I investigate the consequences of Nietzsche's perspectivism for notions of truth and objectivity, and show how the metaphor of visual perspective motivates an epistemology that avoids self-referential difficulties. Perspectivism's claim that every view is only one view, applied to itself, is often supposed to preclude the perspectivist's ability to offer reasons for her epistemology. Nietzsche's arguments for perspectivism depend on “internal reasons”, which have force not only in their own perspective, but also within the standards of alternative perspectives. Internal reasons (...) allow a perspectivist argument against dogmatism without presupposing aperspectival criteria for theory choice. Nietzsche also offers “internal” conceptions of truth and objectivity which reduce them to a matter of meeting our epistemic standards. This view has pluralistic implications, which conflict with common sense, but it is nevertheless consistent and plausible. Nietzsche's position is similar to Putnam's recent internalism, and this is due to their common Kantian heritage. (shrink)

This paper is a contribution to the study of equality-free logic, that is, first-order logic without equality. We mainly devote ourselves to the study of algebraic characterizations of its relation of elementary equivalence by providing some Keisler-Shelah type ultrapower theorems and an Ehrenfeucht-Fraïssé type theorem. We also give characterizations of elementary classes in equality-free logic. As a by-product we characterize the sentences that are logically equivalent to an equality-free one.

A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz–Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable ‘next-state functions’ is extended to (...) a Łukasiewicz–Moisil Topos with an n-valued Łukasiewicz–Moisil Algebraic Logic subobject classifier description that represents non-random and non-linear network activities as well as their transformations in developmental processes and carcinogenesis. The unification of the theories of organismic sets, molecular sets and Robert Rosen’s (M,R)-systems is also considered here in terms of natural transformations of organismal structures which generate higher dimensional algebras based on consistent axioms, thus avoiding well known logical paradoxes occurring with sets. Quantum bionetworks, such as quantum neural nets and quantum genetic networks, are also discussed and their underlying, non-commutative quantum logics are considered in the context of an emerging Quantum Relational Biology. (shrink)

The notion of the rational closure of a positive knowledge base K of conditional assertions θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document} |∼ φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document} (standing for if θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document} then normally φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document}) was first introduced by Lehmann (1989) and developed by Lehmann and Magidor (...) (1992). Following those authors we would also argue that the rational closure is, in a strong sense, the minimal information, or simplest, rational consequence relation satisfying K. In practice, however, one might expect a knowledge base to consist not just of positive conditional assertions, θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document} |∼ φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document}, but also negative conditional assertions, θi φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document} (standing for not if θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document} then normally φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document}. Restricting ourselves to a finite language we show that the rational closure still exists for satisfiable knowledge bases containing both positive and negative conditional assertions and has similar properties to those exhibited in Lehmann and Magidor (1992). In particular an algorithm in Lehmann and Magidor (1992) which constructs the rational closure can be adapted to this case and yields, in turn, completeness theorems for the conditional assertions entailed by such a mixed knowledge base. (shrink)

The Joint International Conference on Logic Programming, sponsored by the Association for Logic Programming, is a major forum for presentations of research, applications, and implementations in this important area of computer science. Logic programming is one of the most promising steps toward declarative programming and forms the theoretical basis of the programming language Prolog and its various extensions. Logic programming is also fundamental to work in artificial intelligence, where it has been used for nonmonotonic and commonsense (...) reasoning, expert systems implementation, deductive databases, and applications such as computer-aided manufacturing. Krzysztof R. Apt is project leader at the Centre for Mathematics and Computer Science in Amsterdam and part-time Professor in Computer Science at the University of Amsterdam. Topics covered: Theory Foundations. Programming Languages. Implementation. Programming Methodologies and Tools. Applications. Deductive Databases. Artificial Intelligence. Parallelism. (shrink)

Problems of logical theory choice are current being widely dis- cussed in the context of anti-exceptionalist views on logic. According to those views, logic is not a special science among others, so, in particular, the methodology for theory choice should be the same in logic as for other scientific disciplines. Richard Routley advanced one such methodology which meshes well with anti-exceptionalism, and argued that it leads one to choosing one single logic, which is a kind of (...) ultralogic. We argue that the choice for only one correct system of logic may be rejected on the basis of the methodology proposed by Routley and, furthermore, that taking anti-exceptionalism about logic seriously recommends that a pluralist view of logic should be accepted. We call this view “full-blooded anti-exceptionalism”, and the resulting view on logic, lacking a proper name, “local pluralism”. (shrink)

It is shown that the notion of the partition of a set can be used to describe in a uniform way the meaning of the expression the same, in its basic uses in transitive and ditransitive sentences. Some formal properties of the function denoted by the same, which follow from such a description are indicated. These properties indicate similarities and differences between functions denoted by the same and generalised quantifiers.

