Universal Logic is not a new logic, but a general theory of logics, considered as mathematical structures. The name was introduced about ten years ago, but the subject is as old as the beginning of modern logic: Alfred Tarski and other Polish logicians such as Adolf Lindenbaum developed a general theory of logics at the end of the 1920s based on consequence operations and logical matrices. The subject was revived after the flowering of thousands of new logics (...) during the last thirty years: there was a need for a systematic theory of logics to put some order in this chaotic multiplicity. This book contains recent works on universal logic by first-class researchers from all around the world. The book is full of new and challenging ideas that will guide the future of this exciting subject. It will be of interest for people who want to better understand what logic is. Tools and concepts are provided here for those who want to study classes of already existing logics or want to design and build new ones. (shrink)

I read Stefan Collini’s What are Universities For? last week with very mixed feelings. In the past, I’ve much admired his polemical essays on the REF, “impact”, the Browne Report, etc. in the London Review of Books and elsewhere: they speak to my heart. If you don’t know those essays, you can get some of their flavour from his latest article in the Guardian yesterday. But I found the book a disappointment. Perhaps the trouble is that Collini is too decent, (...) too high-minded, has too unrealistically exalted a view about what actually happens in universities which is too coloured by attitudes appropriate to the traditional humanities. And he is optimistic to the point of fantasy if he thinks that people are so susceptible to “the romance of ideas and the power of beauty” that they will want, or can be brought to want, lots and lots of universities in order to promote the ideas (as if they would suppose that the task of “conserving, understanding, extending and handing on to subsequent generations the intellectual, scientific, and artistic heritage of mankind” was clearly ill-served when there were only forty universities in England, as opposed to a hundred and whatever). (shrink)

Universal Logic is not a new logic, but a general theory of logics, considered as mathematical structures. The name was introduced about ten years ago, but the subject is as old as the beginning of modern logic: Alfred Tarski and other Polish logicians such as Adolf Lindenbaum developed a general theory of logics at the end of the 1920s based on consequence operations and logical matrices. The subject was revived after the flowering of thousands of new logics (...) during the last thirty years: there was a need for a systematic theory of logics to put some order in this chaotic multiplicity. This bo. (shrink)

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)

The square of opposition is a diagram related to a theory of oppositions that goes back to Aristotle. Both the diagram and the theory have been discussed throughout the history of logic. Initially, the diagram was employed to present the Aristotelian theory of quantification, but extensions and criticisms of this theory have resulted in various other diagrams. The strength of the theory is that it is at the same time fairly simple and quite rich. The theory of oppositions has (...) recently become a topic of intense interest due to the development of a general geometry of opposition (polygons and polyhedra) with many applications. A congress on the square with an interdisciplinary character has been organized on a regular basis (Montreux 2007, Corsica 2010, Beirut 2012, Vatican 2014, Rapa Nui 2016). The volume at hand is a sequel to two successful books: The Square of Opposition - A General Framework of Cognition, ed. by J.-Y. Béziau & G. Payette, as well as Around and beyond the Square of Opposition, ed. by J.-Y. Béziau & D. Jacquette, and, like those, a collection of selected peer-reviewed papers. The idea of this new volume is to maintain a good equilibrium between history, technical developments and applications. The volume is likely to attract a wide spectrum of readers, mathematicians, philosophers, linguists, psychologists and computer scientists, who may range from undergraduate students to advanced researchers. (shrink)

Ancient dialectic started as an art of refutation and evolved into a science akin to our logic, grammar and linguistics. Scholars of ancient philosophy have traditionally focused on Plato's and Aristotle's dialectic without paying much attention to the diverse conceptions and uses of dialectic presented by philosophers after the classical period. To bridge this gap, this volume aims at a comprehensive understanding of the competing Hellenistic and Imperial definitions of dialectic and their connections with those of the classical period. (...) It starts from the Megaric school of the fourth century BCE and the early Peripatetics, via Epicurus, the Stoics, the Academic sceptics and Cicero, to Sextus Empiricus and Galen in the second century CE. The philosophical foundations and various uses of dialectic are closely analysed and systematically examined together with the numerous objections that were raised against them. (shrink)

In the first part of the paper we study arithmetical properties of Pascal triangles modulo a prime power; the main result is the generalization of Lucas' theorem. Then we investigate the structure N; Bpx, where p is a prime, α is an integer greater than one, and Bpx = Rem, px); it is shown that addition is first-order definable in this structure, and that its elementary theory is decidable.

