Logic in Buddhist Philosophy concerns the systematic study of anumāna (often translated as inference) as developed by Dignāga (480-540 c.e.) and Dharmakīti (600-660 c.e.). Buddhist logicians think of inference as an instrument of knowledge (pramāṇa) and, thus, logic is considered to constitute part of epistemology in the Buddhist tradition. According to the prevalent 20th and early 21st century ‘Western’ conception of logic, however, logical study is the formal study of arguments. If we understand the nature of (...) logic to be formal, it is difficult to see what bearing logic has on knowledge. In this paper, by weaving together the main threads of thought that are salient in Dignāga’s and Dharmakīti’s texts, I shall re-conceive the nature of logic in the context of epistemology and demarcate the logical part of epistemology which can be recognised as logic. I shall demonstrate that we can recognise the logical significance of inference as understood by Buddhist logicians despite the fact that its logical significance lies within the context of knowledge. (shrink)

This essay discusses Wittgenstein's conception of logic, early and late, and some of the types of logical system that he constructed. The essay shows that the common view according to which Wittgenstein had stopped engaging in logic as a philosophical discipline by the time of writing Philosophical Investigations is mistaken. It is argued that, on the contrary, logic continued to figure at the very heart of later Wittgenstein's philosophy; and that Wittgenstein's mature philosophy of (...) class='Hi'>logic contains many interesting thoughts that have gone widely unnoticed. (shrink)

In this historical article, Newton da Costa discusses Francisco Miró Quesada’s philosophical ideas about logic. He discusses the topics of reason, logic, and action in Miró Quesada’s work, and in the final section he offers his critical view. In particular, he disagrees with Miró Quesada’s stance on the historicity of reason, for whom “reason is essentially absolute”, whereas for da Costa it “is being constructed in the course of history”. Da Costa concludes by emphasizing the importance of Miró (...) Quesada’s theory of logic and reason, despite it still being incomplete. -/- Historical article by Newton da Costa, annotated and translated by J. C. Cifuentes and L. F. Bartolo Alegre. (shrink)

Putnam, Hilary FPhilosophy of logic. Harper Essays in Philosophy. Harper Torchbooks, No. TB 1544. Harper & Row, Publishers, New York-London, 1971. v+76 pp. The author of this book has made highly regarded contributions to mathematics, to philosophy of logic and to philosophy of science, and in this book he brings his ideas in these three areas to bear on the traditional philosophic problem of materialism versus (objective) idealism. The book assumes that contemporary science (mathematical and (...) physical) is largely correct as far as it goes, or at least that it is rational to believe in it. The main thesis of the book is that consistent acceptance of contemporary science requires the acceptance of some sort of Platonistic idealism affirming the existence of abstract, non-temporal, non-material, non-mental entities (numbers,scientific laws, mathematical formulas, etc.). The author is thus in direct opposition to the extreme materialism which had dominated philosophy of science in the first three quarters of this century. the book can be especially recommended to the scientifically literate, general reader whose acquaintance with these areas is limited to the earlier literature of when it had been assumed that empiricistic materialism was the only philosophy compatible with a scientific outlook. To this group the book presents an eye-opening challenge fulfilling the author’s intention of “shaking up preconceptions and stimulating further discussion”. (shrink)

Philosophers of logic are particularly interested in understanding the aims, epistemology, and methodology of logic. This raises the question of how the philosophy of logic should go about these enquires. According to the practice-based approach, the most reliable method we have to investigate the methodology and epistemology of a research field is by considering in detail the activities of its practitioners. This holds just as true for logic as it does for the recognised empirical and (...) abstract sciences. If we wish to systematically understand the aims and epistemology of logic, we are best placed achieving this by looking at what logicians do, rather than reflecting upon the nature of logic itself. In this entry, we outline the motivations for a practice-based approach towards the philosophy of logic and highlight its advantages over more “top-down” approaches, which attempt to infer conclusions about the nature of logic and its methodology on the basis of traditional assumptions about knowledge, metaphysics, or logic itself. We end by addressing several prominent concerns raised against the practice-based approach. (shrink)

This article discusses the relation between the early Wittgenstein’s and Carnap’s philosophies of logic, arguing that Carnap’s position in The Logical Syntax of Language is in certain respects much closer to the Tractatus than has been recognized. In Carnapian terms, the Tractatus’ goal is to introduce, by means of quasi-syntactical sentences, syntactical principles and concepts to be used in philosophical clarification in the formal mode. A distinction between the material and formal mode is therefore already part of the Tractatus’ (...) view, and its method for introducing syntactical concepts and principles should be entirely acceptable for Carnap by his own criteria. Moreover, despite the Tractatus’ rejection of syntactical statements, there is an important correspondence between Wittgenstein’s saying-showing distinction and Carnap’s object-language-syntax-language distinction: both constitute a distinction between logico-syntactical determinations concerning language and language as determined or described by those determinations. Wittgenstein’s distinction therefore constitutes a precursor of the object-language syntax-language distinction which the latter in a certain sense affirms, rather than simply contradicting it. The saying-showing distinction agrees with Carnap’s position also in marking logic as something that isn’t true/false about either language or reality, which is a conception that underlies Carnap’s principle of tolerance. (shrink)

I take advantage of two recent results: 1) the recognition of an alternative theoretical organization to the deductive-axiomatic one; it is characterized by a sequence of four logical steps belonging to intuitionist logic; 2) the recognition of the logical content of Cusanus’ philosophical works; also this content pertains to intuitionist logic, which Cusanus anticipated by even identifying some its logical laws. Many Cusanus’ books present the alternative theoretical organization; whose yet he did not apply in a clear way (...) its last two steps, the ad absurdum arguing and the application of the principle of sufficient reason. For this reason in the last books his thinking transcended to a metaphysical level. Hegel’s philosophy of logic shares Cusanus’ philosophical effort for exiting out classical logic. He seems to have assumed Cusanus’ anticipation of the new theoretical organization; all goes as if Hegel wanted to improve Cusanus’ poor method, by introducing a process of additions of two negations which however does not agree with the intuitionist logic. Moreover, Hegel presupposes, like Cusanus in his last years, the free application of the principle of sufficient reason to the entire subject of his philosophy of logic without awareness of the logical constraints to which is subject a correct application of this principle; hence, he introduced a metaphysical arguing which according to modern mathematical logic has no consistent content. Also Hegel’s supposed prolongation of Cusanus’ logical discoveries was an essentially metaphysical view. (shrink)

