A common reaction to Hegel’s suggestion that we collapse Kant’s distinction between form and content is that, since such a move would also deprive us of any way of distinguishing the merely logical from the real possibility of our concepts, it is incoherent and ought to be rejected. It is true that these two distinctions are intimately related in Kant, such that if one goes, the other does as well. But it is less obvious that giving them up as Kant (...) conceives them is as incoherent a proposal as many of Hegel’s critics think. It has been the point of a recent account of Hegel’s idealism to demonstrate that his critique of Kant’s dichotomy between form and content or concept and intuition does not commit him to the view that human cognition is materially creative of its content in the manner of a God-like or intuitive intellect—does not, in other words, signify a return to a pre-Critical metaphysics. This is the interpretative stance I adopt here as well, in hope of giving defenders of Kant reasons for taking Hegel more seriously. (shrink)

Demonstrative logic, the study of demonstration as opposed to persuasion, is the subject of Aristotle's two-volume Analytics. Many examples are geometrical. Demonstration produces knowledge (of the truth of propositions). Persuasion merely produces opinion. Aristotle presented a general truth-and-consequence conception of demonstration meant to apply to all demonstrations. According to him, a demonstration, which normally proves a conclusion not previously known to be true, is an extended argumentation beginning with premises known to be truths and containing (...) a chain of reasoning showing by deductively evident steps that its conclusion is a consequence of its premises. In particular, a demonstration is a deduction whose premises are known to be true. Aristotle's general theory of demonstration required a prior general theory of deduction presented in the Prior Analytics. His general immediate-deduction-chaining conception of deduction was meant to apply to all deductions. According to him, any deduction that is not immediately evident is an extended argumentation that involves a chaining of intermediate immediately evident steps that shows its final conclusion to follow logically from its premises. To illustrate his general theory of deduction, he presented an ingeniously simple and mathematically precise special case traditionally known as the categorical syllogistic. (shrink)

In an earlier defense of the view that the fundamental logical properties of logical truth and logical consequence obtain or fail to obtain only relative to contexts, I focused on a variation of Kaplan’s own modal logic of indexicals. In this paper, I state a semantics and sketch a system of proof for a first-order logic of demonstratives, and sketch proofs of soundness and completeness. (I omit details for readability.) That these results obtain for the first-order logic (...) of demonstratives shows that the significance of demonstratives for logic exceeds their behavior as rigid designators in counterfactual reasoning, or reasoning about alternative possibilities. Furthermore, the results in this paper help address one common objection to the view that logical truth and consequence obtain only relative to contexts. According to this objection, the view entails that logical consequence is not formal. (shrink)

This chapter contains sections titled: Introduction How to Read Maimonides' Guide of the Perplexed Belief and Articles of Faith The Art of Biblical Exegesis: Harvesting “Apples of Gold” Language and Logic Philosophy and the Art of Demonstration Conclusion: Implications of Maimonides' Views further reading.

Kaplan (1989a) insists that natural languages do not contain displacing devices that operate on character—such displacing devices are called monsters. This thesis has recently faced various empirical challenges (e.g., Schlenker 2003; Anand and Nevins 2004). In this note, the thesis is challenged on grounds of a more theoretical nature. It is argued that the standard compositional semantics of variable binding employs monstrous operations. As a dramatic first example, Kaplan’s formal language, the Logic of Demonstratives, is shown to contain monsters. (...) For similar reasons, the orthodox lambda-calculus-based semantics for variable binding is argued to be monstrous. This technical point promises to provide some far-reaching implications for our understanding of semantic theory and content. The theoretical upshot of the discussion is at least threefold: (i) the Kaplanian thesis that “directly referential” terms are not shiftable/bindable is unmotivated, (ii) since monsters operate on something distinct from the assertoric content of their operands, we must distinguish ingredient sense from assertoric content (cf. Dummett 1973; Evans 1979; Stanley 1997), and (iii) since the case of variable binding provides a paradigm of semantic shift that differs from the other types, it is plausible to think that indexicals—which are standardly treated by means of the assignment function—might undergo the same kind of shift. (shrink)

This chapter examines the views of seventeenth-century British philosophers on the notion of logic and demonstrative knowledge, particularly Francis Bacon, Thomas Hobbes, and John Locke, offering an overview of traditional Aristotelianism in relation to logic and describing Bacon's approach to demonstration and logic. It also analyzes the contribution of the Cambridge Platonists and evaluates the influence of Cartesianism. The chapter concludes that theorizing about logic and demonstrative knowledge followed an arc familiar from other branches of (...) philosophy such as metaphysics or the philosophy of science. (shrink)

