Machine generated contents note: List of figures. -- Acknowledgments. -- Introduction. -- Part One: Fundamental Issues. -- Part Two: The Transition from the Aristotelian Worldview to the Newtonian Worldview. -- Part Three: Recent Developments in Science and Worldviews. -- Chapter Notes and Suggested Reading. -- References. -- Index.

In lieu of an abstract, here is a brief excerpt of the content:125, HUME'S PROBABILITY ARGUMENT OF?,??,? In the Treatise,?,??,?, Hume presents an follows:' argument which, in the barest of outlines, goes as 1 (Pl) Every proposition has a probability less than one. (P2) If reason were the basis of our beliefs, then we would have no beliefs. (follows from (Pl)) (P3) We in fact do have beliefs. Hence, (P4) Reason is not the basis of our beliefs. The argument has (...) not been particularly well received. D. C. Stove, for example, refers to it as being "not merely defective, but one of the worst 2 arguments ever to impose itself on a man of genius." While not everyone is as unsympathetic as Stove, it nonetheless is difficult to find commentators favorably disposed toward the argument. Various sections of the Treatise are notoriously unclear.?,??,? is such a section; as such, it is difficult to say just what Hume intended his argument to be. My contention in the present paper is that there are two reasonable ways of reconstructing Hume's argument, both consistent with what Hume writes in?,??,?. The first reconstruction is clearly unsound; the second reconstruction fares somewhat better. In particular, my contention will be that this second reconstruction, if not sound, is at least valid 4 and contains no obviously false premises. Allow me to make some preliminary comments before presenting these reconstructions. The reconstructions to follow will primarily be concerned with premise (P2) above; in particular, the 126. reconstructions will focus on how Hume can claim that (P2) follows from (Pl). Premise (Pl) is a common 5 sceptical claim, not obviously false, and certainly not unique to Hume. As such, it strikes me that the more interesting part of the argument is Hume's claim that (P2) follows from (Pl), and such will be the focus of the reconstructions (although (Pl) will be discussed toward the end of this paper). Concerning (P2), why does Hume think this follows from (Pl)? His reasoning is contained in the following passage; Having thus found in every probability, beside the original uncertainty inherent in the subject, a new uncertainty deriv'd from the weakness of that faculty, which judges, and having adjusted these two together, we are oblig'd by our reason to add a new doubt deriv'd from the possibility of error in the estimation we make of the truth and fidelity of our faculties. This is a doubt, which immediately occurs to us, and of which, if we wou'd closely pursue our reason, we cannot avoid giving a decision. But this decision, tho' it shou'd be favourable to our preceeding judgment, being founded only on probability, must weaken still further our first evidence, and must itself be weaken'd by a fourth doubt of the same kind, and so on in infinitum; till at last there remain nothing of the original probability, however great we may suppose it to have been, and however small the diminution by every new uncertainty. No finite object can subsist under a decrease repeated in infinitum; and even the vastest quantity, which can enter into human imagination, must in this manner be reduc'd to nothing. (T182) Not for nothing did I claim that this section of the Treatise is unclear. At best, I can discern only the outline of Hume's reasoning, which seems to go as follows: first, when we assign a probability to some 127, proposition, reason dictates that we re-evaluate this probability. In particular, reason dictates that we "add a new doubt deriv'd from the possibility of error in the estimation we make of the truth and fidelity of our faculties." Note that Hume never specifies the object of this 'new doubt.' He might mean a) that our doubt concerns whether the probability we assigned the proposition is correct, or b) that our doubt concerns the evidence on which we based the assignment of that probability. Whatever the case, this 'new doubt' must "weaken still further our first evidence," presumably resulting in a lowering of the probability we originally assigned to the proposition. We then repeat this doubting process, adding new doubts of the same kind in infinitum, "till at last there remain nothing of the original... (shrink)

In this paper, I identify the source of the differences between classical logic and many-valued logics (including fuzzy logics) with respect to the set of valid formulas and the set of inferences sanctioned. In the course of doing so, we find the conditions that are individually necessary and jointly sufficient for any many-valued semantics (again including fuzzy logics) to validate exactly the classically valid formulas, while sanctioning exactly the same set of inferences as classical logic. This in turn shows, contrary (...) to what has sometimes been claimed, that at least one class of infinite-valued semantics is axiomatizable. (shrink)

This chapter contains sections titled: Introduction The Theory of Relativity Quantum Theory Conclusion References.

