David Sanford

Many philosophic arguments concerned with infinite series depend on the mutual inconsistency of statements of the following five forms: (1) something exists which has R to something; (2) R is asymmetric; (3) R is transitive; (4) for any x which has R to something, there is something which has R to x; (5) only finitely many things are related by R. Such arguments are suspect if the two-place relation R in question involves any conceptual vagueness or inexactness. Traditional sorites arguments show that a statement of form (4) can fail to be true even though it has no clear counter-example. Conceptual vagueness allows a finite series not to have any definite first member. I consider the speculative possibilities that there have been only finitely many non-overlapping hours although there has been no first hour and that space and time are only finitely divisible even though there are no smallest spatial or temporal intervals.

Naive mereology studies ordinary conceptions of part and whole. Parts, unlike portions, have objective boundaries and many things, such as dances and sermons have temporal parts. In order to deal with Mark Heller's claim that temporal parts "are ontologically no more or less basic than the wholes that they compose," we retell the story of Laplace's Genius, here named "Swifty." Although Swifty processes lots of information very quickly, his conceptual repertoire need not extend beyond fundamental physics. So we attempt to follow Swifty's progress in the acquisition of ordinary concepts such as 'table'. (Puzzles of precision and intrusion appear along the way.) Swifty has to understand what tables are before understanding what temporal portions of tables are. This is one reason for regarding tables as ontologically prior to table portions. intrusion appear along the way.)

This article answers John Biro's "Knowability, Believability, and Begging the Question: a Reply to Sanford" in "Metaphilosophy" 15 (1984). Biro and I agree that of two argument instances with the same form and content, one but not the other can beg the question, depending on other factors. These factors include actual beliefs, or so I maintain (against Biro) with the help of some analysed examples. Brief selections from Archbishop Whatley and J S Mill suggest that they also regard reference to actual beliefs as essential to explaining begging the question.

According to John A Barker, whether an argument begs the question is purely a matter of logical form. According to me, it is also a matter of epistemic conditions; some arguments which beg the question in some contexts need not beg the question in every context. I point out difficulties in Barker's treatment and defend my own views against some of his criticisms. In the concluding section, "Alleged difficulties with disjunctive syllogism," I defend the validity of disjunctive syllogism against the views of Alan Ross Anderson and Nuel D Belnap, Jr., ask pointed questions about the notion of intensional disjunction, and suggest how my treatment of begging the question can be extended to deal with the so-called paradoxes of strict implication

Twenty-one paragraphs in this entry begin with a statement of a view about causation. To help organize the entry, the next sentence then classifies the view as 'prevailing, majority, controversial', or 'minority'. The following brief discussions attempt to be clear and fair. Respect for fairness, however, does not prevent the author from referring to his own views. For example, the author classifies "There is no element of genuine a priori reasoning in causal inference" as a majority view. After expounded the central reasons for this majority view, he goes on to criticize these reasons.

Everything red is colored, and all squares are polygons. A square is distinguished from other polygons by being four-sided, equilateral, and equiangular. What distinguishes red things from other colored things? This has been understood as a conceptual rather than scientific question. Theories of wavelengths and reflectance and sensory processing are not considered. Given just our ordinary understanding of color, it seems that what differentiates red from other colors is only redness itself. The Cambridge logician W. E. Johnson introduced the terms determinate and determinable to apply to examples such as red and colored. Chapter XI, of Johnson's Logic, Part I (1921), “The Determinate and the Determinable,” is the main text for discussion of this distinction

If there are vague numbers, it would be easier to use numbers as semantic values in a treatment of vagueness while avoiding precise cut-off points. When we assign a particular statement a range of values (less than 1 and greater than 0) there is no precise sharp cut-off point that locates the greatest lower bound or the least upper bound of the interval, I should like to say. Is this possible? “Vague Numbers” stands for awareness of the problem. I do not present a serious theory of vague numbers. I sketch some reasons for using a many-value semantics. These reasons refer to my earlier treatments of determinacy and definitions of higher-order borderline cases. I also sketch how definitions of independence use the determinacy operator. The distinction between actually assigned values and values whose assignments are acceptable helps avoid unwanted precise cut-off points.

Myles Brand and Marshall Swain advocate the principle that if A is the set of conditions individually necessary and jointly sufficient for the occurrence of B, then if C is a set of conditions individually necessary for the occurrence of B, every member of C is a member of A. I agree with John Barker and Risto Hilpinen who each argue that this principle is not true for causal necessity and sufficiency, but I disagree with their claim that it is true for logical necessity and sufficiency. The original appeal of the principle may be due to confusing two kinds of totality: to say that when every member of set A obtains, then every condition necessary for E obtains is not to say that every condition necessary for E is a member of A. All the authors mentioned believe that causal necessity precludes logical necessity. I deny this on the basis of an example from kinematics. Hume has not refuted definitions of causation in terms of logically necessary and sufficient conditions, nor have Brand and Swain.

The central text of this article is Thomas Reid’s response to Berkeley’s argument for distinguishing tangible from visual shape. Reid is right to hold that shape words do not have different visual and tangible meanings. We might also perceive shape, moreover, with senses other than touch and sight. As Reid also suggests, the visual perception of shape does not require perception of hue or brightness. Contrary to treatments of the Molyneux problem by H. P. Grice and Judith Jarvis Thomson, I argue that breakdowns of a certain kind between tangible and visible shape are conceivable.

Sam signaled a turn by extending his arm out the window. Difficulties in explaining the asymmetry of the by-relation in such examples by reference to acceptable and unacceptable counterfactual conditionals are explored by Hugh McCann in "The Trouble with Level-Generation" ("Mind", October 1982). I refine and defend the following alternative account of one-way dependence of y on x: not only is x necessary for y, but something else, independent from x, is also necessary for y; but there is nothing independent from y such that it and y are each necessary for x.

Unger claims that we can block sorites arguments for the conclusion that there are no ordinary things only by invoking some kind of miracle, but no such miracle is needed if we reject the principle that every statement has a truth value. Wheeler's argument for the nonexistence of ordinary things depends on the assumptions that if ordinary things exist, they comprise real kinds, and that if ordinary predicates really apply to things, the predicates refer to real properties. If we accept Wheeler's criteria for the reality of kinds and properties, we have no good reason to accept these assumptions.

A statement q is a conclusion intermediate between p and h if and only if (1) p justifies h, (2) p justifies q, and (3) (p and not-q) justifies h to a significantly lesser degree than p justifies h. I contend that Gettier-type counterexamples to definitions of factual knowledge violate the following principle: if one knows that h on the basis of p, then all the conclusions intermediate between p and h are true. This principle does not refer to anyone's beliefs that intermediate conclusions are true. I test my contention against several examples which have been discussed in the literature.

This comment on Steven Boer's “Object-Dependent Thoughts” develops two examples: (1) a counterexample to the "axiom of the seamlessness of truth," namely, that there are no propositions, one true and one false, such that knowing the true one requires believing the false one; (2) a story about the first sighting of Neptune, by John Galle on September 23, 1846, that illustrates how one can understand Galle's remark "That is the planet whose position Leverrier calculated" without believing that there is something to which Galle refers.

Fred Dretske holds that if one knows something, one need not eliminate every alternative to it but only the relevant alternatives. Besides defending this view in "The Pragmatic Dimension of Knowledge" ("Phil. Stud.", 40, 363-378, n 81), he makes some tentative suggestions about determining when an alternative is relevant. I discuss these suggestions and conclude that there are problems yet to be solved. I do not conclude that there are insoluble problems or that Dretske's approach is on the wrong track. It is, I believe, on the right track.