In this article I will develop the first steps of a wholly general theory of how indexical and reflexive pronouns function in propositional attitude ascriptions. This will involve a theory of ascriptions of de se beliefs and de se utterances, which can probably be also generalized so as to apply to ascriptions of other attitudes. It will also involve a theory about the ascriptions of beliefs or other attitudes a person has at a time about what happens then (attitudes de (...) praesente, as they are sometimes called) and the beliefs of a person concerning the one whom he is addressing (which I might call beliefs de recipiente) etc.. The most distinctive aspect of the theory will be that I will argue that many phenomena associated with such ascriptions that are nowadays most often viewed as pragmatic are semantic. I will use a system of symbolic logic to formalize such ascriptions. I will start from David Kaplan’s Logic of Demonstratives and generalize it into a logic I call Doxastic Logic of Demonstratives, DLD. Crucial to the semantics of the logic will be an exact definition of the adjustments of a character from one context to another. (shrink)

SummaryThe Science Museum, London, recently acquired some circular logic demonstrators by Charles Mahon, 3rd Earl Stanhope. A study of what exists of Stanhope's unpublished book, notes and letters on the subject allows the development of his demonstrators to be traced. A consideration of Stanhope's characters and interests reveals an Enlightenment figure with aspirations consonant with that era, the logic demonstrators representing the material culmination of his ideals. Yet the demonstrators were not made public during his lifetime, and the (...) final form was greeted with derision 60 years after his death. (shrink)

But to infer is not to be trained in Logic. The primitive persons inferred ; the common layman infers. But they do not know any bit of what is known as ...

In her book Abductive Reasoning Atocha Aliseda stresses the attention to the logical models of abduction, centering on the semantic tableaux as a method for extending and improving both the whole cognitive/philosophical view on it and on other more restricted logical approaches. I will describe the importance of increasing logical knowledge on abduction also taking advantage of some ideas coming from the so-called distributed cognition where logical models are seen as forms of cognitive externalizations of preexistent in-formal human reasoning performances.

Phrases like "That man" are called complex demonstrative phrases. They are usually considered to be directly referential in nature. There are many arguments to suggest that such phrases are not directly referential, but are quantificational. This work examines the philosophical debate over the semantic status of complex demonstratives at length, arriving at the conclusion that the quantificational view is right. A new logical form is also suggested for complex demonstratives.

This paper looks at what David Kaplan's work on indexicals can teach us about logic and the philosophy of logic, and also what Kaplan's logic (i.e. the Logic of Demonstratives) can teach us about indexicals. The lessons are i) that logical consequence is not necessary truth-preservation, ii) that that the linguistic doctrine of necessary truth (also called conventionalism about modality) fails, and iii) that there is a kind of barrier to entailment between non-context-sensitive and context-sensitive claims.

In her book Abductive Reasoning Atocha Aliseda (2006) stresses the attention to the logical models of abduction, centering on the semantic tableaux as a method for extending and improving both the whole cognitive/philosophical view on it and on other more restricted logical approaches. I will provide further insight on two aspects. The first is re-lated to the importance of increasing logical knowledge on abduction: Aliseda clearly shows how the logical study on abduction in turn helps us to extend and modernize (...) the classical and received idea of logic. The second refers to some ideas coming from the so-called distributed cognition and concerns the role of logical models as forms of cognitive exter-nalizations of preexistent in-formal human reasoning performances. The logical externalization in objective systems, communicable and sharable, is able to grant stable perspectives endowed with symbolic, abstract, and rigorous cogni-tive features. I will also emphasize that Aliseda especially stresses that this character of stability and objectivity of logical achievements are not usually present in models of abduction that are merely cognitive and epistemological, and of ex-treme importance from the computational point of view. (shrink)

This is an Editorial Note for the special volume of the journal Manuscrito (42: 4) devoted to Aristotle's theory of demonstration and its logical and metaphysical entanglements, which has been organized by me and Breno Zuppolini (as Guest Editors), with papers authored by Benjamin Morison, Owen Goldin, David Bronstein, Michail Peramatzis, Andrea Falcon, Laura Castelli, Paolo Fait, Joseph Karbowski, Adam Crager, Klaus Corcilius, Robert J. Hankinson, Raphael Zillig and Pieter Sjoerd Hasper.

