When Ockham's logic arrives in Italy, some Dominican philosophers bring into question Ockham's ontological reductionist program. Among them, Franciscus de Prato and Stephanus de Reate pay a great attention to refute Ockham's claim that no universal exists in the extra-mental world. In order to reject Ockham's program, they start by reconsidering the notion of 'real', then the range of application of the rational and the real distinction. Generally, their strategy consists in re-addressing against Ockham some arguments extracted from Hervaeus Natalis's (...) works. Franciscus's and Stephanus's basic idea is that some universals are not acts of cognition, but extra-mental, predicable things. Such things are not separable from singulars, nonetheless they are not the same as those singulars. Consequently, it is not necessary to allow, as Ockham does, that if two things are not really identical, they are really different and hence really separable. According to them, it is possible to hold that two things are not really identical without holding that they are also really non-identical and hence really different. Basically, their reply relies on a different notion of the relation of identity. Identity is regarded as an intersection of classes of things, so that it is possible to say that two things are really identical without saying that they also are the same thing. Franciscus and Stephanus, however, do not seem to achieve completely their aim. (shrink)

Let (L; f) be a finite simple Ockham algebra and let (X;g) be its dual space. We first prove that every connected component of X is either a singleton or a generalised crown (i.e. an ordered set that is connected, has length 1, and all vertices of which have the same degree). The representation of a generalised crown by a square (0,1)-matrix in which all line sums are equal is used throughout, and a complete description of X, including the number (...) of connected components and the degree of the vertices, is given. We then examine the converse problem of when a generalised crown can be made into a connected component of (X; g). We also determine the number of non-isomorphic finite simple Ockham algebras that belong properly to a given subvariety P 2n,0. Finally, we show that the number of fixed points of (L; f) is 0,1, or 2 according to the nature of X. (shrink)

Contemporary analytic philosophers have always been among the most enthusiastic audiences for the volumes in the Cambridge Companion series. And of all the great philosophers of the Middle Ages, perhaps none has appealed more to their sensibilities than <span class='Hi'>William</span> Ockham. It is fitting, therefore, that after the publication of the Companion to Aquinas—the first volume in the series devoted to a medieval philosopher—there should appear a Companion to Ockham. The fifteen chapters comprising this volume survey the entire range of (...) Ockham’s thought and may conveniently be divided into four main parts. The first part (chaps. 2-7) deals with Ockham’s most enduring legacy: his contribution to issues falling within the domain of logic, philosophy of language, and metaphysics. The second part (chaps. 8-9) is devoted to issues in epistemology and philosophy of mind/cognition. The third part (chaps. 10-13) focuses on Ockham’s views in ethics, action theory, and political philosophy. And the fourth part (chaps. 14-15) considers aspects of his philosophical theology. In addition, there is also an historical chapter (chap. 1), placing Ockham’s life and works in their late-medieval intellectual context, and a brief editor’s introduction, including a very useful list of all Ockham’s writings, together with the best (sometimes, the only) Latin editions and English translations available. The volume is well organized and beautifully conceived. Some chapters are quite difficult, and in places contain material that is likely to be unfamiliar even to specialists in medieval philosophy. But the way in which they have been organized maximizes their usefulness and accessibility to specialists and non-specialists alike. The earlier parts of the volume lay the foundation for later ones, and the individual chapters within each of the four parts are arranged so as to build on and compliment one another. This is perhaps most evident in the five chapters comprising the first part.. (shrink)

This paper traces a rather peculiar debate between William Ockham, Walter Chatton, and Robert Holcot over whether it is possible for God to know more than he knows. Although the debate specifically addresses a theological question about divine knowledge, the central issue at stake in it is a purely philosophical question about the nature and ontological status of propositions. The theories of propositions that emerge from the discussion appear deeply puzzling, however. My aim in this paper is to show that (...) there is a way of making sense of these views (and, by implication, of much of what is puzzling about medieval theories of propositions). The key, I argue, lies in getting clear about the precise theoretical roles these thinkers assign to propositions in their accounts of propositional attitudes. (shrink)

It is well-known that Chatton is among the earliest and most vehement critics of Ockham’s theory of judgment, but scholars have overlooked the role Chatton’s criticisms play in shaping Ockham’s final account. In this paper, I demonstrate that Ockham’s most mature treatment of judgment not only contains revisions that resolve the problems Chatton identifies in his earlier theories, but also that these revisions ultimately bring his final account of the objects of judgment surprisingly close to Chatton’s own. Even so, I (...) argue that, at the end of the day, there remain significant differences between their respective analyses of the structure and intentionality of judicative states. (shrink)

