The topic of identity of proofs was put on the agenda of general (or structural) proof theory at an early stage. The relevant question is: When are the differences between two distinct proofs (understood as linguistic entities, proof figures) of one and the same formula so inessential that it is justified to identify the two proofs? The paper addresses another question: When are the differences between two distinct formulas so inessential that these formulas admit of identical proofs? The question appears (...) to be especially natural if the idea of working with more than one kind of derivations is taken seriously. If a distinction is drawn between proofs and disproofs (or refutations) as primitive entities, it is quite conceivable that a proof of one formula amounts to a disproof of another formula, and vice versa. A notion of inherited identity of derivations is introduced for derivations in a cut-free sequent system for Almukdad and Nelson’s constructive paraconsistent logic N4 with strong negation. The notion is obtained by identifying sequent rules the application of which has no effect on the identity of derivations. Then the notion of inherited identity is used to define a bilateralist notion of synonymy between formulas, which is a relation drawing more fine-grained distinctions between formulas than strong equivalence. (shrink)

This chapter is concerned with logical aspects of negation, i.e. with the role of negation in valid inferences and hence with the contribution negation makes to the truth and falsity conditions of declarative expressions. Negation is an important philosophical and logical concept. Often differences between logical systems can ‐ at least partially ‐ be described as differences between the notions of negation used in these logics.

Curry’s paradox is well known. The original version employed a conditional connective, and is not forthcoming if the conditional does not satisfy contraction. A newer version uses a validity predicate, instead of a conditional, and is not forthcoming if validity does not satisfy structural contraction. But there is a variation of the paradox which uses “external validity”. And since external validity contracts, one might expect the appropriate version of the Curry paradox to be inescapable. In this paper we show that (...) this is not the case. We consider two ways of formalising the notion of external validity, and show that in both of these the paradox is not forthcoming without the appropriate forms of contraction. (shrink)

This conflict can be interpreted in both religious and nonreligious ways. However, some intellectuals have identified a common thread parallel to the theological axis. The research study determines the role of existential philosophy in the contemporary religious beliefs. They have interpreted this contradiction as the conflict between our current selves and aspirations. Recognizing our animality and the role that such creatures play in the world is a requirement of our rational side. You may guarantee a well-attended eulogy by eating well, (...) exercising, not being a burden, helping out where you can, raising the next generation, and leaving the area essentially as you found it when it's time to leave. We must deal with this since it is who we are and what we are at our core. However, to be human means to be unhappy with this chilly, conventional assessment. As human beings, we possess the capacity to make decisions that influence our potential. Our destiny is not predetermined and that we can use our willpower to slightly warm the universe's unbreakable laws so that we can bend and shape them into the things we want. In the end, the cosmos prevails, yet we try to become rather than just exist during our brief existence. In the ongoing struggle against finitude, we strive for transcendence. The general framework has secular and strong religious proponents, and this view has been widely referred to as existentialist. (shrink)

A theory of substructural negations as impossibility and as unnecessity based on bi-intuitionistic logic, also known as Heyting-Brouwer logic, has been developed by Takuro Onishi. He notes two problems for that theory and offers the identification of the two negations as a solution to both problems. The first problem is the lack of a structural rule corresponding with double negation elimination for negation as impossibility, DNE, and the second problem is a lack of correspondence between certain sequents and a characterizing (...) frame property. While the identification of negation as impossibility and negation as unnecessity does solve Onishi’s problems, in general it nevertheless seems desirable to keep the two notions separate. The present paper addresses the first problem by introducing a reformulation of Onishi’s display sequent calculus in a language of sequents that incorporates Boolean negation. Instead of identifying negation as impossibility and negation as unnecessity, a notion of weak frame correspondence is defined. It is observed that DNE weakly corresponds with a certain frame property, and two structural sequent rules are presented that together also weakly correspond with that frame property and allow one to derive DNE. Moreover, the reformulated display calculus has an independent motivation by considerations on proof-theoretic semantics. (shrink)

Einführende Bemerkungen zu einem umstrittenen Begriff.

Alexandre Kojève had traveled via Peking. The high official of the French Ministry of the Economy stopped off in Berlin in order to speak to the heads of the German Socialist Student Association. In the Hotel Berliner Hof on Lake Diana, the Parisian guest advised Dutschke & Co. that the most important thing they could do would be to learn Greek. Such an answer to the question “What is to be done?” was not expected from this famous man, whose legendary (...) seminars on Hegel's Phenomenology of Spirit in the Thirties had inspired an entire generation of French scholars and intellectuals. Kojève's long-standing acquaintance, who looked after his guest during his stay in Berlin, was no less baffled to hear from the Hegelian that his next stop was Plettenberg. “Where else should one travel to in Germany? Carl Schmitt is after all the only one with whom it is worthwhile to talk.”. (shrink)

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Betr. u.a. die letzten Briefe Friedrich Nietzsches an Jacob Burckhardt.