Diversity Reading List

Summary: This chapter explores the core thought of the idea of emergentism, that as systems acquire increasingly higher degrees of organizational complexity, they begin to exhibit novel properties which in some sense transcend the properties of their constituent parts, and behave in ways that cannot be predicted on the basis of the laws governing simpler systems. The birth of emergentism can be traced back to John Stuart Mill and his distinction between "heteropathic" and "homeopathic" laws. Academic philosophers contributed to the development of emergence and the attendant doctrines of emergentism, but it is interesting to note that the fundamental idea seems to have had a special appeal to scientists and those outside professional philosophy. In spite of this, emergentism failed to become a visible part of mainstream philosophy of science because philosophy of science was, at the time, shaped by positivist and hyper-empiricist views that dominated Anglo-American philosophy.

Abstract: Trinitarians claim there are three Divine persons each of which is God, and yet there is only one God. It seems they want three to equal one. It just so happens, some metaphysicians claim exactly that. They accept Composition as Identity: each fusion is identical to the plurality of its parts. I evaluate Composition as Identity's application to the doctrine of the Trinity, and argue that it fails to give the Trinitairan any options he or she didn't already have. Further, while Composition as Identity does give us a new way to assert polytheism, its help requires us to endorse a claim that undercuts any Trinitarian motivation for the view.

Abstract: Current formulations of Four-Dimensionalism may be objected to on grounds that they are too inflexible: the formulations do not seem to allow for enough variety in the views they are paired with. For instance, Kit Fine has noted that formulations of Four-Dimensionalism in terms of instantaneous parts may be too demanding for Four-Dimensionalists who believe nothing is instantaneous. And Trenton Merricks has argued that one can think something persists four-dimensionally without taking it to have proper temporal parts, and claims that our formulation of Four-Dimensionalism should be revised to allow for this. I will add my own worries to those of Fine and Merricks. I will note that current formulations of Four-Dimensionalism are not sufficiently neutral with respect to the structure of time, with respect to how liberally objects decompose into parts, and with respect to whether objects and the regions they fill match in mereological structure. I will show that we can formulate Four-Dimensionalism in a sufficiently neutral way, while still producing a view that can do the work we typically require of Four-Dimensionalism.

Summary: Something could be round even if it were the only thing in the universe, unaccompanied by anything distinct from itself. Jaegwon Kim once suggested that we define an intrinsic property as one that can belong to something unaccompanied. Wrong: unaccompaniment itself is not intrinsic, yet it can belong to something unaccompanied. But there is a better Kim-style definition. Say that P is independent of accompaniment iff four different cases are possible: something accompanied may have P or lack P, something unaccompanied may have P or lack P. P is basic intrinsic iff (1) P and not-P are nondisjunctive and contingent, and (2) P is independent of accompaniment. Two things (actual or possible) are duplicates iff they have exactly the same basic intrinsic properties. P is intrinsic iff no two duplicates differ with respect to P.

Publisher's Note: Mary Leng offers a defense of mathematical fictionalism, according to which we have no reason to believe that there are any mathematical objects. Perhaps the most pressing challenge to mathematical fictionalism is the indispensability argument for the truth of our mathematical theories (and therefore for the existence of the mathematical objects posited by those theories). According to this argument, if we have reason to believe anything, we have reason to believe that the claims of our best empirical theories are (at least approximately) true. But since claims whose truth would require the existence of mathematical objects are indispensable in formulating our best empirical theories, it follows that we have good reason to believe in the mathematical objects posited by those mathematical theories used in empirical science, and therefore to believe that the mathematical theories utilized in empirical science are true. Previous responses to the indispensability argument have focussed on arguing that mathematical assumptions can be dispensed with in formulating our empirical theories. Leng, by contrast, offers an account of the role of mathematics in empirical science according to which the successful use of mathematics in formulating our empirical theories need not rely on the truth of the mathematics utilized.

Summary: Surveys the opposition between views of mathematics which take mathematics to represent a independent mathematical reality and views which take mathematical axioms to define or circumscribe their subject matter; and defends the latter view against influential objections.

