We argue that Wittgenstein’s philosophical perspective on Gödel’s most famous theorem is even more radical than has commonly been assumed. Wittgenstein shows in detail that there is no way that the Gödelian construct of a string of signs could be assigned a useful function within (ordinary) mathematics. — The focus is on Appendix III to Part I of Remarks on the Foundations of Mathematics. The present reading highlights the exceptional importance of this particular set of remarks and, more specifically, emphasises (...) its refined composition and rigorous internal structure. (shrink)

The book demonstrates for the first time that transculturality – the mixed constitution of cultures – is by no means only a characteristic of the present, but has de facto determined the composition of cultures since time immemorial. This is demonstated using examples from the arts across all cultures and continents.

This book is about the interrelationship between nature, semiosis, metarepresentation and (self-)consciousness, and the role played by metarepresentation in ...

Concentrating upon applications that are most relevant to modern physics, this valuable book surveys variational principles and examines their relationship to dynamics and quantum theory. Stressing the history and theory of these mathematical concepts rather than the mechanics, the authors provide many insights into the development of quantum mechanics and present much hard-to-find material in a remarkably lucid, compact form. After summarizing the historical background from Pythagoras to Francis Bacon, Professors Yourgrau and Mandelstram cover Fermat's principle of least time, the (...) principle of least action of Maupertuis, development of this principle by Euler and Lagrange, and the equations of Lagrange and Hamilton. Equipped by this thorough preparation to treat variational principles in general, they proceed to derive Hamilton's principle, the Hamilton-Jacobi equation, and Hamilton's canonical equations. An investigation of electrodynamics in Hamiltonian form covers next, followed by a resume of variational principles in classical dynamics. The authors then launch into an analysis of their most significant topics: the relation between variational principles and wave mechanics, and the principles of Feynman and Schwinger in quantum mechanics. Two concluding chapters extend the discussion to hydrodynamics and natural philosophy. Professional physicists, mathematicians, and advanced students with a strong mathematical background will find this stimulating volume invaluable reading. Extremely popular in its hardcover edition, this volume will find even wider appreciation in its first fine inexpensive paperbound edition. (shrink)

We introduce the Relational Responding Task (RRT) as a tool for capturing beliefs at the implicit level. Flemish participants were asked to respond as if they believed that Flemish people are more intelligent than immigrants (e.g., respond “true” to the statement “Flemish people are wiser than immigrants”) or to respond as if they believed that immigrants are more intelligent than Flemish people (e.g., respond “true” to the statement “Flemish people are dumber than immigrants”). The difference in performance between these two (...) tasks correlated with ratings of the extent to which participants explicitly endorsed the belief that Flemish people are more intelligent than immigrants and with questionnaire measures of subtle and blatant racism. The current study provides a first step towards validating RRT effects as a viable measure of implicit beliefs. (shrink)

This monograph presents new material on Francisco Suárez’s comprehensive theory of sense perception. The core theme is perceptual intentionality in Suárez’s theory of the senses, external and internal, as presented in his Commentaria una cum quaestionibus in libros Aristotelis De anima published in 1621. The author targets the question of the multistage genesis of perceptual acts by considering the ontological “items” involved in the procession of sensory information. However, the structural issue is not left aside, and the nature of the (...) relationship due to which our perceptions are mental representations of this or that object is also considered. The heuristic historiographical background includes not only the theories of classical authors, such as Aristotle and Aquinas, but also those of late medieval authors of the fourteenth century. These are headed by John Duns Scotus, John of Jandun, Peter Auriol and Peter John Olivi. Readers will discover the differences between Suárez’s and Aquinas’s views, as well as other sources that may have served as positive inspiration for the Jesuit’s theory. By considering the late medieval philosophy of the fourteenth century, this book helps, to a certain extent, to fill a gap in the historiography of philosophy regarding the link between late medieval and early modern scholasticism. In the first part of the book, the metaphysics of the soul and powers is considered. Chapters on the external senses follow, covering topics such as the sensible species, the causes of sensation, self-awareness, and the ordering of the external senses. A further chapter is devoted to the internal senses and the author argues that by reducing the number and functional scope of the interior senses Suárez deepens the gap between the external senses and the intellect, but he reduces it through emphasizing the unifying efficacy of the soul.This book brings a synthetic and unifying perspective to contemporary research and will particularly appeal to graduate students and researchers in theology and philosophy, especially philosophy of mind. (shrink)

We provide a finite axiomatization of the consequence , i.e. of the set of common sequential rules for and . Moreover, we show that has no proper non-trivial strengthenings other than and . A similar result is true for , but not, e.g., for +.