Tarski "proved" that there cannot possibly be any correct formalization of the notion of truth entirely on the basis of an insufficiently expressive formal system that was incapable of recognizing and rejecting semantically incorrect expressions of language. -/- The only thing required to eliminate incompleteness, undecidability and inconsistency from formal systems is transforming the formal proofs of symbolic logic to use the sound deductive inference model.

P.F. Strawson contributed to many philosophical domains, including the philosophy of language, the history of philosophy, metaphysics, moral philosophy and philosophical methodology. Most of his contributions in these areas have influenced contemporary debates, either because his views are still defended or because they are still considered worthy of detailed responses. His views on the philosophy of logic have been only rarely discussed, however. My aim in this paper is threefold. First, I provide a systematic account (...) of Strawson’s philosophy of logic. I argue that Strawson is an important predecessor of logical expressivism, a contemporary position in the philosophy of logic most notably defended by Robert Brandom. My main focus is on Strawson’s largely-neglected 1982 paper ‘Logical Form and Logical Constants’, which contains his most mature ideas on the topic. Second, while Strawson’s position is of historical and independent philosophical interest, I argue that he leaves many points unclear. Finally, I propose several clarifications of Strawson’s position. (shrink)

C. I. Lewis (I883-I964) was the first major figure in history and philosophy of logic—-a field that has come to be recognized as a separate specialty after years of work by Ivor Grattan-Guinness and others (Dawson 2003, 257).Lewis was among the earliest to accept the challenges offered by this field; he was the first who had the philosophical and mathematical talent, the philosophical, logical, and historical background, and the patience and dedication to objectivity needed to excel. He was (...) blessed with many fortunate circumstances, not least of which was entering the field when mathematical logic, after only six decades of toil, had just reaped one of its most important harvests with publication of the monumental Principia Mathematica. It was a time of joyful optimism which demanded an historical account and a sober philosophical critique. Lewis was one of the first to apply to mathematical logic the Aristotelian dictum that we do not understand a living institution until we see it growing from its birth. (shrink)

I outline the theoretical framework of, and three research programs within American speculative philosophy of science during the period 1900-1931. One program applies verificationism to research in psychology, one investigates the methodology of research programs, and one analyses scientific explanation and other scientific concepts. The primary sources for my outline are works by Morris Raphael Cohen, Grace Andrus de Laguna, Theodore de Laguna, Edgar Arthur Singer Jr., Harold Robert Smart, and Marie Collins Swabey. I also use my outline to (...) provide a partial comparison of American speculative philosophy of science and 1930s logical positivism. My comparison suggests that logical positivism was a proposal for substantially narrowing down and winding back American philosophy of science and was based on positions that were already problematized in the American context. -/- . (shrink)

Gila Sher interviewed by Chen Bo: -/- I. Academic Background and Earlier Research: 1. Sher’s early years. 2. Intellectual influence: Kant, Quine, and Tarski. 3. Origin and main Ideas of The Bounds of Logic. 4. Branching quantifiers and IF logic. 5. Preparation for the next step. -/- II. Foundational Holism and a Post-Quinean Model of Knowledge: 1. General characterization of foundational holism. 2. Circularity, infinite regress, and philosophical arguments. 3. Comparing foundational holism and foundherentism. 4. A post-Quinean model (...) of knowledge. 5. Intellect and figuring out. 6. Comparing foundational holism with Quine’s holism. 7. Evaluation of Quine’s Philosophy -/- III. Substantive Theory of Truth and Relevant Issues: 1. Outline of Sher’s substantive theory of truth. 2. Criticism of deflationism and treatment of the Liar. 3. Comparing Sher’s substantive theory of truth with Tarski’s theory of truth. -/- IV. A New Philosophy of Logic and Comparison with Other Theories: 1. Foundational account of logic. 2. Standard of logicality, set theory and logic. 3. Psychologism, Hanna’s and Maddy’s conceptions of logic. 4. Quine’s theses about the revisability of logic. -/- V. Epilogue. (shrink)

It is often said that ‘every logical truth is obvious’ (Quine 1970: 82), that the ‘axioms and rules of logic are true in an obvious way’ (Murawski 2014: 87), or that ‘logic is a theory of the obvious’ (Sher 1999: 207). In this chapter, I set out to test empirically how the idea that logic is obvious is reflected in the scholarly work of logicians and philosophers of logic. My approach is data-driven. That is to say, (...) I propose that systematically searching for patterns of usage in databases of scholarly works, such as JSTOR, can provide new insights into the ways in which the idea that logic is obvious is reflected in logical and philosophical practice, i.e., in the arguments that logicians and philosophers of logic actually make in their published work. (shrink)

Review of Russell’s Philosophy of Logical Atomism 1897–1905, by Jolen Galaugher (Palgrave Macmillan 2013).

