Alfred North Whitehead was a prominent English mathematician and philosopher who co-authored the highly influential Principia Mathematica with Bertrand Russell. Originally published in 1919, and first republished in 1925 as this Second Edition, An Enquiry Concerning the Principles of Natural Knowledge ranks among Whitehead's most important works; forming a perspective on scientific observation that incorporated a complex view of experience, rather than prioritising the position of 'pure' sense data. Alongside companion volumes The Concept of Nature and The Principle of Relativity, (...) it created a framework for Whitehead's later metaphysical speculations. This is an important book that will be of value to anyone with an interest in the relationship between science and philosophy. (shrink)

The relationship of part to whole is one of the most fundamental there is; this is the first and only full-length study of this concept. This book shows that mereology, the formal theory of part and whole, is essential to ontology. Peter Simons surveys and criticizes previous theories, especially the standard extensional view, and proposes a more adequate account which encompasses both temporal and modal considerations in detail. 'Parts could easily be the standard book on mereology for the next twenty (...) or thirty years.' Timothy Williamson, Grazer Philosophische Studien. (shrink)

I examine the reasons Aristotle presents in Physics VIII 8 for denying a crucial assumption of Zeno’s dichotomy paradox: that every motion is composed of sub-motions. Aristotle claims that a unified motion is divisible into motions only in potentiality (δυνάμει). If it were actually divided at some point, the mobile would need to have arrived at and then have departed from this point, and that would require some interval of rest. Commentators have generally found Aristotle’s reasoning unconvincing. Against David Bostock (...) and Richard Sorabji, inter alia, I argue that Aristotle offers a plausible and internally consistent response to Zeno. I defend Aristotle’s reasoning by using his discussion of what to say about the mobile at boundary instants, transitions between change and rest. There Aristotle articulates what I call the Changes are Open, Rests are Closed Rule: what is true of something at a boundary instant is what is true of it over the time of its rest. By contrast, predications true of something over its period of change are not true of the thing at either of the boundary instants of that change. I argue that this rule issues from Aristotle’s general understanding of change, as laid out in Phys. III. It also fits well with Phys. VI, where Aristotle maintains that there is a first boundary instant included in the time of rest, but not a “first in which the mobile began to change.” I then show how this rule underlies Aristotle’s argument that a continuous motion cannot be composed of actual sub-motions. Aristotle distinguishes potential middles, points passed through en route to a terminus, from actual middles. The Changes are Open, Rests are Closed Rule only applies to actual middles, because only they are boundaries of change that the mobile must arrive at and then depart from. On my reading, Aristotle argues that the instant of arrival, the first instant at which the mobile has come to be at the actual middle, cannot belong to the time of the subsequent motion. If it did, the mobile would already be moving towards the next terminus and thus, per Phys. VI 6, would have already left. But it cannot have moved away from the midpoint at the very same moment it has arrived there. This means that the instant of arrival must be separated from the time of departure by an interval of rest. I show how Aristotle’s reasoning applies generally to rule out any continuous reflexive motion or continuous complex rectilinear motion. On my interpretation, however, the argument does not apply to every change of direction. When, as in the case of projectile motion, multiple movers and their relative powers explain why the mobile changes directions, distinct sub-motions are not involved. Aristotle holds that such motions cannot be continuous, not because they involve intervals of rest, but because they involve multiple causes of motion. My interpretation of the Changes are Open, Rests are Closed Rule allows us to make better sense of Aristotle’s argument than any previous interpretation. (shrink)

There is a longstanding definition of instantaneous velocity. It saysthat the velocity at t 0 of an object moving along a coordinate line is r if and only if the value of the first derivative of the object's position function at t 0 is r. The goal of this paper is to determine to what extent this definition successfully underpins a standard account of motion at an instant. Counterexamples proposed by Michael Tooley (1988) and also by John Bigelow and Robert (...) Pargetter (1990) are reinforced and illuminated by considering the presence or absence of changes to the object's motion. (shrink)

Vectors, we will argue, are not just mathematical abstractions. They are also physical properties--universals. What make them distinctive are the rich and varied essences of these universals, and the complex pattern of internal relations which hold amongst them.

Zeno argued that since at any instant an arrow does not change its location, the arrow does not move at any time, and hence motion is impossible. I discuss the following three views that one could take in view of Zeno's argument:(i) the "at-at" theory, according to which there is no such thing as instantaneous velocity, while motion in the sense of the occupation of different locations at different times is possible,(ii) the "impetus" theory, according to which instantaneous velocities do (...) exist but these are only contingently and causally related to the temporal developments of positions,(iii) the "no instants" theory, according to which instants in time do not exist, and hence instantaneous velocities do not exist, while motion, in the sense of different areas occupied during different time intervals, is possible.I argue that, despite the fact that there have been interesting and relevant developments in mathematics and physics since the time of Zeno, each of these views still has serious drawbacks. (shrink)

First published in 1937. Routledge is an imprint of Taylor & Francis, an informa company.

