Several of these essays have been printed whole in journals; others are in varying degrees new. Two main themes run through them. One is the problem of meaning, particularly as involved in the notion of an analytic statement. The other is the notion of ontological, commitment, particularly as involved in the problem of universals.

Russell's involuted path in the development of his theory of logical types from 1903 to 1910-13 is examined and explained in terms of the development in his early philosophy of the notion of a logical subject vis-a-vis the problem of the one and many; i.e., the problem for russell, first, of a class-as-one as a logical subject as opposed to a class as many, and, secondly, of a propositional function as a single and separate logical subject (...) as opposed to existing only in the many propositions that are its values. (shrink)

Provides an integrated introduction to artificial intelligence. Develops AI representation schemes and describes their uses for diverse applications, from autonomous robots to diagnostic assistants to infobots. DLC: Artificial intelligence.

I argue for a property mereology and for mereological bundle theory. I then apply this theory to the one over many problem (universals) and puzzles concerning persistence and material constitution.

The Mīmāṃsā school of Indian philosophy has for its main purpose the interpretation of injunctions that are found in a set of sacred texts, the Vedas. In their works, Mīmāṃsā authors provide some of the most detailed and systematic examinations available anywhere of statements with a deontic force; however, their considerations have generally not been registered outside of Indological scholarship. In the present article we analyze the Mīmāṃsā theory of Vedic injunctions from a logical and philosophical point of view. (...) The theory at issue can be regarded as a system of reasoning based on certain fundamental principles, such as the distinction between strong and weak duties, and on a taxonomy of ritual actions. We start by reconstructing the conceptual framework of the theory and then move to a formalization of its core aspects. Our contribution represents a new perspective to study Mīmāṃsā and outlines its relevance, in general, for deontic reasoning. (shrink)

This book argues that the meaning of negation, perhaps the most important logical constant, cannot be defined within the framework of the most comprehensive theory of proof-theoretic semantics, as formulated in the influential work of Michael Dummett and Dag Prawitz. Nils Kürbis examines three approaches that have attempted to solve the problem - defining negation in terms of metaphysical incompatibility; treating negation as an undefinable primitive; and defining negation in terms of a speech act of denial - and concludes (...) that they cannot adequately do so. He argues that whereas proof-theoretic semantics usually only appeals to a notion of truth, it also needs to appeal to a notion of falsity, and proposes a system of natural deduction in which both are incorporated. Offering new perspectives on negation, denial and falsity, his book will be important for readers working on logic, metaphysics and the philosophy of language. (shrink)

The main idea that we want to defend in this paper is that the question of what a logic is should be addressed differently when structural properties enter the game. In particular, we want to support the idea according to which it is not enough to identify the set of valid inferences to characterize a logic. In other words, we will argue that two logical theories could identify the same set of validities, but not be the same logic.

The paper analyses the concept of ‘bad infinity’ in connection with Hegel’s critique of infinitesimal calculus and with the belittling of Hegel’s mathematical notions by the representatives of modern logic and the foundations of mathematics. The main line of argument draws on the observation that Hegel’s difference is only derivatively a mathematical one and is primarily of a broadly logico-epistemological nature. Because of this, the concept of bad infinity can be fruitfully utilized, by way of inversion, in an analysis of (...) the conceptual shortcomings of the most prominent foundational attempts at dealing with infinite quanta, such as Cantor’s set theory and Hilbert’s axiomatism. As such, the paper is an attempt at reconstructing Hegel’s philosophy of mathematics and its role in his philosophical system and, more importantly, as a contribution to logic in the more general and radical sense of the word. (shrink)

The aim of this paper is to propose a formal approach to reasoning about desires, understood as logical propositions which we would be pleased to make true, also acknowledging the fact that desire is a matter of degree. It is first shown that, at the static level, desires should satisfy certain principles that differ from those to which beliefs obey. In this sense, from a static perspective, the logic of desires is different from the logic of beliefs. While the (...) accumulation of beliefs tend to reduce the remaining possible worlds they point at, the accumulation of desires tends to increase the set of states of affairs tentatively considered as satisfactory. Indeed beliefs are expected to be closed under conjunctions, while, in the positive view of desires developed here, one can argue that endorsing \ as a desire means to desire \ and to desire \. However, desiring \ and \ at the same time is not usually regarded as rational, since it does not make much sense to desire one thing and its contrary at the same time. Thus when a new desire is added to the set of desires of an agent, a revision process may be necessary. Just as belief revision relies on an epistemic entrenchment relation, desire revision is based on a hedonic entrenchment relation satisfying other properties, due to the different natures of belief and desire. While epistemic entrenchment relations are known to be qualitative necessity relations, hedonic relations obeying a set of reasonable postulates correspond to another set-function in possibility theory, called guaranteed possibility, that drive well-behaved desire revision operations. Then the general framework of possibilistic logic provides a syntactic setting for encoding desire change. The paper also insists that desires should be carefully distinguished from goals. (shrink)

