We study a modal system ¯T, that extends the classical (prepositional) modal system T and whose language is provided with modal operators M inn (nN) to be interpreted, in the usual kripkean semantics, as there are more than n accessible worlds such that.... We find reasonable axioms for ¯T and we prove for it completeness, compactness and decidability theorems.

We present a class of normal modal calculi PFD, whose syntax is endowed with operators M r, one for each r [0,1] : if a is sentence, M r is to he read the probability that a is true is strictly greater than r and to he evaluated as true or false in every world of a F-restricted probabilistic kripkean model. Every such a model is a kripkean model, enriched by a family of regular probability evaluations with range in a (...) fixed finite subset F of [0,1] : there is one such a function for every world w, P F, and this allows to evaluate M ra as true in the world w iff p F r.For every fixed F as before, suitable axioms and rules are displayed, so that the resulting system P FD is complete and compact with respect to the class of all the F-restricted probabilistic kripkean models. (shrink)

We go on along the trend of [2] and [1], giving an axiomatization of S4 0 and proving its completeness and compactness with respect to the usual reflexive and transitive Kripke models. To reach this results, we use techniques from [1], with suitable adaptations to our specific case.

We prove a completeness theorem for Kmath image, the infinitary extension of the graded version K0 of the minimal normal logic K, allowing conjunctions and disjunctions of countable sets of formulas. This goal is achieved using both the usual tools of the normal logics with graded modalities and the machinery of the predicate infinitary logics in a version adapted to modal logic.

Elekes proved that any infinite-fold cover of a σ-finite measure space by a sequence of measurable sets has a subsequence with the same property such that the set of indices of this subsequence has density zero. Applying this theorem he gave a new proof for the random-indestructibility of the density zero ideal. He asked about other variants of this theorem concerning I-almost everywhere infinite-fold covers of Polish spaces where I is a σ-ideal on the space and the set of indices (...) of the required subsequence should be in a fixed ideal ${{\mathcal{J}}}$ on ω. We introduce the notion of the ${{\mathcal{J}}}$ -covering property of a pair ${({\mathcal{A}}, I)}$ where ${{\mathcal{A}}}$ is a σ-algebra on a set X and ${{I \subseteq \mathcal{P}(X)}}$ is an ideal. We present some counterexamples, discuss the category case and the Fubini product of the null ideal ${\mathcal{N}}$ and the meager ideal ${\mathcal{M}}$ . We investigate connections between this property and forcing-indestructibility of ideals. We show that the family of all Borel ideals ${{\mathcal{J}}}$ on ω such that ${\mathcal{M}}$ has the ${{\mathcal{J}}}$ -covering property consists exactly of non weak Q-ideals. We also study the existence of smallest elements, with respect to Katětov–Blass order, in the family of those ideals ${\mathcal{J}}$ on ω such that ${\mathcal{N}}$ or ${\mathcal{M}}$ has the ${\mathcal{J}}$ -covering property. Furthermore, we prove a general result about the cases when the covering property “strongly” fails. (shrink)

Ethicist assumptions about the causes and solutions of environmental problems are widely held within environmental philosophy. It is typically assumed that an important cause of problems are the attitudes towards the natural environment held by individuals and that problems can be solved by getting people to adopt a more ethical orientation towards the environment. This article analyses and criticises these claims. Both the highly mediated nature of the relationship between individuals and the natural environment and the pervasive pressure on firms (...) in market economies to reduce their costs provide reasons to question the ethicist assumptions. (shrink)

The 2012 Varsity Medical Debate between Oxford University and Cambridge University provided a stage for representatives from these famous institutions to debate the motion “This house believes that trainee doctors should be able to use the developing world to gain clinical experience.” This article brings together many of the arguments put forward during the debate, centring around three major points of contention: the potential intrinsic wrong of ‘using’ patients in developing countries; the effects on the elective participant; and the effects (...) on the host community. The article goes on to critically appraise overseas elective programmes, offering a number of solutions that would help optimise their effectiveness in the developing world. (shrink)

The paper aims to investigate the thesis of the so-called Neue Mythologie within the fragment entitled “Das älteste Systemprogramm des deutschen Idealismus” [“The Oldest Systematic Program of German Idealism”]. The latter presents a revolutionary project of social pedagogy linked to the use of the aesthetic character of myth and poetry in the formation of the conscience and the intellect of the people. The program, therefore, formulates a fertile dialogue between the emancipatory potential of the Enlightenment and Jena Romanticism, in that (...) it proposes a re-evaluation of feelings and Sinnlichkeit [sensuousness] in connection to modern rationality and freedom. The links between the rational mythology of the program and Hegelian philosophy will be explored, starting from his early writings, which are strictly concerned with the importance of a popular and sensuous religion (Volksreligion). Secondly, the work will retrace the same sensuous externalization of philosophical ideas within the relationships between art, religion and philosophy in the mature system, addressing the problem of Hegel’s change of heart regarding art and mythology between the two phases of his thought. In the end the value of symbolical mediation of concepts and idea will be established. (shrink)