In this paper I examine William Ockham’s theory of judgment and, in particular, his account of the nature and ontological status of its objects. Commentators, both past and present, habitually interpret Ockham as defending a kind of anti-realism about objects of judgment. My aim in this paper is two-fold. The first is to show that the traditional interpretation rests on a failure to appreciate the ways in which Ockham’s theory of judgment changes over the course of his career. The second, (...) and larger, aim is to show that careful attention to these changes in Ockham’s account (and to the motivations for them) sheds new light on broader developments in his philosophy of mind—specifically, on his views about the nature of concepts and on his account of the nature and structure of intentionality itself. (shrink)

In this paper I challenge recent externalist interpretations of Ockham’s theory of intuitive cognition. I begin by distinguishing two distinct theses that defenders of the externalist interpretation typically attribute to Ockham: a ‘direct reference thesis’, according to which intuitive cognitions are states that lack all internal, descriptive content; and a ‘causal thesis’, according to which intuitive states are wholly determined by causal connections they bear to singular objects. I then argue that neither can be plausibly credited to Ockham. In particular, (...) I claim that the causal thesis doesn’t square with Ockham’s account of supernaturally produced intuition and that the direct reference thesis sits uneasily with Ockham’s characterization of the intentional structure of intuitive states. (shrink)

William of Ockham's semantic theory was founded on the idea that thought takes place in a language not unlike the languages in which spoken and written communication occur. This mental language was held to have a number of features in common with everyday languages. For example, mental language has simple terms, not unlike words, out of which complex expressions can be constructed. As with words, each of these terms has some meaning, or signification; in fact Ockham held that the signification (...) of everyday words derives precisely from the signification of mental terms. Furthermore, the meaning of a mental expression depends directly on the meaning of its constituent terms, as is the case with expressions in more familiar languages. (shrink)

Ockham appeared to maintain that God necessarily knows all true propositions, including future contingent propositions, despite the fact that such propositions have determinate truth values. While some commentators believe that Ockham’s attempt to reconcile divine omniscience with the contingency of true future propositions amounts to little more than a simple-minded assertion of Ockham’s Christian faith, I argue that Ockham’s position is more sophisticated than this and rests on attributing to God a dual knowledge property: God not only knows every true (...) proposition, but knows its modal properties as well. Future contingent propositions are determinately true when actualized, not timelessly, and God’s knowledge of their truth values is knowledge of when the truth value of a proposition is actually determined. (shrink)

Against the background of changing assessments of Nominalism and its meanings before Ockham, this book examines the reception of Ockham's thought at Oxford and ...

This book presents novel formalizations of three of the most important medieval logical theories: supposition, consequence and obligations. In an additional fourth part, an in-depth analysis of the concept of formalization is presented - a crucial concept in the current logical panorama, which as such receives surprisingly little attention.Although formalizations of medieval logical theories have been proposed earlier in the literature, the formalizations presented here are all based on innovative vantage points: supposition theories as algorithmic hermeneutics, theories of consequence analyzed (...) with tools borrowed from model-theory and two-dimensional semantics, and obligations as logical games. For this reason, this is perhaps the first time that these medieval logical theories are made fully accessible to the modern philosopher and logician who wishes to obtain a better grasp of them, but who has always been held back by the lack of appropriate ‘translations' into modern terms.Moreover, the book offers a reflection on the very nature of logic, a reflection that is prompted by the comparisons between medieval and modern logic, their similarities and dissimilarities. It is thus a contribution not only to the history of logic, but also to the philosophy of logic, the philosophy of language and semantics.The analysis of medieval logic is also relevant for the modern philosopher and logician in that, being the unifying methodology used across all disciplines at that time, logic really provided unity to science. It thus presents a unified model of scientific investigation, where logic plays the aggregating role. (shrink)

This thesis is on the history and philosophy of logic and semantics. Logic can be described as the ‘science of reasoning’, as it deals primarily with correct patterns of reasoning. However, logic as a discipline has undergone dramatic changes in the last two centuries: while for ancient and medieval philosophers it belonged essentially to the realm of language studies, it has currently become a sub-branch of mathematics. This thesis attempts to establish a dialogue between the modern and the medieval traditions (...) in logic, by means of ‘translations’ of the medieval logical theories into the modern framework of symbolic logic, i.e. formalizations. One of its conclusions is that, when properly understood within their own framework, the interest of medieval logical theories for modern investigations go beyond mere historical interest, but that a thorough conceptual analysis of such theories must be undertaken in order to avoid conceptual misprojections. While such translations of medieval into modern logic have been attempted before, the approach presented here is innovative in that attention is paid to the similarities as well as to the dissimilarities between the two traditions, and to what can be learned from the medieval masters for modern investigations in logic and semantics. (shrink)

This is collection of Christian treatises written prior to the end of the sixteenth century.