This book is best regarded as a concise essay developing the personal views of a major philosopher of logic and as such it is to be welcomed by scholars in the field. It is not (and does not purport to be) a treatment of a significant portion of those philosophical problems generally thought to be germane to logic. It would be easy to list many popular topics in philosophy of logic which it does not mention. Even (...) its "definition" of logic-"the systematic study of logical truth"-is peculiar to the author and would be regarded as inappropriately restrictive by many logicians There are several standard ways of defining truth using sequences. Quine’s discussions in the 1970 first printing of Philosophy of logic and in previous lectures were vitiated by mixing two. Quine’s logical Two-Method Error, which eluded Quine’s colleagues, was corrected in the 1978 sixth printing. But Quine never explicitly acknowledged, described, or even mentioned the error in print although in correspondence he did thank Corcoran for bringing it to his attention. In regard to style one may note that the book is rich in metaphorical and sometimes even cryptic passages one of the more remarkable of which occurs in the Preface and seems to imply that deductive logic does not warrant distinctive philosophical treatment. Moreover, the author's sesquipedalian performances sometimes subvert perspicuity. (shrink)

This chapter focuses on alternative logics. It discusses a hierarchy of logical reform. It presents case studies that illustrate particular aspects of the logical revisionism discussed in the chapter. The first case study is of intuitionistic logic. The second case study turns to quantum logic, a system proposed on empirical grounds as a resolution of the antinomies of quantum mechanics. The third case study is concerned with systems of relevance logic, which have been the subject of an (...) especially detailed reform program. Finally, the fourth case study is paraconsistent logic, perhaps the most controversial of serious proposals. (shrink)

This paper contributes to explaining the rise of logical empiricism in mid-twentieth century (North) America and to a better understanding of American philosophy of science before the dominance of logical empiricism. We show that, contrary to a number of existing histories, philosophy of science was already a distinct subfield of philosophy, one with its own approaches and issues, even before logical empiricists arrived in America. It was a form of speculative philosophy with a concern for speculative (...) metaphysics, normative issues relating to science and society and issues which later were associated with logical empiricist philosophy of science, issues such as confirmation, scientific explanation, reductionism and laws of nature. Further, philosophy of science was not primarily pragmatist in orientation. We also show, with the help of our historical characterization, that a recent account of the emergence of analytic philosophy applies to the rise of logical empiricism. It has been argued that the emergence of American analytic philosophy is partly explained by analytic philosophers’ use of key institutions, including of journals, to marginalize speculative philosophy and promote analytic philosophy. We argue that this use of institutions included the marginalization of speculative and value-laden philosophy of science and the promotion of logical empiricism. (shrink)

PUTNAM has made highly regarded contributions to mathematics, to philosophy of logic and to philosophy of science, and in this book he brings his ideas in these three areas to bear on the traditional philosophic problem of materialism versus (objective) idealism. The book assumes that contemporary science (mathematical and physical) is largely correct as far as it goes, or at least that it is rational to believe in it. The main thesis of the book is that consistent (...) acceptance of contemporary science requires the acceptance of some sort of Platonistic idealism affirming the existence of abstract, non-temporal, non-material, non-mental entities (numbers, scientific laws, mathematical formulas, etc.). The author is thus in direct opposition to the extreme materialism which had dominated philosophy of science in the first three quarters of this century. The book can be recommended to the scientifically literate, general reader whose acquaintance with these areas is limited to the literature of the 1950’s and before, when it had been assumed that empiricistic materialism was the only philosophy compatible with a scientific outlook. To this group the book presents an eye-opening challenge fulfilling the author’s intention of “shaking up preconceptions and stimulating further discussion”. QUINE’S book is not easy to read, partly because the level of sophistication fluctuates at high frequency between remote extremes and partly because of convoluted English prose style and devilish terminology. Almost all of the minor but troublesome technical errata in the first printing have been corrected [see reviews, e.g., the reviewer, Philos. Sci. 39 (1972), no. 1, 97–99]. In the opinion of the reviewer the book is not suitable for undergraduate instruction, and without external motivation few mathematicians are likely to have the patience to appreciate it. Nevertheless, a careful study of the book will more than repay the effort and one should expect to find frequent references to this book in coming years. (shrink)

The Berlin Group for scientific philosophy was active between 1928 and 1933 and was closely related to the Vienna Circle. In 1930, the leaders of the two Groups, Hans Reichenbach and Rudolf Carnap, launched the journal Erkenntnis. However, between the Berlin Group and the Vienna Circle, there was not only close relatedness but also significant difference. Above all, while the Berlin Group explored philosophical problems of the actual practice of science, the Vienna Circle, closely following Wittgenstein, was more interested (...) in problems of the language of science. The book includes first discussion ever (in three chapters) on Walter Dubislav’s logic and philosophy. Two chapters are devoted to another author scarcely explored in English, Kurt Grelling, and another one to Paul Oppenheim who became an important figure in the philosophy of science in the USA in the 1940s–1960s. Finally, the book discusses the precursor of the Nord-German tradition of scientific philosophy, Jacob Friedrich Fries. Mehr anzeigen Weniger anzeigen . (shrink)

Philosophy of biology is often said to have emerged in the last third of the twentieth century. Prior to this time, it has been alleged that the only authors who engaged philosophically with the life sciences were either logical empiricists who sought to impose the explanatory ideals of the physical sciences onto biology, or vitalists who invoked mystical agencies in an attempt to ward off the threat of physicochemical reduction. These schools paid little attention to actual biological science, and (...) as a result philosophy of biology languished in a state of futility for much of the twentieth century. The situation, we are told, only began to change in the late 1960s and early 1970s, when a new generation of researchers began to focus on problems internal to biology, leading to the consolidation of the discipline. In this paper we challenge this widely accepted narrative of the history of philosophy of biology. We do so by arguing that the most important tradition within early twentieth-century philosophy of biology was neither logical empiricism nor vitalism, but the organicist movement that flourished between the First and Second World Wars. We show that the organicist corpus is thematically and methodologically continuous with the contemporary literature in order to discredit the view that early work in the philosophy of biology was unproductive, and we emphasize the desirability of integrating the historical and contemporary conversations into a single, unified discourse. (shrink)

