Hilbert's program attempts to show that our mathematical knowledge can be certain because we are able to know for certain the truths of elementary arithmetic. I argue that, in the absence of a theory of mathematical truth, Hilbert does not have a complete theory of our arithmetical knowledge. Further, while his deployment of a Kantian notion of intuition seems to promise an answer to scepticism, there is no way to complete Hilbert's epistemology which would answer to his avowed aims.

This pioneering study of Bertrand Russell's social and political thought deals with the years 1896 to 1938, and is the first book to embark on a thorough investigation of the intellectual and cultural context out of which Russell's ideas emerged. Maintaining a sympathetic but critical stance towards Russell's almost innumerable political postures, and focusing in particular on his concern with the intellectual elite, the author renders that thought both plausible and coherent by placing its development against a significant historical background. (...) As well as giving attention to the aspects of Russell's private life which helped determine the direction of his thought, Dr Ironside undertakes an enlightening exploration of the individuals, groups and beliefs by which he was successively influenced. The result is a wide-ranging and highly original view of an important and enduring figure. (shrink)

Arendt Contra Sociology re-assesses the relationship between Hannah Arendt's work and the theoretical foundations of sociology, bringing her insights to bear on key themes within contemporary theoretical sociology. Departing from the view of Arendt as a political theorist who sought to rescue politics from society, and political theory from the social sciences, this book re-examines her distinctions between labour, fabrication and action as a theory of the fundamental ontology of human societies, revisiting her criticism of the tendency of many sociological (...) paradigms to conflate the activity of fabrication with that of action. (shrink)

This book offers a roadmap for determining when and how to regulate risky reproductive technologies on behalf of future children. It starts by explaining our intuitive, but paradoxical, belief that reproductive choices can be both life-giving and harmful. Next, it recommends a case-by-case method for reconciling the interests of future children with the reproductive liberty of prospective parents. Finally, it applies this framework to four past and future medical interventions, including cloning and genetic engineering. Drawing lessons from these case studies, (...) it criticizes the current lack of regulatory oversight. (shrink)

Since Euclid defined a point as “that which has no part” it has been widely assumed that points are necessarily unextended. It has also been assumed that this is equivalent to saying that points or, more properly speaking, degenerate segments, have length zero. We challenge these assumptions by providing models of Euclidean geometry where the points are extended despite the fact that the degenerate segments have null lengths, and observe that whereas the extended natures of the points are not recognizable (...) in the given models, they can be recognized and characterized by structures that are suitable expansions of the models. (shrink)

We show that assuming modest large cardinals, there is a definable class of ordinals, closed and unbounded beneath every uncountable cardinal, so that for any closed and unbounded subclasses $P, Q, {\langle L[P],\in,P \rangle }$ and ${\langle L[Q],\in,Q \rangle }$ possess the same reals, satisfy the Generalised Continuum Hypothesis, and moreover are elementarily equivalent. Examples of such P are Card, the class of uncountable cardinals, I the uniform indiscernibles, or for any n the class $C^{n}{=_{{\operatorname {df}}}}\{ \lambda \, | \, (...) V_{\lambda } \prec _{{\Sigma }_{n}}V\}$ ; moreover the theory of such models is invariant under ZFC-preserving extensions. They also all have a rich structure satisfying many of the usual combinatorial principles and a definable wellorder of the reals. The inner model constructed using definability in the language augmented by the Härtig quantifier is thus also characterized. (shrink)

Can it make sense for someone who appreciates the explanatory power of modern science to continue believing in a traditional religious account of the ultimate nature and purpose of our universe?

Consider syllogisms in which fraction (percentage) quantifiers are permitted in addition to universal and particular quantificrs, and then include further quantifiers which are modifications of such fractions (such as "almost ½ the S are P" and "Much more than ½ the S are P"). Could a syllogistic system containing such additional categorical forms be coherent? Thompson's attempt (1986) to give rules for determining validity of such syllogisms has failed; cf. Carnes & Peterson (forthcoming) for proofs of the unsoundness and incompleteness (...) of Thompson's rules. Building on Peterson (1985), the coherence of such a syllogistic can, however, be demonstrated with an algebra which provides its semantics; e.g., "almost ¾ the S arc P'" is represented as " -(3(SP) » SP)". (shrink)

The widespread impression that recent philosophy of science has pioneered exploration of the “social dimensions of scientific knowledge” is shown to be in error, partly due to a lack of appreciation of historical precedent, and partly due to a misunderstanding of how the social sciences and philosophy have been intertwined over the last century. This paper argues that the referents of “democracy” are an important key in the American context, and that orthodoxies in the philosophy of science tend to be (...) molded by the actual regimes of science organization within which they are embedded. These theses are illustrated by consideration of three representative philosophers of science: John Dewey, Hans Reichenbach, and Philip Kitcher.Author Keywords: Social dimensions of science; Logical positivism; Democracy; Context of discovery/justification; Goals of science. (shrink)

Mackie doubted anything objective could have the motivational properties of a value. In thinking we are morally required to act in a certain way, he said, we attribute objective value to the action. Since nothing has objective value, these moral judgments are all false. As to whether Mackie proved his error theory, opinions vary. But there is broad agreement on one issue. A litany of examples, ranging from amoralism to depression to downright evil, has everyone convinced that Mackie vastly overstated (...) the motivational implications of moral judgment. Mackie did go overboard. But did he have to? I think not. Even on the most modest motivational assumptions, Mackie can make objective value look queer and morality look like a sham. I begin with a sketch. (shrink)

Runkel links Perceptual Control Theory (PCT) thinking to psychological literature and discusses it against that background.