How can the Father, the Son, and the Holy Spirit be distinct and yet identical? Prompted by the doctrine of the divine Trinity, this question sparked centuries of lively debate. In the current context of renewed interest in Trinitarian theology, Russell L. Friedman provides the first survey of the scholastic discussion of the Trinity in the 100-year period stretching from Thomas Aquinas' earliest works to William Ockham's death. Tracing two central issues - the attempt to explain how the (...) three persons are distinct from each other but identical as God, and the application to the Trinity of a 'psychological model', on which the Son is a mental word or concept, and the Holy Spirit is love - this volume offers a broad overview of Trinitarian thought in the thirteenth and fourteenth centuries, along with focused studies of the Trinitarian ideas of many of the period's most important theologians. (shrink)

Is prime matter the same as its potency, its readiness to take on the entire gamut of corporeal substantial forms? This question, arising from a passage in Averroes, lies at the core of later medieval hylomorphism and was hotly debated. The present article looks at three answers to the question by figures from the first half of the fourteenth century: Gerald Ot who takes a Scotistic approach to the issue, John of Jandun and Peter Auriol taking an Averroan tack, and (...) John Buridan with a nominalistic outlook. The discussion reveals a diversity of positions on the nature of potency and its relation to actuality, and in the case of Buridan an unusual view at the heart of his matter theory: the direct inherence of accidental forms in prime matter. (shrink)

This book presents an overview of the later medieval trinitarian theology of the rival Franciscan and Dominican intellectual traditions, and includes detailed studies of thinkers such as Thomas Aquinas, Henry of Ghent, John Duns Scotus, ...

This chapter contains sections titled: The category of relation Philosophical psychology Conceptualism, individuation, and intellectualism.

Since 1991 the Franciscan Francis of Marchia, master of theology at the University of Paris (fl. 1320), has begun receiving his due attention as an exciting and innovative thinker. This volume examines his doctrines in cosmology, physics, metaphysics, ethics, and politics.

Introduction STEN EBBESEN In the second half of the 20th century scholarly research uncovered a wealth of interesting medieval discussions about issues ...

Nella teologia trinitaria di Enrico di Gand, e in particolare nell'uso della nozione di verbum mentis, confluiscono ad avviso dell'A. tre diverse tradizioni che vengono rielaborate in un sistema coerente dal maestro agostiniano. La prima, quella cui aderiscono Tommaso e Bonaventura, insiste sul fatto che le persone sono distinte tra loro proprie per mezzo di relazioni opposte. La seconda, rappresentata da Riccardo di san Vittore, che attribuisce la differenza tra le persone al loro diverso modo di emanazione e di origine. (...) La terza che riprende il modello psicologico della trinità di Agostino ed in particolare l'immagine del Figlio come Verbum. Enrico incorpora i diversi elementi di queste tradizioni in modo originale e sostiene che il Figlio è distinto dalle altre due persone in base al diverso modo di emanazione , ma che è diverso dal Padre e dallo Spirito Santo anche perché è Verbum. L'A. sottolinea la notevole influenza esercitata da Bonaventura sul pensiero trinitario di Enrico, anche dal punto di vista della terminologia utilizzata e ipotizza che ciò sia dovuto al ruolo di «propaganda» delle dottrine bonaventuriane svolto da Ruggero Marston e Matteo d'Aquasparta. (shrink)

This article presents a critical edition from the six surviving witnesses of Landulph Caracciolo’s , Scriptum in I Sententiarum, d. 23, a text that has never appeared in print before. A short introduction begins to set Landulph’s treatment of intentions and intentionality in this text into its historical, philosophical, and theological context, in particular linking it to the positions of John Duns Scotus and Peter Auriol.

The title of this Festschrift to Stephen Brown points to the understanding of medieval philosophy and theology in the longue durée of their traditions and discourses.

