Mathematical proofs generally allow for various levels of detail and conciseness, such that they can be adapted for a particular audience or purpose. Using automated reasoning approaches for teaching proof construction in mathematics presupposes that the step size of proofs in such a system is appropriate within the teaching context. This work proposes a framework that supports the granularity analysis of mathematical proofs, to be used in the automated assessment of students' proof attempts and for the presentation of hints and (...) solutions at a suitable pace. Models for granularity are represented by classifiers, which can be generated by hand or inferred from a corpus of sample judgments via machine-learning techniques. This latter procedure is studied by modeling granularity judgments from four experts. The results provide support for the granularity of assertion-level proofs but also illustrate a degree of subjectivity in assessing step size. (shrink)

If I say “we are now living in England” or “grass is green in summer’ or ‘the cat is on the mat’ what I say will normally be true or false—the statements are true if they correctly report how things are, or correspond to the facts; and if they do not do these things, they are false. Such a statement will only fail to have a truth-value if its referring expressions fail to refer ; or if the statement lies on (...) the border between truth and falsity so that it is as true to say that the statement is true as to say that it is false. Are moral judgments normally true or false in the way in which the above statements are true or false? I will term the view that they are objectivism and the view that they are not subjectivism. The objectivist maintains that it is as much a fact about an action that it is right or wrong as that it causes pain or takes a long time to perform. The subjectivist maintains that saying than an action is right or wrong is not stating a fact about it but merely expressing approval of it or commending it or doing some such similar thing. I wish in this paper, first, to show that all arguments for subjectivism manifestly fail, and secondly to produce a strong argument for objectivism. But, to start with, some preliminaries. (shrink)

On what grounds will the rational man become a Christian? It is often assumed by many, especially non-Christians, that he will become a Christian if and only if he judges that the evidence available to him shows that it is more likely than not that the Christian theological system is true, that, in mathematical terms, on the evidence available to him, the probability of its truth is greater than half. It is the purpose of this paper to investigate whether or (...) not this is a necessary and sufficient condition for the rational man to adopt Christianity. (shrink)

Ethical self-management; an introduction to systematic personality psychology, by M. C. Katz.--Four axiological proofs of the infinite value of man, by R. S. Hartman.--Some thoughts regarding the current philosophy of the behavioral sciences, by C. R. Rogers.--Autonomy and community, by D. Lee.--Synergy in the society and in the individual, by A. H. Maslow.--Human nature: its cause and effect; a theoretical framework for understanding human motivation, by M. C. Katz.--Mental health; a generic attitude, by G. W. Allport.--Love feelings in courtship couples; (...) an analysis, by R. P. Hattis.--Economic policies and human well-being, by W. A. Weisskopf.--The great transformation, by H. F. W. Perk.--Contingencies of reinforcement in the design of a culture, by B. F. Skinner.--For further reading. (shrink)

Mr Olding's recent attack on my exposition of the argument from design gives me an opportunity to defend the central theses of my original article. My article pointed out that there were arguments from design of two types—those which take as their premisses regularities of copresence and those which take as their premisses regularities of succession. I sought to defend an argument of the second type. One merit of such an argument is that there is no doubt about the truth (...) of its premisses. Almost all objects in the world behave in a highly regular way describable by scientific laws. Further, any scientific explanation of such a regularity must invoke some more general regularity. The most general regularities of all are, as such, scientifically inexplicable. The question arises whether there is a possible explanation of another kind which can be provided for them, and whether their occurrence gives any or much support to that explanation. I urged that we do explain some phenomena by explanation of an entirely different kind from the scientific. We explain states of affairs by the action of agents who bring them about intentionally of their own choice. Regularities of succession, as well as other phenomena may be explained in this way. Explanation of this kind I will term intentional explanation. Intentional explanation of some phenomenon E consists in adducing an agent A who brought E about of his own choice and a further end G which, he believed, would be forwarded by the production of E. (shrink)

Arguments move from premises to conclusions. The premises state things taken temporally for granted; if the argument works, the premises provide grounds for affirming the conclusion. A valid deductive argument is one in which the premises necessitate, that is, entail, the conclusion. What I shall call a ‘correct’ inductive argument is one in which the premises in some degree probabilify the conclusion, but do not necessitate it. More precisely, in what I shall call a correct P -inductive argument the premises (...) make the conclusion probable ; in what I shall call a correct C -inductive argument, the premises add to the probability of the conclusion . Arguments only show their conclusions to be true if they start from true premises; arguments of the above types which work and do start from such premises I will call sound arguments. Arguments are only of use to show to an individual that the conclusion is true if he already knows the premises to be true. Most of what I shall have to say today concerns arguments with respect to which there is no doubt that the premises are true. (shrink)

