In the last years of his life, Gerald C. MacCallum, Jr., defied illness to continue his work on the philosophy of law. This book is a monument to MacCallum’s effort, containing fourteen of his essays, five of them published here for the first time. Two of those previously published are widely admired and reprinted: “Legislative Intent,” certainly one of the best papers ever published on its topic, and “Negative and Positive Freedom,” which offered a new way of looking at (...) a distinction that had been canonical for the last two centuries. To complete MacCallum’s unfinished pieces, Marcus G. Singer and Rex Martin painstakingly consulted MacCallum’s notes for planned revisions. MacCallum discusses legal reasoning, the application of rules, the interpretation of statutes and constitutional provisions, and the relation of these matters to morality and justice. In the last decade of his working life, he became greatly concerned with the interrelated themes of integrity, autonomy, conscience, and violence. He wished to relate competition to morality and justice to adversarial systems of law. These themes are woven together in Legislative Intent and constitute the main subject of some of the essays. MacCallum was engaged in a constant search for truth and understanding, and in his life and work lived up to Emerson’s vision of the “American Scholar” as a “human being thinking.” These essays are informed by the author’s deep curiosity, penetrating intelligence, wide knowledge, and outstanding character. They will be treasured wherever these characteristics and true philosophy are treasured. (shrink)

Peter Abelard (1079–1142 ce) was the most wide‐ranging philosopher of the twelfth century. He quickly established himself as a leading teacher of logic in and near Paris shortly after 1100. After his affair with Heloise, and his subsequent castration, Abelard became a monk, but he returned to teaching in the Paris schools until 1140, when his work was condemned by a Church Council at Sens. His logical writings were based around discussion of the “Old Logic”: Porphyry's Isagoge, aristotle'S Categories and (...) On Interpretation and boethius'S textbook on topical inference. They comprise a freestanding Dialectica (“Logic”; probably c.1116), a set of commentaries (known as the Logica [Ingredientibus], c. 1119) and a later (c. 1125) commentary on the Isagoge (Logica Nostrorum Petititoni Sociorum or Glossulae). In a work Abelard called his Theologia, issued in three main versions (between 1120 and c.1134), he attempted a logical analysis of trinitarian relations and explored the philosophical problems surrounding God's claims to omnipotence and omniscience. The Collationes (“Debates,” also known as “Dialogue between a Christian, a Philosopher and a Jew”; probably c.1130) present a rational investigation into the nature of the highest good, in which the Christian and the Philosopher (who seems to be modeled on a philosopher of pagan antiquity) are remarkably in agreement. The unfinished Scito teipsum (“Know thyself,” also known as the “Ethics”; c.1138) analyses moral action. (shrink)

The author takes the reader on a tour that covers such topics as computers, evolution, Descartes, Schrodinger, and the nature of perception, language, and invididuality. He argues that biology provides the key to understanding the brain. Underlying his argument is the evolutionary view that the mind arose at a definite time in history. This book ponders connections between psychology and physics, medicine, philosophy, and more. Frequently contentious, Edelman attacks cognitive and behavioral approaches, which leave biology out of the picture, as (...) well as the currently fashionable view of the brain as a computer. (shrink)

This is a thorough treatment of first-order modal logic. The book covers such issues as quantification, equality (including a treatment of Frege's morning star/evening star puzzle), the notion of existence, non-rigid constants and function symbols, predicate abstraction, the distinction between nonexistence and nondesignation, and definite descriptions, borrowing from both Fregean and Russellian paradigms.

A psychologist offers a detailed study of the genetic underpinnings of human thought, looking at the small number of genes that contain the instructions for building the vastly complex human brain to determine how these genes work, common misconceptions about genes, and their implications for the future of genetic engineering. 30,000 first printing.

Suppose there are several experts, with some dominating others (expert A dominates expert B if B says something is true whenever A says it is). Suppose, further, that each of the experts has his or her own view of what is possible — in other words each of the experts has their own Kripke model in mind (subject, of course, to the dominance relation that may hold between experts). How will they assign truth values to sentences in a common modal (...) language, and on what sentences will they agree? This problem can be reformulated as one about many-valued Kripke models, allowing many-valued accessibility relations. This is a natural generalization of conventional Kripke models that has only recently been looked at. The equivalence between the many-valued version and the multiple expert one will be formally established. Finally we will axiomatize many-valued modal logics, and sketch a proof of completeness. (shrink)

Kleene’s well-known strong three-valued logic is shown to be one of a family of logics with similar mathematical properties. These logics are produced by an intuitively natural construction. The resulting logics have direct relationships with bilattices. In addition they possess mathematical features that lend themselves well to semantical constructions based on fixpoint procedures, as in logic programming.