Summary: Defends an account of mathematical knowledge in which mathematical knowledge is a kind of modal knowledge. Leng argues that nominalists should take mathematical knowledge to consist in knowledge of the consistency of mathematical axiomatic systems, and knowledge of what necessarily follows from those axioms. She defends this view against objections that modal knowledge requires knowledge of abstract objects, and argues that we should understand possibility and necessity in a primative way.

Abstract: We expect there to be a connection between experience and knowledge in many of our ordinary epistemic judgments; this expectation is by no means confined to our knowledge of mental states. Thus, the appeal to a special necessary connection between experience and knowledge of mental states ignores the generality of this phenomenon. More important, however, it takes this phenomenon too seriously: our unreflective expectations about the previous experiences of a person who has knowledge, as I have argued, have little to do with whether these experiences are necessary for knowledge of that sort. Thus, they provide no threat to physicalism, or any other objective theory of mental states. To be sure, it is not hard to see why reductionist theses in the philosophy of mind raise suspicion, as they have often ignored the complexity of our mental lives. In this case, however, the suspicion leads to unwarranted fears about Procrusteans under the bed: it is not the insufficiencies of objectivity, but the vestiges of Empiricism, that suggest that these theories may be inadequate for expressing all the truth about experience that there is.

Abstract: Now THAT THE NEW essentialism is forcing us to reconsider many issues in diverse areas of philosophy, it is appropriate to examine some of the implications of Saul Kripke's work for aesthetics. I shall be focusing on Kripke's "Naming and Necessity." 1 On Kripke's account, the table in my dining room could not have been made out of any other wood than the wood that was, in fact, actually used to make it. It is not merely that this particular kind of wood must have been used, namely oak, but this very piece, otherwise it would not be this particular table. I intend to show how Kripke's line of argument applies to a work of art and to draw the consequences of it for aesthetics. If we do not want to accept these consequences, then we will be forced into a ra- tional reconstruction of the identity issue. My application of Kripke's position is con- fined to painting and sculpture and turns for its example on Michelangelo's David. (Whether or not or how Kripke's analysis and our conclusions can be extended to the other arts is outside the scope of this paper.) Let me be clear about strategy. Through- out I assume without argument Kripke's position. I also assume and, in fact hold, again without argument, that the David is a physical entity. When the consequences of CATHERINE LORD is professor of philosophy at Syra- cuse University. the Kripkean analysis are explored, I engage in a descriptive metaphysics and assume these to be the facts. There is no waffling on the assumption that the David is a physical object. When the consequences of the Kripkean analysis are applied to that assumption, we may not wish to accept them. At that point I engage in a rational reconstruction. The descriptive metaphysics and the rational reconstruction or revisionary meta- physics must not be confused. Following Kripke's analysis, I shall show how it is that Michelangelo could not have made his David out of a different block of marble than the block which he actually used. Since this is counter-intuitive, we may want to protest as follows. Let us pretend that Michelangelo walks into his studio. There are two blocks of marble before him, block A and block B. As the sculptor de- liberates as to which block he will use, he has the work of art in his mind. In fact he has before his mind a perfect image, complete in every detail, of the statue which will result from his efforts. (Here I am not com- mitted to any particular theory of the imagination - one could be Rylean. On any account I see no logical difficulty in supposing that Michelangelo knew exactly what he wanted to do, that he had a representation vivid in every detail of what he would later execute.) We may say, then, that Michelangelo's intention, and I emphasize the word, intention, was to embody a certain idea in matter perhaps even a certain kind of matter, marble, and even perhaps a certain kind of marble. (Again, in speaking of embodying a certain idea, I should not be taken as prejudicing the case in favor of or against any theory of aesthetics.) After examining block A and block B and finding nothing to choose between them, Michelangelo chose block A. Now as far as Michelangelo's intention was concerned it could have been realized in block B. His intention was to create a definite statue which he envisioned in every detail. Accordingly, we seem bound to say that the David might just as readily have been made out of block B as block A. On a Kripkean analysis that is not the case. Had Michelangelo chosen to embody his idea in block B, an entity different from the David would have resulted. It would have looked exactly as the David does in fact look. It might, indeed, have weighed the same amount, etc., but it would not have been identical to the entity to which the David is identical. It would certainly have been a David. ". . . is a David" is a general term which is true of many statues; "the David," as I am using the expression, is a singular