We study the following natural strong variant of destroying Borel ideals: $\mathbb {P}$ $+$ -destroys $\mathcal {I}$ if $\mathbb {P}$ adds an $\mathcal {I}$ -positive set which has finite intersection with every $A\in \mathcal {I}\cap V$. Also, we discuss the associated variants $$ \begin{align*} \mathrm{non}^*(\mathcal{I},+)=&\min\big\{|\mathcal{Y}|:\mathcal{Y}\subseteq\mathcal{I}^+,\; \forall\;A\in\mathcal{I}\;\exists\;Y\in\mathcal{Y}\;|A\cap Y| \omega $ ; (4) we characterise when the Laver–Prikry, $\mathbb {L}(\mathcal {I}^*)$ -generic real $+$ -destroys $\mathcal {I}$, and in the case of P-ideals, when exactly $\mathbb {L}(\mathcal {I}^*)$ $+$ -destroys $\mathcal {I}$ ; (...) and (5) we briefly discuss an even stronger form of destroying ideals closely related to the additivity of the null ideal. (shrink)

This article compares two attempts to return to realism after Kant’s ‘Copernican Revolution’. Quentin Meillassoux, representing the ‘speculative realism’ school, rejects both Kantian and post-Kantian idealism in favour of a materialism based on the epistemology of the modern sciences. But Meillassoux is unaware of the element of choice in his philosophical position, and he does not solve the essential problem posed by idealism which concerns the place of the subject in being. Ricœur, on the other hand, sublates Kant by a (...) deeper embrace of finitude that leads to the self-displacement of the subject, and a ‘Second Copernican Revolution’, one that he freely admits can only be arrived at by Jaspersian ‘Philosophical Faith’. The article concludes by showing how crossing the border into theological faith offers a virtue-ethical perspective on the question of realism and idealism: it is in fact the choice between a childlike humility that receives reality as it is, and an arrogant self-positing that puts the subject in the position of God. (shrink)

Rage against the system : the unity of truth -- A philosophy of hope? The universality of truth -- Absolutely no absolutes? Ricœur's encounter with Thévenaz -- Finitude and the infinite : the God of the philosophers -- Finitude and evil : the crucial distinction -- Rightly relating evil and finitude -- The poetic symbol of creation -- The mysterious unity of creation -- The original goodness of creation -- Conclusion. New frontiers between philosophy and theology.

We continue investigating variants of the splitting and reaping numbers introduced in [4]. In particular, answering a question raised there, we prove the consistency of and of. Moreover, we discuss their natural generalisations $\mathfrak {s}_{\rho }$ and $\mathfrak {r}_{\rho }$ for $\rho \in (0,1)$, and show that $\mathfrak {r}_{\rho }$ does not depend on $\rho $.

We investigate ideals of the form {A⊆ω: Σn∈Axnis unconditionally convergent} where n∈ωis a sequence in a Polish group or in a Banach space. If an ideal onωcan be seen in this form for some sequence inX, then we say that it is representable inX.After numerous examples we show the following theorems: An ideal is representable in a Polish Abelian group iff it is an analytic P-ideal. An ideal is representable in a Banach space iff it is a nonpathological analytic P-ideal.We (...) focus on the family of ideals representable inc0. We characterize this property via the defining sequence of measures. We prove that the trace of the null ideal, Farah’s ideal, and Tsirelson ideals are not representable inc0, and that a tallFσP-ideal is representable inc0iff it is a summable ideal. Also, we provide an example of a peculiar ideal which is representable inℓ1but not in ℝ.Finally, we summarize some open problems of this topic. (shrink)

We investigate which filters onωcan contain towers, that is, a modulo finite descending sequence without any pseudointersection. We prove the following results:Many classical examples of nice tall filters contain no towers.It is consistent that tall analytic P-filters contain towers of arbitrary regular height.It is consistent that all towers generate nonmeager filters, in particular Borel filters do not contain towers.The statement “Every ultrafilter contains towers.” is independent of ZFC.Furthermore, we study many possible logical implications between the existence of towers in filters, (...) inequalities between cardinal invariants of filters $,${\rm{co}}{{\rm{f}}^{\rm{*}}}\left$,${\rm{no}}{{\rm{n}}^{\rm{*}}}\left$, and${\rm{co}}{{\rm{v}}^{\rm{*}}}\left$), and the existence of Luzin type families, that is, if${\cal F}$is a filter then${\cal X} \subseteq {[\omega ]^\omega }$is an${\cal F}$-Luzin family if$\left\{ {X \in {\cal X}:|X \setminus F| = \omega } \right\}$is countable for every$F \in {\cal F}$. (shrink)

We prove the following version of Hechler's classical theorem: For each partially ordered set (Q, ≤) with the property that every countable subset of Q has a strict upper bound in Q, there is a ccc forcing notion such that in the generic extension for each tall analytic P-ideal J (coded in the ground model) a cofinal subset of (J, ⊆*) is order isomorphic to (Q, ≤).