We provide a finite axiomatization of the consequence $\vdash ^{\wedge}\cap \vdash ^{\vee}$ , i.e. of the set of common sequential rules for $\wedge $ and $\vee $ . Moreover, we show that $\vdash ^{\wedge}\cap \vdash ^{\vee}$ has no proper non-trivial strengthenings other than $\vdash ^{\wedge}$ and $\vdash ^{\vee}$ . A similar result is true for $\vdash ^{\leftrightarrow}\cap \vdash ^{\rightarrow}$ , but not, e.g., for $\vdash ^{\leftrightarrow}\cap \vdash ^{+}$.

Aristotle's Categories can easily seem to be a statement of a naïve, pre-philosophical ontology, centered around ordinary items. Wolfgang-Rainer Mann argues that the treatise, in fact, presents a revolutionary metaphysical picture, one Aristotle arrives at by (implicitly) criticizing Plato and Plato's strange counterparts, the "Late-Learners" of the Sophist. As Mann shows, the Categories reflects Aristotle's discovery that ordinary items are things (objects with properties). Put most starkly, Mann contends that there were no things before Aristotle. The author's argument consists (...) of two main elements. First, a careful investigation of Plato which aims to make sense of the odd-sounding suggestion that things do not show up as things in his ontology. Secondly, an exposition of the theoretical apparatus Aristotle introduces in the Categories--an exposition which shows how Plato's and the Late-Learners' metaphysical pictures cannot help but seem inadequate in light of that apparatus. In doing so, Mann reveals that Aristotle's conception of things--now so engrained in Western thought as to seem a natural expression of common sense--was really a hard-won philosophical achievement. Clear, subtle, and rigorously argued, The Discovery of Things will reshape our understanding of some of Aristotle's--and Plato's--most basic ideas. (shrink)

_ Source: _Page Count 31 This paper analyzes the theories of three representatives of Second Scholasticism, namely Francisco Suárez, SJ, John Poinsot, OP, and Francisco de Oviedo, SJ, on the issue of the intuitive and abstractive cognition of the external senses. Based on a comparison of their theories, linked to the historical starting point of the debate in the first decades of the fourteenth century, the paper argues that the doctrinal and argumentative matrix of these authors’ texts is significantly ‘present’ (...) in the Second Scholastics as well. 1) As far as naturally produced sensation is concerned, all these authors, including Poinsot, follow the Scotistic justification of the natural infallibility of the external senses; 2) regarding the possibility of supernaturally caused objectless perception, Poinsot’s position can be labelled, surprisingly, Scotistic; 3) Suárez’s theory, although partly similar to the doctrine of the late Ockham, is an idiosyncratic stance; 4) Oviedo’s conception, even more distant from that of Ockham, can be characterized as ‘Auriolian’ and ‘Chattonian’. (shrink)

This paper analyzes the theories of three representatives of Second Scholasticism, namely Francisco Suárez, sj, John Poinsot, op, and Francisco de Oviedo, sj, on the issue of the intuitive and abstractive cognition of the external senses. Based on a comparison of their theories, linked to the historical starting point of the debate in the first decades of the fourteenth century, the paper argues that the doctrinal and argumentative matrix of these authors’ texts is significantly ‘present’ in the Second Scholastics as (...) well. 1) As far as naturally produced sensation is concerned, all these authors, including Poinsot, follow the Scotistic justification of the natural infallibility of the external senses; 2) regarding the possibility of supernaturally caused objectless perception, Poinsot’s position can be labelled, surprisingly, Scotistic; 3) Suárez’s theory, although partly similar to the doctrine of the late Ockham, is an idiosyncratic stance; 4) Oviedo’s conception, even more distant from that of Ockham, can be characterized as ‘Auriolian’ and ‘Chattonian’. (shrink)