This book traces the development of formal logic from its origins in ancient Greece to the present day. The authors first discuss the work of logicians from Aristotle to Frege, showing how they were influenced by the philosophical or mathematical ideas of their time. They then examine developments in the present century.

Aristotle's treatise De Interpretatione is one of his central works; it continues to be the focus of much attention and debate. C. W. A. Whitaker presents the first systematic study of this work, and offers a radical new view of its aims, its structure, and its place in Aristotle's system, basing this view upon a detailed chapter-by-chapter analysis.By treating the work systematically, rather than concentrating on certain selected passages, Whitaker is able to show that, contrary to traditional opinion, it forms (...) an organized and coherent whole. He argues that the De Interpretatione is intended to provide the underpinning for dialectic, the system of argument by question and answer set out in Aristotle's Topics; and he rejects the traditional view that the De Interpretatione concerns the assertion and is oriented towards the formal logic of the Prior Analytics. In doing so, he sheds valuable new light on some of Aristotle's most famous texts. (shrink)

This paper discusses the debate over whether emotional expressions are spontaneous or intentional actions. We describe a variety of empirical evidence supporting these two possibilities. But we argue that the spontaneous-intentional distinction fails to explain the psychological dynamics of emotional expressions. We claim that a complex systems perspective on intentions, as self-organized critical states, may yield a unified view of emotional expressions as a consequence of situated action. This account simultaneously acknowledges the embodied status of environment, evolution, culture and mind (...) in theories of emotion. (shrink)

We consider several thought and practical experiments, and variations thereof, from which the existence can be inferred of retroactive effects on the assumptions of conservation of linear and angular momentum and of realism defined in a wide sense. Such conclusion is made less counterintuitive by research into the proper physical background of the relativistic length contraction of a moving arrow, viz. the fact that the universe is four-dimensional indeed. In one of the experiments considered, the evidence of retroactivity is more (...) striking and can more easily be actually demonstrated than was the case in earlier proofs. (shrink)

From his own day to the present Socrates has presented a challenge to philosophers and commentators, a challenge at once of a puzzle to be solved and of an ideal to be continually reshaped in response to the demands of shifting historical perspectives. Alexander Nehamas’s intriguing book combines discussion of this ongoing process, specifically of responses to Socrates by Montaigne, Nietzsche, and Foucault, with exemplification of it via his own response to Socrates. The focus of these responses is specified in (...) the book’s title. The Socrates to whom Nehamas himself responds is a figure for whom philosophy is the art of living, that is to say a figure who uses argument and debate as a means to the identification and thereby the achievement of the constituents of the best human life. And the writers on Socrates whom he discusses, sharing that conception of the role of philosophy, pursue it with more or less explicit reference to its pursuit by Socrates. (shrink)

In this dialogue Plato shows the pretensions of the leading sophist, Protagoras, challenged by the critical arguments of Socrates. The dialogue broadens out to consider the nature of the good life and the role of intellect and pleasure.

This book charts new ground, specifically, in its negotiation of a definition of animal welfare, in its systematic discussion of the organizations actually ...

The lexicographic power ΔΓ of chains Δ and Γ is, roughly, the Cartesian power Πγ∈Γ Δ, totally ordered lexicographically from the left. Here the focus is on certain powers in which either Δ = R or Γ = R, with emphasis on when two such powers are isomorphic and on when ΔΓ is 2-homogeneous. The main results are: (1) For a countably infinite ordinal α, Rα* +α ≃ Rα. (2) RR ≄ RQ. (3) For Δ a countable ordinal ≥ 2. (...) ΔR, with its smallest element deleted, is 2-homogeneous. (shrink)

In this paper, it is argued that the prima facie conflict between special relativity and the quantum-mechanical collapse postulate is only apparent, and that the seemingly incompatible accounts of entangled systems undergoing collapse yielded by different reference frames can be regarded as no more than differing accounts of the same processes and events. Attention to the transformation properties of quantum-mechanical states undergoing unitary, non-collapse evolution points the way to a treatment of collapse evolution consistent with the demands of relativity.