William Ernest Johnson was a renowned British logician and economist, and also a fellow of King's College, Cambridge. Originally published in 1922, this book forms the second of a three-volume series by Johnson relating to 'the whole field of logic as ordinarily understood'. The series is widely regarded as Johnson's greatest achievement, making a significant contribution to the tradition of philosophical logic. This book will be of value to anyone with an interest in Johnson's theories, philosophy and the (...) historical development of logic. (shrink)

The aim of this series is to bring together important recent writings in major areas of philosophical inquiry, selected from a variety of sources, mostly periodicals.

In this chapter, I discuss some problems of Kant’s logic corpus while recognizing its richness and potential value. I propose and explain a methodic way to approach it. I then test the proposal by showing how we may use various mate- rials from the corpus to construct a Kantian demonstration of the formal rules of thinking (or judging) that lie at the base of Kant’s Metaphysical Deduction. The same proposal can be iterated with respect to other topics. The (...) said demonstration will have cleared the path for such iterations. (shrink)

This book investigates the central role of reason in Islamic intellectual life. Despite widespread characterization of Islam as a system of belief based only on revelation, John Walbridge argues that rational methods, not fundamentalism, have characterized Islamic law, philosophy and education since the medieval period. His research demonstrates that this medieval Islamic rational tradition was opposed by both modernists and fundamentalists, resulting in a general collapse of traditional Islamic intellectual life and its replacement by more modern but far shallower forms (...) of thought. However, the resources of this Islamic scholarly tradition remain an integral part of the Islamic intellectual tradition and will prove vital to its revival. The future of Islam, Walbridge argues, will be marked by a return to rationalism"--Provided by publisher. (shrink)

This article investigates the nature of Aristotelian syllogistics and shows that the categorical syllogism is fundamentally about showing the connection, in the premises of the syllogism, between the major and minor terms as stated in the conclusion. It discusses how this is important for the use of the syllogism in scientific demonstration. The article then examines modern deductive logic with an eye to they way in which it contrasts with Aristotelian syllogistics. It shows howmodern logic is about (...) making necessary connections between each proposition by means of external or second order rules. In the syllogism, on the other hand, the necessity between the premises as a whole unit and the conclusion is based on the internal middle term. The article concludes with a discussion of Günther Patzig’s claim that Aristotelian syllogisms are best thought of as tautological propositions. If this were the case, then the differences asserted to exist between syllogistic and modern logic would not hold. However, it is shown that Patzig’s assimilation of syllogistics to modern deductive logic is illegitimate. (shrink)

Brouwer's demonstration of his Bar Theorem gives rise to provocative questions regarding the proper explanation of the logical connectives within intuitionistic and constructivist frameworks, respectively, and, more generally, regarding the role of logic within intuitionism. It is the purpose of the present note to discuss a number of these issues, both from an historical, as well as a systematic point of view.

Hao Wang was one of the few confidants of the great mathematician and logician Kurt Gödel. _A Logical Journey_ is a continuation of Wang's _Reflections on Gödel_ and also elaborates on discussions contained in _From Mathematics to Philosophy_. A decade in preparation, it contains important and unfamiliar insights into Gödel's views on a wide range of issues, from Platonism and the nature of logic, to minds and machines, the existence of God, and positivism and phenomenology. The impact of Gödel's (...) theorem on twentieth-century thought is on par with that of Einstein's theory of relativity, Heisenberg's uncertainty principle, or Keynesian economics. These previously unpublished intimate and informal conversations, however, bring to light and amplify Gödel's other major contributions to logic and philosophy. They reveal that there is much more in Gödel's philosophy of mathematics than is commonly believed, and more in his philosophy than his philosophy of mathematics. Wang writes that "it is even possible that his quite informal and loosely structured conversations with me, which I am freely using in this book, will turn out to be the fullest existing expression of the diverse components of his inadequately articulated general philosophy." The first two chapters are devoted to Gödel's life and mental development. In the chapters that follow, Wang illustrates the quest for overarching solutions and grand unifications of knowledge and action in Gödel's written speculations on God and an afterlife. He gives the background and a chronological summary of the conversations, considers Gödel's comments on philosophies and philosophers, and his attempt to demonstrate the superiority of the mind's power over brains and machines. Three chapters are tied together by what Wang perceives to be Gödel's governing ideal of philosophy: an exact theory in which mathematics and Newtonian physics serve as a model for philosophy or metaphysics. Finally, in an epilog Wang sketches his own approach to philosophy in contrast to his interpretation of Gödel's outlook. (shrink)

