Earlier algebraic semantics for Belnapian modal logics were defined in terms of twist-structures over modal algebras. In this paper we introduce the class of BK -lattices, show that this class coincides with the abstract closure of the class of twist-structures, and it forms a variety. We prove that the lattice of subvarieties of the variety of BK -lattices is dually isomorphic to the lattice of extensions of Belnapian modal logic BK . Finally, we describe invariants determining a twist-structure over a (...) modal algebra. (shrink)

The article analyzes the philosophical concept of the “porous self” of J. Rivera. The originality of this concept in the post-phenomenological project is determined by the role of theological constructions that modify the primal experience of self-consciousness. This modification allows us to interpret the phenomenological description of the human self as different from the classical — “porous” temporality, i.e., correlating through “two entrances”—the internal and external—with eternity. Within this approach, the primary phenomenon of the constitution of the "porous" self becomes (...) the inner word, which in the appeal to eternity turns out to be the original self-awareness of the self as a temporality. The secondary phenomenon of the constitution of the “porous” self is not the mundane temporality of M. Heidegger, but Epektasis as an intense striving towards the end of time in General. The worldly temporality of the self, transformed by faith, is phenomenologically revealed as open to eternity in each of its moments. The third phenomenon of the temporality of the self is Memoria, whose interpretation reveals how the structure of the inner consciousness of time by E. Husserl can be framed ontologically and harmoniously integrated into the theological concept. The article shows how, based on this understanding of both the internal and external openness of the “porous” self for eternity, the integral structure of its temporality is formed. The temporality of the porous self is a modification of Husserl’s time diagrams and the intertwining of two streams of temporality at the same time from past to future and from future to past, which itself constitutes a phenomenal field of events of self. This understanding of temporality sets new perspectives for the phenomenological analysis of subjectivity. (shrink)

Veritism is the thesis that the truth is the fundamental epistemic good. According to Duncan Pritchard, the most pressing objections to veritism are the trivial truths objection and the trivial inquiry problem. The former states that veritism entails that trivial truths are as important as deep and important truths. The latter is a problem that a veritist must prefer trivial inquiry that generates many trivial truths to the serious inquiry with the hope but no guarantee to discover some deep and (...) important truth. Both objections arise from the inability of veritism prima facie to properly rate the different types of truths. Pritchard's solution is to approach the truth from the perspective of the intellectually virtuous inquirer who would prefer weighty truth over trivial truth. In my commentary, I criticise the proposed solution as circular reasoning. The necessary virtue for an intellectually virtuous inquirer is that they would prefer the weighty truth over the trivial one and at the same time, the weighty truth is superior because it is the goal for intellectually virtuous inquirer. I suggest another path to substantiate veritism in the face of the two sibling objections. I argue that truth is the fundamental epistemic good as it makes the epistemic realm practically valuable more than any other epistemic good. The weighty truths are preferable to the trivial ones because the practical value of the deep and important truths is usually higher. The suggested path goes away from the attempts to prove the epistemic value of truth only within the epistemic realm, yet I argue it does not compel the intellectually virtuous inquirer to seek the truth only for the sake of practical reasons. (shrink)

And so that there may be less difficulty in understanding what I shall say on this matter, I should like that those not versed in anatomy should take the trouble, before they read this, to have cut up before their eyes the heart of some large animal that has lungs—for it is in all respects sufficiently similar to the heart of man….

Early normative studies of human behavior revealed a gap between the norms of practical rationality (what humans ought to do) and the actual human behavior (what they do). It has been suggested that, to close the gap between the descriptive and the normative, one has to revise norms of practical rationality according to the Quinean, engineering view of normativity. On this view, the norms must be designed such that they effectively account for behavior. I review recent studies of human perception (...) which pursued normative modeling and which found good agreement between the normative prescriptions and the actual behavior. I make the case that the goals and methods of this work have been incompatible with those of the engineering approach. I argue that norms of perception and action are observer-independent properties of biological agents; the norms are discovered using methods of natural sciences rather than the norms are designed to fit the observed behavior. (shrink)

