Three key elements of Aristotle’s theory of demonstration have Pythagorean antecedents. Demonstration is a revelatory discourse that is 1) inferential, 2) explicitly based on premises that are not themselves demonstrated on the basis of more basic premises, and 3) explanatory, insofar as the premises express those basic facts that are explanatory of the conclusion. The Pythagorean Table of Opposites constitutes a kind of protologic making possible a kind of deduction, which Aristotle would have regarded as a “demonstration,” that reveals the (...) reasons behind Pythagorean commands and prohibitions. Philolaus recognizes ultimate explanatory principles. Both he and Archytas recognize the asymmetry of principles and what is explained on their basis. (shrink)

Within the third book of Porphyry's On Abstinence from Animal Food, an ethic of community is developed in order to provide the basis of an account of our ethical obligations to animals. I argue that in spite of Porphyry's rejection of this account, it constitutes a coherent and comprehensive nonanthropocentric ethical theory. It conforms with ethical intuitions insofar as it grants that animals are moral subjects, but does not demand impartiality. By appealing to Theophrastus's notion of to oikeion and to (...) the Stoic notion of oikeic6is it provides the theoretical resources for showing why it is often appropriate to favor human beings over other animals. (shrink)

In response to “Trump and the Trumpists” (Vol. 3, No. 1).

Aristotle’s main objection to Pythagorean number ontology is that it posits as a basic subject what can exist only as inherent in a subject. I then show how contemporary structural realists posit an ontology much like that of Aristotle’s Pythagoreans. Both take the objects of knowledge to be structure, not the subject of structure. I discuss both how pancomputationalists such as Edward Fredkin approach the Pythagorean account insofar as on their account all reality can in principle be expressed as one (...) (very big) number, made up of discrete units, and even more moderate varieties of structural realism, like that of Floridi, share with pancomputationalism the aspect of “Pythagorean” ontology that Aristotle finds so objectionable: positing structure or form with no substrate. I conclude by arguing that Aristotle himself is drawn to something close or (identical) to a structural realist ontology in Metaphysics 7.3. (shrink)

Contrā Dale Jamieson, the study of the metaethical foundations of environmental ethics may well lead students to a more environmentally responsible way of life. For although metaethics is rarely decisive in decision making and action, there are two kinds of circumstances in which it can play a crucial role in our practical decisions. First, decisions that have unusual features do not summon habitual ethical reactions, and hence invite the application of ethical precepts that the study of metaethics and ethical theory (...) isolate and clarify. Second, there are times in which the good of others may well be given greater weight in one’s ethical deliberations if theory has made clear that the good to be promoted is ontologically independent of one’s own good. (shrink)

Human concern over the urgency of current environmental issues increasingly entails wide-ranging discussions of how we may rethink the relationship between humans and the rest of the natural world. In order to provide a context for such discussions this anthology provides a selection of some of the most important, interesting and influential readings on the subject from classical times through to the late nineteenth century. Included are such figures as Xenophon, Plato, Aristotle, Hildegard of Bingen, St Francis of Assisi, Bacon, (...) Decartes, Kant, Mill, Emerson and Thoreau. As the collection as a whole amply demonstrates, the history of western philosophical accounts of nature can help us to better understand current attitudes and problems. Human Life and the Natural World may also be of interest to a broad range of philosophers and students of philosophy, and more generally to those with a concern for the environment that engages the intellect as well as the heart. (shrink)