Analytical jurisprudence and the legal mainstream perceive legal rights in an interactionist fashion, pursuant to a right-obligation duality. The Paper suggests that this is principally because legal positivism and the analytical Anglo-Saxon legal tradition ground their theories on logical positivism and the Wittgensteinian premise that meaning is produced and asserted in social use, i.e. both consensually and contextually. The paper suggests that there is a surplus of meaning which exists beyond social use and which cannot be conceptualized within the (...) sociolinguistic confines of Wittgenstein’s logic of language. This surplus of meaning corresponds to the essential core of legal rights, which, following Aristotle’s induction and philosophy of the essences, constitutes a necessary property and τὸ τί ἦν εἶναι of legal rights, namely a state of affairs or a state of being that cannot be altered without their necessary breach or, indeed, the negation of their very meaning. The Paper discusses the shortcomings of the Wittgensteinian approach and revisits the philosophical foundations of legal rights by employing Aristotle’s induction and theory of the essences, which the Paper connects to the phenomenological method and particularly Ricoeur’s hermeneutics and Husserl’s transcedental phenomenology. This is a process of abstraction and insight, which aspires to induce a rational revisiting of the general theory of legal rights and address the surplus of meaning that Wittgensteinian logic leaves semantically uncovered. (shrink)

Searle’s Chinese Room Argument (CRA) has been the object of great interest in the philosophy of mind, artificial intelligence and cognitive science since its initial presentation in ‘Minds, Brains and Programs’ in 1980. It is by no means an overstatement to assert that it has been a main focus of attention for philosophers and computer scientists of many stripes. It is then especially interesting to note that relatively little has been said about the detailed logic of the argument, whatever significance (...) Searle intended CRA to have. The problem with the CRA is that it involves a very strong modal claim, the truth of which is both unproved and highly questionable. So it will be argued here that the CRA does not prove what it was intended to prove. (shrink)

In 2004, Garrett Cullity made a significant contribution to the literature on what the world’s relatively affluent owe to the world’s relatively poor through the publishing of The Moral Demands of Affluence. In this discussion note, I draw attention to a logical problem in Cullity’s master argument in favor of the view that affluent individuals are justified in spending monetary resources on themselves at a level that lies well above what Peter Singer finds justified. The proposition I defend is (...) that the premises leading to Cullity’s conclusion about the moderate, and not extremely demanding, nature of his position are inconsistent. These premises license any conclusion, including the negation of the one preferred by Cullity. (shrink)

It is shown that the logical theory of belief statements must be prepared to take into account relationships among statements which are subtler and more delicate than is requisite in other contexts. It is necessary here to draw distinctions (of a modal and semantical character) which the standard assertory logic can ignore with impunity. This is due to the fact that it is entirely possible to be in ignorance of various logical relationships (eg., entailment, equivalence, etc.) that in (...) fact obtain among believed statements, and so, for example to believe the premisses of a valid deductive argument, and yet disbelieve the conclusion which follows from them. The implications of such difficulties for the logic of belief statements are examined. (shrink)

We argued [Since this argument appeared in other journals, I am reprising it here, almost verbatim.] (Fulda in J Law Info Sci 2:230–232, 1991/AI & Soc 8(4):357–359, 1994) that the paradox of the preface suggests a reason why machines cannot, will not, and should not be allowed to judge criminal cases. The argument merely shows that they cannot now and will not soon or easily be so allowed. The author, in fact, now believes that when—and only when—they are ready they (...) actually should be so allowed, in the interests of justice. Both the original argument applied and this detailed reconsideration applies exclusively to trial courts, and both specifically exclude(d) sentencing. The argument highlights some key relevant differences between minds and machines and attempts, also, to explain why automation is of far greater import for the first-level justice system (trial courts) than for higher courts. A final section discusses why sentencing was, is, and should be excluded. (shrink)

Following the speech act theory, we take hypotheses and assertions as linguistic acts with different illocutionary forces. We assume that a hypothesis is justified if there is at least a scintilla of evidence for the truth of its propositional content, while an assertion is justified when there is conclusive evidence that its propositional content is true. Here we extend the logical treatment for assertions given by Dalla Pozza and Garola by outlining a pragmatic logic for assertions and hypotheses. On (...) the basis of this extension we analyse the standard logical opposition relations for assertions and hypotheses. We formulate a pragmatic square of oppositions for assertions and a hexagon of oppositions for hypotheses. Finally, we give a mixed hexagon of oppositions to point out the opposition relations for assertions and hypotheses. (shrink)

