This article offers a logical analysis of Slippery Slope Arguments. Such arguments claim that adopting a certain act or policy would take us down a slippery slope to an undesirable bottom and infer from this that we should refrain from this act or policy. Even though a logical assessment of such arguments has not received much careful attention, it is of vital importance to their overall assessment because if the premises fail to support the conclusion an argument (...) is worthless. I partition slippery slope reasoning by means of two dichotomies (reasoning under certainty vs. uncertainty and one-step vs. multiple-step reasoning) into four general categories and evaluate these in turn. The analysis reveals that slippery slope arguments are logically fallacious. (shrink)

In this paper, we give a logical analysis of pluralistic ignorance, which is an important social phenomenon. There has been no consensus about the definition of pluralistic ignorance in the literature. From an epistemic point of view, there are at least three definitions of pluralistic ignorance. We choose three definitions among them, which, for us, are natural to explain many classic examples of phenomenon of pluralistic ignorance in the literature of social and behavioural sciences, e.g., (American) college campuses, (...) The Emperor's New Clothes. To the best of our knowledge, there has been no logical study on the three definitions of pluralistic ignorance yet. We take the three operators of pluralistic ignorance induced by the definitions as first‐class citizens and investigate their logical properties, including the similarities, differences and the interactions, where we find some interesting results; in particular, under the assumption that beliefs are consistent and negatively introspective, a group cannot be second‐order pluralistically ignorant, and thus not be any higher order pluralistically ignorant. This contrasts with Fitch's result in “Ignorance of ignorance” (Kit Fine, Synthese, 2018) that under the same assumption, one may be second‐order ignorant, even though under the assumption of the modal system S4 (semantically, the class of transitive and reflexive frames), one cannot know that one is second‐order ignorant. (shrink)

Husserl and Frege on the analysis of the concept of number and primitive logical concepts.

Following G. E. M. Anscombe, most commentators on Ludwig Wittgenstein’s Tractatus Logico‐philosophicus have held that §6.3751 rules out colour propositions as elementary propositions. However, a careful reading of some passages from The Big Typescript, MS 105 and MS 103, on the logical structure of colour and the logical analysis of colour statements, shows that the elementary propositions of the Tractatus include colour propositions. It follows that Anscombe’s interpretation of §6.3751 is mistaken.

The debate between Zhuangzi and Huizi has profound epistemological significance, however, the main body of their debate comprises logical inferences and refutations. Therefore, this paper mainly focuses on the logical aspects of the debate. Some scholars have suggested that Huizi’s argument is self-contradictory; however, in fact, based on such evaluations of Huizi’s argument, we can conclude that Zhuangzi’s logic is also self-contradictory. By utilizing modern logical analysis tools, this study reveals what and how the propositions and (...) inferences contained in the language of the debate are articulated accurately and strictly. Moreover, by elaborating on the implicit premises omitted by Zhuangzi and Huizi, the actual logical process of the debate can be restored, and the logical fallacy of clandestine change of argumentative issue are revealed. This study presents clear modern logic analysis of the debate; it can also provide a more reliable logical basis for the discussions of Zhuangzi and Huizi’s related philosophical thoughts. (shrink)

Russell’s theory of descriptions in “On Denoting” has long been hailed as a paradigm of the sort of analysis that is constitutiue of philosophical understanding. It is not the only model of logical analysis available to us, however. On Frege’s quite different view, analysis provides not a reduction of some problematic notion to other, unproblematic ones -- as Russell’s analysis does -- but instead a deeper, clearer articulation of the very notion with which we began. (...) This difference, I suggest, is grounded in their two very different conceptions of the nature of language / thought; and it grounds in turn two very different conceptions of the nature of philosophical understanding. (shrink)