In this paper, we introduce a variety bdO of Ockham algebras with balanced double pseudocomplementation, consisting of those algebras of type where is an Ockham algebra, is a double p -algebra, and the operations and are linked by the identities [ f ( x )]* = [ f ( x )] + = f 2 ( x ), f ( x *) = x ** and f ( x + ) = x ++ . We give a description of the (...) congruences on the algebras, and show that there are precisely nine non-isomorphic subdirectly irreducible members in the class of the algebras via the Priestley duality. We also describe all axioms in the variety bdO , and provide a characterization of all subvarieties of bdO determined by 12 none-equivalent axioms, identifying therein the biggest subvariety in which every principal congruence is complemented. (shrink)

Analytic philosophers specializing in medieval philosophy have tended to focus on those aspects of Catholic medieval thought that seem relevant to research programs already firmly established within the mainstream of contemporary academic philosophy. In this way they have tried to convince other philosophers that the Catholic medieval thinkers, despite their theological presuppositions, have something useful to contribute to current discussions. [1] The tendency in question has been especially pronounced in the case of William of Ockham because he is at his (...) best when doing ontology and philosophical semantics, two areas that have figured prominently in recent analytic philosophy and that seem safely removed from distinctively Catholic beliefs. (shrink)

The purpose of this essay is to take issue with two aspects of Marilyn Adams's monumental work William Ockham . Part I deals with Ockham's ontology, arguing (i) that Adams does not sufficiently appreciate the use Ockham makes of the prinicple of ontological parsimony in his attempt to refute the thesis that there are extramental universals or common natures and (ii) that she sets an implausibly high standard of success for Ockham's project of showing that the only singular entities are (...) substances and qualities. Part II argues that Adams fails to provide a convincing defense of Ockham's 'anti-secularist' answer to the question of how Christian thinkers should react to prima facie conflicts between the deliverances of faith and the deliverances of reason. (shrink)

Let me begin somewhat perversely by making clear what I do not intend to do in this paper. I do not propose to offer a general defense of Ockham's resolution of the metaphysical perplexities engendered by the dogma of the Incarnation. In fact, I have argued elsewhere that his account of the hypostatic union is seriously deficient. 1..

Born in England and educated at Oxford, Ockham was the preeminent Franciscan thinker of the mid-fourteenth century. Because of his role in the bitter dispute between the Franciscans and Pope John XXII over evangelical poverty, he was excommunicated in 1328. After that he abandoned philosophy and theology proper, producing instead a series of political tracts on the ecclesiastical and secular power of the papacy.

Distributive bounded lattices with a dual homomorphism as unary operation, called Ockham algebras, were firstly studied by Berman (1977). The varieties of Boolean algebras, De Morgan algebras, Kleene algebras and Stone algebras are some of the well known subvarieties of Ockham algebra. In this paper, new results about the congruence lattice of Ockham algebras are given. From these results and Urquhart's representation theorem for Ockham algebras a complete characterization of the subdirectly irreducible Ockham algebras is obtained. These results are particularized (...) for a large number of subvarieties of Ockham algebras. For these subvarieties a full description of their subdirectly irreducible algebras is given as well. (shrink)

In this note, we give a representation of distributive Ockham algebras via natural hom-functors. In order to do this, we describe two different structures (one algebraic, and the other order-topological) on the set of subsets of the natural numbers. The topological duality previously obtained by A. Urquhart is used throughout.

This work shows the brilliance and the actuality of Ockham's philosophy by giving an analytic introduction to his theory of language, his ontology, and his ...