Let $ be the restriction of usual order relation to integers which are primes or squares of primes, and let ⊥ denote the coprimeness predicate. The elementary theory of $\langle\mathbb{N};\bot, , is undecidable. Now denote by $ the restriction of order to primary numbers. All arithmetical relations restricted to primary numbers are definable in the structure $\langle\mathbb{N};\bot, . Furthermore, the structures $\langle\mathbb{N};\mid, and $\langle\mathbb{N};=,+,x\rangle$ are interdefinable.

Rationals and countable ordinals are important examples of structures with decidable monadic second-order theories. A chain is an expansion of a linear order by monadic predicates. We show that if the monadic second-order theory of a countable chain C is decidable then C has a non-trivial expansion with decidable monadic second-order theory.

The First International Workshop brings together researchers from the theoretical ends of the logic programming and artificial intelligence communities to discuss their mutual interests. Logic programming deals with the use of models of mathematical logic as a way of programming computers, where theoretical AI deals with abstract issues in modeling and representing human knowledge and beliefs. One common ground is nonmonotonic reasoning, a family of logics that includes room for the kinds of variations that can be found (...) in human reasoning. Topics covered: Stable Semantics. Default Logic. AutoEpistemic Logic. Truth Maintenance Systems. Implementation Issues. Diagnosis. Applications. Inheritance Reasoning. Logics of Belief. Inconsistency and Non-Monotonicity. (shrink)

Az egzisztencializmus és irodalma.--A neopozitivizmus és a dolgok művészete.--Az új baloldal művészetfelfogása.--A szocialista realizmus történeti útja és fő jellemzői.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public (...) domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

The first part of this essay develops the idea of logic as the science of thought, articulating, and thus being, the self-consciousness of thought. It explains that logic, so understood, is nothing other than metaphysics, the science of what is in so far as it is. Self-consciousness, then, thought itself, is not empty, but the source of all content. The second part of the essay discusses the opening paragraphs of Hegel’sScience of Logic; it shows how, in (...) these paragraphs, thought is revealed to be the source of its own content in virtue of its original negativity. Thus the second part begins to make concrete the idea of logic provided by the first. (shrink)

I discuss Thomas Aquinas’ views on being, power, and logic, and show how together they provide rebuttals against certain principal objections to the notion of divine omnipotence. The objections I have in mind can be divided into the two classes. One says that the notion of omnipotence ends up in self-contradiction. The other says that it ends up contradicting certain doctrines of traditional theism. Thomas’ account is frequently misunderstood to be a version of what I call a ‘consistent (...) description’ account of omnipotence, which is a standard contemporary account. That account of omnipotence, however, succumbs to certain contemporary objections. Thomas’ account withstands those objections because of his view of logic and, specifically self-contradiction. Moreover, a certain thesis found in Thomas’ understanding of God, but almost entirely absent from contemporary debates about omnipotence, is that God is not just a being, but the source of being. This thesis, I argue, puts Thomas’ account in a position that differs greatly from many contemporary accounts since the scope of possibility, and specifically the scope of what possible powers there are, is ultimately grounded in God’s being. Further still, many contemporary accounts of omnipotence do not seek to establish substantive account of power itself. Thomas, by contrast, has a robust and independent account of what power is. And that account informs his account of what it is to have all powers, or to be omnipotent, in a way that makes his account resistant to contemporary objections. Against contemporary objections, Thomas’ account of omnipotence can sustain the claim that God can do all things. (shrink)

What I think remains sustainable and valid in Hegel's thought is the attempt to regard the ongoing crisis of reason as itself constitutive of self-consciousness. |s Revue Internationale de Philosophie |d 01/10/1996.

This dissertation is a comparative study of Aristotelian and Chinese logic. I briefly overview the reports of difficulties in understanding that derives from cultural differences. I claim that these difficulties not only result from the fact that concepts in each language fail to match properly, but also from the fact that the logical spaces themselves are structured differently. Aristotelian logic is based on the structure of a classificatory system---a hierarchical structure of names for kinds of things organized into (...) genera/species. Chinese logic is based on a Chinese binary system---a yin-yang structure of associative relations. ;I discuss the difficulties of translating the first three chapters of Matthew Lipman's Harry Stottlemeier's Discovery---one of a series of novels used in the Philosophy for Children Project---into Chinese. These chapters discuss the logical relations constituting the Aristotelian Square of Opposition. I find that most translation problems result from the fact that the logical structures of these two languages fail to match. ;I report my research on the responses of American and Chinese school children to reading chapter one of Harry Stottlemeier's Discovery , one in the original English version and the other in Chinese. The study of discussions among older children offers evidence for my claim that logical spaces of Western and Chinese thinking are structured differently, but the study of discussions among younger children gives a hope that there is a chance for there to be communication between the two very different ways of thinking. ;The conclusion is that Aristotelian logic and Chinese logic have two very different objectives, and as a consequence, different patterns for constructing logical relations. These two patterns represent two thinking models. The former is like a tree. It represents a finite number of things according to a presumed order. The latter is like a net; from any point on the net, one can link to any number of related points in an ever-changing world. The possibility of a mutually beneficial rapprochement between Chinese and Aristotelian logic depends on whether we can lay out a way for each side to understand the other in a common discourse. (shrink)