This article investigates the nature of Aristotelian syllogistics and shows that the categorical syllogism is fundamentally about showing the connection, in the premises of the syllogism, between the major and minor terms as stated in the conclusion. It discusses how this is important for the use of the syllogism in scientific demonstration. The article then examines modern deductive logic with an eye to they way in which it contrasts with Aristotelian syllogistics. It shows howmodern logic is about (...) making necessary connections between each proposition by means of external or second order rules. In the syllogism, on the other hand, the necessity between the premises as a whole unit and the conclusion is based on the internal middle term. The article concludes with a discussion of Günther Patzig’s claim that Aristotelian syllogisms are best thought of as tautological propositions. If this were the case, then the differences asserted to exist between syllogistic and modern logic would not hold. However, it is shown that Patzig’s assimilation of syllogistics to modern deductive logic is illegitimate. (shrink)

Since Mates’ seminal Stoic Logic there has been uncertainty and debate about how to treat the term anapodeiktos when used of Stoic syllogisms. This paper argues that the customary translation of anapodeiktos by ‘indemonstrable’ is accurate, and it explains why this is so. At the heart of the explanation is an argument that, contrary to what is commonly assumed, indemonstrability is rooted in the generic account of the Stoic epistemic notion of demonstration. Some minor insights into Stoic (...) class='Hi'>logic ensue. (shrink)

Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes. Yanofsky (...) describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known. Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there. (shrink)

Some demonstrative expressions, those we might term ‘bare demonstratives’, appear without any appended descriptive content (e.g. occurrences of ‘this’ or ‘that’ simpliciter). However, it seems that the majority of demonstrative occurrences do not follow this model. ‘Complex demonstratives’ is the collective term I shall use for phrases formed by adjoining one or more common nouns to a demonstrative expression (e.g. ‘that cat’, ‘this happy man’) and I will call the combination of predicates immediately concatenated with the demonstrative in such phrases (...) the ‘matrix’ of the expression. The question, then, is how we should construe the logical form of such expressions within a semantic theory for our language; and I wish to suggest that some recent answers to this question are, in fact, mistaken. The structure of the paper is as follows: first, I wish to highlight two (often underlying) assumptions about the nature of noun phrases in general, and suggest that, if they are both adopted, they apparently constrain the possible accounts of the logical form of complex demonstratives to just three options. The second and third parts of the paper will be concerned with expanding these options and arguing that none of them are adequate; thus the major part of the paper is concerned with the negative claim that the most obvious moves to make in this area must actually fail on closer inspection. The fourth and final section will then (very briefly) sketch the positive thesis of the paper: that we can deliver a clear and cohesive account of complex demonstratives, armed simply with elements which we will draw from David Kaplan’s theory of demonstratives, but only at the cost of rejecting (or at least refining) one assumption we recognised initially. (shrink)

The scope of my considerations here is defined along two lines, which seem to me of essential relevance for a theory of dialectic. On the one hand, the form of negation that – as self-referring antinomical negation – gains a quasi-semantic expulsory force [Sprengkraft] and therewith a forwarding [weiterverweisenden] character; on the other hand, the notion that every logical category is defective insofar as the explicit meaning of a category does not express everything that is already implicitly presupposed for its (...) meaning. Both lines are tightly interwoven. This I would like to demonstrate with the example of the dialectic of Being and Non-Being at the beginning of the Hegelian Logic. I will first make visible the basic structures of dialectical argumentation (sections II and III) – whereby certain revisions will turn out to be necessary in comparison with Hegel’s actual argument. Thereby it proves essential that the whole apparatus of logical categories and principles must be always already available and utilized for the dialectical explication: proving dialectic as a self-explication of logic by logical means: dialectic, as it were, as the self-fulfillment of logic (sections IV–VI). (shrink)

