We study logical systems for reasoning about equations involving recursive definitions. In particular, we are interested in "propositional" fragments of the functional language of recursion FLR [18, 17], i.e., without the value passing or abstraction allowed in FLR. The "pure," propositional fragment FLR 0 turns out to coincide with the iteration theories of [1]. Our main focus here concerns the sharp contrast between the simple class of valid identities and the very complex consequence relation over several natural classes of models.

We study logical systems for reasoning about equations involving recursive definitions. In particular, we are interested in "propositional" fragments of the functional language of recursion FLR [18, 17], i.e., without the value passing or abstraction allowed in FLR. The "pure," propositional fragment FLR$_0$ turns out to coincide with the iteration theories of [1]. Our main focus here concerns the sharp contrast between the simple class of valid identities and the very complex consequence relation over several natural classes of models.

Individuals are generally held to be morally and legally responsible only for actions carried out freely and deliberately, that is to say, for actions that result from our free choice. However, there is a quite widespread view that all of our actions are the result of the scientific laws that govern our physical bodies. If this should prove to be the case, then human choice would be an illusion, and therefore -- on the generally accepted principle just stated -- personal (...) responsibility would be a meaningless concept and blame and punishment would be inappropriate responses to wicked or criminal acts. In this paper I shall argue that we need to disentangle ‘responsibility’ from ‘choice'. I shall also outline reasons for holding that responsibility is ultimately a first-person matter -- I am responsible if I feel responsible, irrespective of choice -- and I shall briefly consider some of the consequences of this approach. (shrink)

I do not approach the question of free will as a scientist, like Colin Blakemore, or a lawyer, like David Hodgson, or philosopher, like Daniel Dennett, but as a priest -- someone who feels responsible for my own actions and who is called upon to counsel and absolve such as come to me with their shame and their guilt. Should I say that their sense of responsibility is illusory? Or should I encourage them to accept responsibility, and then to deal (...) with it in the various ways -- religious, psychological and practical -- that are open to them? (shrink)

C. A. J. Littlewood approaches Seneca's tragedies as Neronian literature rather than as reworkings of Attic drama, and emphasizes their place in the Roman world and in the Latin literary corpus. The Greek tragic myths are for Seneca mediated by non-dramatic Augustan literature. In literary terms Phaedra's desire, Hippolytus' innocence, and Hercules' ambivalent heroism look back through allusion to Roman elegy, pastoral, and epic respectively. Ethically, the artificiality of Senecan tragedy, the consciousness that its own dramatic worlds, events, and people (...) are literary constructs, responds to the contemporary Stoical dismissal of the public world as mere theatre. (shrink)

Our trust in the word of others is often dismissed as unworthy, because the illusory ideal of "autonomous knowledge" has prevailed in the debate about the nature of knowledge. Yet we are profoundly dependent on others for a vast amount of what any of us claim to know. Coady explores the nature of testimony in order to show how it might be justified as a source of knowledge, and uses the insights that he has developed to challenge certain widespread assumptions (...) in the areas of history, law, mathematics, and psychology. (shrink)

In an article in Philosophy R. G. Swinburne set out to argue that none of Hume's formal objections to the design argument ‘have any validity against a carefully articulated version of the argument’ . This, he maintained, is largely because Hume's criticisms ‘are bad criticisms of the argument in any form’ . The ensuing controversy between Swinburne and Olding 1 has focused upon the acceptable/unacceptable aspects of the dualism presupposed in Swinburne's defence of the design argument; upon whether any simplification (...) is achieved by reducing scientific explanation to agent explanation; and upon the problems which arise from taking a man's acting upon his body as the analogy for understanding a disembodied agent acting upon matter. In this article I shall refer to the Swinburne-Olding controversy when appropriate but my main concern is to return to Swinburne's original article and argue, seriatim , that Hume's individual criticisms of the design argument are for the most part a great deal more powerful than Swinburne allowed. I shall contend that cumulatively they destroy the design argument as any sort of rational foundation for theistic belief. But first I shall indicate briefly the character of the argument together with one or two of the distinctions and refinements in terms of which it has been found helpful to carry on the discussion in recent years. (shrink)

The Aristotle-Kant tradition requires that autonomous activity must originate within the self and points toward a new type of causation (different from natural efficient causation) associated with teleology. Notoriously, it has so far proven impossible to uncover a workable model of causation satisfying these requirements without an increasingly unsatisfying appeal to extra-physical elements tailor-made for the purpose. In this paper we first provide the essential reason why the standard linear model of efficient causation cannot support the required model of agency: (...) its causal thread model of efficient causation cannot support the core requirement that an action is determined by, and thus an expression of, the agent’s nature. We then provide a model that corrects these deficiencies, constructed naturalistically from within contemporary biology, and argue that it provides an appropriate foundation for all the features of genuine agency. Further, we provide general characterisations of freedom and reason suitable to this bio-context (but that also capture the core classical conceptions) and show how this model reconciles them. (shrink)

He that is to govern a whole nation, must read in himself, not this, or that particular man; but mankind. Leviathan is both a magnificent literary achievement and the greatest work of political philosophy in the English language. Permanently challenging, it has found new applications and new refutations in every generation. This new edition reproduces the first printed text, retaining the original punctuation but modernizing the spelling. It offers the most useful annotation available, an introduction that guides the reader through (...) the complexities of Hobbes's arguments, and a substantial index. (shrink)

The paper reviews a number of approaches for handling restricted quantification in relevant logic, and proposes a novel one. This proceeds by introducing a novel kind of enthymematic conditional.