What I think remains sustainable and valid in Hegel's thought is the attempt to regard the ongoing crisis of reason as itself constitutive of self-consciousness. |s Revue Internationale de Philosophie |d 01/10/1996.

This volume may be of interest for all those who wish that philosophy had a scientific character. As an adherent of the Polish Lvov-Warsaw Philosophical School, the author of this collection of papers endeavours to clarify some basic notions of epistemology, ontology and psychology of cognitive acts, such as judgment, existence, being etc. In his investigations he refrains from unnecessary rejection of common-sense knowledge but at the same time searches for suitable patterns in contemporary sciences. Regarding formal logic (...) as a fundamental tool for the precise expression and justification of thoughts, the author tries to clear logic from ontological commitments, shows how to construct logic of norms and how to use safely different definitions in research works. The book presents a new conception of antinomies and an innovatory approach to realistic epistemology. Moreover, some applications of logical methods are illustrated by examples of semantical analyses of the general notion of similarity and the biological concept of homology. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public (...) domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Excerpt from Hegel's Doctrine of Formal Logic: Being a Translation of the First, Section of the Subjective Logic It has been my great good fortune to have freely at my disposal during the preparation of this work the wide knowledge and wise judgement of my friend Dr. James Creed Meredith. I am indeed deeply in his debt for his valuable assistance, ever ready to my call but I can console myself by reflecting that the reader is still (...) more indebted to me for the unstinted use I have made of it. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

If you wish to aid the student whose German is weak to begin reading Hegel, you should compose him a literal crib of the type so helpful to the struggling schoolboy; but you should tell him that he must as soon as possible improve his German and throw away his crutch. If, on the other hand, you are fired by the very different ambition of translating Hegel’s thought truly for the intelligent reader who has no German, then you must write (...) fluent idiomatic English which recalls German forms of speech as little as possible. You may now and then in a footnote or a bracket confess to a liberty taken, but you must always be readable and bold. You must of course know your German, and your Hegelian German, very well, but you must not only prune otiose expletives but not shrink even from metamorphosis. Apart from rash Phaethons like Osmaston who knew little German and less philosophy, too many English translators of Hegel have tried to compromise between the high road and the low road; but partly because they have been baffled by an obscure text, partly because they have clung with misplaced fidelity to the German, they have commonly produced dreary versions which crawl cribwise on the ground. They have forgotten that ineptitudes can be nearly as misleading as errors and far more tedious. (shrink)

The logic of ‘being informed’ gives a formal analysis of a cognitive state that does not coincide with either belief, or knowledge. To Floridi, who first proposed the formal analysis, the latter is supported by the fact that unlike knowledge or belief, being informed is a factive, but not a reflective state. This paper takes a closer look at the formal analysis itself, provides a pure and an applied semantics for the logic of being informed, (...) and tries to find out to what extent the formal analysis can contribute to an information-based epistemology. (shrink)

By playing a crucial role in settling open issues in the philosophical debate about logical consequence, logical evidence has become the holy grail of inquirers investigating the domain of logic. However, despite its indispensable role in this endeavor, logical evidence has retained an aura of mystery. Indeed, there seems to be a great disharmony in conceiving the correct nature and scope of logical evidence among philosophers. In this paper, I examine four widespread conceptions of logical evidence to argue that (...) all should be reconsidered. First, I argue that logical apriorists are more tolerant of logical evidence than empiricists. Second, I argue that evidence for logic should not be read out of natural language. Third, I argue that if logical intuitions are to count as logical evidence, then their evidential content must not be propositional. Finally, I argue that the empiricist proposal of treating experts' judgments as evidence suffers from the same problems as the rationalist conception. (shrink)

Logical monists and pluralists disagree about how many correct logics there are; the monists say there is just one, the pluralists that there are more. Could it turn out that both are wrong, and that there is no logic at all?