Argumentation represents a way of reasoning over a knowledge base containing possibly incomplete and/or inconsistent information, to obtain useful conclusions. As a reasoning mechanism, the way an argumentation reasoning engine reaches these conclusions resembles the cognitive process that humans follow to analyze their beliefs; thus, unlike other computationally reasoning systems, argumentation offers an intellectually friendly alternative to other defeasible reasoning systems. LogicProgrammingisacomputationalparadigmthathasproducedcompu- tationallyattractivesystemswithremarkablesuccessinmanyapplications. Merging ideas from both areas, Defeasible Logic Programming offers a computational reasoning system that uses an argumentation (...) engine to obtain answers from a knowledge base represented using a logic programming language extended with defeasible rules. This combination of ideas brings about a computationally effective system together with a human-like reasoning model facilitating its use in applications. (shrink)

The death of Imre Lakatos on February 2, 1974 was a personal and philosophical loss to the worldwide circle of his friends, colleagues and students. This volume reflects the range of his interests in mathematics, logic, politics and especially in the history and methodology of the sciences. Indeed, Lakatos was a man in search of rationality in all of its forms. He thought he had found it in the historical development of scientific knowledge, yet he also saw rationality endangered (...) everywhere. To honor Lakatos is to honor his sharp and aggressive criticism as well as his humane warmth and his quick wit. He was a person to love and to struggle with. PAUL K. FEYERABEND ROBERT S. COHEN MARX W. WARTOFSKY TABLE OF CONTENTS Preface VII JOHN WORRALL / Imre Lakatos : Philosopher of Mathematics and Philosopher of Science JOSEPH AGASSI / The Lakatosian Revolution 9 23 D. M. ARMSTRONG / Immediate Perception w. W. BAR TLEY, III/On Imre Lakatos 37 WILLIAM BERKSON / Lakatos One and Lakatos Two: An Appreciation 39 I. B. COHEN / William Whewell and the Concept of Scientific Revolution 55 L. JONATHAN COHEN / How Can One Testimony Corroborate Another? 65 R. S. COHEN / Constraints on Science 79 GENE D'AMOUR/ Research Programs, Rationality, and Ethics 87 YEHUDA ELKANA / Introduction: Culture, Cultural System and Science 99 PA UL K. (shrink)

Some of my best friends are women, but I would not want my sister to marry one of them. Modern-minded persons criticize me for manifesting such out-dated prejudices, and would like to send me to Coventry for a compulsory course of reindoctrination. They may be right. It could conceivably be the case that in due course the Sex Discrimination Act will be tightened up, even to the extent of our recognizing that there are no ‘good reasons why the State should (...) not recognize contracts which are in all respects like marriage, except for the sex of the parties concerned’. We can envisage a society so enlightened that the relations between men and women will be purely platonic and it will be a matter of no concern whether two people are members of the opposite sex or not: or, alternatively, our feelings could be so completely homogenized, that it will make no difference to an emotional relationship whether Leslie and Julian have only one Y-chromosome between them, or two, or none at all. In that event I shall be shown to be wrong, and my critics entitled to erect a monument to female equality on my grave. But I have doubts, and suspect that long after I am dead men will go on falling in love with women and women will continue to find their hearts wooed and won by men. And this fact, if it is a fact, makes a profound difference to our social institutions. I want to follow out the logic of social differentiation, relying as little as I can on putative facts about the differences between the sexes. Scientifically attested knowledge is scarce in this field. Many academics take refuge in a safe suspension of judgment, but this is a craven dereliction of duty. We have yet to develop an adequate theory of knowledge in social matters, and only by thrashing out the apparently telling arguments on this and similar issues can we clear our minds about the nature of social knowledge. Moreover, if those who might argue rationally draw back from doing so, they leave the field clear for others who suffer from fewer inhibitions and fewer scruples. And finally, serious social consequences can follow from public confusion about the logic of a situation, and what things are possible and what desirable. There is a danger that in our attempts to remedy the real wrongs done to women we shall only succeed, as with much modern legislation, in making a bad case worse. (shrink)