In this text, a variety of modal logics at the sentential, first-order, and second-order levels are developed with clarity, precision and philosophical insight.

A long-standing theme in discussion of perception and thought has been that our primary cognitive contact with individual objects and events in the world derives from our perceptual contact with them. When I look at a duck in front of me, I am not merely presented with the fact that there is at least one duck in the area, rather I seem to be presented withthisthing (as one might put it from my perspective) in front of me, which looks to (...) me to be a duck. Furthermore, such a perception would seem to put me in a position not merely to make the existential judgment that there is some duck or other present, but rather to make a singular, demonstrative judgment, that that is a duck. My grounds for an existential judgment in this case derives from my apprehension of the demonstrative thought and not vice versa. (shrink)

We study cardinal invariants connected to certain classical orderings on the family of ideals on ω. We give topological and analytic characterizations of these invariants using the idealized version of Fréchet-Urysohn property and, in a special case, using sequential properties of the space of finitely-supported probability measures with the weak* topology. We investigate consistency of some inequalities between these invariants and classical ones, and other related combinatorial questions. At last, we discuss maximality properties of almost disjoint families related to certain (...) ordering on ideals. (shrink)

This book defends antitheodicism, arguing that theodicies, seeking to excuse God for evil and suffering in the world, fail to ethically acknowledge the victims of suffering. The authors argue for this view using literary and philosophical resources, commencing with Immanuel Kant's 1791 "Theodicy Essay" and its reading of the Book of Job. Three important twentieth century antitheodicist positions are explored, including "Jewish" post-Holocaust ethical antitheodicism, Wittgensteinian antitheodicism exemplified by D.Z. Phillips and pragmatist antitheodicism defended by William James. The authors argue (...) that these approaches to evil and suffering are fundamentally Kantian. Literary works such as Franz Kafka'sThe Trial, Samuel Beckett's Waiting for Godot, and George Orwell's Nineteen Eighty-Four, are examined in order to crucially advance the philosophical case for antitheodicism. (shrink)

Temporal Logic: From Ancient Ideas to Artificial Intelligence deals with the history of temporal logic as well as the crucial systematic questions within the field. The book studies the rich contributions from ancient and medieval philosophy up to the downfall of temporal logic in the Renaissance. The modern rediscovery of the subject, which is especially due to the work of A. N. Prior, is described, leading into a thorough discussion of the use of temporal logic in computer science and the (...) understanding of natural language. Temporal Logic: From Ancient Ideas to Artificial Intelligence thus interweaves linguistic, philosophical and computational aspects into an informative and inspiring whole. (shrink)

In his last book, David Armstrong sets out his metaphysical system in a set of concise and lively chapters each dealing with one aspect of the world. He begins with the assumption that all that exists is the physical world of space-time. On this foundation he constructs a coherent metaphysical scheme that gives plausible answers to many of the great problems of metaphysics. He gives accounts of properties, relations, and particulars; laws of nature; modality; abstract objects such as numbers; and (...) time and mind. (shrink)

BackgroundThe amount and value of researchers’ peer review work is critical for academia and journal publishing. However, this labor is under-recognized, its magnitude is unknown, and alternative ways of organizing peer review labor are rarely considered.MethodsUsing publicly available data, we provide an estimate of researchers’ time and the salary-based contribution to the journal peer review system.ResultsWe found that the total time reviewers globally worked on peer reviews was over 100 million hours in 2020, equivalent to over 15 thousand years. The (...) estimated monetary value of the time US-based reviewers spent on reviews was over 1.5 billion USD in 2020. For China-based reviewers, the estimate is over 600 million USD, and for UK-based, close to 400 million USD.ConclusionsBy design, our results are very likely to be under-estimates as they reflect only a portion of the total number of journals worldwide. The numbers highlight the enormous amount of work and time that researchers provide to the publication system, and the importance of considering alternative ways of structuring, and paying for, peer review. We foster this process by discussing some alternative models that aim to boost the benefits of peer review, thus improving its cost-benefit ratio. (shrink)

Concept of African social and political philosophy -- Faces of African freedom -- African socialism and Nyerere -- African personality : a social portrait -- Negritude : a philosophy of social action -- African tribalism : social and political implications -- Apartheid and African social experience -- The African and neo-colonial predicament -- Social self in African philosophy -- Crisis of common good and political instability -- Pan-Africanism as a concept and social philosophy -- African philosophy and social reconstruction.

Is consciousness a purely physical phenomenon? Most contemporary philosophers and theorists hold that it is, and take this to be supported by modern science. But a significant minority endorse non-physicalist theories such as dualism, idealism and panpsychism, among other reasons because it may seem impossible to fully explain consciousness, or capture what it's like to be in conscious states (such as seeing red, or being in pain), in physical terms. This Element will introduce the main non-physicalist theories of consciousness and (...) explain the most important arguments for them, and consider how they each respond to the scientific and other arguments in support of physicalism. This title is also available as Open Access on Cambridge Core. (shrink)