Logical Pluralists maintain that there is more than one genuine/true logical consequence relation. This paper seeks to understand what the position could amount to and some of the challenges faced by its formulation and defence. I consider in detail Beall and Restall’s Logical Pluralism—which seeks to accommodate radically different logics by stressing the way that they each fit a general form, the Generalised Tarski Thesis (GTT)—arguing against the claim that different instances of GTT are admissible precisifications of logical consequence. I (...) then consider what it is to endorse a logic within a pluralist framework and criticise the options Beall and Restall entertain. A case study involving many-valued logics is examined. I next turn to issues of the applications of different logics and questions of which logic a pluralist should use in particular contexts. A dilemma regarding the applicability of admissible logics is tackled and it is argued that application is a red herring in relation to both understanding and defending a plausible form of logical pluralism. In the final section, I consider other ways to be and not to be a logical pluralist by examining analogous positions in debates over religious pluralism: this, I maintain, illustrates further limitations and challenges for a very general logical pluralism. Certain less wide-ranging pluralist positions are more plausible in both cases, I suggest, but assessment of those positions needs to be undertaken on a case-by-case basis. (shrink)

An interesting question is whether deflationism about truth (and falsity) extends to related properties and relations on truthbearers. Lionel Shapiro (2011) answers affirmatively by arguing that a certain deflationism about truth is as plausible as an analogous version of deflationism about logical consequence. I argue that the argument fails on two counts. First, it trivializes to any relation between truthbearers, including substantive ones; in other words, his argument can be used to establish that deflationism about truth is as plausible as (...) deflationism about an arbitrary sentential relation. Second, the alleged analogy between the arguments for deflationism about truth and deflationism about consequence fails. Along the way I consider what implications the failure of the equiplausibility thesis has for deflationism about falsity. (shrink)

One of the open problems in the philosophy of information is whether there is an information logic (IL), different from epistemic (EL) and doxastic logic (DL), which formalises the relation “a is informed that p” (Iap) satisfactorily. In this paper, the problem is solved by arguing that the axiom schemata of the normal modal logic (NML) KTB (also known as B or Br or Brouwer’s system) are well suited to formalise the relation of “being informed”. After (...) having shown that IL can be constructed as an informational reading of KTB, four consequences of a KTB-based IL are explored: information overload; the veridicality thesis (Iap → p); the relation between IL and EL; and the Kp → Bp principle or entailment property, according to which knowledge implies belief. Although these issues are discussed later in the article, they are the motivations behind the development of IL. (shrink)

This paper addresses three problems: the problem of formulating a coherent relativism, the Sorites paradox and a seldom noticed difficulty in the best intuitionistic case for the revision of classical logic. A response to the latter is proposed which, generalised, contributes towards the solution of the other two. The key to this response is a generalised conception of indeterminacy as a specific kind of intellectual bafflement-Quandary. Intuitionistic revisions of classical logic are merited wherever a subject matter is conceived (...) both as liable to generate Quandary and as subject to a broad form of evidential constraint. So motivated, the distinctions enshrined in intuitionistic logic provide both for a satisfying resolution of the Sorites paradox and a coherent outlet for relativistic views about, e.g., matters of taste and morals. An important corollary of the discussion is that an epistemic conception of vagueness can be prised apart from the strong metaphysical realism with which its principal supporters have associated it, and acknowledged to harbour an independent insight. (shrink)

The paper concerns time, change and contradiction, and is in three parts. The first is an analysis of the problem of the instant of change. It is argued that some changes are such that at the instant of change the system is in both the prior and the posterior state. In particular there are some changes from p being true to p being true where a contradiction is realized. The second part of the paper specifies a formal (...) class='Hi'>logic which accommodates this possibility. It is a tense logic based on an underlying paraconsistent prepositional logic, the logic of paradox. (See the author's article of the same name Journal of Philosophical Logic 8 (1979).) Soundness and completeness are established, the latter by the canonical model construction, and extensions of the basic system briefly considered. The final part of the paper discusses Leibniz's principle of continuity: Whatever holds up to the limit holds at the limit. It argues that in the context of physical changes this is a very plausible principle. When it is built into the logic of the previous part, it allows a rigorous proof that change entails contradictions. Finally the relation of this to remarks on dialectics by Hegel and Engels is briefly discussed. (shrink)