Aristotle described the scientific explanation of universal or general facts as deducing them through scientific demonstrations, that is, through syllogisms that met requirements he first formulated of logical validity and explanatoriness. In Chapters 19-23, he adds arguments for the further logical restrictions that scientific demonstrations can neither be indefinitely long nor infinitely extendible through the interposition of new middle terms. Chapters 24-26 argue for the superiority of universal over particular demonstration, of affirmative over negative demonstration, and of direct negative demonstration (...) over demonstration to the impossible. Chapters 27 34 discuss different aspects of sciences and scientific understanding, allowing us to distinguish between sciences, and between scientific understanding and other kinds of cognition, especially opinion. Philoponus' comments on these chapters are interesting especially because of his metaphysical analysis of universal predication and his understanding of the notion of subordinate sciences. We learn from his commentary that Philoponus believed in Platonic Forms as inherent in, and posterior to, the Divine Intellect, but ascribed to Aristotle an interpretation of Plato's Forms as independent substances, prior to the Demiurgic Intellect. A very important notion from Aristotle's Posterior Analytics is that of the 'subordination' of sciences, i.e. the idea that some sciences depend on 'higher' ones for some of their principles. Philoponus goes beyond Aristotle in suggesting a taxonomy of sciences, in which the subordinate science is the same in genus as the superordinate, but different in species. (shrink)

In Explaining an Eclipse, Owen Goldin provides a book-length treatment of the first ten chapters of book 2 of the Posterior Analytics. Goldin’s aim is to answer one question: how can an Aristotelian demonstration show anything of scientific interest if all the premises are definitions? To this question Goldin gives his undivided attention.

Aristotle’s account of epistēmē is foundationalist. In contrast, the web of dialectical argumentation that constitutes justification for scientific principles is coherentist. Aristotle’s account of explanation is structurally parallel to the argument for a foundationalist account of justification. He accepts the first argument but his coherentist accounts of justification indicate that he would not accept the second. Where is the disanalogy? For Aristotle, the intelligibility of a demonstrative premise is the cause of the intelligibility of a demonstrated conclusion and causation is (...) asymmetric. Within the Posterior Analytics itself, Aristotle does not account for this, but elsewhere he develops the resources for doing so: the cause is what acts on a substrate to actualize a potential in that substrate, resulting in the effect. On the other hand, it may well happen that two propositions entail each other, in which case one may as well justify the one on the basis of the other as vice versa. (shrink)

At Metaphysics A 5 986a22-b2, Aristotle refers to a Pythagorean table, with two columns of paired opposites. I argue that 1) although Burkert and Zhmud have argued otherwise, there is sufficient textual evidence to indicate that the table, or one much like it, is indeed of Pythagorean origin; 2) research in structural anthropology indicates that the tables are a formalization of arrays of “symbolic classification” which express a pre-scientific world view with social and ethical implications, according to which the presence (...) of a principle on one column of the table will carry with it another principle within the same column; 3) a close analysis of Aristotle's arguments shows that he thought that the table expresses real causal relationships; and 4) Aristotle faults the table of opposites with positing its principles as having universal application and with not distinguishing between those principles that are causally prior and those that are posterior. Aristotle's account of scientific explanation and his own explanations that he developed in accordance with this account are in part the result of his critical encounter with this prescientific Pythagorean table. (shrink)

abstract What gives ethical and political validity to a state? This is to ask what a state is for and to provide a means to determine whether or not a constitution is just. In this paper I compare the account given by Tamir in Liberal Nationalism with that of Rawls, in order to clarify the decisive differences. Although both recognize the importance of particular associations and the moral imperative to be fair, Tamir places priority on the first and Rawls on (...) the second. I explore their practical implications in regard to the ethical defensibility of Israel's self‐identification as a Jewish state and to conflicting nationalistic territorial claims for the Temple Mount in Jerusalem. I suggest that if Tamir is correct in her analysis of nationalism, the Israeli‐Palestinian conflict is a problem that is without the sort of solution that is sought by those who are both interested parties and rational agents of good will. (shrink)

This book is an attempt to meet the arguments of scholars who have denied that within the Philebus, generally recognized as a late dialogue, the theory of Forms of the middle dialogues is advocated or plays an important role. Accordingly, instead of a commentary on the argument of the Philebus as a whole, Benitez presents a painstaking analysis of those passages that promise to shed light on Plato's metaphysical and epistemological views at the time of the writing of the Philebus. (...) The result is not for the casual reader, since much of the book is devoted to a careful examination of the Greek text and alternative interpretations. Nonetheless this book will prove profitable for all who are interested in Platonic metaphysics, for Benitez concentrates on developing cogent interpretations of the One-Many problems and the Heavenly Tradition and the Fourfold Classification, two of the most difficult and provocative passages in the Platonic corpus. (shrink)