The following well-known problem motivated my handling more general problems. As we surely know, our pupils and even students are confronted with much more trouble when learning mathematics (and even physics) than when they learn ‘empirical’ sciences like biology, mineralogy etc. There are many factors that can at least partially explain this phenomenon. I would however mention one factor that is not too frequently adduced: mathematics, logic, and much of physics use concepts that are abstract while the empirical sciences seem (...) to support understanding by using expressions concerning (denoting? expressing?) concrete objects. Therefore the first topic to be explained (or explicated) is: Abstract vs. concrete. The second point will consist of applying the first point to explanation of the trouble with learning mathematics. The third point will ask Logical Analysis of Natural Language how to tell abstract expressions from concrete ones. The fourth point will confront the concept described in the foregoing point with conceptions trying to abandon the distinction between analytic and empirical expressions. Here it will be shown that the empiricism representing this latter conception deprives semantics as applied to Natural language of important features of expressivity. (shrink)

Cognitive, or knowledge, agents, who are in some way aware of describing their own view of the world (based on their mental concepts), need to become concerned with the expressions of their own conceptions. My main supposition is that agents’ conceptions are mainly expressed in the form of linguistic expressions that are spoken, written, and represented based on e.g. letters, numbers, or symbols. This research especially focuses on symbolic conceptions (that are agents’ conceptions that are manifested in the form of (...) their symbols). I attempt to logically (and using????LSYM) analyse symbolic conceptions in terminological systems.????LSYM is an assertional fragment of my developed Conception Language (????L), which is utilised as a formal-logical system for representing and explicating agents’ conceptions of the world. Keywords: assertional logic; cognitive agent; knowledge agent; conception language; conception; symbol; symbolic conception. (shrink)

Die Arbeit schlägt eine beweistheoretische Analyse der mathematischen Physik im Gegensatz zu gegenwärtigen modelltheoretischen Ansätzen vor. Über eine oberflächliche Analogie hinaus haben beweistheoretische Techniken und Renormalisationsverfahren ein gemeinsames Ziel: die Ausschaltung von Unendlichkeiten in einer konsistenten Theorie. Die Geschichte der Renormalisation in Quantenfeldtheorien wird kurz skizziert und eine allgemeine These über die Natur und Justizfizierung von Theorien in der mathematischen Physik vorgeschlagen. Wir schließen mit den Grundlinien für ein Forschungsprogramm für eine physikalische Logik.

The primary aim is the reconstruction of the main argument of the second chapter of Anselm’s Proslogion. To be proved is the statement that God, or something than which nothing greater can be thought, exists in reality. I proceed by a piecemeal analysis of every sentence of the Latin original and its subsequent translation into a formal second-order language with choice operator. Reconstructing Anselm’s reasoning demands interpretative input and additions. For example, the formula ‘quod maius est’ has to be (...) suitably interpreted and expanded. Furthermore, I try to explicate Anselm’s maius predicate in terms of a perfection predicate and to develop a general proof for Anselm’s theorem, i.e. the statement that something/that than which something greater cannot be thought has all greater-making attributes. (shrink)

In this paper, I will present a puzzle for logical analyses, such as Russell’s analysis of definite descriptions and Recanati’s analysis of ‘that’-clauses. I will argue that together with Kripke’s disquotational principles connecting sincere assent and belief such non-trivial logical analyses lead to contradictions. Following this, I will compare the puzzle about logical analysis with Frege’s puzzle about belief ascriptions. We will see that although the two puzzles do have similarities, the solutions to Frege’s (...) puzzle cannot be applied mutatis mutandis to the puzzle about logical analysis. Hence, to say it with Kripke, the main thesis of this paper is that the puzzle is a puzzle. A complete solution to the puzzle promises a better understanding of both logical analyses and belief ascriptions. (shrink)

