• Korean Journal of Logic
• /
• v.22 no.3
• /
• pp.417-446
• /
• 2019

The operation theory of the Wittgenstein's Tractatus Logico-Philosophicus is the essential basis of the philosophy of mathematics of the Tractatus. Wittgenstein presents the definition of cardinal numbers on the basis of operation theory, and suggests the proof of "$2{\times}2=4$" by using the theory of operations in 6.241. Therefore, in order to explicate correctly the philosophy of mathematics, it is required to understand rigorously the theory of operations in the Tractatus. Accordingly in this paper, I will endeavor to explicate operation theory of the Tractatus as a preliminary study for explicating the philosophy of mathematics of the Tractatus. In this process, we can ascertain Frascolla's important contributions and fallacies in his reconstruction of 6.241. In particular, we can understand the background that in 6.241 Wittgenstein made mistakes and that there he dealt with the addition operation of the theory of operations, and on the basis of this, we can reconstruct correctly 6.241.

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

In the Tractatus, 'logical space' raises the several puzzles as follows. What are logical space, logical coordinates and logical place? What is the point of such analogies and what do they refer to exactly in the Tractatus? And what do occupy logical space? Can facts, proposition, propositional sign, situation and contradiction occupy it respectively? Or is it impossible to reconcile the remarks concerning logical place in the Tractatus? Futhermore, why did Wittgenstein need the concept of logical space? What is the problem that he tried to solve through this concept? In this paper, I will endeavor to answer to these problems. Logical space in the Tractatus is the system of propositions with senses. And it is the concept which Wittgenstein contrived by making model of Hertz's configuration space. Wittgenstein's fundamental coordinates are in some ways similar to geometrical ones. On the other hand logical coordinates are completely different from geometrical ones. Hence attempts to understand logical space by a kind of geometrical spaces cannot be right at all.

• Korean Journal of Logic
• /
• v.21 no.1
• /
• pp.1-37
• /
• 2018

As is well known, Wittgenstein criticizes Russell's theory of types explicitly in the Tractatus. What, then, is the point of Wittgenstein's criticism of Russell's theory of types? In order to answer this question I will consider the theory of types on its philosophical aspect and its logical aspect. Roughly speaking, in the Tractatus Wittgenstein's logical syntax is the alternative of Russell's theory of types. Logical syntax is the sign rules, in particular, formation rules of notation of the Tractatus. Wittgenstein's distinction of saying-showing is the most fundamental ground of logical syntax. Wittgenstein makes a step forward with his criticism of Russell's theory of types to the view that logical grammar is arbitrary and a priori. His criticism of Russell's theory of types is after all the challenge against Frege-Russell's conception of logic. Logic is not concerned with general truth or features of the world. Tautologies which consist of logic say nothing.

• Korean Journal of Logic
• /
• v.21 no.2
• /
• pp.231-268
• /
• 2018

Wittgenstein asserts in the Tractatus Logico-Philosophicus 5.542 that "A believes that p" is of the form "'p' says p" and "here we have no co-ordination of a fact and an object, but a co-ordination of facts by means of a co-ordination of their objects." What does, then, it mean exactly that 'p' says p? What are "facts" and "a co-ordination" in the expression "a co-ordination of facts"? Are propositional attitude statements significant propositions or not? Furthermore, what is the point of Wittgenstein's criticism of Russell's theory of judgement? In this paper, I will answer these questions on the basis of Wittgenstein's explication of the concept of thought and Ramsey's relevant remark on propositional attitude. Meanwhile propositional attitude statements are bound up with solipsism of the Tractatus Logico-Philosophicus and some of them have senses. Hence both of assertions that all the propositional attitude statements are significant and all of them are nonsense in the Tractatus Logico-Philosophicus are not correct.