The Analysis of Matter is perhaps best known for marking Russell's rejection of phenomenalism and his development of a variety of Lockean representationalism–-Russell's causal theory of perception. This occupies Part 2 of the work. Part 1, which is certainly less well known, contains many observations on twentieth-century physics. Unfortunately, Russell's discussion of relativity and the foundations of physical geometry is carried out in apparent ignorance of Reichenbach's and Carnap's investigations in the same period. The issue of conventionalism (...) in its then contemporary form is simply not discussed. The only writers of the period who appear to have had any influence on Russell's conception of the philosophical issues raised by relativity were Whitehead and Eddington. Even the work of A. A. Robb fails to receive any extended discussion;1 although Robb's causal theory is certainly relevant to many of Russell's concerns, especially those voiced in Part 3, regarding the construction of points and the topology of space-time. In the case of quantum mechanics, the idiosyncrasy of Russell's selection of topics is more understandable, since the Heisenberg and Schrödinger theories were only just discovered. Nevertheless, it seems bizarre to a contemporary reader that Russell should have given such emphasis2 to G. N. Lewis's suggestion that an atom emits light only when there is another atom to receive it–-a suggestion reminiscent of Leibniz, and one to which Russell frequently returns. In short, the philosophical problems of modern physics with which Russell deals seem remote from the perspective of post-positivist philosophy of physics. (shrink)

This article offers the first critical edition of the most important version of Francis of Marchia's famous question 1 of his commentary on Book IV of the Sentences, in which the Franciscan theologian puts forth his virtus derelicta theory of projectile motion. The introduction attempts to place Marchia's theory in its proper context. The theory might seem to us an obvious improvement on Aristotle, but rather than an immediate and complete break with tradition that all scholastics quickly adopted, Marchia's virtus (...) derelicta was more a stage in a gradual process that had begun many decades before and did not find universal acceptance among his first successors. Moreover, Marchia himself did not take the theory to what might seem the obvious conclusion that Jean Buridan would draw, because Marchia employed the virtus derelicta to explain more phenomena than just projectile motion. (shrink)

Both Morain and Largent (2023) and Garland, Morain, and Sugarman (2023) recognize the ethical challenges inherent in clinician participation in embedded research. Focusing on the question of integr...

Russell’s way out of his paradox via the impredicative theory of types has roughly the same logical power as Zermelo set theory - which supplanted it as a far more flexible and workable axiomatic foundation for mathematics. We discuss some new formalisms that are conceptually close to Russell, yet simpler, and have the same logical power as higher set theory - as represented by the far more powerful Zermelo-Frankel set theory and beyond. END.

Rudolf Carnap is increasingly regarded as one of the most important philosophers of the twentieth century. He was one of the leading figures of the logical empiricist movement associated with the Vienna Circle and a central figure in the analytic tradition more generally. He made major contributions to philosophy of science and philosophy of logic, and, perhaps most importantly, to our understanding of the nature of philosophy as a discipline. In this volume a team of contributors explores the major themes (...) of his philosophy and discusses his relationship with the Vienna Circle and with philosophers such as Frege, Husserl, Russell, and Quine. New readers will find this the most convenient and accessible guide to Carnap currently available. Advanced students and specialists will find a conspectus of recent developments in the interpretation of Carnap. (shrink)

Alexander Moritzi is one of the most obscure figures in the early history of evolutionary thought. Best known for authoring a flora of Switzerland, Moritzi also published Réflexions sur l’espèce en histoire naturelle, a remarkable book about evolution with an overtly materialist viewpoint. In this work, Moritzi argues that the generally accepted line between species and varieties is artificial, that varieties can over time give rise to new species, and that deep time and turnover of species in the fossil record (...) clearly support an evolutionary interpretation of biological diversity. Moritzi was also a gradualist and viewed relationships between taxa as best represented by a ramifying tree. Although Réflexions was the first full book to be written on the topic of evolution following Lamarck’s Philosophie zoologique, Moritzi’s evolutionist contribution was stillborn, read by almost no one in his lifetime and ultimately absent from the many historiographies of evolutionary thought. This is unfortunate since many of the arguments Moritzi marshaled on behalf of an evolutionary explanation of life can be found in subsequent transmutationist writings by Frédéric Gérard, Robert Chambers, Henri Lecoq, Baden Powell, Charles Naudin, Herbert Spencer, Alfred Russel Wallace, and Charles Darwin—none of whom is likely to have ever known of the existence of Réflexions. Finally, Moritzi’s arguments, along with those found in Darwin’s private essay on evolution of the same year, provide an excellent window into the state of evolutionary thought and debate over the nature of species at the beginning of the 1840s. (shrink)

Russell’s way out of his paradox via the impre-dicative theory of types has roughly the same logical power as Zermelo set theory - which supplanted it as a far more flexible and workable axiomatic foundation for mathematics. We discuss some new formalisms that are conceptually close to Russell, yet simpler, and have the same logical power as higher set theory - as represented by the far more powerful Zermelo-Frankel set theory and beyond. END.

