We address the problem of musical variation (identification of different musical sequences as variations) and its implications for mental representations of music. According to reductionist theories, listeners judge the structural importance of musical events while forming mental representations. These judgments may result from the production of reduced memory representations that retain only the musical gist. In a study of improvised music performance, pianists produced variations on melodies. Analyses of the musical events retained across variations provided support for the reductionist account (...) of structural importance. A neural network trained to produce reduced memory representations for the same melodies represented structurally important events more efficiently than others. Agreement among the musicians' improvisations, the network model, and music‐theoretic predictions suggest that perceived constancy across musical variation is a natural result of a reductionist mechanism for producing memory representations. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 503 sufferings of Job, which she finds instructively different from the sort of account which would come naturally to people of our own time. We are apt to wonder how a good God could possibly permit the many and frightful evils which infest the world. Aquinas, however, believed that all human beings are afflicted with "a terminal cancer of soul," for which pain and suffering are the (...) divinely-appointed remedies (340). If we are not cured, we will lose for ever the ultimate bliss of communion with God. At this rate we are to expect that the best people are precisely those who are liable to suffer the most (342). Aquinas would agree with Pope Gregory, who says that it is frequently difficult to understand the ways of providence, but never more so than "when things go ill with good people and well with bad people" (343). Stump concludes that what Aquinas's interpretation of Job, and his overall account of evil, has to show us is "that our approach to the problem of evil is a consequence of our attitude towards much larger issues, such as the nature of human happiness and the goal of human life" (356). The reader will have inferred that this is a remarkable volume. None of the contributions is to be sneezed at, and some are very impressive indeed. HUGO MEYNELL University of Calgary Calgary, Alberta, Canada Christ the 'Name' ofGod: Thomas Aquinas on Naming Christ. By HENK J. M. SCHOOT. Nijmegen: Peeters Leuven, 1993. Pp. 231 (Paper). The hiddenness of God in Christ and "the relation between the Word Incarnate and human words for this Word" animate this study of Aquinas's christological epistemology; it is a study of Aquinas's understanding of "the mystery of Christ, and [of] human ways of signifying him" (1). And because "all human understanding and signification fails [sic] to reach Christ as he is," Schoot believes that all christological knowledge is primarily negative and heavily reliant on analogy (1). He applies to the names of Christ what another author (Mark Jordan) has applied to the divine names: "the surest approach to the divine is by the scrutiny of linguistic failure" (153). The structure of the book reflects these insights. In the first chapter the author stresses the negative character of christological language by reflecting upon Aquinas's use of mysterium in christology. The second chapter is an analysis of his use of "the concepts of signification, supposition, predication and reduplication," in the context of the most current knowledge of medieval grammar and logic (7). It is here that the author stresses Aquinas's strongly linguistic approach to christology, as well as the distinction between supposition ("standing for") and predication ("sig- 504 BOOK REVIEWS nification"), which will be crucial to his analysis of the hypostatic union in later chapters. In fact, "the whole of christology is built on the distinction between signification and supposition" (55). Schoot believes that Aquinas, following medieval "modist" grammarians, thought that "a fundamental parallel exists between different modes of signification, modes of understanding and modes of being" (43), and hence a linguistic approach is often a decisive entry into questions of theological (and christologiocal) epistemology and metaphysics. In this context, the author examines the distinction Aquinas made between a number of modes of signification. Chapter Three is devoted to Aquinas as a biblical theologian. His use of biblical names of Christ {over ninety in his commentary on Isaiah alone) suggests that "a large part of Aquinas' treatment of the person and life of the Word Incarnate is devoted to a discussion of names" (104), and that the fact that Christ is a mystery "is rooted in (his] being the 'name' of God" (105). Schoot finds that "Aquinas employs the same rules concerning signification examining those names as he does concerning the divine names" (193). Chapter Four applies the key insights of Aquinas's "theory of supposition to the theology of Christ incarnate" (194). Following an analysis of such key concepts as first and second substance, esse, suppositum, singularis, particularis, and individuum, Schoot concludes that The subject-term having both signification and supposition expresses a linguistic unity that Aquinas deems analogous to the... (shrink)

