This paper outlines three broad ways one might think about logical correctness: the Realist approach, the One-Language approach and my own Neo-Carnapian view. Although the realist and one-language views have dominated the philosophy of logic in recent years, I argue against them, favouring of the Neo-Carnapian approach.

In Baghdad in the mid twelfth century Abū al-Barakāt proposes a radical new procedure for finding the conclusions of premise-pairs in syllogistic logic, and for identifying those premise-pairs that have no conclusions. The procedure makes no use of features of the standard Aristotelian apparatus, such as conversions or syllogistic figures. In place of these al-Barakāt writes out pages of diagrams consisting of labelled horizontal lines. He gives no instructions and no proof that the procedure will yield correct results. So the (...) reader has to work out what his procedure is and whether it is correct. The procedure turns out to be insightful and entirely correct, but this paper may be the first study to give a full description of the procedure and a rigorous proof of its correctness. (shrink)

The article "The logic of hatred and its social and historical expressions: From the great witch-hunt to terror and present-day djihadism," written by Jean Greisch, was originally published electronically on the publisher’s Internet portal on March 2020 with open access.

This erratum is to correct in the paper of Daniele Chiffi and Ahti-Veikko Pietarinen, On the Logical Philosophy of Assertive Graphs.

The original version of this article unfortunately contains several errors introduced by the typesetter during the publishing process. It has been corrected.

The original version of this article unfortunately contains mistakes introduced by the publisher during the production process. The mistakes and corrections are described in the following list.

Recent work on analyticity distinguishes two kinds, metaphysical and epistemic. This paper argues that the distinction allows for a new view in the philosophy of logic according to which the claims of logic are metaphysically analytic and have distinctive modal profiles, even though their epistemology is holist and in many ways rather Quinean. It is argued that such a view combines some of the more attractive aspects of the Carnapian and Quinean approaches to logic, whilst avoiding some famous problems.

This note corrects an error in my paper 'Normalisation and Subformula Property for a System of Classical Logic with Tarski's Rule' (Archive for Mathematical Logic 61 (2022): 105-129, DOI 10.1007/s00153-021-00775-6): Theorem 2 is mistaken, and so is a corollary drawn from it as well as a corollary that was concluded by the same mistake. Luckily this does not affect the main result of the paper.

We show that the polynomial translation of the classical propositional normal modal logic S4 into the intuitionistic propositional logic Int from Fernández is incorrect. We give a modified translation and prove its correctness, and provide implementations of both translations to allow others to test our results.

This is a correction to: Gemma Robles, José M. Méndez, A note on functional relations in a certain class of implicative expansions of FDE related to Brady’.

순자의 논리학은 인식론으로 이해해야 한다. 순자는 ｢正名｣편에서 현상을 인식하는 방법으로 名을 바로 지어야 實을 바로 볼 수 있다고 한다. 중국에서 名은 實(현상)의 존재를 인식하는 방법으로 받아들였다. 이를 名實論이라고 말한다. 순자의 ‘논리’는 명제에 대한 참과 거짓의 판별 방법은 아니다. 순자는 사람이 현상을 인식함에 대한 설명을 한다. 즉 사람의 마음을 설명하고, 마음이 현상을 인식하는 수단으로서 名이 사용된다. 이러한 설명은 『荀子』｢正名｣에서 발견할 수 있다. ｢正名｣에는 正名의 논리적 체계에서 諸家를 비판하기 위한 근거로서 制名의 三原則이 제시되고 있다. ‘制名’에 대한 순자의 사상은 바로 유교적 군주인 ‘聖王’ (...) 아래에서 이루어지는 현실과 이념의 결합을 명실론 차원에서 표명한 것이다. 명칭을 제정하는 일이 가능한 이유는, 사람들이 공유한 바의 감각기관과 그것을 바탕으로 분석·종합하고 반성·추리할 수 있는 心의 기능에 있는 것이다. ‘諸子’사상의 집약자인 순자의 명실론은 그의 사상 전체의 성격과 유기적으로 연계되어 있으며, 순자의 논리학인 ｢正名｣에 자세하게 열거되어 있음을 이 논문은 밝힌다. (shrink)

A Correction to this paper has been published: 10.1007/s11225-021-09980-z.

In the original publication of the article, in Definition 4, the sixth line which reads as.

This is a just a notice stating that Springer has made some of the corrections they neglected to make at the proof stage.