We present a way out of Russell’s paradox for sets in the form of a direct weakening of the usual inconsistent full comprehension axiom scheme, which, with no additional axioms, interprets ZFC. In fact, the resulting axiomatic theory 1) is a subsystem of ZFC + “there exists arbitrarily large subtle cardinals”, and 2) is mutually interpretable with ZFC + the scheme of subtlety.

A recursive enumerator for a function h is an algorithm f which enumerates for an input x finitely many elements including h(x), f is a k(n)-enumerator if for every input x of length n, h(x) is among the first k(n) elements enumerated by f. If there is a k(n)-enumerator for h then h is called k(n)-enumerable. We also consider enumerators which are only A-recursive for some oracle A. We determine exactly how hard it is to enumerate the Kolmogorov function, which (...) assigns to each string x its Kolmogorov complexity: • For every underlying universal machine U, there is a constant a such that C is k(n)-enumerable only if k(n) ≥ n/a for almost all n. • For any given constant k, the Kolmogorov function is k-enumerable relative to an oracle A if and only if A is at least as hard as the halting problem. • There exists an r.e., Turing-incomplete set A such for every non-decreasing and unbounded recursive function k, the Kolmogorov function is k(n)-enumerable relative to A. The last result is obtained by using a relativizable construction for a nonrecursive set A relative to which the prefix-free Kolmogorov complexity differs only by a constant from the unrelativized prefix-free Kolmogorov complexity. Although every 2-enumerator for C is Turing hard for K, we show that reductions must depend on the specific choice of the 2-enumerator and there is no bound on the quantity of their queries. We show our negative results even for strong 2-enumerators as an oracle where the querying machine for any x gets directly an explicit list of all hypotheses of the enumerator for this input. The limitations are very general and we show them for any recursively bounded function g: • For every Turing reduction M and every non-recursive set B, there is a strong 2-enumerator f for g such that M does not Turing reduce B to f. • For every non-recursive set B, there is a strong 2-enumerator f for g such that B is not wtt-reducible to f. Furthermore, we deal with the resource-bounded case and give characterizations for the class ${\rm S}_{2}^{{\rm P}}$ introduced by Canetti and independently Russell and Sundaram and the classes PSPACE, EXP. • ${\rm S}_{2}^{{\rm P}}$ is the class of all sets A for which there is a polynomially bounded function g such that there is a polynomial time tt-reduction which reduces A to every strong 2-enumerator for g. • PSPACE is the class of all sets A for which there is a polynomially bounded function g such that there is a polynomial time Turing reduction which reduces A to every strong 2-enumerator for g. Interestingly, g can be taken to be the Kolmogorov function for the conditional space bounded Kolmogorov complexity. • EXP is the class of all sets A for which there is a polynomially bounded function g and a machine M which witnesses A ∈ PSPACEf for all strong 2-enumerators f for g. Finally, we show that any strong O(log n)-enumerator for the conditional space bounded Kolmogorov function must be PSPACE-hard if P = NP. (shrink)

Peter Abelard (1079–1142 ce) was the most wide‐ranging philosopher of the twelfth century. He quickly established himself as a leading teacher of logic in and near Paris shortly after 1100. After his affair with Heloise, and his subsequent castration, Abelard became a monk, but he returned to teaching in the Paris schools until 1140, when his work was condemned by a Church Council at Sens. His logical writings were based around discussion of the “Old Logic”: Porphyry's Isagoge, aristotle'S Categories and (...) On Interpretation and boethius'S textbook on topical inference. They comprise a freestanding Dialectica (“Logic”; probably c.1116), a set of commentaries (known as the Logica [Ingredientibus], c. 1119) and a later (c. 1125) commentary on the Isagoge (Logica Nostrorum Petititoni Sociorum or Glossulae). In a work Abelard called his Theologia, issued in three main versions (between 1120 and c.1134), he attempted a logical analysis of trinitarian relations and explored the philosophical problems surrounding God's claims to omnipotence and omniscience. The Collationes (“Debates,” also known as “Dialogue between a Christian, a Philosopher and a Jew”; probably c.1130) present a rational investigation into the nature of the highest good, in which the Christian and the Philosopher (who seems to be modeled on a philosopher of pagan antiquity) are remarkably in agreement. The unfinished Scito teipsum (“Know thyself,” also known as the “Ethics”; c.1138) analyses moral action. (shrink)