In this inaugural lecture I offer, against the background of a discussion of knowledge representation and its tools, an overview of my research in the philosophy of science. I defend a relational model-theoretic realism as being the appropriate meta-stance most congruent with the model-theoretic view of science as a form of human engagement with the world. Making use of logics with preferential semantics within a model-theoretic paradigm, I give an account of science as process and product. I demonstrate the (...) power of the full-blown employment of this paradigm in the philosophy of science by discussing the main applications of model-theoretic realism to traditional problems in the philosophy of science. I discuss my views of the nature of logic and of its role in the philosophy of science today. I also specifically offer a brief discussion on the future of cognitive philosophy in South Africa. My conclusion is a general look at the nature of philosophical inquiry and its significance for philosophers today. South African Journal of Philosophy Vol. 25 (4) 2006: pp. 275-289. (shrink)

My analysis here is an attempt to bring out the main through-line in the development of Bulgarian philosophy of law today. A proper account of Bulgarian philosophy of law in the 20th century requires an attempt to find, on the one hand, a solution to epistemological and methodological problems in law and, on the other, a clear-cut influence of the Kantian critical tradition. Bulgarian philosophy of law follows a complicated path, ranging from acceptance and revision of Kantian (...) philosophy to the development of interesting theories on the logic of legal reasoning. (shrink)

This paper introduces the special issue on Logic and Philosophy of Religion of the journal Sophia: International Journal of Philosophy and Traditions (Springer). The issue contains the following articles: Logic and Philosophy of Religion, by Ricardo Sousa Silvestre and Jean-Yvez Béziau; The End of Eternity, by Jamie Carlin Watson; The Vagueness of the Muse—The Logic of Peirce’s Humble Argument for the Reality of God, by Cassiano Terra Rodrigues; Misunderstanding the Talk(s) of the Divine: Theodicy (...) in the Wittgensteinian Tradition, by Ondřej Beran; On the Concept of Theodicy, by Ricardo Sousa Silvestre; The Logical Problem of the Trinity and the Strong Theory of Relative Identity, by Daniel Molto; Thomas Aquinas on Logic, Being, and Power, and Contemporary Problems for Divine Omnipotence, by Errin D. Clark. -/- . (shrink)

The received view in the history of the philosophy of psychology is that the logical positivists—Carnap and Hempel in particular—endorsed the position commonly known as “logical” or “analytical” behaviourism, according to which the relations between psychological statements and the physical-behavioural statements intended to give their meaning are analytic and knowable a priori. This chapter argues that this is sheer legend: most, if not all, such relations were viewed by the logical positivists as synthetic and knowable only a posteriori. It (...) then traces the origins of the legend to the logical positivists’ idiosyncratic extensional or at best weakly intensional use of what are now considered crucially strongly intensional semantic notions, such as “translation,” “meaning” and their cognates, focussing on a particular instance of this latter phenomenon, arguing that a conflation of explicit definition and analyticity may be the chief source of the legend. (shrink)

The title of the present paper might arouse some curiosity among the minds of the readers. The very first question that arises in this respect is whether India produced any logic in the real sense of the term as has been used in the West. This paper is centered only on the three systems of Indian philosophy namely Nyāya, Buddhism and Jainism. We have been talking of Indian philosophy, Indian religion, Indian culture and Indian spirituality, but not (...) that which are of more fundamental concepts for any branch of knowledge whether it is social sciences or humanities. No aspect of human life and the universe has been left unexamined by Indian philosophers, and this leads to a totality of vision in both philosophical and psychological fields. In this paper we will discuss the main thinkers, sources and main concepts related to Indian Logic. (shrink)

Logic diagrams have seen a resurgence in their application in a range of fields, including logic, biology, media science, computer science and philosophy. Consequently, understanding the history and philosophy of these diagrams has become crucial. As many current diagrammatic systems in logic are based on ideas that originated in the 18th and 19th centuries, it is important to consider what motivated the use of logic diagrams in the past and whether these reasons are still (...) valid today. This paper proposes that transcendental philosophy was a key inspiration for the development of logic diagrams and that such diagrams can be employed in transcendental arguments, even after the linguistic turn. (shrink)

Relevant logics are a family of non-classical logics characterized by the behavior of their implication connectives. Unlike some other non-classical logics, such as intuitionistic logic, there are multiple philosophical views motivating relevant logics. Further, different views seem to motivate different logics. In this article, we survey five major views motivating the adoption of relevant logics: Use Criterion, sufficiency, meaning containment, theory construction, and truthmaking. We highlight the philosophical differences as well as the different logics they support. We end with (...) some questions for future research. (shrink)

Broadly speaking, two views of modernity are prevalent in contemporary debates. According to the first view, i.e. “modernization theory,” there is one single form of modernity, which is tantamount to liberal, capitalist modernity. The West has already and fully achieved modernity; non-Western societies have lagged behind and must simply catch up with the West. In contrast, according to the second view, “post-colonial theory,” there is no such thing as modernity. What the West erroneously calls “modernity” is nothing but a highly (...) parochial way of thought, and of economic and political organization, that developed by accident first in the West and then by the exercise of military violence or economic power was subsequently “universalized.” In this chapter, I argue that Hegel, read properly, provides a third conception of modernity, one which, contrary to the modernization theory, respects differences between societies, and yet, contrary to post-colonial theory, does not engage in dividing the human species into fundamentally different or incommensurate groups. I argue that Hegel’s theory of modernity must be sought at the conjunction of the Science of Logic (specifically the logic of the Concept) and the Philosophy of Right. I then elaborate on Hegel’s theory of modernity, thus construed. (shrink)