Lewis Gordon's Fear of Black Consciousness is a resolute response to the ongoing pessimism present in contemporary culture and academia regarding Black life. As a towering figure in Black existential philosophy, Gordon seamlessly weaves together discussions of contemporary and historical Western philosophers such as Gabriel Marcel and Friedrich Nietzsche with his analyses of film, music, culture, and more. Across the text's twelve chapters, Gordon reveals the pervasiveness of anti-black ideologies while challenging his readers to affirm various forms of resistance to (...) violence, invisibility, and erasure. The book is written for an audience beyond academia, and is invested in telling a practical philosophical story about generating an empowering sense of Black consciousness. Sprinkled with personal stories, witty anecdotes, and powerful arguments, the book encourages readers to rethink historical descriptions of anti-black violence as well as the vocabulary used to talk about race and racism today. An example of this is Gordon's discussion of various slave trades across the planet. He writes, ‘Only the Arab designation is correct, since it refers to Arabs trading in the enslavement of peoples. The others should properly be called the European slave trade and the East Indian slave trade or Asian slave trade. Oceans do not trade people’ (pp. 52). Another insightful aspect of the text is the author's study of films like Jordan Peele's Get Out, Boots Riley's Sorry to Bother You, and Ryan Coogler's Black Panther. Through these films, he provides a detailed look at how cinematic representation engages complex dialogues of anti-Blackness and Black power, as well as anti-capitalism. Overall, Gordon's book is a wonderful resource for anyone curious about cultivating a resistant and critical lens on contemporary culture. The aim of this review is to highlight a few of the book's major contributions for academics, casual readers, and those interested in ongoing discussions within Africana philosophy. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Explorations in the Theology of Benedict XVI ed. by John C. CavadiniJeffrey L. MorrowExplorations in the Theology of Benedict XVI. Edited by John C. Cavadini. Notre Dame, Ind.: University of Notre Dame Press, 2012. Pp. viii + 318. $30.00 (cloth). ISBN: 978-0-268-02309-6.Pope Emeritus Benedict XVI is arguably the greatest theologian to ascend to the chair of St. Peter in centuries. His theological output even prior (...) to becoming pope is staggering. It is thus fitting that an edited volume examine his theological oeuvre; there is a need for many more such volumes. The essays collected in this book were originally presented at a conference on the theology of Pope Benedict at the University of Notre Dame. Each contribution brings something insightful and unique to the volume. The book is divided into three sections: “The Dynamic of Advent,” encompassing chapters 2–5; “Caritas in Veritate,” encompassing chapters 6–7; and “God is Love,” encompassing the remaining chapters 8–11. The initial chapter-length introduction and the first chapter fall outside of this division because in many ways they set the stage for the entire volume.John Cavadini’s introduction (1–20) could serve as a useful overview of the theological work of Pope Benedict. Cavadini provides a preview of each chapter but also underscores the significance of Benedict’s theological work. He emphasizes how “one of Benedict’s major achievements is the demonstration of Augustine’s original insight into the unity of the theological tasks of understanding and of engendering understanding” (3).Cyril O’Regan’s very fine essay, “Benedict the Augustinian” (21–60), examines the Augustinian nature of Benedict’s theology. O’Regan maintains, “throughout his career Benedict not only turns again and again to Augustine as his theological model, but also... in Benedict’s self-understanding[,] the basic figuration of his theology is Augustinian” (22). This Augustinian texture to Benedict’s theology involves, among other things, his “real familiarity with and admiration” for “the classic” works of Augustine, his use of Augustine’s “theological style,” his use of shared themes, and the manner in which he consciously “articulates substantive theological positions” typical of Augustine. Moreover, O’Regan points to “Benedict’s sense that he is living in a time of crisis and senescence similar to that of Augustine” (21–22). Some of the similarities O’Regan observes in the theological work of Augustine and Benedict pertain to eschatology, the relationship between faith and reason, biblical interpretation, culture, the role of the liturgy, and the centrality of prayer. O’Regan’s essay is undoubtedly the best piece I have read on the importance of Augustine for Benedict.The thesis of Peter Casarella’s “Culture and Conscience in the Thought of Joseph Ratzinger/Pope Benedict XVI” (63–86) is that for Benedict, “the witness to truth is the key to seeing how culture and conscience are necessarily intertwined” (64). Casarella initiates his investigation with the pope’s critique of relativism. The first major section examines what he terms Benedict’s “theology of culture.” For Benedict, this has a moral dimension, and thus [End Page 493] Caserella spends the entire second portion of his essay looking at conscience and its formation in the context of culture. This is a very helpful essay that makes an important contribution to Benedict’s thought as it relates to moral theology.The late Fr. Edward Oakes’s contribution, “Resolving the Relativity Paradox: Pope Benedict XVI and the Challenge of Christological Relativism” (87–113), explores Benedict’s problem with relativism, but homes in on relativism in the context of Christology. Oakes argues, “the challenge of relativism cannot be met unless it is done first and foremost in Christological terms” (93), and he thinks Benedict does precisely this. Oakes’s overview of Ernst Troeltsch’s discussion of historical criticism as corrosive to Christology is enlightening:what most undermines Christocentrism is the historical-critical method, not so much because of the results arising from that method as from its very use.... Historical criticism... is marked by three key methodological principles: (1) the principle of criticism, that no historical document... can be taken on its own terms as automatically reliable but must... (shrink)