Dans la seconde moitié des années 1900, Bertrand Russell et Hugh MacColl échangèrent sans s’entendre sur les questions de l’implication et de l’existence, dans le cadre d’un débat plus général sur la nature de la logique. Il est tentant de voir dans cet échange une opposition entre le moniste logique Russell et le pluraliste MacColl. Dans cet article, j’affirme que cette interprétation est inexacte, et que les deux hommes étaient tous deux monistes, bien qu’ayant des allégeances différentes. La transition du (...) monisme au pluralisme ne s’effectue en réalité qu’à partir du début des années 1910, peu après la mort de MacColl en 1909. Les premiers signes de cette transition sont à trouver particulièrement chez le philosophe américain C. I. Lewis, le mathématicien néerlandais L. E. J. Brouwer, et le logicien polonais Jan Łukasiewicz. Ces auteurs sont des exemples de l’avènement graduel de la métalogique. (shrink)

This book aims to offer an account of conscious experience and of concepts that help us understand empirical reasoning and empirical dialectic. The account offered possesses, it is claimed, two virtues. First, it provides great theoretical freedom. It allows the theoretician freedom to radically reconceive the world. The theoretician may, for example, begin with the conception that colors are genuine qualities of physical bodies and may, in light of empirical findings, shift to the conception that colors are not genuine qualities (...) at all. Second, the account grants empirical reason a great power to constrain: empirical reason can force a particular conception of the self and the world on the rational inquirer. These seemingly contrary virtues are reconciled through a novel treatment of presentation and appearances in the account offered of conscious experience and a novel treatment of ostensive definitions in the account offered of concepts. The argument of the book is buttressed by a critical study of the principal approaches to experience and reason found in the philosophical literature.--. (shrink)

Dr Seuren's study deals with the problem of presenting an adequate model of grammatical description. The model he proposes conforms in its main outlines to the transformational generative grammar established by Chomsky, but differs in important respects. These mainly affect that part of Chomsky's syntactic component known as the 'base', which generates basic or 'deep' structures. In the model of the base proposed here two main constituents are distinguished for every deep structure representation of a sentence, vis-a-vis the operators and (...) the nucleus. The deep structure of a sentence is thus seen to be very similar to the logical structure of a proposition. The arguments given in support of this analysis are based on mainly on considerations of simplicity and semantic adequacy. (shrink)

A new frame of reference, which in its fundamental structuring differs radically from the structuring of the familiar western Indo-European viewpoints (logical, mathematical, scientific, philosophical, etc.), already exists. Recently, by the strategem of systematically disallowing a previously unnoticed untenable assumption encoded in the traditional Western symbolic logics, set theories, etc., in particular and in the Western World-View in general, this frame of reference has generated its own, entirely non-traditional, formalized language. The Notre Dame Journal of Formal Logic has accepted (...) for publication a first paper presenting this non-standard formalized language (Hilgartner, 1975).As one of its accomplishments, this new frame of reference delivers a general theory of living. This theory purports to span the entire domain of what we call living systems, human or non-human. (shrink)

Two experiments examined the role of conditional reasoning in the logical deduction game, Mastermind . An analysis suggested that Modus Tollens (MT) reasoning could be used to determine the code structure, for example, in determining if any of the colours in the code are repeated. Consistent with this analysis, Experiment 1 showed that only MT errors are correlated with the number of hypotheses advanced in Mastermind . A subsequent analysis showed that conditional reasoning such as Affirming the Consequent (AC) (...) and Denying the Antecedent (DA) could lead to particularly damaging inferences only when the code was four different colours. When that was known before play, Experiment 2 showed that AC errors, but not MT errors, were significantly correlated with Mastermind hypotheses advanced. A stepwise multiple regression analysis supported these findings: When the solvers knew they were playing a four-colour code, there was a slight diminution in the variance explained by MT errors, and a significant increase in the variance explained by AC errors. An analysis of the number of different possible codes that could be consistent with hypotheses actually played showed that the number of such codes is far fewer when the code consists of four different colours than when its structure is not known. This analysis suggests that reasoners are therefore unlikely to discover many alternative causes for the feedback given when the code consists of four different colours, and it is under these conditions that humans are most likely to engage in AC reasoning. (shrink)

The standard notion of formal theory, in logic, is in general biased exclusively towards assertion: it commonly refers only to collections of assertions that any agent who accepts the generating axioms of the theory should also be committed to accept. In reviewing the main abstract approaches to the study of logical consequence, we point out why this notion of theory is unsatisfactory at multiple levels, and introduce a novel notion of theory that attacks the shortcomings of the received notion (...) by allowing one to take both assertions and denials on a par. This novel notion of theory is based on a bilateralist approach to consequence operators, which we hereby introduce, and whose main properties we investigate in the present paper. (shrink)