Abu Nasr Muhammad Al-Farabi (870–950 AD), the second outstanding representative of the Muslim peripatetic after al Kindi (801–873 AD), was born in Turkestan about 870 AD. Al-Farabi’s studies commenced in Farab, then he travelled to Baghdad, where he studied logic with a Christian scholar named Yuhanna b. Hailan. Al-Farabi wrote numerous works dealing with almost every branch of science in the medieval world. In addition to a large number of books on logic and other sciences, he came to (...) be known as the “Second Teacher” (al-Mou’allim al-Thani), Aristotle being the first. One of Al-Farabi’s most important contributions was clarifying the func- tions of logic as follows: 1. He defined logic and compared it with grammar, and discussed the clas- sification and fundamental principles of science in a unique and useful manner. 2. He made the study of logic easier by dividing it into two categories: Takhayyul (idea) and Thubut (proof). 3. He believed that the objective of logic is to correct faults we may find in ourselves and in others, and faults that others find in us. 4. He said that if we do not comprehend logic, we must either have faith in all people, or mistrust all people, or differentiate between them. Such actions would be undertaken without a basis of evidence or experimen- tation. In this paper, I will analyse the functions of logic in Al-Farabi’s works, Enumeration of the Sciences, Book on the Syllogism, Book on Dialectic, Book on Demonstration and Ring Stones of Wisdom, in order to present his contributions in the field of logic. (shrink)

In his book The Boundary Stones of Thought, Ian Rumfitt considers five arguments in favour of intuitionistic logic over classical logic. Two of these arguments are based on reflections concerning the meaning of statements in general, due to Michael Dummett and John McDowell. The remaining three are more specific, concerning statements about the infinite and the infinitesimal, statements involving vague terms, and statements about sets.Rumfitt is sympathetic to the premisses of many of these arguments, and takes some of (...) them to be effective challenges to Bivalence, the following principle: Each statement is either true or false.However, he argues that counterexamples to Bivalence do not immediately lead to counterexamples to Excluded Middle, and so do not immediately refute classical logic; here, Excluded Middle is taken to be the following principle: For each statement A, is true.Much... (shrink)

CORCORAN RECOMMENDS COCCHIARELLA ON TYPE THEORY. The 1983 review in Mathematical Reviews 83e:03005 of: Cocchiarella, Nino “The development of the theory of logical types and the notion of a logical subject in Russell's early philosophy: Bertrand Russell's early philosophy, Part I”. Synthese 45 (1980), no. 1, 71-115 .

This paper demonstrates that Edmund Husserl’s frequently overlooked 1890 manuscript, “On the Logic of Signs,” when closely investigated, reveals itself to be the hermeneutical touchstone for his seminal 1891 Philosophy of Arithmetic. As the former comprises Husserl’s earliest attempt to account for all of the different kinds of signitive experience, his conclusions there can be directly applied to the latter, which is focused on one particular type of sign; namely, number signs. Husserl’s 1890 descriptions of motivating and replacing (...) signs will be respectively employed to clarify his 1891 understanding of the authentic and inauthentic presentations of numbers via number signs. Moreover, his schematic classification of replacement-signs in Semiotic will illuminate the reasons why he believed the number system to be necessary for the operation of replacing number signs. (shrink)

This paper deals with the study of the nature of mind, its processes and its relations with the other filed known as logic, especially the contribution of most notable contemporary analytical philosophy Ludwig Wittgenstein. Wittgenstein showed a critical relation between the mind and logic. He assumed that every mental process is logical. Mental field is field of space and time and logical field is a field of reasoning (inductive and deductive). It is only with the advancement in (...) logic, we are today in the era of scientific progress and technology. Logic played an important role in the cognitive part or we can say in the ‗philosophy of mind‘ that this branch is developed only because of three crucial theories i.e. rationalism, empiricism, and criticism. In this paper, it is argued that innate ideas or truth are equated with deduction and acquired truths are related with induction. This article also enhance the role of language in the makeup of the world of mind, although mind and the thought are the terms that are used by the philosophers synonymously but in this paper they are taken and interpreted differently. It shows the development in the analytical tradition subjected to the areas of mind and logic and their critical relation. (shrink)

The first beginnings of modern logic in Croatia are recognizable as early as in the middle of the 19th century in Vatroslav Bertić. At the turn of the 20th century, Albin Nagy, who was teaching in Italy, made contributions to algebraic logic and to the philosophy of logic. At that time, a distinctive author Mate Meršić stood out, also working on algebraic logic. In the Croatian academic philosophy, until the publication of Gajo Petrović's textbook (...) (1964) and the contributions by Heda Festini, a critical or indifferent attitude toward modern logic prevailed. The first comprehensive modern logic textbook in Croatian was written by mathematician Vladimir Devidé (1964), known, for example, for his axiomatizations of natural numbers and classical propositional logic. In the Croatian philosophy of the 1980s and 1990s, influential logicians are Goran Švob and mathematician Zvonimir Šikić. At the turn of the 21st century, logical investigations are being intensified and extended to various branches of the contemporary logic. (shrink)

This thesis is about the metaphysics of logic. I argue against a view I refer to as ‘logical realism’. This is the view that the logical constants represent a particular kind of metaphysical structure, which I dub ‘logico-metaphysical structure’. I argue instead for a more metaphysically lightweight view of logic which I dub ‘logical expressivism’. -/- In the first part of this thesis (Chapters I and II) I argue against a number of arguments that Theodore Sider has given (...) for logical realism. In Chapter I, I present an argument of his to the effect that logico-metaphysical structure provides the only good explanation of the semantic determinacy of the logical constants. I argue that other explanations are possible. In Chapter II, I present another argument of his to the effect that logico-metaphysical structure is something that comes along with ontological realism: the view that there is a non-language-relative fact of the matter about what exists. I argue that the connection between logical and ontological realism is not as close as Sider makes it out to be. -/- In the second part of this thesis (Chapters III – V) I set out a positive view of the logical constants that can explain both why their meanings are semantically determinate, and why they form part of our vocabulary. On that view, the primary bearers of logical structure are propositional attitudes, and the logical constants are in our language as vehicles for the expression of logically complex propositional attitudes. In Chapter III, I set out an expressivist theory of propositional logic. In Chapter IV, I use this theory to explain how the logical connectives end up having determinate meanings. In Chapter V, I extend the expressivist theory to predicate logic. (shrink)