In this paper, the author develops a theory of concepts and shows that it captures many of the ideas about concepts that Leibniz expressed in his work. Concepts are first analyzed in terms of a precise background theory of abstract objects, and once concept summation and concept containment are defined, the axioms and theorems of Leibniz's calculus of concepts (in his logical papers) are derived. This analysis of concepts is then seamlessly connected with Leibniz's modal metaphysics of complete individual concepts. (...) The fundamental theorem of Leibniz's modal metaphysics of concepts is proved, namely, whenever an object x has F contingently, then (i) the individual concept of x contains the concept F and (ii) there is a (counterpart) complete individual concept y which doesn't contain the concept F and which `appears' at some other possible world. Finally, the author shows how the concept containment theory of truth can be made precise and made consistent with a modern conception of truth. (shrink)

Historians of philosophy are often challenged to discern the relative impacts of the ideas and the actions of ancient philosophers. The ideas of these thinkers often stand alone in an almost disembodied fashion, set apart from the physicality of a philosopher, his or her personality, and even their intellectual development over time. This article considers the tension between the people, the ideas, and the social context in Late Antique Athens and Alexandria and investigates the way in which genial and difficult (...) personalities influence the fate of Neoplatonic schools in the two cities in the late fifth and early sixth centuries AD. (shrink)

This book tackles the issues that arise in connection with intensional logic -- a formal system for representing and explaining the apparent failures of certain important principles of inference such as the substitution of identicals and existential generalization -- and intentional states --mental states such as beliefs, hopes, and desires that are directed towards the world. The theory offers a unified explanation of the various kinds of inferential failures associated with intensional logic but also unifies the study of intensional contexts (...) and intentional states by grounding the explanation of both phenomena in a single theory. When an axiomatized realm of abstract entities is added to the metaphysical structure of the world, we can use them to identify and individuate the contents of directed mental states. The special abstract entities can be viewed as the objectified contents of mental files, and they play a crucial role in the analysis of truth conditions of the sentences involved in inferential failures. (shrink)

The so-called ergodic hierarchy (EH) is a central part of ergodic theory. It is a hierarchy of properties that dynamical systems can possess. Its five levels are egrodicity, weak mixing, strong mixing, Kolomogorov, and Bernoulli. Although EH is a mathematical theory, its concepts have been widely used in the foundations of statistical physics, accounts of randomness, and discussions about the nature of chaos. We introduce EH and discuss its applications in these fields.

