Protophysics and Special Theory of Relativity. First, a proposal for a constructive foundation of the Special Theory of Relativity by M. Buth is criticized and confronted with an alternative proposal by the author. The main idea is to solve the problem of transforming coordinates between inertial systems in terms of the General Theory of Measurement. Regarding transformations of co-ordinates as transformations of thecorresponding “functions of measurement” these functions have to meet two demands. 1. To identify measured values which are related (...) to different inertial systems and measuring procedures as the same magnitude, the ratio scale of length and duration has to be defined with respect to the whole class of inertial systems. 2. Using the concept of a certain physical magnitude, propositions about measuring devices are made which are invariant with respect to measuring procedures. As aconsequence every transformation between functions of measurement has to be an equivalence relation. The first demand leads to linearity, the second one reduces the set of permissible transformations between inertial systems to the alternative of Galilei- and Lorentz-transformation. The (im)possibility of putting an absolute simultaneity into practice decides between these transformations. (shrink)

Journal Name: Cognitive Linguistics Issue: Ahead of print.

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 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)

There is a tacit assumption that interpretation comes naturally, that human beings live by constantly interpreting. In this sense, we might even rephrase Descartes by saying: We interpret, therefore we are. While such a basic human disposition makes interpretation appear to come naturally, the forms it takes, however, do not. In this work, Iser offers a fresh approach by formulating an "anatomy of interpretation" through which we can understand the act of interpretation in its many different manifestations. For Iser, there (...) are several different genres of interpretation, all of which are acts of translation designed to transpose something into something else. Perhaps the most obvious example of interpretation involves canonical texts, such as the Rabbinical exegesis of the Torah or Samuel Johnson's reading of Shakespeare. But what happens when the matter that one seeks to interpret consists not of a text but of a welter of fragments, as in the study of history, or when something is hidden, as in the practice of psychoanalysis, or is as complex as a culture or system? Iser details how, in each of these cases, the space that is opened up by interpretation is negotiated in a different way, thus concluding that interpretation always depends on what it seeks to translate. For students of philosophy, literary and critical theory, anthropology, and cultural history, Iser's elucidation of the mechanics by which we translate and understand, as well as his assessment of the anthropological roots of our drive to make meaning, will undoubtedly serve as a revelation. (shrink)