هذا الكتاب هو الجانب الأكبر من أطروحتي للدكتوراه من جامعة القاهرة "فلسفة اللغة والمنطق عند كواين" وهو أول دراسة عربية عن هذا المنطقي الفيلسوف. تنقسم الدراسة إلى خمسة فصول يسبقها مدخل ويلحقها خاتمة. يحدد المدخل المراد بفلسفة اللغة وفلسفة المنطق، وتيارات فلسفة اللغة المعاصرة وموقع كواين منها. ويناقش الفصل الأول مشكلة التحليلية. ويشرح الثاني نظرية كواين التجريبية السلوكية في دراسة اللغة والإشارة. ويعالج الفصل الثالث مشكلة المعنى. ويحلل الرابع دعوى اللاتحديد في الترجمة. ويبحث الخامس آراء كواين في فلسفة المنطق. وفي (...) الخاتمة تأصيل لفلسفة كواين التي تسمى التجريبية الطبيعية أحيانا أو التجريبية البراجماتية أحيانا أخرى. ويقع الكتاب في 356 صفحة . (shrink)

The Art of Logic by Avi Sion is a collection of recent essays on various topics in logic theory and in applied logic. The same faculty and art of logic is called for in formulating theoretical logic and in applying its findings to diverse fields. The essays here collected deal with some very important issues in logic, philosophy, and spirituality, which he had not previously treated in as much detail if at all.

An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts of the (...) physical world and are objects of mathematics. Though some mathematical structures such as infinities may be too big to be realized in fact, all of them are capable of being realized. Informed by the author's background in both philosophy and mathematics, but keeping to simple examples, the book shows how infant perception of patterns is extended by visualization and proof to the vast edifice of modern pure and applied mathematical knowledge. (shrink)

