A theory of magnitudes involves criteria for their equivalence, comparison and addition. In this article we examine these aspects from an abstract viewpoint, by focusing on the so-called De Zolt’s postulate in the theory of equivalence of plane polygons (“If a polygon is divided into polygonal parts in any given way, then the union of all but one of these parts is not equivalent to the given polygon”). We formulate an abstract version of this postulate and derive it from some (...) selected principles for magnitudes. We also formulate and derive an abstract version of Euclid’s Common Notion 5 (“The whole is greater than the part”), and analyze its logical relation to the former proposition. These results prove to be relevant for the clarification of some key conceptual aspects of Hilbert’s proof of De Zolt’s postulate, in his classicalFoundations of Geometry(1899). Furthermore, our abstract treatment of this central proposition provides interesting insights for the development of a well-behaved theory ofcompatiblemagnitudes. (shrink)

The introduction and elimination rules for material implication in natural deduction are not complete with respect to the implicational fragment of classical logic. A natural way to complete the system is through the addition of a new natural deduction rule corresponding to Peirce's formula → A) → A). E. Zimmermann [6] has shown how to extend Prawitz' normalization strategy to Peirce's rule: applications of Peirce's rule can be restricted to atomic conclusions. The aim of the present paper is to extend (...) Seldin's normalization strategy to Peirce's rule by showing that every derivation Π in the implicational fragment can be transformed into a derivation Π' such that no application of Peirce's rule in Π' occurs above applications of →-introduction and →-elimination. As a corollary of Seldin's normalization strategy we obtain a form of Glivenko's theorem for the classical {→}-fragment. (shrink)

Logic does not have purely existential theorems: the only existential sentences that are valid are those with valid universal analogues. Here, we show indeed this is so, when properly interpreted: every existential validity has a simple universal analogue, which is also valid. We also characterize existential and universal validities in terms of tautologies.

Evidence suggests that humans might have neurological specializations for music processing, but a compelling adaptationist account of music and dance is lacking. The sexual selection hypothesis cannot easily account for the widespread performance of music and dance in groups (especially synchronized performances), and the social bonding hypothesis has severe theoretical difficulties. Humans are unique among the primates in their ability to form cooperative alliances between groups in the absence of consanguineal ties. We propose that this unique form of social organization (...) is predicated on music and dance. Music and dance may have evolved as a coalition signaling system that could, among other things, credibly communicate coalition quality, thus permitting meaningful cooperative relationships between groups. This capability may have evolved from coordinated territorial defense signals that are common in many social species, including chimpanzees. We present a study in which manipulation of music synchrony significantly altered subjects’ perceptions of music quality, and in which subjects’ perceptions of music quality were correlated with their perceptions of coalition quality, supporting our hypothesis. Our hypothesis also has implications for the evolution of psychological mechanisms underlying cultural production in other domains such as food preparation, clothing and body decoration, storytelling and ritual, and tools and other artifacts. (shrink)

The use of negative probabilities is discussed for certain problems in which a stochastic process approach is indicated. An extension of probability theory to include signed (negative and positive) probabilities is outlined and both philosophical and axiomatic examinations of negative probabilities are presented. Finally, a class of applications illustrates the use and implications of signed probability theory.

To begin with, there is a conceptual necessity implied in the very concept of cause itself, and in all concepts that have a causal element; and this definitional "must," far from being conventional or arbitrary, reflects the natural necessity of those physical systems which in fact constitute the nature of our universe. The conceptual necessity of the concept of cause can be pointed up in the following way. Assume that we have good reason for saying at to that f, g, (...) h, and i are jointly sufficient to E and hence C of E. What would we say at t1 if f, g, h, and i occurred but not E? We would clearly not say then, or ever, that while ordinarily these conditions are jointly sufficient for E, this time they were not; rather we would say that somehow we were mistaken in thinking that f, g, h, and i at t1 were identical with f, g, h, and i at t0. We might have been mistaken in either of two ways. We might have mis-identified one of the conditions at t1, erroneously thinking, say, that p was an f; or one or more of the conditions might have had its nature altered, losing some capacity or power it once had. In either case, we would withdraw the claim at t1 that C was the cause of E. Since we would withdraw the use of C at t1 and would never admit that f, g, h, and i at any t, if genuine instances of f, g, h, and i, would not produce E, we are clearly using C in such a way that actually producing E is part of its meaning. On the assumption that the conditions are genuinely the same, it follows, so to speak, from the principle of identity that they must produce the same effect. (shrink)

Implicit in the scottish tradition is a metaphilosophy of commonsense which deserves as much attention as that recently given to scottish presentative realism and agent causality. The author articulates this metaphilosophy by (a) sketching a systematic metaphilosophy of commonsense, (b) considering to what extent thomas reid fits this pattern, And (c) deciding to what extent asa mahan, One of the ablest of the american realists, Fits it. The result is a characterization of a coherent scottish metaphilosophy still worthy of consideration. (...) He also explores the question whether the metaphilosophy that emerges from (b) and (c) is part of an ongoing tradition. It has been suggested that there are important similarities between the scottish view and g e moore's concept of analysis. While he agrees that there are analogies he stresses the disanalogies as more enlightening about the nature of both. (shrink)

What do we learn about language from reading Wittgenstein'sPhilosophical Investigations? This question gains urgency from Wittgenstein's alleged animus against philosophical theorizing and his indirectness. Section 1 argues that Wittgenstein's goal is to prevent philosophical questioning about the foundations of language from the beginning. This conception of his aim is not in tension with Wittgenstein's use of the notion of community; community interpretations of his views betray a misguided commitment to the coherence of the idea that language might need grounding. Wittgenstein's (...) goal is not to enjoin us not to step outside of language-games, but to show that we have insufficiently clear grasp of the terms we try to use to express the limits of intelligibility. Section 2 suggests that appreciating Wittgenstein's moral concerning the relation between language and philosophizing about it involves allowing him to teach us how to read his book. What makes readingPhilosophical Investigations possible is openness to learning how not to forget our lives in language. (shrink)