This paper concerns the debate on the nature of Rudolf Carnap'sproject in his 1928 book The Logical Structure of the Worldor Aufbau. Michael Friedman and Alan Richardson haveinitiated much of this debate. They claim that the Aufbauis best understood as a work that is firmly grounded inneo-Kantian philosophy. They have made these claims in oppositionto Quine and Goodman's ``received view'' of the Aufbau. Thereceived view sees the Aufbau as an attempt to carry out indetail Russell's external world program. (...) I argue that both sidesof this debate have made errors in their interpretation ofRussell. These errors have led these interpreters to misunderstandthe connection between Russell's project and Carnap's project.Russell in fact exerted a crucial influence on Carnap in the1920s. This influence is complicated, however, due to the factthat Russell and Carnap disagreed on many philosophical issues. Iconclude that interpretations of the Aufbau that ignoreRussell's influence are incomplete. (shrink)

M. H. A. Newman (1928) criticized Russell's structuralist philosophy of science. Demopoulos and Friedman have discussed Newman's critique, showing its relevance to the structuralist positions held by Schlick and Carnap, and to Putnam's argument against "metaphysical realism". I discuss Richard Braithwaite's (1940) appeal to Newman in a critique of Arthur Eddington. Braithwaite believed Newman had shown that "structure depends upon content". Eddington, in his reply, misunderstood the generality of Newman's argument.

In lieu of an abstract, here is a brief excerpt of the content:Black Deconstruction: Russell Atkins and the Reconstruction of African-American CriticismAldon Lynn Nielsen (bio)“What does that signify?” “It don’t signify nothin’ Mr. Warner.”—Russell Atkins, MaleficiumThere are, everywhere unheard (as one might see deep in an electron microscope) rigidities violently breaking—Russell Atkins, WhicheverCritical debates about the applicability of recent literary theories to the reading of African-American writing have often been marked by curious lacunae. Despite the rapid proliferation (...) of critical texts addressing themselves to black writing, it remains the case that many critics come to black writing with methodologies and agendas already in hand, while few critics have taken upon themselves the task of rereading the critical history of African-American work in theory. This has often resulted in a sort of critical shortsightedness, with the field of black literary theory presented as a foreshortened, if now more level, playing field. While some have engaged in arguments about the question of whether or not African-American writing should be engaged by poststructuralist theorists (a question that seems to begin with the assumption that poststructuralism is a particularly white mode of mythology), the fact is that a form of deconstruction had been theorized by an African-American poet long before deconstruction had entered the American academy. That this fact is largely unknown among contemporary critics is the result of a continuing practice of not reading the theoretical work of black poets who have published outside the established circuit of the academic press. With the prominent exceptions of poets like Amiri Baraka, June Jordan, Larry Neal, and Haki Madhabuti, the critical writings of recent African-American poets have seldom been collected and circulated in any very effective way. Characteristically, Neal’s essays were gathered into a book posthumously, and Madhabuti’s have been published and distributed primarily through his own publishing house. Even Baraka’s collections have been allowed to pass out of print in most instances, only the books on music remaining readily available throughout his career. This may change for black poets who write in more mainstream modes in the near future. Now that Rita Dove has served a term as Poet Laureate of the United States and Derek Walcott has won the Nobel Prize, we might expect a modest increase in interest by publishers and readers in critical works by poets whose forms are less troubling than their content. And black poets who attain academic credentials and write scholarly/critical essays, such as Nathaniel Mackey and Harryette Mullen, may succeed in getting their works published by the university presses. However, surveys of shelves in bookstores and [End Page 86] libraries will confirm that there has been little concern among even university and small presses to collect and preserve the critical legacy of black experimentalists in the way that the essays of Charles Olson, Ed Dorn, or Robert Creeley have been maintained before a public.Russell Atkins has been one of the most prolific and demanding of black poets writing criticism and theory in the last four decades, but like Percy Johnston, central figure of the Dasein group of poets centered at Howard University in the 1950s, he has had to publish most of this work through his own magazine and workshop press, and there has never been a published collection of his critical work. The special Russell Atkins number of the Free Lance, a journal with which Atkins was associated for two decades, included a section surveying his work in critical prose, but little of that work has found its way into the broader critical discourse of literary scholars (it has fared a little better with musicologists), and Atkins’s prose is infrequently cited. As eccentric as Atkins’s prose can sometimes be, these works are important early signs of a break with the “rigidities” of traditional humanist discourse among African-American writers. Atkins’s statements on music, literature, politics, and education parallel the works by Baraka leading into and out of the Black Arts Movement, but Atkins, as he does in his verse, travels an independent and often disturbing path.Speaking of Anthony Braxton’s experimentalism, Ronald Radano observes that it “emerged from the changing landscape of urban American life, from... (shrink)