: This article focuses on one aspect of the late mediaeval debate over divine power, as it was discussed by Oxford philosophers Walter Chatton (d. 1343) and William Ockham (d. 1347). Chatton and Ockham would have agreed, for example, that God is ultimately responsible for the existence of the works of Pablo Picasso, but they would not agree over wheher it violates God's omnipotence to say that he cannot make something that Picasso made, for example, the painting Guernica, without using (...) Picasso himself as an intermediate cause. The context of their dispute was a larger debate regarding the ontological status of relations. This article (1) explains how these two issues, omnipotence and relations, became so interestingly tangled together, (2) tries to see which of the two men mentioned above got the better of their exchange, and finally (3) draws out some important consequences for fourteenth-century discussions of causality, occasionalism, and omnipotence. (shrink)

6 Abstract. I propose that empirical procedures, like computational procedures, are justified in 7 terms of truth-finding efficiency. I contrast the idea with more standard philosophies of science 8 and illustrate it by deriving Ockham’s razor from the aim of minimizing dramatic changes of 9 opinion en route to the truth.

Saint Francis's desire to follow the life of Jesus made him go to great lengths to dissociate himself from power, property and legal rights of any kind. The witness to Christian humility that his small group gave was so attractive to his contemporaries that soon his fellowship became a large organisation entrusted by the Church with a preaching mission throughout Europe and beyond. By 1300 there were Franciscans in Beijing.

My talk tonight comes under the heading of history of theology. It may take you away somewhat from the study of early Christianity, but perhaps it can come under the head of the history of the history of early Christianity—my topic is a dispute involving Marsilius and Ockham over Peter’s role in the early Church and the use Ockham made of early Christian documents, or what he thought were such.

A passage on the origin of property in Grotius, De iure praedae , pp. 226-230 [Note 1] seems to contain echoes of the controversy between pope John XXII and William of Ockham on Franciscan poverty. Grotius's note (b) on p. 227 refers to the decretals..

The best way of becoming acquainted with William of Ockham and his Dialogue would be to read A.S. McGrade's "Introduction", "Principal Dates in Ockham's Life", and "Suggestions for Further Reading" in..

Remember that for Ockham there is nothing in the universe that is in any way universal except a concept or word: there are no real natures shared by many things. However, things do resemble one another, some things more closely than others. So the various degrees of resemblance give a foundation in reality for our conceptual structures, such as Porphyry's tree. Now resemblance (or similitude or likeness) is a relation. If such relations are realities, then we can say that there (...) are realities out there that correspond to our conceptual structures. But it won't surprise you to hear that Ockham denies that relations are realities out there in the world: or more exactly, he denies that relations are out there as realities additional to the things that are related. He wants to say that if Socrates is white and Plato is white then they are similar in respect of their whiteness, but their similarity is not something additional to Socrates and Plato and Socrates' whiteness and Plato's whiteness. Nothing is out there except absolute things. (shrink)

Philosophiques 32 (2005), 435-447. [An English version is available here.].

That it is: According to the Commentator, Met. 7 com. 11 ([Iuntina 8 fol. 76r]): The definition is the same as the substance of the thing. Hence it is in some way outside the soul, and consequently all its parts are in some way outside the soul. But the definition is composed of universals. Hence [the universal is outside the soul].

In his admirably clear, beautifully argued study, Claude Panaccio has provided an able defense of Ockham’s position in response to an argument I presented against Ockham in a discussion with Peter King eight years ago at a meeting in Pittsburgh.1 But after eight years, and even after Claude’s book, I still stand by that argument. So, in these comments I will attempt to explain why I think Ockham may still not be off the hook.

It is well known that Francis of Marchia and William of Ockham joined Michael of Cesena's rebellion against the pope, together escaping from Avignon and signing documents supporting Cesena's defence of Franciscan poverty. The relationship between the works of the two thinkers, on the other hand, is the subject of ongoing investigation. After discussing Francis' rejection in his Commentary on the Sentences of Ockham's theory of quantity, this paper shows how Francis' Improbatio became a source for Ockham's Opus Nonaginta Dierum. (...) Building on Offler's ground-breaking critical edition of the latter work, it is argued that Ockham made extensive use of Francis' Improbatio, even though on several points he felt it necessary to reformulate the arguments of his confrère or even to substantially modify his positions. The two Franciscan theologians differed deeply both in their basic philosophical commitments and in their methodological attitude. These differences emerged even when they were—so to speak—fighting on the same front. (shrink)

CHAPTER ONE Simple cognition Ockham's epistemology is founded upon the primacy of individual cognition. As coming first in the order of knowing, ...

