offer a non-skeptical solution to the paradox. If Kripke had noticed that the later Wittgenstein was a deflationist about truth, he could have avoided his skeptical conclusion.

• Korean Journal of Logic
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• v.15 no.1
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• pp.155-190
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• 2012

As far as Hilbert's Program is concerned, there seems to be important differences in the development of Wittgenstein's thoughts. Wittgenstein's main claims on this theme in his middle period writings, such as Wittgenstein and the Vienna Circle, Philosophical Remarks and Philosophical Grammar seem to be different from the later writings such as Wittgenstein's Lectures on the Foundations of Mathematics (Cambridge 1939) and Remarks on the Foundations of Mathematics. To show that differences, I will first briefly survey Hilbert's program and his philosophy of mathematics, that is to say, formalism. Next, I will illuminate in what respects Wittgenstein was influenced by and criticized Hilbert's formalism. Surprisingly enough, Wittgenstein claims in his middle period that there is neither metamathematics nor proof of consistency. But later, he withdraws his such radical claims. Furthermore, we cannot find out any evidences, I think, that he maintained his formerly claims. I will illuminate why Wittgenstein does not raise such claims any more.