What lies behind Aristotle’s declarations that an attribute or feature that is demonstrated to belong to a scientific subject is proper to that subject? The answer is found in APo. 2.8-10, if we understand these chapters as bearing not only on Aristotle theory of definition but also as clarifying the logical structure of demonstration in general. If we identify the basic subjects with what has no different cause, and demonstrable attributes with what do have ‘a different cause’, the definitions of (...) demonstrable attributes necessarily have the minor terms of the appropriate demonstrations in their definitions, for which reason the subjects and demonstrable attributes are coextensive. (shrink)

Heraclitus accepts as a principle that any particular insight into things is necessarily partial and perspectival. Edward Halper has discussed how, for this reason, it is in principle impossible for a particular thinker to attain the perspective of the Logos by which the whole can be made intelligible. So, metaphysics itself tells us that metaphysics is impossible. According to Halper, Heraclitus was wrong to take the Logos as applying to itself, as the Logos should properly be understood as applying only (...) to what is not a product of human agency. I argue that Halper’s move cannot serve as a corrective patch to Heraclitus’ metaphysical thought, since it posits a distinction between the human and the rest of reality which Heraclitus could never accept. Although not a radical monist who denies the reality of all multiplicity, a fundamental principle of his thought is that all distinctions and oppositions are grounded in a more fundamental unity. I instead approach the Heraclitean paradox by appealing to the strategy, familiar from a number of ancient Greek philosophers, of making a distinction between different levels of knowledge inherent within the same knower. (shrink)

What is it for a philosophical account to be atomist? What is the attraction of an atomistic metaphysics? These questions are best approached by considering representative varieties of atomism. The present paper offers a preliminary account of atomism in general and then, in order to shed light on atomism in general and its appeal, considers two very different varieties of atomism: that of Democritus and that of Fredkin’s “digital ontology.” Atomistic accounts are philosophically attractive for two related reasons. First, on (...) an atomistic account, the units of explanation are determinate, and for that reason are in principle ultimately intelligible, as are the complexes derived from them. Both examples of atomism that the author takes as examples display these features. Second, atomism is reductionistic. Ancient atomism has this feature, but it is not an inevitable result of an atomistic strategy. It is absent from Fredkin’s digital ontology. (shrink)

This commentary on Aristotle’s Metaphysics is in a style familiar from the writings of Leo Strauss and his students. The reader is presented with a paraphrase of the whole of Aristotle’s text, marked by seemingly odd omissions, emphases, and offhand remarks. One soon sees that the book is written in code. Only as the book progresses is the author more explicit concerning what he takes to be the main lines of Aristotle’s esoteric teaching, which is as follows.Aristotle writes the Metaphysics (...) for students being initiated into philosophy. These students have already left behind a mythical world-view, but not all are.. (shrink)

There is agreement neither concerning the point that is being made in Posterior analytics 96b15–25 nor the issue Aristotle intends to address. There are two major lines of interpretation of this passage. According to one, sketched by Themistius and developed by Philoponus and Eustratius, Aristotle is primarily concerned with determining the definitions of the infimae species that fall under a certain genus. They understand Aristotle as arguing that this requires collating definitional predictions, seeing which are common to which species. Pacius, (...) on the other hand, takes Aristotle to be saying that a genus is studied scientifically through first determining the infimae species that fall under that genus. This interpretation attributes to Aristotle a distinction between primary and derivative subjects. I argue for Pacius’s interpretation, defending it against Barnes’s objections.Author Keywords: Demonstration; Definition; Aristotle; Species; Principles. (shrink)