This paper is concerned with a propositional modal logic with operators for necessity, actuality and apriority. The logic is characterized by a class of relational structures defined according to ideas of epistemic two-dimensional semantics, and can therefore be seen as formalizing the relations between necessity, actuality and apriority according to epistemic two-dimensional semantics. We can ask whether this logic is correct, in the sense that its theorems are all and only the informally valid formulas. This paper gives outlines of two (...) arguments that jointly show that this is the case. The first is intended to show that the logic is informally sound, in the sense that all of its theorems are informally valid. The second is intended to show that it is informally complete, in the sense that all informal validities are among its theorems. In order to give these arguments, a number of independently interesting results concerning the logic are proven. In particular, the soundness and completeness of two proof systems with respect to the semantics is proven (Theorems 2.11 and 2.15), as well as a normal form theorem (Theorem 3.2), an elimination theorem for the actuality operator (Corollary 3.6), and the decidability of the logic (Corollary 3.7). It turns out that the logic invalidates a plausible principle concerning the interaction of apriority and necessity; consequently, a variant semantics is briefly explored on which this principle is valid. The paper concludes by assessing the implications of these results for epistemic two-dimensional semantics. (shrink)

In a series of studies children show increasing mastery of irregular plural forms (such as mice) simply by producing erroneous over‐regularized versions of them (such as mouses). We explain this phenomenon in terms of successive approximation in imitation: Children over‐regularize early in acquisition because the representations of frequent, regular plural forms develop more quickly, such that at the earliest stages of production they interfere with children's attempts to imitatively reproduce irregular forms they have heard in the input. As the strength (...) of the representations that determine children's productions settle asymptotically, the early advantage for the frequent regular forms is negated, and children's attempts to imitate the irregular forms they have observed become more likely to succeed (a process that produces the classic U‐shape in children's acquisition of plural inflection). These data show that children can acquire correct linguistic behavior without feedback in a situation where, as a result of philosophical and linguistic analyses, it has often been argued that it is logically impossible for them to do so. (shrink)

In an earlier paper entitled Synonymous Logics, the authors attempted to show that there are two modal logics so that each is exactly translatable into the other, but they are not translationally equivalent. Unfortunately, there is an error in the proof of this result. The present paper provides a new example of two such logics, and a proof of the result claimed in the earlier paper.

In this paper we investigate total correctness in Nonstandard Dynamic Logic . Here we show that despite of the celebrated Kfoury-Park [5] result, termination is a rst order notion if approached properly.

As we all know, metaphysics and objective truth are basically antagonistic, while dialectical materialism and objective truth are uniform. This is the common sense of Marxist philosophy and needs no argument. What, then, is the relationship between formal logic as a science and objective truth? This involves the problem of the correctness of thought form and the truthfulness of thought content. As shown, this problem is still an unsettled dispute in philosophy and logic circles. There are two opposite views: (...) one view holds that formal logic should concern itself with the correctness of thought form and the truthfulness of thought content; the other holds that formal logic should concern itself only with the correctness of thought form, but not the truthfulness of thought content. The substance of the issue involves the problem of the relationship between formal logic and objective truth. We consider that the science of formal logic itself does not and cannot assume the task of solving objective truth, since it is basically distinguished from the philosophy of dialectical materialism. However, formal logic does not exclude objective truth. It differs basically from metaphysics in that formal logic is a science. Thus, there is no inherent and necessary link between formal logic and objective truth. Formal logic does not study the problem of objective truth. (shrink)

This paper presents a new correctness criterion for marked Danos-Reginer graphs (D-R graphs, for short) of Multiplicative Cyclic Linear Logic MCLL and Abrusci's non-commutative Linear Logic MNLL. As a corollary we obtain an affirmative answer to the open question whether a known quadratic-time algorithm for the correctness checking of proof nets for MCLL and MNLL can be improved to linear-time.

The Tractatus revolves around the connection between two central topics – the preconditions of symbolic representation and the nature of logic-cum-philosophy. Proper philosophy is an activity, namely of revealing the hidden structures that allow language to represent reality by way of logical analysis. At the same time the main purpose of such logical analysis consists in revealing metaphysical statements to be nonsensical. In the subsequent development of analytic philosophy, these two ideas parted company. The positive aim of revealing (...) the logical form of sentences resulted in a program closely associated with Davidson, namely a theory of meaning for natural languages that yields metaphysical corollaries. The negative aim of overcoming metaphysics ushered in the activity of dissolving conceptual confusions through conceptual rather than logical analysis, propelled by the later Wittgenstein. My presentation pursues these historical lines of influence. But the ultimate aim is a substantive one, namely to establish whether the two projects can be kept apart. With the later Wittgenstein, I criticize the claim that formal calculi constitute the hidden structure of natural languages. But I also contend that the hope of engaging in anti-metaphysical dialectic without relying on logico-conceptual analysis of some kind falls prey to a “myth of mere method”. (shrink)