Anselm of Cantorbery wrote Proslogion, where is formulated the famous ‘Unum argumentum’ about the existence of God. This argument was been disputed and criticized by numerous logicians from an extensional view point. The classical predicate logic is not able to give a formal frame to develop an adequate analysis of this argument. According to us, this argument is not an ontological proof; it analyses the meaning of the “quo nihil maius cogitari posit”, a characterization of God, and establish, by (...) absurd, that “quod non posit cogitare non esse” by using the hypothesis: “to think in re” is taller than “to think in solo intelectu”. We discuss this relation and the difference between the meanings of the elementary predicates ‘to be in re’, ‘to be in intellectu’ and ‘to be in solo intellectu’. We propose a new logical approach of this ‘Unum argumentum’ of Anselm by using Curry’s Combinatory Logic. Indeed, Combinatory Logic is an abstract applicative formalism of operators applied to operands; in this formalism, the predicates, viewed as specific operators, can be composed and can be transformed, by an intrinsic way, into more complex predicates, by means of abstract operators, called “combinators”, studied by Combinatory Logic. We show that this formalism is a logical frame where it becomes possible to discuss and to formulate cognitive representations of the meanings of predicates used inside of the ‘Unum argumentum’ and to explain how the argument runs. (shrink)

This article proposes the use of temporal logic for an analysis of instrumentality inspired by the work of G.H. von Wright. The first part of the article contains the philosophical foundations. We discuss von Wright’s general theory of agency and his account of instrumentality. Moreover, we propose several refinements to this framework via rigorous definitions of the core notions involved. In the second part, we develop a logical system called Temporal Logic of Action and Expectations (TLAE). The logic (...) is inspired by a fragment of propositional dynamic logic based on indeterministic time. The system is proven to be weakly complete relative to its given semantics. We then employ TLAE to formalise and analyse the instrumentality relations defined in the first part of the paper. Last, we point out philosophical implications and possible extensions of our work. (shrink)

Hintikka and Sandu’s independence-friendly logic is a conservative extension of first-order logic that allows one to consider semantic games with imperfect information. In the present article, we first show how several variants of the Monty Hall problem can be modeled as semantic games for IF sentences. In the process, we extend IF logic to include semantic games with chance moves and dub this extension stochastic IF logic. Finally, we use stochastic IF logic to analyze the Sleeping Beauty problem, leading to (...) the conclusion that the thirders are correct while identifying the main error in the halfers’ argument. (shrink)

Any philosophical method that treats the analysis of the meaning of a sentence or expression in terms of a decomposition into a set of conceptually basic constituent parts must do some theoretical work to explain the puzzles of intensionality. This is because intensional phenomena appear to violate the principle of compositionality, and the assumption of compositionality is the principal justification for thinking that an analysis will reveal the real semantical import of a sentence or expression through a method (...) of decomposition. Accordingly, a natural strategy for dealing with intensionality is to argue that it is really just an isolable, aberrant class of linguistic phenomena that poses no general threat to the thesis that meaning is basically compositional. On the other hand, the later Mohists give us good reason to reject this view. What we learn from them is that there may be basic limitations in any analytical technique that presupposes that meaning is perspicuously represented only when it has been fully decomposed into its constituent parts. The purpose of this paper is to (a) explain why the Mohists found the issue of intensionality to be so important in their investigations of language, and (b) defend the view that Mohist insights reveal basic limitations in any technique of analysis that is uncritically applied with a decompositional approach in mind, as are those that are often pursued in the West in the context of more general epistemological and metaphysical programs. (shrink)

The mind-body problem is—despite appearances—still the inevitable basic issue of unending discussions in recent philosophy. Various types of epistemologies and metaphysics, European and American, have offered their widely divergent “solutions” of the dreaded Cartesian tangle. Is there any hope of reaching a universally acceptable view?

The aim of this paper will be to show how significant the logical theories of judgement which were worked out at the end of the nineteenth century have been for the ontological thought during the twentieth century. Against the classical - Aristotelian and Scholastic - analysis of predicative judgement, Franz Brentano on one hand and Gottlob Frege on the other hand have leveled two different criticisms, which then generated two radically divergent ontological paradigms. On one side, despite Brentano’s (...) own nominalistic stands, there was a tremendous extension of the general category of “object” as well as of the notion of “being” with, as a consequence, the exceptionnally luxuriant ontologies of Brentano’s heirs. On the other side, notwithstanding Frege’s own Platonistic affinities, there was a drastic deflation of the realm of objects to the benefit of the realm of concepts taken as classifying functions, and therefore a strong nominalistic trend among Frege’s heirs. The development of quantified modal logics at the middle of twentieth century however forced contemporary ontology to reconsider this simple alternative in order to give place to some hybrid entities such as individual concepts or other kinds of “intensional objects”. (shrink)