The work aims to demonstrate that at the heart of Eriugena’s approach to Christian theology there lies a profoundly philosophical interest in the necessity of a cardinal shift in the paradigms of thinking – namely, that from the metaphysical to the dialectical one, which wins him a reputation of the ‘Hegel of the ninth century,’ as scholars in Post-Hegelian Germany called him. The prime concern of Eriugena’s discourse is to prove that the actual adoption of the salvific truth of Christ’s (...) revelation about all humans’ Sonship to God directly depends on the way the truth of God’s Oneness is consistently thought of. It is exactly the dialectic of the universal and particular which allows Eriugena both to tackle the dichotomy between being and non-being and to proceed towards raising a question how the totality of God’s being can be approached so as to let him radically reconsider a predominantly metaphysical view of creation the theological reflection traditionally relies on. According to the dialectical understanding of unity that Eriugena does adhere to, the reality of creation cannot be thought of, and therefore known, otherwise than in the way of being inseparable from the universal Principle of all. This is the Principle abandoned by nothing, unless the mind corrupted by the senses thinks otherwise and, following the metaphysical pattern of dichotomy, improperly sets the creation and its Principle apart. Restoration of the mind to the proper rational motion of recta ratio freed, as Eriugena argues, from the dictates of senses therefore becomes the way of both the epistemological breakthrough to the infinite whole and practical return from the world of finite things to living in the divine reality of creation. The work’s argument is based on the assumption of close affinity between Eriugena’s discourse and that of his Islamic contemporaries, who developed their dialectical ideas within the Mu’tazilah tradition of a philosophically disciplined approach to the truth of God’s Oneness. In particular, al-Nazzam’s engagement with Parmenides’ Periphyseon and his resistance to the danger of a dualistic interpretation of its ontology seem to provoke Eriugena’s innovative approach to Christian theology with a view to suggesting a mode of overcoming dualism as the main obstacle on the way to the Truth revealed. This vision of the meaning of Eriugena’s undertaking allows us not only to better understand the novelty of his approach to Christian theology, but also reconsider some of the key points of his discourse that seem to have become a sort of commonplace in Eriugenian studies: 1. Unlike the prevalent opinion, not the forms of the division of Nature but the modes of interpreting being and non-being are to be understood to constitute the genuine subject-matter of each book of the Periphyseon and, hence, of the five parts of his system. 2. The fourfold division of Nature is to be interpreted not as a basic structure of the system offered by Eriugena, but as a means of introducing dialectic to the body of theology by refuting Augustine’s metaphysical vision of a hierarchical model of the universe and indicating the way of resolution of the cardinally theological contradiction – God does and does not create at the same time. 3. All this gives reason to disagree with a general tendency of associating Eriugena’s work with exploration of the division of God’s Nature and to reinterpret it as an immense anti-division project to be understood as an important turn in the history of Christian thought entirely focused on the truth of God’s Oneness and human life in conformity to it. *** I affirm that this thesis is entirely my own work and has not been submitted for examination in any form elsewhere. (shrink)

The present paper is devoted to computational aspects of propositional inconsistency-adaptive logics. In particular, we prove (relativized versions of) some principal results on computational complexity of derivability in such logics, namely in cases of CLuN r and CLuN m , i.e., CLuN supplied with the reliability strategy and the minimal abnormality strategy, respectively.

We prove here that the intuitionistic theory $T_{0}\upharpoonright + UMID_{N}$ , or even $EEJ\upharpoonright + UMID_{N}$ , of Explicit Mathematics has the strength of $\prod_{2}^{1} - CA_{0}$ . In Section I we give a double-negation translation for the classical second-order $\mu-calculus$ , which was shown in [ $M\ddot{o}02$ ] to have the strength of $\prod_{2}^{1}-CA_{0}$ . In Section 2 we interpret the intuitionistic $\mu-calculus$ in the theory $EETJ\upharpoonright + UMID_{N}$ . The question about the strength of monotone inductive definitions in (...) $T_{0}$ was asked by S. Feferman in 1982, and - assuming classical logic - was addressed by M. Rathjen. (shrink)

Historical entitlement theories of property rights, which claim that individuals can acquire moral property rights over natural resources by appropriating them, traditionally face a strong objection: it is widely implausible that a single individual can unilaterally impose duties on everyone around him and yet, apparently, this is exactly what such theories allow. In this essay, I argue that the same problem appears in all other theories of distributive justice and if this problem was a reason to reject historical entitlement theories, (...) it would also be a reason to reject all rival theories. Which means that as long, as one is committed to any theory of distributive justice at all, she, at the risk of inconsistency, cannot rely on the aforementioned objection to criticize historical entitlement theories. (shrink)

The word “encyclopedia” comes to us from the Greek or, more precisely, is the deformed transcription, through Latin, of a erase in which we recognize a word composed of two elements, enkyklios and paideia, found in Quintilian in the ancient editions of De institutione oratoria (I, 10, 1). The expression itself, enkyklios paideia, appears only later, in the Hellenistic Age, under Roman domination, beginning with Dionysius of Halicarnassus (around the first century B.C.), but the concept goes back to the Eleatics, (...) especially to Hippias of Elis who, if we can believe the account in Plato's Dialogues, taught this total knowledge, later known with the term enkyklopaideia. (shrink)