This book philosophically discusses the educational challenges of dwelling poetically, which, according to Martin Heidegger, means learning from great poems how to live a worthy life and relate authentically to beings and to Being. The gifts of great poetry are carefully described and concrete approaches are presented that the educator can adopt.

Existentialism and Sociology is the first work to systematically and critically analyze the existential ideas of Jean-Paul Sartre and to demonstrate their importance and connection to central sociological categories found in the theories of Weber, Durkheim, Freud, Mead, and others.

In chapter one I cover the basic concepts developed in Being and Nothingness, notable those of "temporality," "negation," "anguish" and "bad faith." In chapter two I move from the individual as the center of free action, to the individual in relation to the Other. In chapter three I attempt to unify the perspectives in the first two chapter and present a theory of action. In chapter four I introduce the reader to the Critique and establish its thematic links with Being (...) and Nothingness. In chapter five I analyze the ramifications of the concept of the practico-inert, which, for Sartre, is inseparable from human sociality. In chapter six I deal with the concept of organization, which refers to the contradictions within the social group as it moves into advanced stages of social integration. In chapter seven I cover the concepts of power and authority. Chapter eight deals with the idea of dialectical humanism and highlights essential concepts in the work by way of concluding it. --Introduction. (shrink)

Christian economic theology is distinguished from Christian social ethics by its methodological reflection on the emergence, formation, and proper boundaries of the economic sphere, as well as transcendental reflection on the conditions of possibility of economic science. In practice, this often amounts to anxiety about the authority of Christianity in the economic sphere, as well as about the extent to which Christianity can be held responsible for the system of impersonal economic domination known as capitalism. This review essay draws upon (...) three recent works on or about Christian economic theology, and argues that this genre's anxiety about Christian authority manifests in the ways that it draws temporal boundaries between ancient, medieval, and modern economies. Ultimately, its ambivalence about economy itself is traceable to Aristotle's understanding of money as containing two natures, one defined by quality (use value) and the other by quantity (exchange value). Christianity here becomes a cipher for quality. (shrink)

_ Source: _Volume 25, Issue 1, pp 72 - 94 Politics has never been considered Martin Buber’s forte. This paper considers the range of Buber’s reception as a political thinker by considering it in the form of three “moments,” each from a different point in his career, and each through the eyes of a different figure who either read or worked with Buber politically: Theodor Herzl, Gustav Landauer, and Hans Kohn. The three moments are structured around a discussion of the (...) classic criticism that Buber’s politics are naïve or utopian; the paper seeks to respond, as Buber did, in a way that raises questions about the borders of politics itself. (shrink)

ḥeleḳ 1. Maʼamar rishon -- ḥeleḳ 2. Maʼamar sheni -- ḥeleḳ 3. Maʼamar shelishi -- ḥeleḳ 4. Maʼamar reviʻi-ḥamishi.

How did one of the greatest Jewish thinkers of the 20th century grapple with the founding of Israel and the Israeli-Palestinian conflict—one of the most significant political conflicts of his time? Samuel Hayim Brody traces the development of Martin Buber's thinking and its implications for the Jewish religion, for the problems posed by Zionism, and for the Zionist-Arab conflict. Beginning in turbulent Weimar Germany, Brody shows how Buber's debates about Biblical meanings had concrete political consequences for anarchists, socialists, Zionists, Nazis, (...) British, and Palestinians alike. Brody further reveals how Buber's passionate commitment to the rule of God absent an intermediary came into conflict in the face of a Zionist movement in danger of repeating ancient mistakes. Brody argues that Buber's support for Israel stemmed from a radically rich and complex understanding of the nature of the Jewish mission on earth that arose from an anarchist reading of the Bible. (shrink)

We formulate epsilon substitution method for elementary analysisEA (second order arithmetic with comprehension for arithmetical formulas with predicate parameters). Two proofs of its termination are presented. One uses embedding into ramified system of level one and cutelimination for this system. The second proof uses non-effective continuity argument.