In this paper, the author derives the Dedekind-Peano axioms for number theory from a consistent and general metaphysical theory of abstract objects. The derivation makes no appeal to primitive mathematical notions, implicit definitions, or a principle of infinity. The theorems proved constitute an important subset of the numbered propositions found in Frege's *Grundgesetze*. The proofs of the theorems reconstruct Frege's derivations, with the exception of the claim that every number has a successor, which is derived from a modal axiom that (...) (philosophical) logicians implicitly accept. In the final section of the paper, there is a brief philosophical discussion of how the present theory relates to the work of other philosophers attempting to reconstruct Frege's conception of numbers and logical objects. (shrink)

Some recently-proposed counterexamples to the traditional definition of essential property do not require a separate logic of essence. Instead, the examples can be analysed in terms of the logic and theory of abstract objects. This theory distinguishes between abstract and ordinary objects, and provides a general analysis of the essential properties of both kinds of object. The claim ‘x has F necessarily’ becomes ambiguous in the case of abstract objects, and in the case of ordinary objects there are various ways (...) to make the definition of ‘F is essential to x’ more fine-grained. Consequently, the traditional definition of essential property for abstract objects in terms of modal notions is not correct, and for ordinary objects the relationship between essential properties and modality, once properly understood, addresses the counterexample. (shrink)

The foregoing set of theorems forms an effective foundation for the theory of situations and worlds. All twenty-five theorems seem to be basic, reasonable principles that structure the domains of properties, relations, states of affairs, situations, and worlds in true and philosophically interesting ways. They resolve 15 of the 19 choice points defined in Barwise (1989) (see Notes 22, 27, 31, 32, 35, 36, 39, 43, and 45). Moreover, important axioms and principles stipulated by situation theorists are derived (see Notes (...) 33, 37, and 38). This is convincing evidence that the foregoing constitutes a theory of situations. Note that worlds are just a special kind of situation, and that the basic theorems of world theory, which were derived in previous work, can still be derived in this situation-theoretic setting. So there seems to be no fundamental incompatibility between situations and worlds — they may peacably coexist in the foundations of metaphysics. The theory may therefore reconcile two research programs that appeared to be heading off in different directions. And we must remind the reader that the general metaphysical principles underlying our theory were not designed with the application to situation theory in mind. This suggests that the general theory and the underlying distinction have explanatory power, for they seem to relate and systematize apparently unrelated phenomena. (shrink)

The formulation of propositional modal logic is revised by interposing a domain of structured propositions between the modal language and the models. Interpretations of the language (i.e., ways of mapping the language into the domain of propositions) are distinguished from models of the domain of propositions (i.e., ways of assigning truth values to propositions at each world), and this contrasts with the traditional formulation. Truth and logical consequence are defined, in the first instance, as properties of, and relations among, propositions. (...) -/- These definitions have certain interesting consequences. One is that they resolve a question that cannot be answered by the traditional analysis, in which Kripke models directly interpret modal language. The question is, is the reason a modal sentence has a different truth value at other possible worlds due to the fact that the sentence has a different meaning at that world or due to a change in the world? The philosophical conception elaborates the second answer. Another interesting consequence is that modal language, properly speaking, is not intensional, at least according to the classic tests for, and definitions of, intensionality. (shrink)

Mathematical pluralism can take one of three forms: (1) every consistent mathematical theory consists of truths about its own domain of individuals and relations; (2) every mathematical theory, consistent or inconsistent, consists of truths about its own (possibly uninteresting) domain of individuals and relations; and (3) the principal philosophies of mathematics are each based upon an insight or truth about the nature of mathematics that can be validated. (1) includes the multiverse approach to set theory. (2) helps us to understand (...) the significance of the distinguished non‐logical individual and relation terms of even inconsistent theories. (3) is a metaphilosophical form of mathematical pluralism and hasn't been discussed in the literature. In what follows, I show how the analysis of theoretical mathematics in object theory exhibits all three forms of mathematical pluralism. (shrink)

The appeal to possible worlds in the semantics of modal logic and the philosophical defense of possible worlds as an essential element of ontology have led philosophers and logicians to introduce other kinds of `worlds' in order to study various philosophical and logical phenomena. The literature contains discussions of `non-normal worlds', `non-classical worlds', `non-standard worlds', and `impossible worlds'. These atypical worlds have been used in the following ways: (1) to interpret unusual modal logics, (2) to distinguish logically equivalent propositions, (3) (...) to solve the problems associated with propositional attitude contexts, intentional contexts, and counterfactuals with impossible antecedents, and (4) to interpret systems of relevant and paraconsistent logic. However, those who have attempted to develop a genuine metaphysical theory of such atypical worlds tend to move too quickly from philosophical characterizations to formal semantics. (shrink)