The object of this paper is to examine what evidence we can have for or against the truth of determinism, a doctrine often set forward by the proposition ‘every event has a cause’. I understand in this context by the cause of an event a set of prior conditions jointly sufficient for the occurrence of the event. Since the determinist is concerned with all physical states and not merely with changes of states, which are most naturally termed events, we may (...) phrase this claim more precisely as follows: There is for every physical state at some earlier instant a set of conditions jointly sufficient for its occurrence. (shrink)

An alleged moral right to informational privacy assumes that we should have control over information about ourselves. What is the philosophical justification for this control? I think that one prevalent answer to this question—an answer that has to do with the justification of negative rights generally—will not do.

The most common view of suicide today is that it is intentional self-killing. 1 Because of the self-killing component, suicide is often described as self-inflicted death or as dying by one's own hand, and the victim is in turn often described as having done himself to death or as having taken his own life. But must one's death be self-inflicted in order to be suicide? The answer, I want to suggest, is arguably no.

EMPIRICIST THEORIES OF PERSONAL IDENTITY STATE THAT THE IDENTITY OF A PERSON OVER TIME IS A MATTER OF BODILY CONTINUITY AND/OR SIMILARITY OF MEMORY AND CHARACTER. IN CONTRAST, THIS PAPER ARGUES THAT WHILE BODILY CONTINUITY AND SIMILARITY OF MEMORY AND CHARACTER ARE EVIDENCE OF PERSONAL IDENTITY, THEY DO NOT CONSTITUTE IT. IT IS SOMETHING UNDEFINABLE. THE DIFFICULTY OF KNOWING WHAT TO SAY IN PUZZLE CASES DOES NOT SHOW THAT PERSONAL IDENTITY EXISTS IN DIFFERENT DEGREES OR THAT WE HAVE TO MAKE (...) ARBITRARY JUDGMENTS ABOUT IT. IT SHOWS ONLY THAT SOMETIMES WE CANNOT KNOW WHO IS WHO. (shrink)

In the past ten years, there has been growing interest in and concern about protecting the privacy of personal medical information. Insofar as medical records increasingly are stored electronically, and electronic information can be shared easily and widely, there have been legislative efforts as well as scholarly analyses calling for greater privacy protections to ensure that patients can feel safe disclosing personal information to their health-care providers. At the same time, the volume of biomedical research conducted in this country continues (...) to grow. The budget of the National Institutes of Health, for example, was $20,298 million in 2001, having more than doubled from a budget of $9,218 million 10 years before. This growing body of research includes increased efforts to use stored medical records as a source of data for health services, epidemiologic, and clinical studies. (shrink)

In the past ten years, there has been growing interest in and concern about protecting the privacy of personal medical information. Insofar as medical records increasingly are stored electronically, and electronic information can be shared easily and widely, there have been legislative efforts as well as scholarly analyses calling for greater privacy protections to ensure that patients can feel safe disclosing personal information to their health-care providers. At the same time, the volume of biomedical research conducted in this country continues (...) to grow. The budget of the National Institutes of Health, for example, was $20,298 million in 2001, having more than doubled from a budget of $9,218 million 10 years before. This growing body of research includes increased efforts to use stored medical records as a source of data for health services, epidemiologic, and clinical studies. (shrink)

ARGUMENTS FROM DESIGN TO THE EXISTENCE OF GOD MAY TAKE AS THEIR PREMISS EITHER THE EXISTENCE OF REGULARITIES OF COPRESENCE OR THE EXISTENCE OF REGULARITIES OF SUCCESSION. THERE ARE NO VALID FORMAL OBJECTIONS TO A CAREFULLY ARTICULATED ARGUMENT OF THE LATTER TYPE. AGAINST SUCH AN ARGUMENT NONE OF THE OBJECTIONS IN HUME’S "DIALOGUES" HAVE ANY WORTH. THE ARGUMENT MAY HOWEVER GIVE ONLY A SMALL DEGREE OF SUPPORT TO ITS CONCLUSION.

(I UNDERSTAND BY A MIRACLE, A VIOLATION OF A LAW OF NATURE BY A GOD.) A VIOLATION OF A LAW OF NATURE IS THE OCCURRENCE OF A NON-REPEATABLE COUNTER-INSTANCE TO IT. CONTRARY TO HUME’S VIEW, THERE COULD BE GOOD HISTORICAL EVIDENCE BOTH THAT A VIOLATION HAD OCCURRED AND THAT IT WAS DUE TO THE ACT OF A GOD.