This paper investigates the basis arguments of so-called legal logic and their relation to logic in its standard meaning. There is no doubt that legal arguments belong to logic in the wide sense (sensu largo), but their reduction to schemes of formal logic (logica sensu stricto) is a controversial issue. It can be demonstrated that only some legal arguments fall under explicit rules of formal logic, that is, having a deductive character. Most such reasoning is (...) fallible, and its correctness depends on appealing to extra-logical principles taken from legal norms. For instance, if we say, “If it is permitted more, then it is permitted less” (argumentum a maiori ad minus), we assume that the concepts expressed by the words “more” and “less” are already defined. (shrink)

What corresponds to the present-day ‘transcendental-pragmatic’ concept of ultimate grounding in Hegel is his claim to absoluteness of the logic. Hegel’s fundamental intuition is that of a ‘backward going grounding’ obtaining the initially unproved presuppositions, thereby ‘wrapping itself into a circle’ – the project of the self-grounding of logic, understood as the self-explication of logic by logical means. Yet this is not about one of the multiple ‘logics’ which as formal constructs cannot claim absoluteness. It is rather (...) a fundamental logic that only makes logical textures possible at all and so owns transcendental character. The non-contradiction-principle is an example for this. Es- sential is that it is ‘under-cover-effcient’ as soon as meaningful concepts are used. Self-explication of the fundamental logic then means explicating its implicit under-cover validity, in fact by means of the fundamental logic itself. As is shown this is the affair of dialectic which thereby is to be understood as ultimate grounding of the fundamental logic. This is analyzed in detail using the example of the being/non-being-dialectic. As is demonstrated each explication step generates a new implicit issue and therewith a new explication-discrepancy inducing an antinomical structure that anew forwards the explication procedure. So this is entirely determined by itself. Decisive for the ultimate grounding argumentation is that thereby an objectively verifyable procedure is found, which is apparently possible only in a Hegelian framework. In contrast the immediate evidence of a speech act claimed by the transcendental-pragmatic position has only private character, which is grounding-theoretically irrelevant. (shrink)

Complex demonstrative phrases, in English, are phrases such as ‘that woman in the department’ and ‘that car on the corner’. They are of particular interest to philosophers for two related reasons. The first involves the problem of intentionality. If there are phrases that are candidates for “latching directly onto the world,” they are such phrases, and their “simple” counterparts, as in the occurrences of ‘that’ in ‘that is nice’. As a result, philosophers interested in intentionality, from the sense-data theorists to (...) contemporary philosophers of mind, have devoted considerable attention to the question of how a demonstrative thought links to its object. The second reason involves issues in semantics and the philosophy of language. In the course of investigations into the model theory for modal logic in the 1950s and 1960s, philosophers recognized that the simplest way to treat terms was as modally rigid, namely as designating their actual designations relative to any possible world in which they existed, and nothing else in other worlds. It was soon recognized that this semantic property could be elegantly explained by the assumption that the semantics of singular terms reflects the role of singular terms in linking representations directly to the world. If the semantic contribution of a singular term to a thought is simply the object it denotes, and the thought is the object of modal evaluation, then the modal rigidity of the class of terms falls out as a consequence. Demonstrative phrases, both simple and complex, have always been taken to be among the paradigms for this picture of reference, which has come to be known as “the direct reference” model. (shrink)

The Demonstrative Theory holds that quoted matter is logically external to the quoting sentence, that quotation marks are (demonstratively) referential, and that quotation marks are grammatically required for autonomous mentioning. In contrast, the Identity Theory holds that quoted matter is integral to its quoting sentence, that quotation marks serve merely as disambiguating punctuation, and that mentionings need not be quotation-marked. I support the Identity Theory by pointing out fallacies in the arguments for demonstrative theories and by considering empty quotation, ordinary (...) language as found in casual use and in novels and plays, and historical and developmental facts about quotation. (shrink)