This book investigates Aristotle’s views on abstraction and explores how he uses it. In this work, the author follows Aristotle in focusing on the scientific detail first and then approaches the metaphysical claims, and so creates a reconstructed theory that explains many puzzles of Aristotle’s thought. Understanding the details of his theory of relations and abstraction further illuminates his theory of universals. Some of the features of Aristotle’s theory of abstraction developed in this book include: abstraction is a relation; perception (...) and knowledge are types of abstraction; the objects generated by abstractions are relata which can serve as subjects in their own right, whereupon they can appear as items in other categories. The author goes on to look at how Aristotle distinguishes the concrete from the abstract paronym, how induction is a type of abstraction which typically moves from the perceived individuals to universals and how Aristotle’s metaphysical vocabulary is "relational.’ Beyond those features, this work also looks at how of universals, accidents, forms, causes and potentialities have being only as abstract aspects of individual substances. An individual substance is identical to its essence; the essence has universal features but is the singularity making the individual substance what it is. These theories are expounded within this book. One main attraction in working out the details of Aristotle’s views on abstraction lies in understanding his metaphysics of universals as abstract objects. This work reclaims past ground as the main philosophical tradition of abstraction has been ignored in recent times. It gives a modern version of the medieval doctrine of the threefold distinction of essence, made famous by the Islamic philosopher, Avicenna. (shrink)

This book examines the birth of the scientific understanding of motion. It investigates which logical tools and methodological principles had to be in place to give a consistent account of motion, and which mathematical notions were introduced to gain control over conceptual problems of motion. It shows how the idea of motion raised two fundamental problems in the 5th and 4th century BCE: bringing together being and non-being, and bringing together time and space. The first problem leads to the exclusion (...) of motion from the realm of rational investigation in Parmenides, the second to Zeno's paradoxes of motion. Methodological and logical developments reacting to these puzzles are shown to be present implicitly in the atomists, and explicitly in Plato who also employs mathematical structures to make motion intelligible. With Aristotle we finally see the first outline of the fundamental framework with which we conceptualise motion today. (shrink)

How do we know what we "know"? How did we –as individuals and as a society – come to accept certain knowledge as fact? In _Human Knowledge,_ Bertrand Russell questions the reliability of our assumptions on knowledge. This brilliant and controversial work investigates the relationship between ‘individual’ and ‘scientific’ knowledge. First published in 1948, this provocative work contributed significantly to an explosive intellectual discourse that continues to this day.

This book investigates what change is, according to Aristotle, and how it affects his conception of being. Mark Sentesy argues that change leads Aristotle to develop first-order metaphysical concepts such as matter, potency, actuality, sources of being, and the teleology of emerging things. He shows that Aristotle’s distinctive ontological claim—that being is inescapably diverse in kind—is anchored in his argument for the existence of change. -/- Aristotle may be the only thinker to have given a noncircular definition of change. When (...) he gave this definition, arguing that change is real was a losing proposition. To show that it exists, he had to rework the way philosophers understood reality. His groundbreaking analysis of change has long been interpreted through a Platonist lens, however, in which being is conceived as unchanging. Offering a comprehensive reexamination of the relationship between change and being in Aristotle, Sentesy makes an important contribution to scholarship on Aristotle, ancient philosophy, the history and philosophy of science, and metaphysics. (shrink)

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...) preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Some authors have recently arguedthat an objects velocity is logicallyindependent of its locations throughout time.Their aim is to deny the Russellianview that motion is merely a change oflocation, and to promote a rival account onwhich the connection between velocities andtrajectories is provided by the laws ofnature. I defend the Russellian view of motionagainst these attacks.

Consider a circle and a pair of its semicircles. Which is prior, the whole or its parts? Are the semicircles dependent abstractions from their whole, or is the circle a derivative construction from its parts? Now in place of the circle consider the entire cosmos (the ultimate concrete whole), and in place of the pair of semicircles consider the myriad particles (the ultimate concrete parts). Which if either is ultimately prior, the one ultimate whole or its many ultimate parts?

According to Aristotle, the way in which the parts of a whole are is different from the way in which the whole exists. Parts of an object are only potentially, whereas the whole exists actually. Although commentators agree that Aristotle held this doctrine, little effort has been made to spell out precisely what it could mean to say that the parts are only potentially. In this paper, I shall attempt to elucidate that claim and explain the philosophical motivation behind it. (...) I will argue that the motivation of mereological potentialism is to account for the unity of material substance. For a part to be potentially is, I will argue, a form of ontological dependence of the part on the whole. Potential parts have their being as a possible division of the whole. I will further explain this by specifying how the parts are grounded in the capacities of the whole and how the parts are individuated by the whole. (shrink)