Using a general model of corruption that explains and accounts for corruption across different corporate and professional activities, the paper will examine how certain practices in the media, especially in areas where journalism, advertising and public relations regularly intersect and converge, can be construed as instances of corruption. By applying this general model of corruption the paper will then offer a taxonomy of media corruption by identifying most if not all the major types of media corruption. It will be argued (...) that such corruption is regular and systematic. (shrink)

There are a standard number of replies to the riddle of induction, none of which has gained ascendency. It seems that a new approach is needed that concedes less to the Humean dialectic. Humeans, both traditional and contemporary, unwittingly play on the ambiguity of the phrase "change in the course of nature," and that is why `C· ∼ E' appears to be self-consistent, though in fact it is not. I provide an analysis of 'cause' and 'natural necessity' which gives inductive (...) inference that internal warrant we assume it to have in ordinary and scientific thinking and rebut in advance contemporary Humean objections based on the erroneous assumption that 'x is necessary' and 'x is a priori' are materially equivalent. (shrink)

HAMILTON WORRIED THAT THERE WERE REPRESENTATIVE ELEMENTS\nIN REID'S EPISTEMOLOGY, WHILE J S MILL FLATLY CHARACTERIZED\nTHE SCOT AS A REPRESENTATIVE REALIST. I ARGUE THAT HAMILTON\nAND MILL WERE MISTAKEN AND THAT THEIR MISTAKES AROSE FROM\nAN INSUFFICIENT UNDERSTANDING AND APPRECIATION OF THE\nNATIVISTIC ELEMENTS OF THE UNDERSTANDING INTRODUCED BY\nREID; AND TO INSUFFICIENT AWARENESS OF REID'S\nCHARACTERIZATION OF PERCEPTION AS ACTIVE IN CONTRAST TO\nBRITISH EMPIRICIST RELIANCE ON A PASSIVELY GIVEN EPISTEMIC\nBASE. REID REJECTED EVERY VARIETY OF THE "MESSENGER"\nTHEORY.

IN the recent past there has been a resurgence of interest in the work of Thomas Reid; several new editions of his work have appeared as well as a series of articles concerning various aspects of his systematic philosophy. Interest has generalized to the whole Scottish tradition, including numerous figures in the history of American philosophy who were deeply influenced by Reid and Dugald Stewart. In addition, several recent and contemporary philosophers have used Reid's epistemic views as a point of (...) departure in developing their own adverbial theories of sensing and appearing. Others have used Reid's theory of agency in formulating their own views on freedom and responsibility. (shrink)

The recent transnational wave of destruction that was caused by the earthquake-induced tsunamis in South East Asia has raised the issue of global justice in terms of the rights of victims to expect aid relief and the moral responsibility of the rest of the world to provide it. In this paper I will discuss the issue of global ethics in terms of positive rights that people have to assistance from others when they cannot provide such assistance themselves. The main object (...) of the paper is to demonstrate that positive rights are universal and global in scope and cannot therefore be restricted by any national, religious, cultural or other social boundaries. Such rights provide a rational and ethical foundation for global justice that is cosmopolitan. The argument for the position offered in the paper will be broadly based on the moral philosophy of Alan Gewirth.1. (shrink)

At Epistles 2.2.87–9 Horace introduces an argument against writing poetry based on the unpleasant mutual admiration required in poetic society with an anecdote about an orator and a jurisconsult: †frater erat Romae† consulti rhetor, ut alter alterius sermone meros audiret honores, Gracchus ut hic illi, foret huic ut Mucius ille.

At Epistles 2.2.87–9 Horace introduces an argument against writing poetry based on the unpleasant mutual admiration required in poetic society with an anecdote about an orator and a jurisconsult: †frater erat Romae† consulti rhetor, ut alter alterius sermone meros audiret honores, Gracchus ut hic illi, foret huic ut Mucius ille.

Probability and Frequency. Aristotle frequently used the concept of probability, but apparently he did not make any persistent effort to clarify or analyze it. His description of a fortiori argument in The Topics, e.g., depends upon “the more or less likely or probable,” but he does not explore this notion. In The Rhetoric, where he applies himself to a puzzle about probability which the Sophists had advanced, he comes closer to an analysis of probability. Aristotle quotes Agathon, One might perchance (...) say this was probable—That things improbable oft will hap to men, and elaborates thusly: “For what is improbable does happen [often], and therefore it is probable that improbable things will happen. Granted this, one might argue that ‘what is improbable is probable.’ “ Aristotle believes that one can avoid this imposture by distinguishing between “general” and “specific” probability, and apparently intends by the former the statistical sense of frequent occurrence; but he does not establish what he might mean by the probability of an individual event and so leaves the notion of “specific probability” unclear. (shrink)

Most philosophers of science nowadays hold a network or postulational view of the meaning of theoretical words. However, there are many nuances to this view, and after explicitly separating them, we show what we take to be wrong with each one. While we reject the postulational view we do not defend its traditional alternatives either; rather we show the pointlessness of insisting on a single source for the meaning of theoretical words. We also point out the shortcomings of Carnap's newest (...) meaning criterion which depends upon a network view. But, again, we suggest not only that this new rendition of the criterion is faulty but also that there is something misguided about any search at all for such a criterion. (shrink)