Henry Leonard and Karel Lambert first introduced so-called presupposition-free (or just simply: free) logics in the 1950’s in order to provide a logical framework allowing for non-denoting singular terms (be they descriptions or constants) such as “the largest prime” or “Pegasus” (see Leonard [1956] and Lambert [1960]). Of course, ever since Russell’s paradigmatic treatment of definite descriptions (Russell [1905]), philosophers have had a way to deal with such terms. A sentence such as “the..

In this book G. W. Leibniz presents not only his reflections on predestination and election but also a more detailed account of the problem of evil than is found in any of his other works apart from the _Theodicy_. Surprisingly, his _Dissertation on Predestination and Grace_ has never before been published in any form. Michael J. Murray's project of translating, editing, and providing commentary for the volume will therefore attract great interest among scholars and students of Leibniz's philosophy and theology. (...) Leibniz addresses such topics as free will, moral responsibility, divine causation, justice, punishment, divine foreknowledge, and human freedom, revealing crucial aspects of the genesis of his mature metaphysics and the theological motivations behind it. (shrink)

In this paper we introduce the notion of a set algebra S satisfying a system E of equations. After defining a notion of freeness for such algebras, we show that, for any system E of equations, set algebras that are free in the class of structures satisfying E exist and are unique up to a bisimulation. Along the way, analogues of classical set-theoretic and algebraic properties are investigated.

Aldo Antonelli offers a novel view on abstraction principles in order to solve a traditional tension between different requirements: that the claims of science be taken at face value, even when involving putative reference to mathematical entities; and that referents of mathematical terms are identified and their possible relations to other objects specified. In his view, abstraction principles provide representatives for equivalence classes of second-order entities that are available provided the first- and second-order domains are in the equilibrium dictated by (...) the abstraction principles, and whose choice is otherwise unconstrained.entities are the referents of abstraction terms: such referents are to an extent indeterminate, but we can still quantify over them, predicate identity or non-identity, etc. Our knowledge of them is limited, but still substantial: we know whatever has to be true no matter how the representatives are chosen, i.e., what is true in all models of the corresponding abstraction principles. This view is backed up by an “austere” conception of universals, according to which these are first-order objects, i.e., ways of collecting first-order objects. Antonelli thus claims that second-order logic does not import any novel ontological commitment beyond ontology of first-order, naturalistically acceptable, objects. Moreover, in the case of arithmetic, even if Hume’s Principle is construed as described above, Frege’s Theorem goes through unaffected, since there is nothing in its proof that depends on an account of the “true nature” of numbers. A viable construal of logicism is then given by the combination of semantic nominalism and a naturalistic conception of abstraction. [Editors note]. (shrink)