With the advent of classical logic we are continuing to observe an adherence to the laws of logic. Moreover, the system of classical logic exhibits a prominent role within analytic philosophy. Given that the laws of logic have persistently endured in actively defining classical logic and its preceding system of logic, it begs the question as to whether it actually proves to be consistent with Islam. To consider this inquiry in a broader manner; it (...) would be an investigation into the consistency between Islam and the logic which has been the predominant driving force of analytic philosophy. Despite the well documented engagement and novel contributions made in the field of logic by Arab and Islamic theologians/logicians, I think this question deserves examination not just in terms of classical logic but also from perspectives which go beyond classical logic, namely, non-classical logic. Doing so, would I believe, retain this inquiry within the purview of analytic philosophy despite the reference to non-classical logic. To be more specific, this question would be directed toward the Islamic theologian who espouses the system of classical logic in attempting to make sense of an absolute ineffable God of Islam. The inquiry would seek to determine if classical logic is consistent (amenable) in making sense of an absolute ineffable God of Islam. This would principally involve an analysis which determines whether the metaphysical assumptions of the laws of logic (more specifically the law of non-contradiction) are consistent in making sense of an absolute ineffable God of Islam. I shall argue that it is inconsistent. I shall establish my position on this matter by demonstrating why classical logic is inconsistent (not amenable) with an absolute ineffable God of Islam. Although, I am principally concerned with classical logic, my argument is as applicable to all earlier systems of logic as much as it is to classical logic. This is on the basis that both systems of logic, namely, all preceding systems and classical logic, consider the laws of logic as defining features. (shrink)

Some expressions of English, like the demonstratives ‘this’ and ‘that’, are referentially promiscuous: distinct free occurrences of them in the same sentence can differ in content relative to the same context. One lesson of referentially promiscuous expressions is that basic logical properties like validity and logical truth obtain or fail to obtain only relative to a context. This approach to logic can be developed in just as rigorous a manner as David Kaplan’s classic logic of demonstratives. The result (...) is a logic that applies to arguments in English containing multiple occurrences of referentially promiscuous expressions. (shrink)

The writings of Nishida Kitar , whose name has become almost synonymous with Japanese philosophy, continue to attract attention around the world. Yet studies of his thought in Western languages have tended to overlook two key areas: first, the influence of the generation of Japanese philosophers who preceded Nishida; and second, the logic of basho (place), the cornerstone of Nishida's mature philosophical system. The Logic of Nothingness addresses both of these topics. Robert Wargo argues that the overriding concern (...) of Nishida's mature philosophy, the attempt to give a reasonable account of reality that includes the reasonableness of that account itself--or what Wargo calls the problem of completeness--has its origins in Inoue Enryo's (1858-1919) and Inoue Tetsujiro's (1855-1944) preoccupation with the problem of standpoints. A translation of one of Nishida's most demanding texts, included here as an appendix, demonstrates the value of Wargo's insightful analysis of the logic of basho as an aid to deciphering the philosopher's early work. (shrink)

In order to capture our intuitions about the logical consistency of sentences and the logical validity of arguments, a semantics for a natural language has to allow for the fact that different occurrences of a single bare demonstrative, such as “this”, may refer to different objects. But it is not obvious how to formulate a semantic theory in order to achieve this result. This paper first criticizes several proposals: that we should formulate our semantics as a semantics for tokens, not (...) expressions, Kaplan’s idea that syntax associates a demonstration with each occurrence of a demonstrative, Braun’s idea that a context may specify shifts in context across the evaluation of the expressions in a sentence; and Predelli’s idea that we should countenance different classes of contexts. Finally, a solution is proposed that allows that a natural language persists across the addition of basic lexical items but defines logical properties in terms of language stages. A surprising result is that we do not need to think of demonstratives as taking different referents in different situations. (shrink)

Given the plethora of competing logical theories of validity available, it’s understandable that there has been a marked increase in interest in logical epistemology within the literature. If we are to choose between these logical theories, we require a good understanding of the suitable criteria we ought to judge according to. However, so far there’s been a lack of appreciation of how logical practice could support an epistemology of logic. This paper aims to correct that error, by arguing for (...) a practice-based approach to logical epistemology. By looking at the types of evidence logicians actually appeal to in attempting to support their theories, we can provide a more detailed and realistic picture of logical epistemology. To demonstrate the fruitfulness of a practice-based approach, we look to a particular case of logical argumentation—the dialetheist’s arguments based upon the self-referential paradoxes—and show that the evidence appealed to support a particular theory of logical epistemology, logical abductivism. (shrink)

In the Posterior Analytics Aristotle contrasts demonstrations with syllogisms through signs. In the Prior Analytics he defines a sign as a demonstrative premise. One is thus led to ask: is a sign a demonstration? This book reconstructs the history of the notion of "demonstration through signs" from roughly the third through to the thirteenth century. It examines the work of Aristotle's Greek, Arabic, and Latin commentators, both within and outside the tradition of the Posterior Analytics.