THE PAPER BEGINS BY CONSIDERING THREE ALTERNATIVE DEFINITIONS OF "ANALYTIC," ONE IN TERMS OF LOGICAL TRUTH, ONE IN TERMS OF THE MEANINGS OF WORDS, AND ONE IN TERMS OF SELF-CONTRADICTION OR INCOHERENCE. NEXT, FIVE DEFINITIONS OF "NECESSARY" ARE CONSIDERED, ONE IN TERMS OF ANALYTICITY, AND ONE PICKING OUT THE BROADER KIND OF LOGICAL NECESSITY DISCUSSED BY KRIPKE AND PLANTINGA. FINALLY, THREE DEFINITIONS OF "A PRIORI" ARE CONSIDERED. ONLY ON A FEW OF THESE DEFINITIONS DO THE CATEGORIES OF ANALYTIC, NECESSARY, AND (...) A PRIORI COINCIDE. (shrink)

CONTRARY TO GOODMAN’S VIEW, A CLEAR DISTINCTION CAN BE MADE BETWEEN QUALITATIVE AND POSITIONAL PREDICATES. HENCE WE CAN EXPLAIN THAT WE OUGHT TO PROJECT ’GREEN’ RATHER THAN ’GRUE’ BECAUSE THE LATTER IS A POSITIONAL PREDICATE, RATHER THAN BECAUSE THE LATTER IS LESS WELL ENTRENCHED. A PREDICATE IS POSITIONAL IF, TO FIND OUT AS CERTAINLY AS WE CAN WHETHER IT APPLIES TO AN OBJECT, WE HAVE TO FIND OUT THE LATTER’S SPATIO-TEMPORAL LOCATION.

For a theist, a man's duty is to conform to the announced will of God. Yet a theist who makes this claim about duty is faced with a traditional dilemma first stated in Plato's Euthyphro—are actions which are obligatory, obligatory because God makes them so, or does God urge us to do them because they are obligatory anyway? To take the first horn of this dilemma is to claim that God can of his free choice make any action obligatory or (...) non-obligatory. The critic claims that the theist cannot take this horn, for God cannot make bad actions good. (shrink)

This article investigates the claim that some truths are fundamentally or really true — and that other truths are not. Such a distinction can help us reconcile radically minimal metaphysical views with the verities of common sense. I develop an understanding of the distinction whereby Fundamentality is not itself a metaphysical distinction, but rather a device that must be presupposed to express metaphysical distinctions. Drawing on recent work by Rayo on anti-Quinean theories of ontological commitments, I formulate a rigourous theory (...) of the notion. In the final sections, I show how this package dovetails with ' interpretationist' theories of meaning to give sober content to thought that some things — perhaps sets, or gerrymandered mereological sums — can be 'postulated into existence'. (shrink)

Philosophy of history is not a subject which has hitherto attracted much attention in this country. Preoccupation with the methods and achievements of the natural sciences, and distaste for the sort of rationale of history as a whole which Hegel and others offered under the title in the early nineteenth century, have served to make most British philosophers accord its problems only the most casual recognition. It is therefore all the more interesting to find an English writer of unusual powers (...) both of argument and expression, who was himself an historian of distinction in his special field, devoting a large part of his philosophical thinking to the problems of historical knowledge and their wider implications. Unfortunately, R. G. Collingwood was not able to begin the major work on philosophy of history, to writing which, as we are told in the introduction to the present book, he had looked forward for twenty-five years, until his powers were seriously affected by bad health, and he did not live to complete it. But though the full results of his thinking on the subject are lost, we are now able, thanks to the skilful work of his friend Professor T. M. Knox, to study what is in effect an extensive interim report on it. Professor Knox has produced The Idea of History largely on the basis of lectures which Collingwood prepared in 1936, supplemented by two essays already published which date from the same period and a certain amount of material from the unfinished Principles of History written in 1939. (shrink)

This paper examines two puzzles of indeterminacy. The first puzzle concerns the hypothesis that there is a unified phenomenon of indeterminacy. How are we to reconcile this with the apparent diversity of reactions that indeterminacy prompts? The second puzzle focuses narrowly on borderline cases of vague predicates. How are we to account for the lack of theoretical consensus about what the proper reaction to borderline cases is? I suggest (building on work by Maudlin) that the characteristic feature of indeterminacy is (...) alethic normative silence, and use this to explain both plurality and lack of consensus. (shrink)

The object of this paper is to show that there are no valid formal objections to the argument from design, so long as the argument is articulated with sufficient care. In particular I wish to analyse Hume's attack on the argument in Dialogues Concerning Natural Religion and to show that none of the formal objections made therein by Philo have any validity against a carefully articulated version of the argument.