This essay considers the implications for the powers metaphysic of the no-successor problem: As there are no successors in the set of real numbers, one state cannot occur just after another in continuous time without there being a gap between the two. I show how the no-successor problem sets challenges for various accounts of the manifestation of powers. For powers that give rise to a manifestation that is a new state, the challenge of no-successors is similar to that faced on (...) Bertrand Russell's analysis by causal relations. Powers whose manifestation is a processes and powers that manifest through time are challenged differently. To avoid powers appearing enigmatic, these challenges should be addressed, and I point to some possible ways this might be achieved. A prerequisite for addressing these challenges is a careful focus on the nature and timing of the manifesting and manifestation of powers. (shrink)

Aristotle’s solution to Zeno’s arrow paradox differs markedly from the so called at-at solution championed by Russell, which has become the orthodox view in contemporary philosophy. The latter supposes that motion consists in simply being at different places at different times. It can boast parsimony because it eliminates velocity from the ontology. Aristotle, by contrast, solves the paradox by denying that the flight of the arrow is composed of instants; rather, on my reading, he holds that the flight is a (...) unity which is ontologically prior to the temporal parts that may be abstracted from it. I label this position temporal holism; and an entity that is ontological prior to its temporal parts lasting. Lasting, I argue, is the key to Aristotle’s solution to the arrow paradox, but it has received insufficient attention in the relevant literature. I therefore set out here to investigate lasting and highlight its major role in Aristotle’s metaphysics more broadly, and in his solution to other problems of change. I show, too, how lasting within a contemporary context underwrites a parsimonious and intuitive solution to the arrow paradox that retains instantaneous velocity, and hence solves a problem for those who think velocity is required within the ontology to underwrite certain causal roles. (shrink)

A staunch hylomorphism involves a commitment to a sparse theory of universals and a sparse theory of composite material objects, as well as to an ontology of fundamental causal powers. Faint-hearted hylomorphism, in contrast, lacks one or more of these elements. On the staunch version of HM, a substantial form is not merely some structural property of a set of elements—it is rather a power conferred on those elements by that structure, a power that is the cause of the generation (...) (by fusion) and persistence of a composite whole through time. Bernard Williams discussed (and rejected) a faint-hearted version of HM in 1986, and faint-hearted HM has been defended more recently by Mark Johnston (2006) and Kathrin Koslicki (2008). I defend the superiority of the staunch version, in spite of its heavier ontological commitments, as a way of accounting for a real distinction between living organisms and heaps of matter, without recourse to dualism or vitalism, and as a way of combining a powers ontology with the possibility of gunk. (shrink)

Aristotle's Physics is one of the least studied "great books"--physics has come to mean something entirely different than Aristotle's inquiry into nature, and stereotyped Medieval interpretations have buried the original text. Sach's translation is really the only one that I know of that attempts to take the reader back to the text itself. -- Leon Cass, University of Chicago.

The first exhaustive study of Aristotle's concept of chance.

Zeno’s Paradoxes In the fifth century B.C.E., Zeno offered arguments that led to conclusions contradicting what we all know from our physical experience—that runners run, that arrows fly, and that there are many different things in the world. The arguments were paradoxes for the ancient Greek philosophers. Because many of the arguments turn crucially on … Continue reading Zeno’s Paradoxes →.

I. In some celebrated passages, the Physics conveys to us that.

‘The Union of Cause and Effect in Aristotle : Physics III 3’, Oxford Studies in Ancient Philosophy, 32, pp. 205-232, May 2007.: I argue that Aristotle introduced a unique realist account of causation, which has not hitherto been appreciated in the history of philosophy: causal realism without a causal relation. In his account, cause and effect are unified by the ectopic actualization of the agent’s potentiality in the patient. His solution consists in the introduction of a property that belongs to (...) one subject but is realized in another subject on whose state this realization depends. I identify and analyze the multiple ontological dependencies between the causal state of the agent and that of the patient during their causal activity. (shrink)

Almost everything that we know about Zeno of Elea is to be found in the opening pages of Plato's Parmenides. There we learn that Zeno was nearly 40 years old when Socrates was a young man, say 20. Since Socrates was born in 469 BC we can estimate a birth date for Zeno around 490 BC. Beyond this, really all we know is that he was close to Parmenides (Plato reports the gossip that they were lovers when Zeno was young), (...) and that he wrote a book of paradoxes defending Parmenides' philosophy. Sadly this book has not survived, and what we know of his arguments is second-hand, principally through Aristotle and his commentators (here I have drawn particularly on Simplicius, who, though writing a thousand years after Zeno, apparently possessed at least some of his book). There were apparently 40 ‘paradoxes of plurality’, attempting to show that ontological pluralism — a belief in the existence of many things rather than only one — leads to absurd conclusions; of these paradoxes only two definitely survive, though a third argument can probably be attributed to Zeno. Aristotle speaks of a further four arguments against motion (and by extension change generally), all of which he gives and attempts to refute. In addition Aristotle attributes two other paradoxes to Zeno. Sadly again, almost none of these paradoxes are quoted in Zeno's original words by their various commentators, but in paraphrase. (shrink)