• Korean Journal of Logic
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• v.18 no.3
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• pp.337-358
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• 2015

Vann Mcgee produced "counterexamples" to Modus Ponens in "A Counterexample to Modus Ponens". Discussions about the examples tended to focus on a probabilistic reading of conditional statements. This article attempts to establish both (1) Modus Ponens is a deductively valid rule of inference, and (2) the counterexample-like appearance of Mcgee's example can be (and should be) explained without making a reference to the notion of conditional probability. The reason why his examples seem to counter Modus Ponens is found rather within the ambiguity a conditional statement exhibits. That is, Mcgee's examples are cases of equivocation on the conditional statements involved.

• Korean Journal of Logic
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• v.15 no.3
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• pp.375-392
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• 2012

In a previous paper I argued that the denial of the uncontested principle results in the denial of modus ponens. In his reply Byeong Deok Lee explicitly says that he does not deny the validity of modus ponens though he still does not accept the uncontested principle. In this paper I show that his view is untenable.

• Korean Journal of Logic
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• v.16 no.1
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• pp.87-115
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• 2013

In my previous article "The Uncontested Principle and Wonbae Choi's Objections", I argued that the validity of modus ponens (as a deductive inference) is compatible with the claim that the Uncontested Principle is controversial. In his recent paper "The Uncontested Principle and Modus Ponens", Wonbae Choi criticizes my view again by making the following three claims: First, even though I do not take an inference of the form 'If A then (probably) C. A. $\therefore$ C' as an instance of modus ponens, this form of inference can be taken to be such an instance. Second, there is no grammatical indicator which allows us to distinguish between an indicative conditional based on a deductive inference and an indicative conditional based on an inductive inference, so that inferences based on these conditionals should not be treated as different types of inferences. Third, if we allow an indicative conditional based on an inductive inference, we thereby violate the so-called 'principle of harmony', which any logical concept should preserve. In this paper, I reply that his criticisms are all implausible.

• Korean Journal of Logic
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• v.19 no.2
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• pp.233-251
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• 2016

In their recent paper published in this journal Shin Kim and Jinyong Lee have attacked some previous studies on the counterexample to modus ponens. Among their arguments I would like to discuss the following two; first, those attempts to explain van McGee's example by reference to conditional probability do not accord with van McGee's position, second, van McGee'e example is to be best seen as an argument containing the fallacy of equivocation. I show that the first argument is not correct, the second one is not so persuasive as it seemed first.

• Korean Journal of Logic
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• v.14 no.3
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• pp.85-100
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• 2011

Recently Byeong Deok Lee has denied the validity of the so-called uncontested principle, which says that the indicative conditional implies the material conditional. I show that his denial means that modus ponens is not valid and that the truth-conditions of indicative conditionals are weaker than that of material conditionals. It seems that what made him hold this view is related to some misunderstanding of indicative conditionals.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.5
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• pp.674-678
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• 2007

Baldwin defined the approximate reasoning using truth function mapping. In paper [4], we defined two truth function mappings and applied these truth function mappings to generalized modus ponens. In this paper, we introduce the results of generalized modus tollens using these two truth function mappings.

• Korean Journal of Logic
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• v.15 no.2
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• pp.273-294
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• 2012

In my previous article "An Inferentialist Account of Indicative Conditionals" and "An Inferentialist Account of Indicative Conditionals and Hasuk Song's Objections", I argued that the so-called Uncontested Principle is not uncontestable. According to the Uncontested Principle, an indicative conditional '$A{\rightarrow}C$' logically implies a material conditional '$A{\supset}C$'. In his recent paper "On the Recent Controversies surrounding the Uncontested Principle" Wonbae Choi presents three objections to my claim. First, my denial of the Uncontested Principle implies rejecting modus ponens. Second, my denial of the Uncontested Principle is tantamount to taking the truth-conditions of an indicative conditional as weaker than those of a material conditional, which are usually taken to be the weakest among conditionals. Third, my view that we can warrantedly assert '$A{\rightarrow}C$' even when 'A ${\therefore}$ C' is inductively justified is based on a misunderstanding of the way in which indicative conditionals are justified. In this paper I argue that Choi's objections are all based on misunderstandings of my view. First, I do not deny the validity of modus ponens (as a form of deductive reasoning). Second, the fact that the inductive warrantability of 'A ${\therefore}$ C' does not imply the truth of '$A{\supset}C$' does not show that the truth-conditions of an indicative conditional is weaker than those of a material conditional. Third, Choi's claim that a contingent conditional '$A{\rightarrow}C$' is true only when 'C' can be deductively derived from 'A' in conjunction with a hidden premiss is not well grounded, nor does it fit the facts.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.40-41
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• 2003

A new method, the Triple I method is proposed for solving the problem of fuzzy reasoning. The Triple I method for solving fuzzy modus ponens is compared with the CRI method i.e., Compositional Rule of Inference and reasonableness of the Triple I method is clarified. Moreover the Triple I method can be generalized to provide a theory of sustentation degrees. Lastly, the Triple I method can be bring into the framework of classic logics.

• Korean Journal of Logic
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• v.5 no.1
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• pp.63-79
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• 2001

반 멕기는 전건 긍정 규칙(modus ponens)에 대한 이른바 반례들을 제시하고, 이런 예는 전건 긍정 규칙이 '엄밀히 타당한'것은 아님을 보여준다고 주장하였다. 그런데 최근 들어 카츠는 이런 반 멕기의 주장을 논박하고 있다. 이 논문은 카츠의 이런 논박이 어느 정도 성공적인지를 검토하고 있다. 이를 위해 우선 반 멕기의 반례가 제시되고, 그 다음 카츠의 반박이 자세히 분석되고 정식화된다. 이런 정식화에 바탕을 두고 카츠의 논증이 평가되며, 그 결과 카츠의 논증이 흠이 있음이 드러난다. 이런 이유로 논자는 카츠의 논박이 반 멕기가 내세운 전건 긍정 규칙의 반례를 무효화하지 못했으며, 따라서 반례는 여전히 유효하다고 주장한다.

• Journal of Educational Research in Mathematics
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• v.18 no.1
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• pp.123-135
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• 2008

This study analysed the schemata which are requisite to understand and prove examples of mathematical induction, and examined students' construction of the schemata. We verified that the construction of implication-valued function schema and modus ponens schema needs function schema and proposition-valued function schema, and needs synthetic coordination for successive mathematical induction schema. Given this background, we establish $1{\sim}4$ levels for students' understanding of the mathematical induction. Further, we analysed cognitive difficulties of students who studying mathematical induction in connection with these understanding levels.