By logic I mean the subject Aristotle started in Prior Analytics. Logic studies demonstration and everything necessary for demonstration, and also many things that come to mind in the course of such studies—including axiomatic method as described in my short “Axiomatic method”. By young I mean less than about 40 years old. By logicians I mean people who have dedicated their lives to advancing and criticizing logic: to discovering and establishing new additions and also to (...) clarifying and correcting what has or had been accepted. More specifically, my advice is for people who have already embarked on their careers: from fresh PhDs, instructors, and assistant professors to young professors looking forward to reaping the fruits of their long years of study and research. My advice is for people who have mastered logic and who want to improve their mastery. I would write something very different for students, something along the lines of my “Logic teaching in the 21st century”. Some of the things I recommend you have already done. Please do not think that my recommending something suggests that I think you have not already done it. Moreover, I am fully aware that other retired logicians are as qualified as I to give advice that will help you make the most of your remaining years as an active logician. I hope you seek their advice. I can tell you with certainty that some of their advice will conflict with mine and that some of their advice will serve you better. Temperaments vary; this advice will not be suitable for all temperaments. Be careful whose advice you accept. The lessons of my paper “Critical thinking and pedagogical license” apply here. I recommend that you consider its implications for career decisions. (shrink)

The chapters in this timely volume aim to answer the growing interest in Arthur Schopenhauer’s logic, mathematics, and philosophy of language by comprehensively exploring his work on mathematical evidence, logic diagrams, and problems of semantics. Thus, this work addresses the lack of research on these subjects in the context of Schopenhauer’s oeuvre by exposing their links to modern research areas, such as the “proof without words” movement, analytic philosophy and diagrammatic reasoning, demonstrating its continued relevance to current discourse (...) on logic. -/- Beginning with Schopenhauer’s philosophy of language, the chapters examine the individual aspects of his semantics, semiotics, translation theory, language criticism, and communication theory. Additionally, Schopenhauer’s anticipation of modern contextualism is analyzed. The second section then addresses his logic, examining proof theory, metalogic, system of natural deduction, conversion theory, logical geometry, and the history of logic. Special focus is given to the role of the Euler diagrams used frequently in his lectures and their significance to broader context of his logic. In the final section, chapters discuss Schopenhauer’s philosophy of mathematics while synthesizing all topics from the previous sections, emphasizing the relationship between intuition and concept. -/- Aimed at a variety of academics, including researchers of Schopenhauer, philosophers, historians, logicians, mathematicians, and linguists, this title serves as a unique and vital resource for those interested in expanding their knowledge of Schopenhauer’s work as it relates to modern mathematical and logical study. (shrink)

Throughout the twentieth century, the classical logic of Frege and Russell dominated the field of formal logic. But, as Ross Brady argues, a new type of weak relevant logic may prove to be better equipped to present new solutions to persistent paradoxes. _Universal Logic _begins with an overview of classical and relevant logic and discusses the limitations of both in analyzing certain paradoxes. It is the first text to demonstrate how the main set-theoretic and semantic (...) paradoxes can be solved in a systematic way and as such will be of great interest to both scholars and students of logic. (shrink)

Logic is a celebrated representation language because of its formal generality. But there are two senses in which a logic may be considered general, one that concerns a technical ability to discriminate between different types of individuals, and another that concerns constitutive norms for reasoning as such. This essay embraces the former, permutation-invariance conception of logic and rejects the latter, Fregean conception of logic. The question of how to apply logic under this pure invariantist view (...) is addressed, and a methodology is given. The pure invariantist view is contrasted with logical pluralism, and a methodology for applied logic is demonstrated in remarks on a variety of issues concerning non-monotonic logic and non-monotonic inference, including Charles Morgan’s impossibility results for non-monotonic logic, David Makinson’s normative constraints for non-monotonic inference, and Igor Douven and Timothy Williamson’s proposed formal constraints on rational acceptance. (shrink)

In this paper I argue that demonstrative induction can deal with the problem ofthe underdetermination of theory by evidence. I present the historical case studyof spectroscopy in the early 1920s, where the choice among different theorieswas apparently underdetermined by spectroscopic evidence concerning the alkalidoublets and their anomalous Zeeman effect. By casting this historical episodewithin the methodological framework of demonstrative induction, the localunderdetermination among Bohr's, Heisenberg's, and Pauli's rival theories isresolved in favour of Pauli's theory of the electron's spin.