In the years spanning the first half of the 20th century Bertrand Russell wavered between two incompatible accounts of physical reality. On one account, physical objects were taken to be logical constructs of phenomenal entities, the immediate data of sense experience. Such a view roughly fits the familiar characterization of being a combination of “Hume plus mathematical logic.” This type of phenomenalism, in the empiricist tradition, contrasted starkly with a variant of scientific realism, including a realistic account of causal (...) connections as relations between universals, that Russell developed between 1912 and 1927, and which was derived from Kant’s distinction between a noumenal and a phenomenal world. My concern in this paper is with the viability of the unique form of scientific realism Russell developed, the role of universals and causal explanation in it, and criticisms that have been directed at it. I will argue that an early refutation of Russell’s realism by the mathematician M. Newman and a recent revival of that refutation by W. Demopoulos and M. Friedman ignore the critical role universals play in Russell’s scientific realism and hence fail to refute his view. I will also briefly consider a recent “anti-realist” argument that repeats Newman’s mistake: interpreting predicates in terms of extensions and not as referring to universal properties and relations. (shrink)

According to Michael Friedman, Ernst Cassirer’s “outstanding contribution [to Neo-Kantianism] was to articulate, for the first time, a clear and coherent conception of formal logic within the context of the Marburg School” (Friedman 2000, p. 30). In his paper “Kant und die moderne Mathematik” (1907), Cassirer argued not only that the new relational logic of Frege1 and Russell was a major breakthrough with profound philosophical implications, but also that the logicist thesis itself was a “fact” of modern (...) mathematics. Cassirer summarizes his evaluation of Russell’s work: Here logic and mathematics have been fused into a true, henceforth indissoluble unity; and from this inner connection there arises for each... (shrink)

The theme of this paper was inspired by studies related to the subject of my doctoral dissertation,1 and, more specifically, by the work of A. Richardson and M. Friedman on the same subject presented in their two recently published books.2 The material in these books which addresses the connection between Russell and Carnap’s Der logische Aufbau der Welt reveals the same basic perspective in both authors and, in fact, represents the first in depth enquiry of this connection, despite (...) certain fairly essential limitations which I hope to reveal in this paper. The line of investigation I intend to take in the following may therefore be outlined as such; to examine, albeit briefly, the extent to which Richardson’s and Friedman’s perspective can offer us a correct historical and philosophical approach to the influence of Russell’s philosophy on the Aufbau, and, by confirming the existence of the limitations alluded to, to determine whether this perspective may be adequately reformulated independently of their existence, and to determine how, in general terms, it may in fact be reformulated. Thus, although my analyses and commentaries do not fall within a strictly historiographical framework, as is the case in the work developed by Richardson and Friedman, it is nevertheless possible to achieve certain objectives characteristic of this framework which, eventually, may become the subject of a future historiography of the philosophy of Russell and his influence on the Aufbau.3 In order to achieve these objectives my main aim is neither negative nor destructive but essentially philosophical; I see myself together with the authors in question as partners in the investigation and resolution of problems arising from the presentation, discussion and testing of competitive theories, an example of what occurs in the scientific enquiry. In these circumstances, and from this point of view, I see myself as a philosopher who points to certain difficulties and problems in the theory put forward by these authors to explain the Aufbau, and, with particular reference to Russell’s philosophy, concludes by suggesting an alternative theory. (shrink)