This chapter contains sections titled: What Does Philosophy Have to Do with Science? Philosophical Issues in Scientific Practice Philosophical Issues in Scientific Foundations Conclusion References.

The past twenty or so years have seen the sorites paradox receive a good deal of philosophical air-time. Yet, in what is surely a sign of a good puzzle, no consensus has emerged. It is perhaps a good time to stop and take stock of the current status of the sorites paradox. My main contention is that the proposals offered to date as ways of blocking the paradox are seriously deficient, and hence there is, at present, no acceptable solution to (...) the sorites. In the final section I argue that, although vagueness is the source of the threat to modus ponens engendered by the sorites, it is also vagueness that protects modus ponens from clear counterexample. (shrink)

The past twenty or so years have seen the sorites paradox receive a good deal of philosophical air-time. Yet, in what is surely a sign of a good puzzle, no consensus has emerged. It is perhaps a good time to stop and take stock of the current status of the sorites paradox. My main contention is that the proposals offered to date as ways of blocking the paradox are seriously deficient, and hence there is, at present, no acceptable solution to (...) the sorites. In the final section I argue that, although vagueness is the source of the threat to modus ponens engendered by the sorites, it is also vagueness that protects modus ponens from clear counterexample. (shrink)

In a Sentences Commentary written about 1250 the Franciscan Richard Rufus subjects Anselm’s argument for God’s existence in his Proslogion to the most trenchant criticism since Gaunilon wrote his response on behalf of the “fool.” Anselm’s argument is subtle but sophistical, claims Rufus, because he fails to distinguish between signification and supposition. Rufus therefore offers five reformulations of the Anselmian argument, which we restate in modern formal logic and four of which we claim are valid, the fifth turning on a (...) possible scribal error. Rufus’s final conclusion is that the formulation in Proslogion, chapter 3, is convincing, but not that of chapter 2. (shrink)

The Copernican revolution of the 1500s and 1600s was in large part due to new theories and discoveries, which indicated that the general view of the universe – the more or less Aristotelian, teleological view – was no longer viable. This revolution eventually resulted in a substantially different view on the sort of universe we inhabit. New discoveries in recent years, involving Bell’s theorem, quantum theory, and the outcome of carefully designed and replicated experiments, strongly suggest that the general view (...) of the universe we have had since the Copernican revolution is no longer viable. The main goals of this paper are (i) to present Bell’s theorem and the results of these recent experiments in a way accessible to a non-technical audience, and (ii) to explore the question of whether these new discoveries place us in a similar situation to that of our predecessors in the early years of the 1600s, or roughly, whether we are in the beginning stages of a modern Copernican revolution. (shrink)

In recent years, a number of well-known intentional realists have focused their energy on attempts to provide a naturalized theory of mental representation. What tends to be overlooked, however, is that a naturalized theory of mental representation will not, by itself, salvage intentional realism. Since most naturalistic properties play no interesting causal role, intentional realists must also solve the problem of showing how intentional properties , even if naturalized, could be causally efficacious. Because of certain commitments, this problem is especially (...) difficult for intentional realists such as Fodor. In the current paper I focus on the problem as it arises for such realists, and I argue that the best-known solution proposed to date is inadequate. If what I say is correct, then such intentional realists are left with an additional and substantial problem, and one that has generally not been sufficiently appreciated. (shrink)