We develop a bottom-up approach to truth-value semantics for classical logic of partial terms based on equality and apply it to prove the conservativity of the addition of partial description and selection functions, independently of any strictness assumption.

Let V be the cumulative set theoretic hierarchy, generated from the empty set by taking powers at successor stages and unions at limit stages and, following [2], let the primitive language of set theory be the first order language which contains binary symbols for equality and membership only. Despite the existence of ∀∀-formulae in the primitive language, with two free variables, which are satisfiable in V but not by finite sets ([5]), and therefore of ƎƎ∀∀ sentences of the same language, (...) which are undecidable in ZFC without the Axiom of Infinity, truth in V for Ǝ*∀∀-sentences of the primitive language, is decidable ([1]). Completeness of ZF with respect to such sentences follows. (shrink)

Let HF be the collection of the hereditarily finite well-founded sets and let the primitive language of set theory be the first-order language which contains binary symbols for equality and membership only. As announced in a previous paper by the authors, "Truth in V for ∃*∀∀-sentences is decidable," truth in HF for ∃*∀∀-sentences of the primitive language is decidable. The paper provides the proof of that claim.

We show that the Axiom of Foundation, as well as the Antifoundation Axiom AFA, plays a crucial role in determining the decidability of the following problem. Given a first-order theory T over the language , and a sentence F of the form with quantifier-free in the same language, are there models of T in which F is true? Furthermore we show that the Extensionality Axiom is quite irrelevant in that respect.

This landmark work provides a systematic introduction to systems of modal logic and stands as the first presentation of what have become central ideas in philosophy of language and metaphysics, from the "new theory of reference" and non-linguistic necessity and essentialism to "Kripke semantics.".

We show that the replacement rule of the sequent calculi ${\bf G3[mic]}^= $ in [8] can be replaced by the simpler rule in which one of the principal formulae is not repeated in the premiss.

Appearing in English for the first time, Schelling’s 1842 lectures develop the idea that many philosophical concepts are born of religious-mythological notions.

The axiom of infinity can be expressed by stating the existence of sets satisfying a formula which involves restricted universal quantifiers only, even if the axiom of foundation is not assumed.

The still unsettled decision problem for the restricted purely universal formulae 0-formulae) of the first order set-theoretic language based over =, ∈ is discussed in relation with the adoption or rejection of the axiom of foundation. Assuming the axiom of foundation, the related finite set-satisfiability problem for the very significant subclass of the 0-formulae consisting of the formulae involving only nested variables of level 1 is proved to be semidecidable on the ground of a reflection property over the hereditarily finite (...) sets, and various extensions of this result are obtained. When variables are restricted to range only over sets, in universes with infinitely many urelements the set-satisfiability problem is shown to be solvable provided the axiom of foundation is assumed; if it is not, then the decidability of a related derivability problem still holds. That, in turn, suggests the alternative adoption of an antifoundation axiom under which the set-satisfiability problem is also solvable . Turning to set theory without urelements, assuming a form of Boffa's antifoundation axiom, the complement of the set-satisfiability problem for the full class of Δ0-formulae is shown to be semidecidable; a result that is known not to hold, for the set-satisfiability problem itself, even for a very restricted subclass of the Δ0-formulae. (shrink)

With precision and profundity born of 30 years of devoted study, John Boyle offers an essential introduction to St. Thomas Aquinas on Scripture, shedding helpful light on the goals, methods, and commitments that animate the Angelic Doctor's engagement with the sacred page. Because the genius of St. Thomas's approach to the Bible lies not so much in its novelty but rather in the fidelity and clarity with which he recapitulates the riches of the preceding interpretive Tradition, this initiation into St. (...) Thomas's vision of Scripture is itself an orientation to the Church's vision of Scripture, from the Fathers through and beyond the Middle Ages. St. Thomas's embeddedness within the Church's Tradition and his own historical context is integral to his approach to Scripture, yet it sets him at some distance from modern readers, for whom his interpretive vision may seem perplexing or even impenetrable. In this Primer, Boyle first provides an acclimation to this medieval context through a survey and explanation of pertinent technical terminology used by St. Thomas and characteristic of the scholastic theology of the time. With an eye to the medieval practice of considering Scripture according to the fourfold division of causes, Boyle builds on this initial foundation by exploring in turn St. Thomas's accounts of the end or use of Scripture (final cause), its divine and human authorship (efficient cause), its order and division (material cause), and its literary styles or genres (formal cause). Drawing on writings from across St. Thomas's corpus, but especially his work On the Commendation and Division of Sacred Scripture and the prologues to his biblical commentaries, Boyle masterfully elucidates both the hermeneutical principles and deep wisdom of the Angelic Doctor's approach to Scripture, imparting invaluable guidance not only for reading and understanding St. Thomas and other great masters of the Tradition, but also-and ultimately-for understanding Scripture in light of this Tradition and reading it with greater benefit and joy. (shrink)

We show that if the structural rules are admissible over a set \ of atomic rules, then they are admissible in the sequent calculus obtained by adding the rules in \ to the multisuccedent minimal and intuitionistic \ calculi as well as to the classical one. Two applications to pure logic and to the sequent calculus with equality are presented.