Gödel's Philosophical Legacy Kurt Gödel's contributions to philosophy extend beyond his incompleteness theorems. He engaged deeply with the work of other philosophers, including Immanuel Kant and Edmund Husserl, and explored topics such as the nature of time, the structure of the universe, and the relationship between mathematics and reality. Gödel's philosophical writings, though less well-known than his mathematical work, offer rich insights into his views on the nature of existence, the limits of human knowledge, and the interplay between the (...) finite and the infinite. His work continues to inspire and challenge philosophers, mathematicians, and scientists, inviting them to explore the profound and often enigmatic questions at the heart of human understanding. -/- Kurt Gödel's Broader Contributions to Philosophy Kurt Gödel, while primarily known for his monumental incompleteness theorems, made significant contributions that extended beyond the realm of mathematical logic. His philosophical pursuits deeply engaged with the works of eminent philosophers like Immanuel Kant and Edmund Husserl. Gödel's explorations into the nature of time, the structure of the universe, and the relationship between mathematics and reality reveal a profound and multifaceted intellectual legacy. -/- Engagement with Immanuel Kant Gödel held a deep interest in the philosophy of Immanuel Kant. He admired Kant's critical philosophy, particularly the distinction between the noumenal and phenomenal worlds. Kant posited that human experience is shaped by the mind’s inherent structures, leading to the conclusion that certain aspects of reality (the noumenal world) are fundamentally unknowable. Gödel’s incompleteness theorems echoed this Kantian theme, illustrating the limits of formal systems in capturing the totality of mathematical truth. Gödel believed that mathematical truths exis t independently of human thought, akin to Kant's noumenal realm. This philosophical alignment provided a robust foundation for Gödel's Platonism, which asserted the existence of mathematical objects as real, albeit abstract, entities. -/- Influence of Edmund Husserl Gödel was also profoundly influenced by Edmund Husserl, the founder of phenomenology. Husserl's phenomenology emphasizes the direct investigation and description of phenomena as consciously experienced, without preconceived theories about their causal explanation. Gödel saw Husserl's work as a pathway to bridge the gap between the abstract world of mathematics and concrete human experience. Husserl's ideas about the structures of consciousness and the intentionality of thought resonated with Gödel's views on mathematical intuition. Gödel believed that human minds could access mathematical truths through intuition, a concept that draws on Husserlian phenomenological methods. -/- The Nature of Time and the Universe Gödel's philosophical inquiries extended to the nature of time and the structure of the universe. His collaboration with Albert Einstein at the Institute for Advanced Study led to the development of the "Gödel metric" in 1949. This solution to Einstein's field equations of general relativity described a rotating universe where time travel to the past was theoretically possible. Gödel's model challenged conventional notions of time and causality, suggesting that the universe might have a more intricate structure than previously thought. Gödel's exploration of time was not just a mathematical curiosity but a profound philosophical statement about the nature of reality. He questioned whether time was an objective feature of the universe or a construct of human consciousness. His work hinted at a timeless realm of mathematical truths, aligning with his Platonist view. -/- Mathematics and Reality Gödel's philosophical outlook extended to the broader relationship between mathematics and reality. He believed that mathematics provided a more profound insight into the nature of reality than empirical science. For Gödel, mathematical truths were timeless and unchangeable, existing independently of human cognition. This perspective led Gödel to critique the materialist and mechanistic views that dominated 20th-century science and philosophy. He argued that a purely physicalist interpretation of the universe failed to account for the existence of abstract mathematical objects and the human capacity to understand them. Gödel's philosophy suggested a more integrated view of reality, where both physical and abstract realms coexist and inform each other. -/- Gödel's Exploration of Time Kurt Gödel, one of the most profound logicians of the 20th century, ventured beyond the confines of mathematical logic to explore the nature of time. His inquiries into the concept of time were not merely theoretical musings but were grounded in rigorous mathematical formulations. Gödel's exploration of time challenged conventional views and opened new avenues of thought in both physics and philosophy. -/- Gödel and Einstein Gödel’s interest in the nature of time was significantly influenced by his friendship with Albert Einstein. Both were faculty members at the Institute for Advanced Study in Princeton, where they engaged in deep discussions about the nature of reality, time, and space. Gödel's exploration of time culminated in his solution to Einstein's field equations of general relativity, known as the Gödel metric. -/- The Gödel Metric In 1949, Gödel presented a model of a rotating universe, which became known as the Gödel metric. This solution to the equations of general relativity depicted a universe where time travel to the past was theoretically possible. Gödel’s rotating universe contained closed timelike curves (CTCs), paths in spacetime that loop back on themselves, allowing for the possibility of traveling back in time. The Gödel metric posed a significant philosophical challenge to the conventional understanding of time. If time travel were possible, it would imply that time is not linear and absolute, as commonly perceived, but rather malleable and subject to the geometry of spacetime. This raised profound questions about causality, the nature of temporal succession, and the very structure of reality. -/- Philosophical Implications Gödel’s exploration of time extended beyond the mathematical implications to broader philosophical inquiries: Nature of Time: Gödel questioned whether time was an objective feature of the universe or a construct of human consciousness. His work suggested that our understanding of time as a linear progression from past to present to future might be an illusion, shaped by the limitations of human perception. -/- Causality and Free Will: The existence of closed timelike curves in Gödel’s model raised questions about causality and free will. If one could travel back in time, it would imply that future events could influence the past, potentially leading to paradoxes and challenging the notion of a deterministic universe. -/- Temporal Ontology: Gödel's work contributed to debates in temporal ontology, particularly the debate between presentism (the view that only the present exists) and eternalism (the view that past, present, and future all equally exist). Gödel’s rotating universe model seemed to support eternalism, suggesting a block universe where all points in time are equally real. Philosophy of Science: Gödel’s exploration of time had implications for the philosophy of science, particularly in the context of understanding the limits of scientific theories. His work underscored the importance of considering philosophical questions when developing scientific theories, as they shape our fundamental understanding of concepts like time and space. -/- Legacy Gödel’s exploration of time remains a significant and controversial contribution to both physics and philosophy. His work challenged established notions and encouraged deeper inquiries into the nature of reality. Gödel’s rotating universe model continues to be a topic of interest in theoretical physics and cosmology, inspiring new research into the nature of time and the possibility of time travel. In philosophy, Gödel’s inquiries into time have prompted ongoing debates about the nature of temporal reality, the relationship between mathematics and physical phenomena, and the limits of human understanding. His work exemplifies the intersection of mathematical rigor and philosophical inquiry, demonstrating the profound insights that can emerge from such an interdisciplinary approach. The Temporal Ontology of Kurt Gödel Kurt Gödel's profound contributions to mathematics and logic extend into the realm of temporal ontology—the philosophical study of the nature of time and its properties. Gödel's insights challenge conventional perceptions of time and suggest a more intricate, layered understanding of temporal reality. This essay explores Gödel's contributions to temporal ontology, particularly through his engagement with relativity and his philosophical reflections. -/- Gödel's Rotating Universe One of Gödel’s most notable contributions to temporal ontology comes from his work in cosmology, specifically his solution to Einstein’s field equations of general relativity, known as the Gödel metric. Introduced in 1949, the Gödel metric describes a rotating universe with closed timelike curves (CTCs). These curves imply that, in such a universe, time travel to the past is theoretically possible, presenting a significant challenge to conventional views of linear, unidirectional time. -/- Implica tions for Temporal Ontology Gödel's rotating universe model has profound implications for our understanding of time: Eternalism vs. Presentism: Gödel’s model supports the philosophical stance known as eternalism, which posits that past, present, and future events are equally real. In contrast to presentism, which holds that only the present moment exists, eternalism suggests a "block universe" where time is another dimension like space. Gödel’s rotating universe, with its CTCs, reinforces this view by demonstrating that all points in time could, in principle, be interconnected in a consistent manner. Non-linearity of Time: The possibility of closed timelike curves challenges the idea of time as a linear sequence of events. In Gödel’s universe, time is not merely a straight path from past to future but can loop back on itself, allowing for complex interactions between different temporal moments. This non-linearity has implications for our understanding of causality and the nature of temporal succession. Objective vs. Subjective Time: Gödel’s work invites reflection on the distinction between objective time (the time that exists independently of human perception) and subjective time (the time as experienced by individuals). His model suggests that our subjective experience of a linear flow of time may not correspond to the objective structure of the universe. This raises questions about the relationship between human consciousness and the underlying temporal reality. -/- Gödel and Philosophical Reflections on Time Gödel’s engagement with temporal ontology was not limited to his cosmological work. He also reflected deeply on philosophical questions about the nature of time and reality, drawing on the ideas of other philosophers and integrating them into his own thinking. Kantian Influences: Gödel was influenced by Immanuel Kant’s distinction between the noumenal world (things as they are in themselves) and the phenomenal world (things as they appear to human observers). Gödel’s views on time echoed this distinction, suggesting that our perception of time might be a phenomenon shaped by the limitations of human cognition, while the true nature of time (the noumenal aspect) might be far more complex and non-linear. Husserlian Phenomenology: Gödel’s interest in Edmund Husserl’s phenomenology also informed his views on time. Husserl’s emphasis on the structures of consciousness and the intentionality of thought resonated with Gödel’s belief in the importance of intuition in accessing mathematical truths. Gödel’s reflections on time incorporated a phenomenological perspective, considering how temporal experience is structured by human consciousness. Mathematical Platonism: Gödel’s Platonist views extended to his understanding of time. Just as he believed in the independent existence of mathematical objects, Gödel saw time as an objective entity with a structure that transcends human perception. His work on the Gödel metric can be seen as an attempt to uncover this objective structure, revealing the deeper realities that underlie our experience of time. (shrink)

