David Sanford

Naive mereology studies ordinary, common-sense beliefs about part and whole. Some of the speculations in this article on naive mereology do not bear directly on Peter van Inwagen's "Material Beings". The other topics, (1) and (2), both do. (1) Here is an example of Peter Unger's "Problem of the Many". How can a table be a collection of atoms when many collections of atoms have equally strong claims to be that table? Van Inwagen invokes fuzzy sets to solve this problem. I claim that an alternative treatment of vagueness, supervaluations over many-value valuations, provides a better solution. (2) The Special Composition Question asks how parts compose a whole. One who rejects van Inwagen's answer in terms of constituting a life need not provide some alternative answer. Even if all answers to the Special Question fail, there are a multitude of less general composition questions that are not so difficult.

I criticize and emend J L Mackie's account of causal priority by replacing ‘fixity’ in its central clause by 'x is a causal condition of y, but y is not a causal condition of x'. This replacement works only if 'is a causal condition of' is not a symmetric relation. Even apart from our desire to account for causal priority, it is desirable to have an account of nonsymmetric conditionship. Truth, for example, is a condition of knowledge, but knowledge is not a condition of truth. My definitions of 'sufficient condition for' and 'necessary condition for' do not imply that p is a sufficient condition of q if and only if q is a necessary condition of p.

The primary objects of hearing are sounds: everything we hear we hear by hearing a sound. (This claim differs from Berkeley’s that we hear only sounds and from Aristotle’s that we only hear sounds.) Colored regions are primary objects of sight, and pressure resistant regions are primary objects of perception by touch. By definition, the primary objects of perception are physical. The properties of the primary objects of perception are exactly the properties sense-datum theories attribute to sense-data. Indirect Realism holds that awareness of sense-data (or something similar) mediates our perception of primary objects. Direct Realism denies this. The question when the perception of a primary object, such as parts of the surfaces of a hat and coat, is thereby the perception of a non-primary object, such as a person, is independent of the disagreement between Direct and Indirect Realism.

Hume's arguments for the contention that causal necessity precludes logical necessity depend on the questionable principle that a cause must precede its effect. Hobbes' definition of entire cause, although it fails to account for causal priority, is not refuted by Hume. The objections of Myles Brand and Marshall Swain (Philosophical Studies, 1976) to my counterexample against Hume (Philosophical Studies, 1975) are ineffective. Their other objections to my criticisms of their argument against defining causation in terms of necessary and sufficient conditions (Synthese, 1970) are also mostly ineffective.

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.

A primary purpose of argument is to increase the degree of reasonable confidence that one has in the truth of the conclusion. A question begging argument fails this purpose because it violates what W. E. Johnson called an epistemic condition of inference. Although an argument of the sort characterized by Robert Hoffman in his response (Analysis 32.2, Dec 71) to Richard Robinson (Analysis 31.4, March 71) begs the question in all circumstances, we usually understand the charge that an argument is question begging with reference to the beliefs of the person, or the sort of person, to whom the argument is directed.

Two fusions can be in the same place at the same time. So long as a house made of Tinkertoys is intact, the fusion of all its Tinkertoys parts coincides with the fusion of it walls and its roof. If none of the Tinkertoys is destroyed, their fusion persists through the complete disassembly of the house. (So the house is not a fusion of its Tinkertoy parts.) The fusion of the walls and roof does not persist through the complete disassembly because the walls and the roof themselves do not persist. (So the walls and the roof are also not fusions of their Tinkertoy parts.)

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

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.

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.

Examples of sensory illusion show the failure of the attempt of traditional sense-datum theory to account for something's phenomenally appearing to be F by postulating the existence of a sense-datum that is actually F. the Muller-Lyer Illusion cannot be explained by postulating two sensibly presented lines that actually have the lengths the physical lines appear to have. Illusions due to color contrast cannot be explained by postulating sense-data that actually have the colors the physical samples appear to have.

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.

Philosophers have had difficulty in explaining the difference between disjunctive and non-disjunctive predicates. Purely syntactical criteria are ineffective, and mention of resemblance begs the question. I draw the distinction by reference to relations between borderline cases. The crucial point about the disjoint predicate 'red or green', for example, is that no borderline case of 'red' is a borderline case of 'green'. Other varieties of disjunctive predicates are: inclusively disjunctive (such as 'red or hard'), disconnected (such as 'grue' on the usual definitions), and skew (such as 'grue' on an emended definition). 'Green' is not a disjunctive predicate. Nelson Goodman's new riddle of induction elicits yet another response.

Although Aranyosi's claim that McTaggart's "set of parts" is a set rather than a fusion is correct, his attempt to restate McTaggart's conception needs revision. Aranyosi argues that "the fusion of cats is identical with the fusion of all cat-parts, 'regardless of whether all cat-parts are parts of cats or not.'" Fusions have unique decompositions into what David Lewis calls "nice parts." Cats are nice parts of cat fusions, as are maximal spatio-temporally connected parts. Part of Aranyosi's argument fails when it deals with cats; part of it fails when it deals with maximal spatio-temporally connected parts. He does not identify one kind of nice part that allows his whole argument to go through.

McTaggart argues that the A series, which orders events with reference to past, present, and future, involves an inescapable contradiction. The significant difference between the earlier version of his argument (Mind, 1908) and the version in The Nature of Existence, Volume II, Chapter 33 (1927), has often gone unnoticed. His arguments are all invalid; the conclusion can be rejected without rejecting any premiss. It is therefore unnecessary to adopt any philosophical thesis about time (e.g., that some token-reflexive analysis of tensed statements is adequate) to avoid McTaggart's final conclusion that time is unreal.

I revise J L Mackie's first account of casual direction by replacing his notion of "fixity" by a newly defined notion of "sufficing" that is designed to accommodate indeterminism. Keeping Mackie's distinction between casual order and casual direction, I then consider another revision that replaces "fixity" with "one-way conditionship". In response to the charge that all such accounts of casual priority beg the question by making an unjustified appeal to temporal priority, i maintain that one-way conditionship explains rather that assumes objective temporal dependence as well as objective casual dependence.

Hume, in "An Enquiry Concerning Human Understanding", holds (1) that all causal reasoning is based on experience and (2) that causal reasoning is based on nothing but experience. (1) does not imply (2), and Hume's good reasons for (1) are not good reasons for (2). This essay accepts (1) and argues against (2). A priori reasoning plays a role in causal inference. Familiar examples from Hume and from classroom examples of sudden disappearances and radical changes do not show otherwise. A priori causal reasoning is closely related to understanding causal mechanisms. One uncovers the intelligibility of a causal process by understanding its mechanism.

To accommodate vague statements and predicates, I propose an infinite-valued, non-truth-functional interpretation of logic on which the tautologies are exactly the tautologies of classical two-valued logic. iI introduce a determinacy operator, analogous to the necessity operator in alethic modal logic, to allow the definition of first-order and higher-order borderline cases. On the interpretation proposed for determinacy, every statement corresponding to a theorem of modal system T is a logical truth, and I conjecture that every logical truth on the interpretation corresponds to a theorem of T. the interpretation is extended to predicate logic. A borderline case of a predicate 'F’ is neither determinately F nor determinately not-F. Traditional sorites arguments are seen to fall apart early in their gradual stepwise passage from truth to falsity.

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.