Bilattices, introduced by M. Ginsberg, constitute an elegant family of multiple-valued logics. Those meeting certain natural conditions have provided the basis for the semantics of a family of logic programming languages. Now we consider further restrictions on bilattices, to narrow things down to logic programming languages that can, at least in principle, be implemented. Appropriate bilattice background information is presented, so the paper is relatively self-contained.

One approach to the paradoxes of self-referential languages is to allow some sentences to lack a truth value (or to have more than one). Then assigning truth values where possible becomes a fixpoint construction and, following Kripke, this is usually carried out over a partially ordered family of three-valued truth-value assignments. Some years ago Matt Ginsberg introduced the notion of bilattice, with applications to artificial intelligence in mind. Bilattices generalize the structure Kripke used in a very natural way, while making (...) the mathematical machinery simpler and more perspicuous. In addition, work such as that of Yablo fits naturally into the bilattice setting. What I do here is present the general background of bilattices, discuss why they are natural, and show how fixpoint approaches to truth in languages that allow self-reference can be applied. This is not new work, but rather is a summary of research I have done over many years. (shrink)

Nested sequent systems for modal logics are a relatively recent development, within the general area known as deep reasoning. The idea of deep reasoning is to create systems within which one operates at lower levels in formulas than just those involving the main connective or operator. Prefixed tableaus go back to 1972, and are modal tableau systems with extra machinery to represent accessibility in a purely syntactic way. We show that modal nested sequents and prefixed modal tableaus are notational variants (...) of each other, roughly in the same way that tableaus and Gentzen sequent calculi are notational variants. This immediately gives rise to new modal nested sequent systems which may be of independent interest. We discuss some of these, including those for some justification logics that include standard modal operators. (shrink)

The variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and many-valued logic, lattice theory, game theory, and topology. One source of this richness is the inherent non-monotonicity of its negation, something that does not have close parallels with the machinery of other programming paradigms. Nonetheless, much of the work on logic programming semantics seems to exist side by side with similar work done for imperative and functional programming, with relatively minimal contact (...) between communities. In this paper we summarize one variety of approaches to the semantics of logic programs: that based on fixpoint theory. We do not attempt to cover much beyond this single area, which is already remarkably fruitful. We hope readers will see parallels with, and the divergences from the better known fixpoint treatments developed for other programming methodologies. (shrink)

First - order modal logic is very much under current development, with many different semantics proposed. The use of rigid objects goes back to Saul Kripke. More recently, several semantics based on counterparts have been examined, in a development that goes back to David Lewis. There is yet another line of research, using intensional objects, that traces back to Richard Montague. I have been involved with this line of development for some time. In the present paper, I briefly sketch several (...) of the approaches to first - order modal logic. Then I present one that I call FOIL in the Montague tradition that, I believe, is both expressive and natural. I briefly discuss in what sense it can be made to encompass the other approaches. Finally, I provide tableau rules to go with the FOIL semantics. (shrink)

Agents do not merely have duties – they often have directed duties to others. This paper first reveals problems with traditional attempts to equate these directed duties with claims and claim rights. It then defends a novel account of directionality that locates the unifying element of directed duties in a counterparty’s prioritization of the duties owed to her. If one agent has a directed duty to another, then the degree to which fulfilling the duty matters to the agent to whom (...) it is owed itself matters – in a distinctive, special and inherent sense. This subject-determined normative significance of directed duties can be used to articulate a priority account of directionality, an account that can demonstrate why many have taken control powers, interests or the authority to demand compliance to be so important in analyzing the directed duties we owe to others. (shrink)