The focus of this chapter is the rise of investigations in philosophical aesthetics in the mid-1950s and continuing through to the mid-1960s. This salient issue had to do with the foundations of philosophical aesthetics in the context of the Marxist-Leninist worldview. That this became an issue was due in large part to the appearance, in 1956, of the first Russian translation of Marx’s Economic and Philosophical Manuscripts of 1844. Marx’s emphasis in these writings on the self-constituting, transformative potential of labor (...) suggested possibilities for an aesthetic that did not sit comfortably with the dogmatic principles of dialectical and historical materialism. In effect, the foundational question for a Soviet aesthetics went to the heart of Marxism-Leninism: could young Marx’s anthropocentrism be reconciled with the established Soviet doctrine beholden to, on the one hand, Engels’ metaphysics of “matter-in-motion” and, on the other hand, Lenin’s copy theory of knowledge? Among the aestheticians, the issue surfaced in a debate about the nature of beauty: is beauty relative to man or is it an objectively cognizable material property? To the degree that the parties to this debate addressed the underlying issue, they tended to remain ambivalent toward the result that neither side—those favoring creative expression versus the defenders of objective beauty—simply conceded nor rejected the views of the other. As I argue, a systematic philosophical aesthetics within the scope of Soviet philosophy never saw the light of day. By the mid-1960s, research was ramifying into a variety of adjacent considerations, for example, value theory, theories of culture and cultural artifacts, the history of aesthetic categories, the social and pedagogical functions of art, art and morality in relation to the “socialist way of life,” art in the era of the “scientific-technological revolution,” and so on—of which only some recalled the spirit, rarely the letter, of the initial “aesthetics” discussion. (shrink)

The author describes an interpreted modal language and produces some clear examples of logical and analytic truths that are not necessary. These examples: (a) are far simpler than the ones cited in the literature, (b) show that a popular conception of logical truth in modal languages is incorrect, and (c) show that there are contingent truths knowable ``a priori'' that do not depend on fixing the reference of a term.

Late in life, Józef Maria Bocheński set out to examine the age-old preoccupation with the question “how to live as well and as long as possible?” A traditional answer has been, “live wisely.” In his Handbook of Worldly Wisdom (2020), Bocheński analyzes this answer arguing that, conceptually, living wisely is distinct from obeying moral commandments, prescribing ethical rules, and recognizing authority (e.g., piety, free submission to divine authority). He claims that ethics consists solely in what moral philosophers label as “metaethics” (...) — a theoretical discipline interested in the conceptual status of moral discourse qua discourse. However, Bocheński remains silent about a substantive ethics — that is, how a life led one way or another subscribes to some guiding value-set. As regards wisdom, therefore, the consequence of this position is that Bocheński’s account is ethically neutral. I argue that such a position entails a tension and dichotomy between, on the one hand, prudential rationality concerned with getting on in the moment — that is, wisdom — and, on the other hand, unconditional moral commandments. For his part, Bocheński does not recommend living according to wisdom’s precepts as he analyses them; his own path through life, he tells us, has been a commitment to Christian values, piety abetted by observance of moral commandments, a perspective that, I submit, is not ethically neutral: on the contrary, it entails thick, substantive value-choice. Bocheński’s avowal suggests a second dichotomy and tension, that between the worldly conduct of life, with moderate acknowledgment of moral principles, and an extra-worldly perspective (the “folly of the Cross”). Bocheński does not attempt to resolve either dichotomy, to seek a possible point of their convergence and integration, for instance by inquiring into moral psychology (i.e., the construction of self, the nature of the will, etc.). I believe that this set of views stems from conclusions Bocheński reached in advance of producing the Handbook that bear on, first, how philosophy should be conducted — as logical analysis hostile to grandiloquent speculation and synthesis (“worldviews”); and second, his utter dismissal as nefarious of anthropocentric views. Indeed, Bocheński asserts, without a blush, that almost everything “we” have come to believe about ourselves is superstition writ large. I trace what I consider to be difficulties with Bocheński’s account of wisdom — in relation to his take on morality, (meta-)ethics, and piety — to these idiosyncratic views. (shrink)