The philosophy of superdeterminism is based on a single scientific fact about the universe, namely that cause and effect in physics are not real. In 2020, accomplished Swedish theoretical physicist, Dr. Johan Hansson published a physics proof using Albert Einstein’s Theory of Special Relativity that our universe is superdeterministic meaning a predetermined static block universe without cause and effect in physics. In the absence of cause and effect in physics, past, present and future events must all exist equally in (...) logical relationship. Our experience of time must be an illusion, because our experience of change in our world is not actually caused in time. Rather, the change we experience in our world is caused by the changing appearances in our static block universe in the static fourth dimension of time. We should think of time as a distance in the fourth dimension of time from our present position in the dimension of time to another position either towards or away from the beginning of the universe. Because physical reality is not actually caused to change in our static block universe, then static physical reality is actually timeless. But, because very good evidence supports the creation of timeless physical reality, then non-temporal causation of timeless physical reality outside of time is real. (shrink)

The identity theory’s rise to prominence in analytic philosophy of mind during the late 1950s and early 1960s is widely seen as a watershed in the development of physicalism, in the sense that whereas logical behaviourism proposed analytic and a priori ascertainable identities between the meanings of mental and physical-behavioural concepts, the identity theory proposed synthetic and a posteriori knowable identities between mental and physical properties. While this watershed does exist, the standard account of it is misleading, as it (...) is founded in erroneous intensional misreadings of the logical positivists’—especially Carnap’s—extensional notions of translation and meaning, as well as misinterpretations of the positivists’ shift from the strong thesis of translation-physicalism to the weaker and more liberal notion of reduction-physicalism that occurred in the Unity of Science programme. After setting the historical record straight, the essay traces the first truly modern identity theory to Schlick’s pre-positivist views circa 1920 and goes on to explore its further development in Feigl, arguing that the fundamental difference between the Schlick-Feigl identity theory and the more familiar and influential Place-Smart-Armstrong identity theory has resurfaced in the deep and seemingly unbridgeable gulf in contemporary philosophy of consciousness between inflationary mentalism and deflationary physicalism. (shrink)

Logic has a fundamental role in the philosophy of Franjo Marković (1845-1914). His theory of concepts and reasoning is analyzed, especially with respect to the essential role of the principle of sufficient reason and in connection with the concept of causality. The interplay of various types of evidence in Marković's inductive-deductive logic is analysed by means of contemporary justification logic tools.

In the paper, various notions of the logical semiotic sense of linguistic expressions – namely, syntactic and semantic, intensional and extensional – are considered and formalised on the basis of a formal-logical conception of any language L characterised categorially in the spirit of certain Husserl's ideas of pure grammar, Leśniewski-Ajdukiewicz's theory of syntactic/semantic categories and, in accordance with Frege's ontological canons, Bocheński's and some of Suszko's ideas of language adequacy of expressions of L. The adequacy ensures their unambiguous syntactic and (...) semantic senses and mutual, syntactic and semantic correspondence guaranteed by the acceptance of a postulate of categorial compatibility of syntactic and semantic (extensional and intensional) categories of expressions of L. This postulate defines the unification of these three logical senses. There are three principles of compositionality which follow from this postulate: one syntactic and two semantic ones already known to Frege. They are treated as conditions of homomorphism of partial algebra of L into algebraic models of L: syntactic, intensional and extensional. In the paper, they are applied to some expressions with quantifiers. Language adequacy connected with the logical senses described in the logical conception of language L is, obviously, an idealisation. The syntactic and semantic unambiguity of its expressions is not, of course, a feature of natural languages, but every syntactically and semantically ambiguous expression of such languages may be treated as a schema representing all of its interpretations that are unambiguous expressions. (shrink)

This paper reconstructs the American reception of logical positivism in the early 1930s. I argue that Moritz Schlick (who had visiting positions at Stanford and Berkeley between 1929 and 1932) and Herbert Feigl (who visited Harvard in the 1930-31 academic year) played a crucial role in promoting the *Wissenschaftliche Weltauffassung*, years before members of the Vienna Circle, the Berlin Group, and the Lvov-Warsaw school would seek refuge in the United States. Building on archive material from the Wiener Kreis Archiv, the (...) Harvard University Archives, and the Herbert Feigl Papers, as well as a large number of publications in American philosophy journals from the early 1930s, I reconstruct the subtle transformation of the American philosophical landscape in the years immediately preceding the European exodus. I argue that (1) American philosophical discussions about meaning and significance and (2) internal dynamics in the Vienna Circle between 1929 and 1931 significantly impacted the way in which US philosophers came to perceive logical positivism. (shrink)

A key question in the philosophy of logic is how we have epistemic justification for claims about logical entailment (assuming we have such justification at all). Justification holism asserts that claims of logical entailment can only be justified in the context of an entire logical theory, e.g., classical, intuitionistic, paraconsistent, paracomplete etc. According to holism, claims of logical entailment cannot be atomistically justified as isolated statements, independently of theory choice. At present there is a developing interest in—and endorsement (...) of—justification holism due to the revival of an abductivist approach to the epistemology of logic. This paper presents an argument against holism by establishing a foundational entailment-sentence of deduction which is justified independently of theory choice and outside the context of a whole logical theory. (shrink)

The paper begins by acknowledging that weakened systematic precision in phenomenology has made its application in philosophy of science obscure and ineffective. The defining aspirations of early transcendental phenomenology are, however, believed to be important ones. A path is therefore explored that attempts to show how certain recent developments in the logic of self-reference fulfill in a clear and more rigorous fashion in the context of philosophy of science certain of the early hopes of phenomenologists. The resulting (...) dual approach is applied to several problems in the philosophy of science: on the one hand, to proposed rejections of scientific objectivity, to the doctrine of radical meaning variance, and to the Quine-Duhem thesis, and or. the other, to an analysis of hidden variable theory in quantum mechanics. (shrink)