There are two kinds of logical errors. Either you use a non-valid scheme of an argument or your analysis of the premises is mistaken. No extensional or intensional theory can solve the following problem connected with analyzing NL expressions: The Leibniz principle of substituting identical for identical contains the condition a = b. Extensional as well as intensional systems (at least if intensions are defined as functions from possible worlds) analyzing this condition as formulated in natural language are (...) happy if a is contingently or logically or analytically equivalent with b, while this may be insufficient for applying Leibniz. Examples are adduced that show the absurdity of applying Leibniz in such cases. A following remedy is thinkable: one could try to formulate some axioms or perhaps meta-formulated rules that would eliminate the critical cases. This would mean however that a new theory came into being just to shield us from incorrectly applying Leibniz rule. Instead a procedural analysis of NL expressions is offered that makes it possible to unambiguously determine their sense and so their denotation in such a way that the above mentioned critical cases cannot set in. It is shown that the hyperintensional system defined by Transparent intensional logic is able to generally solve the main problems connected with using NL expressions. (shrink)

Excerpt from Primer of Logical Analysis: For the Use of Composition Students To be sure, then, that we understand a sentence, we must be able to say, when any new and equally well-understood sentence is put beside the first, whether the new sentence is in meaning equivalent to the first, or consistent with the first, or deducible from the first, or opposed to the first. Yet other questions may be asked about the relative force of two sentences; but (...) these are enough for the present. Let us explain what we mean by them. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

In this paper, we analyze the relationship between commitment and obligation from a logical viewpoint. The principle of commitment implying obligation is proven in a specific logic of action preference which is a generalization of Meyer 's dynamic deontic logic. In the proposed formalism, an agent's commitment to goals is considered as a special kind of action which can change one's deontic preference andone's obligation to take some action is based on the preference and the effects of the action. (...) In this logic, it is shown that an agent has the obligation to take any action which is necessary for achieving as many committed goals as possible. The semantics of our logic is based on the possible world models for the dynamic logic of actions. A binary preference relation between possible worlds is associated with the model. Then the preference between actions are determined by comparing that of their consequences. According to the semantics, while the preference will influence the agent's choice of action, commitment is a kind of action that will change the agent's preference. Thus we can show how obligations arise from commitments via updating of deontic preference. The integrated semantics make it possible to express and reason about the mutual relationship among these mental attitudes in a common logic. (shrink)

The present attempt to indicate the general manner in which the kinship system of a people can be stated as an interpreted axiomatic system, with utilization of the symbolism of modern mathematical logic, is intended as a demonstration of the applicability of contemporary logical methods to problems in the social sciences. Aside from the obvious general advantages in the way of clarity and logical rigour to be gained by an application of axiomatic method, there emerges as by-products a (...) convenient system of kinship symbolization and what is believed to be a solution to the long-standing controversy concerning the use of the terms ‘descriptive’ and ‘classificatory’ in reference to kinship systems. Since kinship terms are words in languages, the present exposition is perhaps of interest in that it shows how meaning in a semantic field of related terms can be defined by logical methods. So all the directional or temporal terms in a specific language might be treated as kinship terms are here. The possibility of a systematic treatment of the semantic aspects of linguistics which so far have resisted this type of treatment should be of interest to linguists. (shrink)

We analyse the behaviour of definite descriptions and proper names terms in mathematical logic. We show that in formal arithmetic, wether some axioms are fixed or not, proper names cannot be considered rigid designators and have the same behaviour as definite descriptions. In set theory, sometimes two names for the same object are introduced. It seems that this can be explained by the notion of meaning. The meaning of such proper names can be considered as fuzzy sets of equivalent co-designative (...) definite descriptions and their references as sets of all equivalent co-designative definite descriptions. (shrink)