G. E. M. Anscombe; IX—Parmenides, Mystery and Contradiction, Proceedings of the Aristotelian Society, Volume 69, Issue 1, 1 June 1969, Pages 125–132, https://do.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:C. Suetonius Tranquillus: De Grammaticis et RhetoribusJames E. G. ZetzelR. A. Kaster, ed. C. Suetonius Tranquillus: De Grammaticis et Rhetoribus. Edited with a translation, introduction, and commentary. Oxford: Clarendon Press. lx 1 370 pp. Cloth, $72.00.From a very early stage, the Romans were interested in their own literary history. In the second century B.C.E., Accius composed his didascalica; in the first century, Varro, Cornelius Nepos, and Julius Hyginus (...) all wrote biographies of literary figures; and early in the second century c.e. Suetonius wrote a set of books De uiris illustribus, giving accounts of the lives of Roman poets, historians, orators, philosophers—and teachers of grammar and rhetoric. Our knowledge of the first four categories of writers is exiguous: aside from Cicero’s Brutus, which is of more importance for chronology than for biography proper, we have the versions of some of Suetonius’ lives of the poets that are attached to scholia and the one-sentence notices excerpted from Suetonius by Jerome in his adaptation of Eusebius’ Chronicle; we also have occasional anecdotes in the elder Seneca, Aulus Gellius, and a few other sources. The vagaries of textual transmission, however, have left us much better off with the last of Suetonius’ rubrics: a single manuscript survived to the middle ages containing (along with Tacitus’ minor works) the portion of De uiris illustribus known as De grammaticis et rhetoribus (DGR). The text is badly preserved, and it is also incomplete: of the sixteen professors of rhetoric once included, lives of only five remain. Even so, it is a text of considerable importance for students of Roman education and, indeed, of Roman intellectual life: not only does it describe the origins of grammatical and rhetorical education at Rome, it discusses the origins, character, and students of the men who taught the elite of Rome; it preserves anecdotes involving the leading political and literary figures of the first centuries B.C.E. and c.e.; and along the way it offers quotations, otherwise unknown, from such figures as Valerius Cato, Helvius Cinna, Furius Bibaculus, Cicero, Asinius Pollio, and Asinius Gallus.Until now, DGR has been an extraordinarily difficult text to understand or [End Page 475] to use. Suetonius’ chronology is vague, his biographical reconstructions obscure, and his narratives maddeningly brief and anecdotal—not to mention the fact that the text itself is so corrupt that the words themselves are not always easy to ascertain. No longer: with Robert Kaster’s magnificent edition, DGR is a text that cannot only be read, but understood, used, and even (at times) admired. In some respects, K. is the perfect match for Suetonius: like Suetonius, K.’s principal interest is not in the internal history of ancient education, but in its external history, above all in the social context and significance of teaching at Rome. It should also be said, however, that in other ways K. is far better than Suetonius: where the ancient text is brief, elliptical, and anecdotal, K. is thorough, patient, and extraordinarily learned. K.’s edition includes a long introduction, a new critical text and facing translation, and an exhaustive commentary, followed by four appendices (of which the longest and most important concerns Suetonius’ use of the elder Seneca). A brief review can scarcely do justice to K.’s achievement; a few comments will have to suffice.Introduction: Although DGR is perhaps the portion of De uiris illustribus that modern scholars would most happily have done without, K. turns the very obscurity of the subject matter to good advantage. In writing of poets, historians, and the rest, Suetonius could make full use of earlier biographers such as Nepos and Hyginus; with the teachers, he had no such sources. As a result, DGR provides an excellent laboratory in which to observe Suetonius’ working methods: K. analyzes brilliantly the way in which he collected his information, how it is related to his research for the lives of literary figures, and the strengths and weaknesses of Suetonius’ approach. In both the introduction and the commentary (to singularly good effect in his analysis of DGR1–4 on the origins of grammatical teaching at Rome), K. pays close attention... (shrink)

Markov, A. A. On constructive mathematics.--Ceĭtin, G. S. Mean value theorems in constructive analysis.--Zaslavskiĭ, I. D. and Ceĭtlin, G. S. On singular coverings and properties of constructive functions connected with them.--Maslov, S. Ju. Certain properties of E. L. Post's apparatus of canonical calculi.--Zaslavskiĭ, I. D. Graph schemes with memory.

Contemporary religious studies contains many studies of Orthodox theology of the twentieth century, but there are almost no studies of the most prominent modern trend in Orthodox theology, neo-patristics. In particular, in the works of L. Voronkova, G. Gabinsky, M. Gordienko, Y. Kalinin, P. Kurochkin, I. Mozgovy, V. Molokov, M. Novikov, N. Petelinskaya, V. Chertikhin, A. Chertkov, a thorough analysis of tendencies was carried out Modernism of Orthodox theology of the Russian Church. Of these, only M. Novikov briefly criticizes the (...) views of V. Lossky, a representative of Neopatristics, but the researcher does not realize the originality of this trend in Orthodox theology. Especially the tendencies of the development of Orthodox theology of spiritual academic schools of the XIX-beg. XX century. M. Ivanov, M. Glubokovsky, I. Kondratieva, G. Pankov, O. Pechurina, O. Sarapin, L. Fokina were thoroughly researched, but these studies were usually conducted outside the context of all Orthodox theology of the XX century. (shrink)

The Baire algebra of a topological space X is the quotient of the algebra of all subsets of X modulo the meager sets. We show that this Boolean algebra can be endowed with a natural closure operator, resulting in a closure algebra which we denote $\mathbf {Baire}(X)$. We identify the modal logic of such algebras to be the well-known system $\mathsf {S5}$, and prove soundness and strong completeness for the cases where X is crowded and either completely metrizable and continuum-sized (...) or locally compact Hausdorff. We also show that every extension of $\mathsf {S5}$ is the modal logic of a subalgebra of $\mathbf {Baire}(X)$, and that soundness and strong completeness also holds in the language with the universal modality. (shrink)