Quasi-Nelson logic (QNL) was recently introduced as a common generalisation of intuitionistic logic and Nelson's constructive logic with strong negation. Viewed as a substructural logic, QNL is the axiomatic extension of the Full Lambek Calculus with Exchange and Weakening by the Nelson axiom, and its algebraic counterpart is a variety of residuated lattices called quasi-Nelson algebras. Nelson's logic, in turn, may be obtained as the axiomatic extension of QNL by the double negation (or involutivity) axiom, and intuitionistic logic as the (...) extension of QNL by the contraction axiom. A recent series of papers by the author and collaborators initiated the study of fragments of QNL, which correspond to subreducts of quasi-Nelson algebras. In the present paper we focus on fragments that contain the connectives forming a residuated pair (the monoid conjunction and the so-called strong Nelson implication), these being the most interesting ones from a substructural logic perspective. We provide quasi-equational (whenever possible, equational) axiomatisations for the corresponding classes of algebras, obtain twist representations for them, study their congruence properties and take a look at a few notable subvarieties. Our results specialise to the involutive case, yielding characterisations of the corresponding fragments of Nelson's logic and their algebraic counterparts. (shrink)

This article argues that the causal loops that occur in some time-travel scenarios and in certain solutions of the theory of relativity are no more mysterious than the infinitely descending causal chains familiar from Newtonian mechanics.

This very brief paper provides plausible answers to the two residual questions that Jamie Tappenden states, but leaves unanswered, in his 2024 paper ‘Following Bobzien: Some notes on Frege’s development and engagement with his environment’, namely, why Frege read Sigwart’s Logik and what caused Frege to read Prantl.

Ullin Thomas Place died on 2nd January 2000 at the age of seventy-five. I had met him a little over three years earlier, in November 1996, during the annual 'Mind and Brain' symposium organized by Peter Fenwick and held at the Institute of Psychiatry in London. At that meeting Professor Place delivered a slightly shortened version of the paper reproduced here, in which he told his personal story — a pilgrim's progress? — recounting, as he put it, 'the history of (...) a thought process leading from an adolescent interest in mystical experience to an article entitled‘Is consciousness a brain process?’[Place, 1956] in which I argued for an affirmative answer to that question'. (shrink)

Summary I try to apply Lakatos's metacriterion of the rationality of normative philosophies of science to normative political theories, stressing that Lakatos's metacriterion is not only an extension of Popper's idea of tests by potentially falsifyingdescriptive basic judgments to tests by potentially falsifyingnormative judgments. Rather, its application is a test by demonstrating the tested theory's capability of reconstructing its own history as rational. Finally I argue that the tradition of utilitarian political theories is fittest to be confirmed by a Lakatosian (...) test. (shrink)

PurposeThe paper suggests overcoming the polarization of today's debate on peer‐to‐peer systems by defining a fair balance between the principle of precaution and the principle of openness. Threats arising from these file sharing applications‐systems should not be a pretext to limit freedom of research, speech or the right “freely to participate in the cultural life of the community”, as granted by the Universal Declaration of Human Rights from 1948. The paper aims to take sides in today's debate.Design/methodology/approachThe paper adopts an (...) interdisciplinary approach, including network theory, law and ethics. The method draws on both theoretical and empirical material so as to stress the paradox of the principle of precaution applied to P2P systems and why the burden of proof should fall on the party proposing that one refrain from action.FindingsCensors and opponents of P2P systems who propose to apply the principle of precaution to this case deny the premise upon which that principle rests. “Levels of evidence” required by the precautionary principle show that – in many cases in which the outcomes of technology are ignored – another principle is needed for orienting action, namely, the principle of openness.Social implicationsAlarm about how P2P systems undermine crucial elements of the societies often led to the ban of this technology. The paper illustrates why it should not be the case: rather than shutting these networks down, they should be further developed.Originality/valueThe paper provides the comprehensive picture of a far too often fragmented debate. (shrink)

This paper offers a critique of the Bayesian interpretation of quantum mechanics with particular focus on a paper by Caves, Fuchs, and Schack containing a critique of the “objective preparations view” or OPV. It also aims to carry the discussion beyond the hardened positions of Bayesians and proponents of the OPV. Several claims made by Caves et al. are rebutted, including the claim that different pure states may legitimately be assigned to the same system at the same time, and the (...) claim that the quantum nature of a preparation device cannot legitimately be ignored. Both Bayesians and proponents of the OPV regard the time dependence of a quantum state as the continuous dependence on time of an evolving state of some kind. This leads to a false dilemma: quantum states are either objective states of nature or subjective states of belief. In reality they are neither. The present paper views the aforesaid dependence as a dependence on the time of the measurement to whose possible outcomes the quantum state serves to assign probabilities. This makes it possible to recognize the full implications of the only testable feature of the theory, viz., the probabilities it assigns to measurement outcomes. Most important among these are the objective fuzziness of all relative positions and momenta and the consequent incomplete spatiotemporal differentiation of the physical world. The latter makes it possible to draw a clear distinction between the macroscopic and the microscopic. This in turn makes it possible to understand the special status of measurements in all standard formulations of the theory. Whereas Bayesians have written contemptuously about the “folly” of conjoining “objective” to “probability,” there are various reasons why quantum-mechanical probabilities can be considered objective, not least the fact that they are needed to quantify an objective fuzziness. But this cannot be appreciated without giving thought to the makeup of the world, which Bayesians refuse to do. Doing this on the basis of how quantum mechanics assigns probabilities, one finds that what constitutes the macroworld is a single Ultimate Reality, about which we know nothing, except that it manifests the macroworld or manifests itself as the macroworld. The so-called microworld is neither a world nor a part of any world but instead is instrumental in the manifestation of the macroworld. Quantum mechanics affords us a glimpse “behind” the manifested world, at stages in the process of manifestation, but it does not allow us to describe what lies “behind” the manifested world except in terms of the finished product—the manifested world, for without the manifested world there is nothing in whose terms we could describe its manifestation. (shrink)

It is shown that the boolean prime ideal theorem BPIT: every boolean algebra has a prime ideal, does not follow from the order-extension principle OE: every partial ordering can be extended to a linear ordering. The proof uses a Fraenkel-Mostowski model, where the family of atoms is indexed by a countable universal-homogeneous boolean algebra whose boolean partial ordering has a `generic' extension to a linear ordering. To illustrate the technique for proving that the order-extension principle holds in the model we (...) also study Mostowski's ordered model, and give a direct verification of OE there. The key technical point needed to verify OE in each case is the existence of a support structure. (shrink)