term referring to only one. Al- though there is a possible world in which Michelangelo embodies his idea in block B and in which the resulting sculpture comes to be put in the Academia in Florence and even to be enjoyed in precisely the same way as we do in fact enjoy the David, the object of our attention in that possible world is not to be identified with the entity in the Academia, i.e., with the David we ac- tually do enjoy. To grasp Kripke's central contention, let us consider it in its most dramatic formula- tion where he argues that Socrates could not possibly have come from different parents. More precisely, Kripke is willing to allow that the sperm and egg from which Socrates came might possibly have been transplanted from the bodies of his mother and father to the bodies of a different man and woman. Had such a transplantation taken place, Socrates might well have come from differ- ent parents, as the term is ordinarily under- stood. The key issue can be brought out as follows. Suppose that Socrates' parents had died in an earthquake in their early youth at a time before they first met. There is such a possible world. Now suppose that some other Athenian couple gave birth to a son on the precise date on which Socrates, our Socrates, was born. Suppose that this son was snub-nosed like Socrates, indeed looked exactly like him at every stage of his life. We may even suppose that his per- sonality, his genetic make-up, etc. was the same as our Socrates. We can imagine his living a life from birth to death just like the life Socrates lived, even becoming the teacher of Plato and being given the hem- lock. Would that person have been our Socrates? The answer for Kripke is No. Somewhere in outer space there may now, in fact, be a double of Gerald Ford. He may live on a planet qualitatively indistin- guishable in every respect down to the last detail from the planet Earth. He may even be president of a country exactly like ours, etc., but he would not be Gerald Ford even though his name may be "Gerald Ford." Qualitative similarity cannot suffice to es- tablish identity. To return to the table in my dining room, in traditional Aristotelian terms, Kripke in- sists that essential to the table is both its form and its matter, its being a table, on the one hand, and its being made of the very wood it is indeed made of, on the other. Supposing Michelangelo had chosen block B instead of block A for embodying his idea. Suppose also that Leonardo da Vinci had stepped into his studio and absconded with block A.2 Suppose that by some extraordi- nary coincidence Michelangelo and Leo- nardo, working separately, each produced a statue qualitatively indistinguishable from the David which is in the Academia. Which of the two works, that of Michelangelo or that of Leonardo would be the David, Michelangelo's made out of block B or Leo- nardo's made out of block A? Take a simpler case. Suppose that Michelangelo had worked on both blocks of marble and produced two qualitatively indistinguish- able statues. Let the one made from block A find its way to the Uffizi or the Louvre and the one made from block B find its way to the Academia (perhaps in the manner of Kripkean Approach To Identity of Art Work those statues of Daedelus). There is no logical reason why our David should have found its way to the Academia. There is, however, a necessity - an onto- logical necessity - that the David should have been made out of block A, though the truth of the sentence, "The David was made out of block A," cannot be established on the basis of a purely a priori reflection. We have here, then, a necessary a posteriori proposition. And it is the a posteriori char- acter of the proposition that encourages one to suppose that we could have discovered that the David was made out of granite. If we discover that the David is made out of granite, not marble, then we have dis- covered that the David is necessarily made out of granite. This is merely an epistemic possibility. We could even now, in a scepti- cal frame of mind, say that as far as we know David might in fact have been made out of granite. But since, in fact, the David is made out of marble and made from block A, in all possible worlds it is made of marble and from block A. There is no ontologically possible world in which we discover it to be made of granite or out of block B.

Publisher's Note: Our much-valued mathematical knowledge rests on two supports: the logic of proof and the axioms from which those proofs begin. Naturalism in Mathematics investigates the status of the latter, the fundamental assumptions of mathematics. These were once held to be self-evident, but progress in work on the foundations of mathematics, especially in set theory, has rendered that comforting notion obsolete. Given that candidates for axiomatic status cannot be proved, what sorts of considerations can be offered for or against them? That is the central question addressed in this book. One answer is that mathematics aims to describe an objective world of mathematical objects, and that axiom candidates should be judged by their truth or falsity in that world. This promising view - realism - is assessed and finally rejected in favour of another - naturalism - which attends less to metaphysical considerations of objective truth and falsity, and more to practical considerations drawn from within mathematics itself. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be helpfully applied in the assessment of candidates for axiomatic status in set theory. Maddy's clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.