One of Ockham's fundamental tenets about the human intellect is that its acts constitute a mental language. Although this language of thought shares some of the features of conventional language, thought is commonly considered as prior to conventional language. This paper tries to show that this consensus is seriously challenged in Ockham's early writings. I shall argue that, in claiming the priority of conventional language over mental language, Ockham established a novel explanation of the systematicity of thought—an explanation which anticipates (...) the idea that thought becomes systematic through the acquisition of conventional language. (shrink)

ence of language that we call “logic” brings forth for the followers of truth, while reason and experience clearly confirm and prove [it].2 Hence Aristotle, the main originator of this science, calls [it] now an introductory method, now a way of knowing, now a science common to all [things] and the way to truth. By these [phrases] he indicates that the entryway to wis-.

In this elegantly written book, Russell Friedman offers a fascinating account of Trinitarian theology in the period 1250-1350. Chapter 1 compares Aquinas's and Bonaventure's explanation of the identity and distinction of the three divine Persons. For Aquinas, the properties constitutive of the divine Persons are strictly relational properties, grounded in relations of opposition in the order of origin. Bonaventure accepts the role of relational properties, but he emphasizes the distinct way that each Person emanates: the Father is unemanated, the Son (...) emanates as generated by the Father ("by way of nature"), and the Holy Spirit emanates as freely spirated by the Father and the Son ("by way of will"). As Friedman .. (shrink)

The mediaeval logic of Aristotelian privation, represented by Ockham's expositionof All A is non-P as All S is of a type T that is naturally P and no S is P, iscritically evaluated as an account of privative negation. It is argued that there aretwo senses of privative negation: (1) an intensifier (as in subhuman), the dualof Neoplatonic hypernegation (superhuman), which is studied in linguistics asan operator on scalar adjectives, and (2) a (often lexicalized) Boolean complementrelative to the extension of (...) a privative negation in sense (1) (e.g., Brute). Thissecond sense, which is the privative negation discussed in modern linguistics, isshown to be Aristotle's. It is argued that Ockham's exposition fails to capture muchof the logic of Aristotelian privation due to limitations in the expressive power of thesyllogistic. (shrink)

Ockham’s razor is the principle that, all other things being equal, scientists ought to prefer simpler theories. In recent years, philosophers have argued that simpler theories make better predictions, possess theoretical virtues like explanatory power, and have other pragmatic virtues like computational tractability. However, such arguments fail to explain how and why a preference for simplicity can help one find true theories in scientific inquiry, unless one already assumes that the truth is simple. One new solution to that problem is (...) the Ockham efficiency theorem (Kelly 2002, 2004, 2007a-d, Kelly and Glymour 2004), which states that scientists who heed Ockham’s razor retract their opinions less often and sooner than do their non-Ockham competitors. The theorem neglects, however, to consider competitors following random (“mixed”) strategies and in many applications random strategies are known to achieve better worst-case loss than deterministic strategies. In this paper, we describe two ways to extend the result to a very general class of random, empirical strategies. The first extension concerns expected retractions, retraction times, and errors and the second extension concerns retractions in chance, times of retractions in chance, and chances of errors. (shrink)

According to a widespread view in medieval scholarship, theories of supposition are the medieval counterparts of theories of reference, and are thus essentially extensional theories. I propose an alternative interpretation: theories of supposition are theories of properties of terms, but whose aim is to allow for the interpretation of sentences. This holds especially of Ockham’s supposition theory, which is the main object of analysis in this paper. In particular, I argue for my intensional interpretation of his theory on the basis (...) of two key-phrases in his Summa Logicae: ‘denotatur’ and ‘propositio est distinguenda’. Finally, I offer a reconstruction of his theory as a set of instructions to be carried out in order to generate the possible readings of (certain) sentences. (shrink)

I propose to examine the issue of whether the ancient tradition in logic continued to be developed in the later medieval period from the vantage point of the relations between two specific groups of theories, namely the medieval theories of supposition and the (originally) ancient theories of fallacies. More specifically, I examine whether supposition theories absorbed and replaced theories of fallacies, or whether the latter continued to exist, with respect to one particular author, William of Ockham. I compare different parts (...) of Ockham's Summa Logicae, namely III-4 (on fallacies), and the final chapters of part I and first chapters of part II (on supposition). I conclude that there is overlap of conceptual apparatus and of goals (concerning propositions that must be distinguished) in Ockham's theories of supposition and of fallacies, but that the respective conceptual apparatuses also present substantial dissimilarities. Hence, theories of supposition are better seen as an addition to the general logical framework that medieval authors had inherited from ancient times, rather than the replacement of an ancient tradition by a medieval one. Indeed, supposition theories and fallacy theories had different tasks to fulfil, and in this sense both had their place in fourteenth century logic. (shrink)