This is an anthology in which all but one of the essays have been previously published. Western religious thought has made use of, or appropriated, or remained in dialogue with every major philosophical development from Platonism to Marxism. One of the latest versions of such appropriation, discovered as many would think in a most unlikely place, is the appropriation of analytic philosophy. A new natural theology is abroad in the land, and this volume attempts quite successfully to capture its current (...) state. If Flew and MacIntyre offered the first version of this dialogue and found analytic philosophy detrimental to western theism, this volume recognizes that more recent analytic philosophy has offered a second version and discovered analytic methodology as supportive of theistic philosophical persuasions. Essays by Ross, Rowe, Swinburne and Horsburgh consider the contribution of modal logic. Other essays by Alston, Bennett, and Hick, discuss the divine nature. Language and religion is developed by Ross, Pike, Plantinga, Rowe, Kenny, Mavrodes, Savage, and Donnelly. Miracle language is investigated by Holland and Dietl, while Gill discusses verification, and Chisholm the self. Although one may regret that some writers, Geach or Phillips, for example, are not included, it is time to recognize that natural theology has revived in our day by means of analytic philosophy, and this collection is an early and very successful reminder, as well as functioning as a good text for courses in the latest in philosophical theology on the Anglo-Saxon scene.—H. A. D. (shrink)

심리적 쾌락의 반대개념은 무엇인가? 대부분의 사람들은 ‘고통’이라고 대답한다. 그러나 고통이 아니라 불쾌(不快)와 무쾌(無快)가 심리적 쾌락의 반대개념임을 논증하는 것이 본 논문의 목적이다. 이를 위하여 필자는 양극대립이라는 논리적 관계와 쾌락에 무관심한 심리적 상태에 주목한다. 불쾌는 쾌락의 양극대립자이다. 쾌락에 무관심한 심리적 상태인 무쾌는 쾌락의 중립적 대립자이다. 무쾌는 쾌락과 불쾌 사이의 진정한, 그리고 자연적인 경계이다. 무쾌는 독특한 방법으로 쾌락과 불쾌 둘 다에 관련되는 공간을 분할한다. 심리적 사건을 구성하고 있는 것은 유쾌한 사건이거나 불쾌한 사건 둘 중의 어느 하나이지만, 쾌락과 불쾌를 구성요소로 하여 생기는 사건은 무쾌일 (...) 수도 있다. 유쾌하지도 않고 불쾌하지도 않다는 의미에서가 아니라 불쾌함과 마찬가지로 유쾌함도 포함한다는 의미에서 그렇다. 극과 극의 방식으로 쾌-불쾌 공간을 조직하는 것은 독특한 중심점의 존재이다. 쾌락과 불쾌의 대립을 이해하는 데 무쾌가 결정적으로 중요한 이유가 바로 여기에 있다. (shrink)

"Testability and Meaning" is one of Carnap's best-known works. It has been usually seen as one of the main sources of the received view of the philosophy of science, and it is normally read in the hght of the tradition it originated. Nevertheless, this reading detaches the text from the philosophical project to which it belongs. This paper aims to situate Camap's article in its proper philosophical place, which is found in the programme initiated in the Logische Syntax, a programme (...) which essentially remained alive throughout the rest of Camap's career. The paper shows how this view opens up a natural way of understanding Carnap's important article in a different light, more interesting and coherent. (shrink)

In theology, by W.L. Rowe.--Divine foreknowledge and human freedom, by A. Kenny.--Some puzzles concerning omnipotence, by G.I. Mavrodes.--The paradox of the stone, by C.W. Savage.--Creation ex nihilo, by J. Donnelly.--The miraculous, by R.F. Holland.--On miracles, by P.J. Dietl.--The tacit structure of religious knowing, by J.H. Gill.--On the observability of the self, by R.M. Chisholm.--Re-examining Kierkegaard's "Teleological suspension of the ethical," by J. Donnelly.