Cut reductions are defined for a Kripke-style formulation of modal logic in terms of indexed systems of sequents. A detailed proof of the normalization (cutelimination) theorem is given. The proof is uniform for the propositional modal systems with all combinations of reflexivity, symmetry and transitivity for the accessibility relation. Some new transformations of derivations (compared to standard sequent formulations) are needed, and some additional properties are to be checked. The display formulations [1] of the systems considered can be presented as (...) encodings of Kripke-style formulations. (shrink)

Dynamic topological logic provides a context for studying the confluence of the topological semantics for S4, topological dynamics, and temporal logic. The topological semantics for S4 is based on topological spaces rather than Kripke frames. In this semantics, □ is interpreted as topological interior. Thus S4 can be understood as the logic of topological spaces, and □ can be understood as a topological modality. Topological dynamics studies the asymptotic properties of continuous maps on topological spaces. Let a dynamic topological system (...) be a topological space X together with a continuous function f. f can be thought of in temporal terms, moving the points of the topological space from one moment to the next. Dynamic topological logics are the logics of dynamic topological systems, just as S4 is the logic of topological spaces. Dynamic topological logics are defined for a trimodal language with an S4-ish topological modality □, and two temporal modalities, ○ and *, both interpreted using the continuous function f. In particular, ○ expresses f’s action on X from one moment to the next, and * expresses the asymptotic behaviour of f. (shrink)

Dynamic topological logic provides a context for studying the confluence of the topological semantics for S4, topological dynamics, and temporal logic. The topological semantics for S4 is based on topological spaces rather than Kripke frames. In this semantics, □ is interpreted as topological interior. Thus S4 can be understood as the logic of topological spaces, and □ can be understood as a topological modality. Topological dynamics studies the asymptotic properties of continuous maps on topological spaces. Let a dynamic topological system (...) be a topological space X together with a continuous function f. f can be thought of in temporal terms, moving the points of the topological space from one moment to the next. Dynamic topological logics are the logics of dynamic topological systems, just as S4 is the logic of topological spaces. Dynamic topological logics are defined for a trimodal language with an S4-ish topological modality □ , and two temporal modalities, ○ and * , both interpreted using the continuous function f. In particular, ○ expresses f’s action on X from one moment to the next, and * expresses the asymptotic behaviour of f. (shrink)

Intuitionistic logic is presented here as part of familiar classical logic which allows mechanical extraction of programs from proofs. to make the material more accessible, basic techniques are presented first for propositional logic; Part II contains extensions to predicate logic. This material provides an introduction and a safe background for reading research literature in logic and computer science as well as advanced monographs. Readers are assumed to be familiar with basic notions of first order logic. One device for making this (...) book short was inventing new proofs of several theorems. The presentation is based on natural deduction. The topics include programming interpretation of intuitionistic logic by simply typed lambda-calculus (Curry-Howard isomorphism), negative translation of classical into intuitionistic logic, normalization of natural deductions, applications to category theory, Kripke models, algebraic and topological semantics, proof-search methods, interpolation theorem. The text developed from materal for several courses taught at Stanford University in 1992-1999. (shrink)

A Short Introduction to Modal Logic presents both semantic and syntactic features of the subject and illustrates them by detailed analyses of the three best-known modal systems S5, S4 and T. The book concentrates on the logical aspects of ...

This paper considers the computational complexity of the disjunction and existential properties of intuitionistic logic. We prove that the disjunction property holds feasibly for intuitionistic propositional logic; i.e., from a proof of A v B, a proof either of A or of B can be found in polynomial time. For intuitionistic predicate logic, we prove superexponential lower bounds for the disjunction property, namely, there is a superexponential lower bound on the time required, given a proof of A v B, to (...) produce one of A and B which is true. In addition, there is superexponential lower bound on the size of terms which fulfill the existential property of intuitionistic predicate logic. There are superexponential upper bounds for these problems, so the lower bounds are essentially optimal. (shrink)

