On the dominant contemporary accounts of how practical considerations affect what we ought to believe, practical considerations either encroach on epistemic rationality by affecting whether a belief is epistemically justified, or constitute distinctively practical reasons for belief which can only affect what we ought to believe by conflicting with epistemic rationality. This paper argues that Søren Kierkegaard offers a promising alternative view on which practical considerations can affect what we ought to believe without either encroaching on or (necessarily) conflicting with (...) epistemic rationality by determining which among the epistemically permitted outright doxastic attitudes one should all‐things‐considered adopt. (shrink)

We prove that any 1-closed (see def 1.1) model of the Π 2 consequences of PA satisfies ¬Cons PA which gives a proof of the second Godel incompleteness theorem without the use of the Godel diagonal lemma. We prove a few other theorems by the same method.

We prove that the Gödel incompleteness theorem holds for a weak arithmetic T = IΔ0 + Ω2 in the form where Cons H (T) is an arithmetic formula expressing the consistency of T with respect to the Herbrand notion of provability.

We formulate a Π1 sentence τ which is a version of the Tableau consistency of GlΔ0. The sentence τ is true and is provable in GlΔ0 + exp. We construct a model M of GlΔ0+Ω1+τ+BGs1 which has no proper end-extension to a model of GlΔ0+Ω1+τ. Also we prove that GlΔ0+Ω1+τ is not Π1 conservative over GlΔ0+τ.

We prove that: • if there is a model of I∆₀ + ¬ exp with cofinal Σ₁-definable elements and a Σ₁ truth definition for Σ₁ sentences, then I∆₀ + ¬ exp +¬BΣ₁ is consistent, • there is a model of I∆₀ Ω₁ + ¬ exp with cofinal Σ₁-definable elements, both a Σ₂ and a ∏₂ truth definition for Σ₁ sentences, and for each n > 2, a Σ n truth definition for Σ n sentences. The latter result is obtained by (...) constructing a model with a recursive truth-preserving translation of Σ₁ sentences into boolean combinations of $\exists \sum {\begin{array}{*{20}{c}} h \\ 0 \\ \end{array} } $ sentences. We also present an old but previously unpublished proof of the consistency of I∆₀ + ¬ exp + ¬BΣ₁ under the assumption that the size parameter in Lessan's ∆₀ universal formula is optimal. We then discuss a possible reason why proving the consistency of I∆₀ + ¬ exp + ¬BΣ₁ unconditionally has turned out to be so difficult. (shrink)

We show that for each n ≥ 1, if T2n does not prove the weak pigeonhole principle for Σbn functions, then the collection scheme B Σ1 is not finitely axiomatizable over T2n. The same result holds with Sn2 in place of T 2n.

For a fixed q  ℕ and a given Σ1 definition φ(d,x), where d is a parameter, we construct a model M of 1 Δ0 + ¬ exp and a non standard d  M such that in M either φ has no witness smaller than d or phgr; is equivalent to a formula ϕ(d,x) having no more than q alternations of blocks of quantifiers.

For any n, we construct a model of in which each formula is equivalent to an formula.

This book compiles and reviews the most prominent linguistic theories into a single source that serves as an essential reference for future solutions to one of the most important challenges of our age.

Purpose. Romanticism as a movement developed in Germany, where, becoming the philosophy of time in the 18th-19th centuries, spread to all European countries. The "mobility" of the Romantic doctrine, its diversity, sometimes contradictory views, attitude to man as a free, harmonious, creative person led to the susceptibility of this movement by ethnic groups, different in nature and mentality. Its ideas found a wide response in Ukraine with its "cordocentric" type of culture in the early nineteenth century. Since the peculiarity of (...) "Ukrainian Romanticism" was its "literary-centric" nature, the purpose of this study is to analyse and comprehend the place of man in the national philosophy and literature of this period. Accordingly, the main tasks of the work are as follows: to determine the main features, the nature of Ukrainian Romanticism; to trace the main vectors of comprehension and image of man in the literature of this time. Theoretical basis. The ideas of European Romanticism were creatively rethought and assimilated during the emergence of new Ukrainian literature. It provided samples of highly artistic works, unique names of talented writers – creators and thinkers, who in their works reflected the philosophy of time. Based on the works of F. Schlegel, partly E. Husserl, M. Heidegger, K. Jaspers, Romanticism in the Ukrainian humanities, in terms of philosophy, culturology, as well as at the intersection with literature, was studied by T. Bovsunivska, Y. Hrybkova, S. Efremov, N. Kalenichenko, S. Kozak, T. Komarynets, D. Nalyvayko, Y. Nakhlik, I. Ogorodnyk, V. Ogorodnyk, A. Sinitsyna, D. Chyzhevsky, M. Yatsenko, E. Kyryliuk, M. Biletsky, D. Dontsov, S. Efremov, G. Kostyuk, S. Krymsky, Y. Sherekh and others. Originality. The authors of the article prove that Romanticism in Ukraine, being "literary-centric" inherently, having absorbed the main ideas and features of European Romanticism, has its own features and vectors of formation and development. Man in this kind of movement, thanks to the means of art, appears very clearly as a spiritually rich, sensitive, vulnerable and strong person. For him or her, the highest value is freedom, the ability to make freely independent fateful decisions. Conclusions. Ukrainian writers, reflecting the philosophical ideas of Romanticism, saw in man a harmonious combination of "natural" and "social", through which he indirectly carries out his own national existence. In addition to the objective realities of the external world, in their works, Romantic writers appeal to the subjective, internal, spiritual, "ideal" world of the hero, who interacts with reality through his own system of values. At each level of development of the humanities and methodology of cognition, this allows a new reading of these works. (shrink)

The authors study opera from the perspective of the theories of psychoanalyst Jacques Lacan, and argue that opera's second death corresponded with the rise of psychoanalysis in the early 20th century. With a preface by Lanfossi and an afterword by Alberto Toscano.