In this paper we attempt to formulate logical foundations for a theory of actions or performance. Human beings act in various ways, and their actions are intimately interrelated with their use of language. But precisely how actions and the use of language are interrelated is not very clear. One of the reasons is perhaps that we have no precise vocabulary in terms of which such interrelations may be handled. There is need for developing a systematic theory in which different kinds (...) of actions may be discussed, contrasted, and compared. Then the various interrelations between actions and linguistic usage may perhaps be discussed rather more carefully and thoroughly than heretofore. Although much important preliminary work has been done in the analysis of actions, no one it seems has attempted to develop a strict logical theory for such analysis. A few tentative and programmatic steps were taken in the author's Toward a Systematic Pragmatics. Let us attempt here to improve those and take a few more. Any first attempts of this kind are of course fraught with difficulties. There inevitably will be some oversimplification or some overelaboration here or there. Ultimately of course we are interested in interrelating performance with various notions from syntax, semantics, and quantitative pragmatics. But this is not easy and only a few tentative suggestions toward such a development can be given here. In section 1 the distinction between action-kinds and action-events is drawn, and the character of the primitive or primitives needed for the theory of performance is discussed. In section 2 some further notions are then defined. Certain Rules of Performance are suggested in section 3. In section 4 there is discussion of the somewhat tenuous notion of acceptance as a basis for action. In section 5 the fundamental notions required for Parsons and Shils' theory of social action is discussed briefly. In section 6 we attempt to define the two basic notions required in Leonard's recent papers concerning authorship and purpose. Finally, in section 7, the theory of performance is interrelated with von Wright's deontic logic, in which such notions as permission and obligation are considered. (shrink)

This book is less about disjunction than about the English word ‘or’, and it is less for than against formal logicians—more exactly, against those who maintain that formal logic can be applied in certain ways to the evaluation of reasoning formulated in ordinary English. Nevertheless, there are many things to interest such of those persons who are willing to overlook the frequent animadversions directed against their kind in the book, and this review will concentrate on them.

The author, who pioneered this argument in 1961, here places it in the context of traditional discussions of the problem, and answers various criticisms that have been made.

In this paper I am merely analysing the meaning of Phaedo 99–107 without discussing either its historical significance or its value as a contribution to the logic of science. The paper attempts in fact to be little more than a paraphrase of the Greek, which aims only at accuracy of statement, but I am adding in the third section a note on the relation of this passage to the discussion of method in Republic VI, mainly in order to minimize (...) its relevance. The first section of the paper deals with the linguistic analysis of the text, the second, very sketchily, with the general doctrine. (shrink)

Minimality ranks in the style of Deissler are one way of measuring the structural complexity of minimal extensions of first-order structures. In particular, positive Deissler rank measures the complexity of the injective envelope of a module as an extension of that module. In this paper we solve a problem of the second author by showing that certain injective envelopes have the maximum possible positive Deissler rank complexity. The proof shows that this complexity naturally reflects the internal structure of the injective (...) extension in the form of the levels of the Matlis hierarchy. (shrink)

The four authors present their speculations about the future developments of mathematical logic in the twenty-first century. The areas of recursion theory, proof theory and logic for computer science, model theory, and set theory are discussed independently.

In this analysis, I employ Husserl’s three-part description of intentionality to show how a player/play act/play object model for consciousness helps us see play more clearly. I review Suits’ logic-based attempts to amend Huizinga’s overly inclusive characterization of play. However, I do so on what I see as stronger phenomenological grounds by describing four kinds of experience embedded in Suits’ work-play dichotomy. I analyze two species of play-fortified work – namely, work that requires intrinsic enhancement and work that does (...) not. I also describe two species of play – namely, play that is compromised and play that is unfettered. I conclude by summarizing advantages of phenomenological analyses and underlining the important distinctions this philosophic method uncovers within traditional work and play categories. (shrink)

Given a structure for a first-order language L, two objects of its domain can be indiscernible relative to the properties expressible in L, without using the equality symbol, and without actually being the same. It is this relation that interests us in this paper. It is called Leibniz equality. In the paper we study systematically the problem of its definibility mainly for classes of structures that are the models of some equality-free universal Horn class in an infinitary language Lκκ, where (...) κ is an infinite regular cardinal. (shrink)