The dominant theory of the evolution of moral cognition across a variety of fields is that moral cognition is a biological adaptation to foster social cooperation. This chapter argues, to the contrary, that moral cognition is likely an evolutionary exaptation: a form of cognition where neurobiological capacities selected for in our evolutionary history for a variety of different reasons—many unrelated to social cooperation—were put to a new, prosocial use after the fact through individual rationality, learning, and the development and transmission (...) of social norms. This chapter begins with a brief overview of the emerging behavioral neuroscience of moral cognition. It then outlines a novel theory of moral cognition that I have previously argued explains these findings better than alternatives. Finally, it shows how the evidence for this theory of moral cognition and human evolutionary history together suggest that moral cognition is likely not a biological adaptation. Instead, like reading sheet music or riding a bicycle, moral cognition is something that individuals learn to do—in this case, in response to sociocultural norms created in our ancestral history and passed down through the ages to enable cooperative living. (shrink)

In general, offers a good discussion of Dworkin's theory of interpretation. Postema is critically concerned with whether Dworkin commits himself to individualistic and privatistic sense of interpretation and how Dworkin articulates the logical independency of pre-interpretive paradigm instances or social facts which form the object of interpretation and the end which is interpretively posited in the act of interpretation. Criticisms, for the most part, appear to be compatible with Dworkin's overall theory and may simply be additional explication of the character (...) of interpretation. "There is nothing in Dworkin's meta-theory of interpretation of social practices that requires attention to the interpretive activities of fellow participants. Herein lies the strong "protestantism" of Dworkin's theory. Not only is each participant encouraged to take up the interpretive enterprise...but each individual participant also has access to the truth, as it were, about what the practice is and requires, though private interpretation of the practice-text. While Dworkin seems to recognize that the practice is common, he counsels participants to live as if each had a private understanding of his own." "It is problematic because it makes interpretation of social practices insufficiently practical, insufficiently intersubjective, and thus insufficiently political." Notes that the interpretive attitude when acting in a practice is relatively rare, usually becoming part of a practice is more like learning a discipline or technique. "[I]t may not be possible intelligibly to separate that point from the activies and rules in which it is expressed. The same meaning may, conceivably, be expressed in some other way, but this does not imply that the meaning is logically independent of the medium of expression." "That is, the behavior is logically separable from its interpretation only on pain of denying that the practice is common activity yielding common principles." "Often an agent may only come to understand his actions long after he has performed them, or may later come to see his actions in a very different light...First, on this view meaningful action is a primitive. Action is expressive of its meaning or purpose, but not resolvable into distinct behavior and purpose. But, since this purpose or meaning may not be fully or clearly articulated, interpretation can be seen as the activity of re-formulating and articulating it. Second, the 'meaning' of an action cannot be regarded as a private matter for the agent alone.". (shrink)

How can we acquire a grasp of cardinal numbers, even the first very small positive cardinal numbers, given that they are abstract mathematical entities? That problem of cognitive access is the main focus of this paper. All the major rival views about the nature and existence of cardinal numbers face difficulties; and the view most consonant with our normal thought and talk about numbers, the view that cardinal numbers are sizes of sets, runs into the cognitive access problem. The source (...) of the problem is the plausible assumption that cognitive access to something requires causal contact with it. It is argued that this assumption is in fact wrong, and that in this and similar cases we should accept that a certain recognise-and-distinguish capacity is sufficient for cognitive access. We can then go on to solve the cognitive access problem, and thereby support the set-size view of cardinal numbers, by paying attention to empirical findings about basic number abilities. To this end some selected studies of infants, pre-school children and a trained chimpanzee are briefly discussed. (shrink)

Several justification logics have been created, starting with the logic LP, [1]. These can be thought of as explicit versions of modal logics, or of logics of knowledge or belief, in which the unanalyzed necessity (knowledge, belief) operator has been replaced with a family of explicit justification terms. We begin by sketching the basics of justification logics and their relations with modal logics. Then we move to new material. Modal logics come in various strengths. For their corresponding justification logics, differing (...) strength is reflected in different vocabularies. What we show here is that for justification logics corresponding to modal logics extending T, various familiar extensions are actually conservative with respect to each other. Our method of proof is very simple, and general enough to handle several justification logics not directly corresponding to distinct modal logics. Our methods do not, however, allow us to prove comparable results for justification logics corresponding to modal logics that do not extend T. That is, we are able to handle explicit logics of knowledge, but not explicit logics of belief. This remains open. (shrink)

