The set-theoretic axiom WISC states that for every set there is a set of surjections to it cofinal in all such surjections. By constructing an unbounded topos over the category of sets and using an extension of the internal logic of a topos due to Shulman, we show that WISC is independent of the rest of the axioms of the set theory given by a well-pointed topos. This also gives an example of a topos that is not a predicative topos (...) as defined by van den Berg. (shrink)

We combine intuitionistic logic and classical logic into a new, first-order logic called polarized intuitionistic logic. This logic is based on a distinction between two dual polarities which we call red and green to distinguish them from other forms of polarization. The meaning of these polarities is defined model-theoretically by a Kripke-style semantics for the logic. Two proof systems are also formulated. The first system extends Gentzenʼs intuitionistic sequent calculus LJ. In addition, this system also bears essential similarities to Girardʼs (...) LC proof system for classical logic. The second proof system is based on a semantic tableau and extends Dragalinʼs multiple-conclusion version of intuitionistic sequent calculus. We show that soundness and completeness hold for these notions of semantics and proofs, from which it follows that cut is admissible in the proof systems and that the propositional fragment of the logic is decidable. (shrink)

This paper provides a partial solution to the completeness problem for Joyal's axiomatization of open and etale maps, under the additional assumption that a collection axiom holds.

The goal of this paper is to sketch and defend a new interpretation or 'theory' of objective chance, one that lets us be sure such chances exist and shows how they can play the roles we traditionally grant them. The account is 'Humean' in claiming that objective chances supervene on the totality of actual events, but does not imply or presuppose a Humean approach to other metaphysical issues such as laws or causation. Like Lewis (1994) I take the Principal Principle (...) (PP) to be the key to understanding objective chance. After describing the main features of Humean objective chance (HOC), I deduce the validity of PP for Humean chances, and end by exploring the limitations of Humean chance. (shrink)

The present article is concerned with Proclus’ highly original and profoundly influential account of the symbolic function of poetry, the pedagogic as well as the hieratic value of myths and the soteriological power of allegorical interpretation. Thus, the paper begins with a brief discussion of Plato’s dismissal of poetry as μέγιστον ψεῦδος. Subsequently, Proclus’ theory of three kinds of poetry is examined, upon which attention is paid to his revolutionary idea that σύμβολα rather than μιμήματα are the tools of the (...) highest kind of poetry. Then, Proclus’ views on the difference between Plato’s and Homer’s μυθοποιΐα are considered. While the article concludes with an analysis of Proclus’ conviction about the functional similarity of symbols in myths and those in magic rites, allegoresis is shown to have the same salvational role that Proclus ascribes to theurgy. (shrink)

The new …eld of judgment aggregation aims to …nd collective judgments on logically interconnected propositions. Recent impossibility results establish limitations on the possibility to vote independently on the propositions. I show that, fortunately, the impossibility results do not apply to a wide class of realistic agendas once propositions like “if a then b” are adequately modelled, namely as subjunctive implications rather than material implications. For these agendas, consistent and complete collective judgments can be reached through appropriate quota rules (which decide (...) propositions using acceptance thresholds). I characterise the class of these quota rules. I also prove an abstract result that characterises consistent aggregation for arbitrary agendas in a general logic. (shrink)

While current doctrines try to separate conflicts within two distinct categories – conventional versus irregular, there are, however, a series of contemporary conflicts that challenge this western view on war showing that the disjunctive manner of classification in ‘big and conventional’ versus ‘small and irregular’ is limited and simplistic. The military strategists as well as the academics used a series of concepts in order to describe the main shifts in the character of war – from the Fourth Generation Warfare (4GW) (...) and ‘new wars’ to hybrid wars. This article aims to identify these mutations in war evolution in the new, post-Cold War international context. The traditional image we have on this well-known ‘labor division’ within the military field no longer reflects reality. (shrink)

During the Italian Renaissance, artists and anatomists compared man to various mechanical devices, in an attempt to uncover knowledge about the structure and processes of the human body. In so doing, they drew on ancient Greek notions of instrumentality and proportion. During the early Scientific Revolution, the metaphor of Man the machine played a key role in the development of mechanistic philosophy. During the Enlightenment, it served views on materialism and atheism. By the nineteenth century, when the Industrial Revolution was (...) in full swing, a fundamental change in the relationship of man to machine had come about. Whereas, for Protagoras, man had been the measure of all things, now suddenly the machine was the standard by which the capacities and limits of man were judged. Man the machine was a key feature in the development of the totalitarian ideology of Communism. Moreover, for over a century now, the technocratic viewpoint has guided many technological innovations. Tracing a history of this metaphor, through Leonardo, Vesalius, Harvey, Descartes, Hobbes, Leibniz, La Mettrie, d'Holbach, Marx and Wells, places man's relationship with technology and his gradual loss of identity since the Renaissance in a new context. (shrink)