Thomas Hobbes was the first great philosopher to write in English. His account of the human condition, first developed in The Elements of Law, which comprises Human Nature and De Corpore Politico, is a direct product of the intellectual and political strife of the seventeenth century. It is also a remarkably penetrating look at human nature, and a permanently relevant analysis of the fears and self-seeking that result in the war of `each against every man'. In The Elements of Law (...) Hobbes memorably sets out both the main lines of his general philosophy, later augmented in De Corpore, and the moral and political philosophy later made famous in Leviathan. Copies of Human Nature and De Corpore Politico, until 1889 printed as separate works, are rare antiques or scarcely less rare scholarly texts; this is the first complete popular edition. It is here supplemented by chapters from De Corpore and Three Lives, two from Hobbes's original Latin. These have never before been published together in English. (shrink)

The inverse of the distance between two structures $\mathscr{A} \not\equiv \mathscr{B}$ of finite type τ is naturally measured by the smallest integer q such that a sentence of quantifier rank q - 1 is satisfied by A but not by B. In this way the space $\operatorname{Str}^\tau$ of structures of type τ is equipped with a pseudometric. The induced topology coincides with the elementary topology of $\operatorname{Str}^\tau$ . Using the rudiments of the theory of uniform spaces, in this elementary note (...) we prove the convergence of every Cauchy net of structures, for any type τ. (shrink)

The inverse of the distance between two structures $\mathscr{A} \not\equiv \mathscr{B}$ of finite type $\tau$ is naturally measured by the smallest integer $q$ such that a sentence of quantifier rank $q - 1$ is satisfied by $\mathscr{A}$ but not by $\mathscr{B}$. In this way the space $\operatorname{Str}^\tau$ of structures of type $\tau$ is equipped with a pseudometric. The induced topology coincides with the elementary topology of $\operatorname{Str}^\tau$. Using the rudiments of the theory of uniform spaces, in this elementary note we (...) prove the convergence of every Cauchy net of structures, for any type $\tau$. (shrink)

Dr Ian Ramsey has made considerable use of the word ‘disclosure’ in what he has to say about religion and in his attempts to give an account of the meaning of religious language. He sometimes speaks of ‘discernment’ or ‘insight’ but ‘disclosure’ is the word he normally favours. In what follows I shall ask: what a disclosure is, to what extent Dr Ramsey's use of the notion leads to confusions, and what questions have to be faced in order to resolve (...) these confusions. (shrink)

In this article I try to refute the so-called "libertarian" theory of free will, and to examine how our conclusion ought to modify our common attitudes of praise and blame. In attacking the libertarian view, I shall try to show that it cannot be consistently stated. That is, my dscussion will be an "analytic-philosophic" one. I shall neglect what I think is in practice an equally powerful method of attack on the libertarian: a challenge to state his theory in such (...) a way that it will fit in the modern biology and psychology, which are becoming increasingly physicalistic. (shrink)

Is a whole something more than the sum of its parts? Are there things composed of the same parts? If you divide an object into parts, and divide those parts into smaller parts, will this process ever come to an end? Can something lose parts or gain new ones without ceasing to be the thing it is? Does any multitude of things (including disparate things such as you, this book, and the tail of a cat) compose a whole of some (...) sort? Questions such as these have occupied us for at least as long as philosophy has existed. They define the field that has come to be known as mereology-the study of all relations of part to whole and of part to part within a whole-and have deep and far-reaching ramifications in metaphysics as well as in logic, the foundations of mathematics, the philosophy of language, the philosophy of science, and beyond. In Mereology, A. J. Cotnoir and Achille C. Varzi have compiled decades of advanced research into a comprehensive, up-to-date, and formally rigorous picture. The early chapters cover the more classical aspects of mereology; the rest of the book deals with variants and extensions. Whether you are an established professional philosopher, an interested student, or a newcomer, inside you will find all the tools you need to join this ever-evolving field of inquiry and theorize about all things mereological. (shrink)

David Hume is the greatest and also one of the most provocative philosophers to have written in the English language. No philosopher is more important for his careful, critical, and deeply perceptive examination of the grounds for belief in divine powers and for his sceptical accounts of the causes and consequences of religious belief, expressed most powerfully in the Dialogues Concerning Natural Religion and The Natural History of Religion. The Dialogues ask if belief in God can be inferred from the (...) nature of the universe or whether it is even consistent with what we know about the universe. The Natural History of Religion investigates the origins of belief, and follows its development from harmless polytheism to dogmatic monotheism. Together they constitute the most formidable attack upon the rationality of religious belief ever mounted by a philosopher. This edition also includes Section XI of The Enquiry Concerning Human Understanding and a letter concerning the Dialogues, as well as particularly helpful critical apparatus and abstracts of the main texts, enabling the reader to locate or relocate key topics. (shrink)

THERE ARE TWO CONCEPTS OF MIRACLE: AS (A) THE VIOLATION OF A NATURAL LAW, AND AS (B) A STRIKING COINCIDENCE WITHIN NATURAL LAW. DIFFICULTIES IN (A) HAVE BEEN WIDELY DISCUSSED, E.G., BY R SWINBURNE. THOSE IN (B) HAVE NOT. I ARGUE THAT IF DIFFICULTIES IN (A) FORCE A RETREAT TO (B), THEN A PLACE MUST BE FOUND FOR A GOD TO ACT TO PRODUCE (B). SEVERAL POSSIBILITIES ARE CONSIDERED; NONE ARE FOUND SATISFACTORY EXCEPT POSSIBLY THE GOD INFLUENCING UNNOTICED AN ANIMATE (...) OBJECT. I CONCLUDE WITH A NEW AND FAVORABLE LOOK AT HUME’S CONTRARY MIRACLES ARGUMENT. (shrink)