We establish the decidability, with respect to open formulas in the first order language with equality =, the membership relation , the constant for the empty set, and a binary operation w which, applied to any two sets x and y, yields the results of adding y as an element to x, of the theory NW having the obvious axioms for and w. Furthermore we establish the completeness with respect to purely universal sentences of the theory , obtained from NW (...) by adding the Extensionality Axiom E and the Regularity Axiom R, and of the theory obtained by adding to NW (a slight variant of) the Antifoundation Axiom AFA. (shrink)

"The chief business of twentieth-century philosophy” is “to reckon with twentieth-century history," claimed R. G. Collingwood. In this remarkable collection of essays, Frank Ankersmit demonstrates the prescience of that remark and goes a long way toward meeting its challenge. Responding to the work of Hayden White, Arthur Danto, and Hans-Georg Gadamer, he examines such issues as the difference between historical representation and artistic expression, the status of metaphor in historical description, and the relation of postmodernism to historicism. Ankersmit's fluent grasp (...) of European thought and his ability to incorporate concepts from literary theory, art history, the philosophy of science, and political thought into his analyses assure that this collection will interest readers throughout the humanities. (shrink)

The problem is addressed of establishing the satisfiability of prenex formulas involving a single universal quantifier, in diversified axiomatic set theories. A rather general decision method for solving this problem is illustrated through the treatment of membership theories of increasing strength, ending with a subtheory of Zermelo-Fraenkel which is already complete with respect to the ∀*∀ class of sentences. NP-hardness and NP-completeness results concerning the problems under study are achieved and a technique for restricting the universal quantifier is presented.

Ethics for Enemies comprises three original philosophical essays on torture, terrorism, and war. F. M. Kamm deploys ethical theory in her challenging new treatments of these most controversial practical issues. First she considers the nature of torture and the various occasions on which it could occur, in order to determine why it might be wrong to torture a wrongdoer held captive, even if this were necessary to save his victims. In the second essay she considers what makes terrorism wrong--whether it (...) is the intention to harm civilians, rather than harm to them being 'collateral damage,' or something else--and whether terrorism is always wrong. The third essay discusses whether having a right reason, in the sense of a right intention, is necessary in order for a war to be just. Kamm then examines ways in which the harms of war can be proportional to the achievement of the just cause and other goods that war can bring about, so as to make the declaration of war permissible. (shrink)

This is an English translation of Schelling's Ideas for a Philosophy of Nature (first published in 1797 and revised in 1803), one of the most significant works in the German tradition of philosophy of nature and early nineteenth-century philosophy of science. It stands in opposition to the Newtonian picture of matter as constituted by inert, impenetrable particles, and argues instead for matter as an equilibrium of active forces that engage in dynamic polar opposition to one another. In the revisions of (...) 1803 Schelling incorporated this dialectical view into a neo-Platonic conception of an original unity divided upon itself. The text is of more than simply historical interest: its daring and original vision of nature, philosophy, and empirical science will prove absorbing reading for all philosophers concerned with post-Kantian German idealism, for scholars of German Romanticism, and for historians of science. (shrink)

The limited aim here is to explain what John Dewey might say about the formulation of the grue example. Nelson Goodman’s problem of distinguishing good and bad inductive inferences is an important one, but the grue example misconstrues this complex problem for certain technical reasons, due to ambiguities that contemporary logical theory has not yet come to terms with. Goodman’s problem is a problem for the theory of induction and thus for logical theory in general. Behind the whole discussion of (...) these issues over the last several decades is a certain view of logic hammered out by Russell, Carnap, Tarski, Quine, and many others. Goodman’s nominalism hinges in essential ways on a certain view of formal logic with an extensional quantification theory at its core. This raises many issues, but the one issue most germane here is the conception of predicates ensconced in this view of logic. (shrink)

The essays in this collection address different aspects of Dewey's philosophy of logic, from his work at the beginning of the twentieth century to the culmination of his logical thought in the 1938 volume, Logic: The Theory of Inquiry.

Laughter as superiority -- The elements of laughter -- The one necessary thing -- Objections to the normative thesis -- Comic virtues and vices -- The social virtues -- The charismatic virtues -- Machine law -- Machine scholarship -- Machine art and machine cities -- The battle of the norms -- Resistance to laughter -- The sociability thesis -- Conclusion.

Neuroscience has studied deductive reasoning over the last 20 years under the assumption that deductive inferences are not only de jure but also de facto distinct from other forms of inference. The objective of this research is to verify if logically valid deductions leave any cerebral electrical trait that is distinct from the trait left by non-valid deductions. 23 subjects with an average age of 20.35 years were registered with MEG and placed into a two conditions paradigm (100 trials for (...) each condition) which each presented the exact same relational complexity (same variables and content) but had distinct logical complexity. Both conditions show the same electromagnetic components (P3, N4) in the early temporal window (250–525 ms) and P6 in the late temporal window (500–775 ms). The significant activity in both valid and invalid conditions is found in sensors from medial prefrontal regions, probably corresponding to the ACC or to the medial prefrontal cortex. The amplitude and intensity of valid deductions is significantly lower in both temporal windows (p = 0.0003). The reaction time was 54.37% slower in the valid condition. Validity leaves a minimal but measurable hypoactive electrical trait in brain processing. The minor electrical demand is attributable to the recursive and automatable character of valid deductions, suggesting a physical indicator of computational deductive properties. It is hypothesized that all valid deductions are recursive and hypoactive. (shrink)

I present a possible worlds semantics for a hyperintensional belief revision operator, which reduces the logical idealization of cognitive agents affecting similar operators in doxastic and epistemic logics, as well as in standard AGM belief revision theory. (Revised) belief states are not closed under classical logical consequence; revising by inconsistent information does not perforce lead to trivialization; and revision can be subject to ‘framing effects’: logically or necessarily equivalent contents can lead to different revisions. Such results are obtained without resorting (...) to non-classical logics, or to non-normal or impossible worlds semantics. The framework combines, instead, a standard semantics for propositional S5 with a simple mereology of contents. (shrink)

razdel I. Istoriko-filosofskie issledovanii︠a︡ -- razdel II. Filosofskie i sot︠s︡ialʹno-politicheskie problemy -- razdel III. Istorii︠a︡ v lit︠s︡akh.