• Korean Journal of Logic
• /
• v.22 no.2
• /
• pp.253-290
• /
• 2019

Wittgenstein presents so-called picture theory in the Tractatus Logico-Philosophicus. What is, then, the point of the picture theory? What are the philosophical problems which the picture theory tries to solve? In this paper, I will endeavor to show that the object of a picture is different from the sense of a picture, that the representing relation is different from the projective relation, that picture theory is applied to composite propositions as well as elementary propositions and that on the one hand the basic problems that picture theory tries to solve are problem of theory of meaning and that of theory of truth, but on the other hand the more important problem is what Wittgenstein calls "the mystery of negation." From these discussions, we can see that it is not correct at all to interpret that the picture theory in the Tractatus Logico-Philosophicus is nothing but an analogy which does not have a significant content.

• Korean Journal of Logic
• /
• v.18 no.1
• /
• pp.1-39
• /
• 2015

Are properties and relations objects in the Tractatus Logico-Philosophicus? In this paper I will discuss essentially important problems concerning that question. That is, I will try to show that in a sense the concept of objects of the Tractatus is closely intertwined with that of Frege, and moreover the former was suggested to overcome Frege's predicament concerning the concept of objects. In the process of our discussions, it must be kept in mind that these discussions have no relations with metaphysical disputes, but proceed only from a logical point view. Futhermore it is Ramsey that made a most decisive contribution on these problems. In this paper I will try to show that in the Tractatus, properties and relations are objects via the discussions of Ramsey who was under the direct influences of Wittgenstein.

• Korean Journal of Logic
• /
• v.17 no.1
• /
• pp.1-32
• /
• 2014

Both 5.52 and 5.521 of the Tractatus Logico-Philosophicus raise several questions. In this paper I will explicate Wittgenstein's concept of generality by answering such questions. These questions and problems are closely intertwined. I will try to show what follows. It is ${\xi}$-conditions that are most decisive on the concept of generality of the Tractatus. Except Ramsey, commentators such as Anscombe, Glock, Kenny etc. failed in accurately grasping the Wittgenstein's thoughts concerning ${\xi}$-condition and their claims are not fair at all. Futhermore, from a view point of history of logic, 5.52 has very important significances. That is to say, it anticipates for the first time a possibility of infinitary logic and the concept of universe of discourse in model theory.

• Korean Journal of Logic
• /
• v.23 no.2
• /
• pp.117-159
• /
• 2020

In the early Wittgenstein's Tractatus, both philosophy of logic and that of mathematics belong to the most crucial subjects of it. What is the philosophical view of the early Wittgenstein in the Tractatus? Did he, for example, accept Frege and Russell's logicism or reject it? How did he stipulate the relation between logic and mathematics? How should we, for example, interpretate "Mathematics is a method of logic."(6.234) and "The Logic of the world which the proposition of logic show in the tautologies, mathematics shows in equations."(6.22)? Furthermore, How did he grasp the relation between mathematical equations and tautologies? In this paper, I will endeavor to answer these questions.

• Korean Journal of Logic
• /
• v.19 no.2
• /
• pp.253-293
• /
• 2016

In Wittgenstein's Tractatus, the concept of 'identity' gives rise to several puzzles as follows. What is an equation(Gleichung) in the Tractatus? Is an equation identical with so called an identity statement? Frege asserts that identity is not a relation between signs but one between objects or of a thing to itself. Then how does Wittgenstein criticize this Frege's conception? Furthermore Wittgenstein explicitly criticizes about Russell's definition of identity. Then What is the point of such Wittgenstein's critique? In a nutshell, what is early Wittgenstein's idea on the nature of identity? In this paper, I will endeavor to answer these questions.

• Korean Journal of Logic
• /
• v.20 no.2
• /
• pp.163-196
• /
• 2017

Wittgenstein declares in the Tractatus Logico-Philosophicus that he resolved Russell's Paradox. According to him, a function cannot be its own argument. If we assume that a function F(fx) can be its own argument, a proposition "F(F(fx))" will be given, where the outer function F has a meaning different from the inner function F. In consequence, "F(F(fx))" will not be able to have a definite sense. Why, however, does Wittgenstein call into question a function F(fx) and "F(F(fx))"? To answer this question, we must examine closely Russell's own resolution of Russell's Paradox. Only when we can understand Russell's resolution can we do Wittgenstein's resolution. In particular, I will endeavor to show that the idea in Wittgenstein's 1913 letter to Russell provides a decisive clue for this problem.