This is an expository paper in which the basic ideas of a family of Justification Logics are presented. Justification Logics evolved from a logic called LP, introduced by Sergei Artemov [1, 3], which formed the central part of a project to provide an arithmetic semantics for propositional intuitionistic logic. The project was successful, but there was a considerable bonus: LP came to be understood as a logic of knowledge with explicit justifications and, as such, was capable of addressing in a (...) natural way long-standing problems of logical omniscience. Since then, LP has become one member of a family of related logics, all logics of knowledge with explicit knowledge terms. In this paper the original problem of intuitionistic foundations is discussed only briefly. We concentrate entirely on issues of reasoning about knowledge. (shrink)

LP can be seen as a logic of knowledge with justifications. See [S. Artemov, The logic of justification, The Review of Symbolic Logic 1 477–513] for a recent comprehensive survey of justification logics generally. Artemov’s Realization Theorem says justifications can be extracted from validities in the more conventional Hintikka-style logic of knowledge S4, in which they are not explicitly present. Justifications, however, are far from unique. There are many ways of realizing each theorem of S4 in the logic LP. If (...) the machinery of justifications is to be applied to artificial intelligence, or better yet, to everyday reasoning, we will need to work with whatever justifications we may have at hand—one version may not be interchangeable with another, even though they realize the same S4 formula. In this paper we begin the process of providing tools for reasoning about justifications directly. The tools are somewhat complex, but in retrospect this should not be surprising. Among other things, we provide machinery for combining two realizations of the same formula, and for replacing subformulas by equivalent subformulas. The results are algorithmic in nature—semantics for LP plays no role. We apply our results to provide a new algorithmic proof of Artemov’s Realization Theorem itself. This paper is a much extended version of [M.C. Fitting, Realizations and LP, in: S. Artemov, A. Nerode , Logical Foundations of Computer Science—New York ’07, in: Lecture Notes in Computer Science, vol. 4514, Springer-Verlag, 2007, pp. 212–223]. (shrink)

Medical practitioners of all specialisms are identified by their professional titles. Their function is determined by their regulators, and subject to voluntary employment contracts....

The family of all stable models for a logic program has a surprisingly simple overall structure, once two naturally occurring orderings are made explicit. In a so-called knowledge ordering based on degree of definedness, every logic program P has a smallest stable model, sk P — it is the well-founded model. There is also a dual largest stable model, S k P, which has not been considered before. There is another ordering based on degree of truth. Taking the meet and (...) the join, in the truth ordering, of the two extreme stable models sk P and S.. (shrink)

Act-utilitarianism comes in two standard varieties: ‘subjective’ act-utilitarianism, which tells agents to attempt to maximize utility directly, and ‘objective’ act-utilitarianism, which permits agents to use non-utilitarian decision-making procedures. This article argues that objective actutilitarianism is exposed to a dilemma. On one horn of it is the contention that objective act-utilitarianism makes inconsistent claims about the rightness of acts. On the other horn of it is the contention that objective act-utilitarianism collapses back into what is, essentially, subjective act-utilitarianism. Three objective act-utilitarian (...) responses to this dilemma are explored and rejected. The recommended conclusion is that a consistent utilitarian must either embrace subjective act-utilitarianism, or abandon act-utilitarianism altogether. Key Words: act-utilitarianism • subjective • objective • decision-making procedure • criterion of rightness • dilemma. (shrink)

A well-known problem with Hintikka-style logics of knowledge is that of logical omniscience. One knows too much. This breaks down into two subproblems: one knows all tautologies, and one’s knowledge is closed under consequence. A way of addressing the second of these is to move from knowledge simpliciter, to knowledge for a reason. Then, as consequences become ‘further away’ from one’s basic knowledge, reasons for them become more complex, thus providing a kind of resource measurement. One kind of reason is (...) a formal proof. Sergei Artemov has introduced a logic of explicit proofs, LP. I present a semantics for this, based on the idea that it is a logic of knowledge with explicit reasons. A number of fundamental facts about LP can be established using this semantics. But it is equally important to realize that it provides a natural logic of more general applicability than its original provenance, arithmetic provability. (shrink)