The completeness of the modal logic S4 for all topological spaces as well as for the real line , the n-dimensional Euclidean space and the segment etc. was proved by McKinsey and Tarski in 1944. Several simplified proofs contain gaps. A new proof presented here combines the ideas published later by G. Mints and M. Aiello, J. van Benthem, G. Bezhanishvili with a further simplification. The proof strategy is to embed a finite rooted Kripke structure for S4 into a (...) subspace of the Cantor space which in turn encodes . This provides an open and continuous map from onto the topological space corresponding to . The completeness follows as S4 is complete with respect to the class of all finite rooted Kripke structures. (shrink)

A simple cut elimination proof for arithmetic with the epsilon symbol is used to establish the termination of a modified epsilon substitution process. This opens a possibility of extension to much stronger systems.

If politics is about the state, can a stateless people be political? The field of Jewish political thought examines how Jewish individuals and communal organizations have behaved politically both within and beyond statehood. The study of Jewish political thought promises to expand received conceptions of what counts as "political.".

The epsilon substitution method was proposed by D. Hilbert as a tool for consistency proofs. A version for first order predicate logic had been described and proved to terminate in the monograph “Grundlagen der Mathematik”. As far as the author knows, there have been no attempts to extend this approach to the second order case. We discuss possible directions for and obstacles to such extensions.

We present a survey of proof theory in the USSR beginning with the paper by Kolmogorov [1925] and ending (mostly) in 1969; the last two sections deal with work done by A. A. Markov and N. A. Shanin in the early seventies, providing a kind of effective interpretation of negative arithmetic formulas. The material is arranged in chronological order and subdivided according to topics of investigation. The exposition is more detailed when the work is little known in the West or (...) the original presentation can be improved using notions or results which appeared later. This includes such topics as Novikov's cut-elimination method (regular formulas) and Maslov's inverse method for the predicate logic. (shrink)

Ackermann proved termination for a special order of reductions in Hilbert's epsilon substitution method for the first order arithmetic. We establish termination for arbitrary order of reductions.

A simple and complete proof of strong normalization for first- and second-order intuitionistic natural deduction including disjunction, first-order existence and permutative conversions is given. The paper follows the Tait–Girard approach via computability predicates and saturated sets. Strong normalization is first established for a set of conversions of a new kind, then deduced for the standard conversions. Difficulties arising for disjunction are resolved using a new logic where disjunction is restricted to atomic formulas.

We describe a short model-theoretic proof of an extended normal form theorem for derivations in predicate logic which implies in PRA a normal form theorem for the arithmetic derivations . Consider the Gentzen-type formulation of predicate logic with invertible rules. A derivation with proper variables is one where a variable b can occur in the premiss of an inference L but not below this premiss only in the case when L is () or () and b is its eigenvariable. Free (...) variables of such derivation are eigenvariables and free variables of its last sequent. Then any sequent derivable in predicate logic has a cut-free derivation with proper variables where the main formula of any antecedent rule is underivable. The proof is by a simple modification of the construction of a countermodel of the formula from the open branch of its canonical proof-search tree. It extends to intuitionistic and higher order systems. The proof of the corresponding normalization theorem outlined in [8] uses the passage to the infinitary derivations enriched by finitary derivations. The normal form after a modification to make it decidable can be considered as a realization of Gentzen's idea stated at the end of [2], that his notion of reduction for arithmetic can be extended to other fields of mathematics. (shrink)

We describe a natural deduction system NDIL for the second order intuitionistic linear logic which admits normalization and has a subformula property. NDIL is an extension of the system for !-free multiplicative linear logic constructed by the author and elaborated by A. Babaev. Main new feature here is the treatment of the modality !. It uses a device inspired by D. Prawitz' treatment of S4 combined with a construction $<\Gamma>$ introduced by the author to avoid cut-like constructions used in $\otimes$ (...) -elimination and global restrictions employed by Prawitz. Normal form for natural deduction is obtained by Prawitz translation of cut-free sequent derivations. (shrink)

A survey of works on automatic theorem-proving in the ussr 1964-1970. the philosophical problems are not touched.