In this essay I argue that Albert would reject the need for a separate fourth mode of common personal supposition, and that his view of merely confused supposition has not been fully explicated by modern scholars. I first examine the various examples of conjunct descent given by modern scholars from his Perutilis logica , and show that Albert clearly adopts it in resolving the sophistic examples involved. Second, I explicate the view of merely confused supposition that Albert defends in his (...) Sophismata , and then attempt to answer the question: which view of merely confused supposition was his final view, the view articulated in the Perutilis logica or the view in the Sophismata ? I conclude that based upon his Sophismata view of merely confused supposition, Albert came to realize the logical strength his revised theory of personal supposition afforded, and consequently, that he is one of the earliest 14th-century logicians to adopt conjunct terminal descent to resolve various sophisms, a move which gave his theory of personal supposition a logical symmetry having two sorts of propositional descents to singulars, and two sorts of terminal descents to singulars. (shrink)

This article summarizes Ockham's interpretation of Aristotle's categories, showing how his account of connotative concepts introduced a revision in the Aristotelian doctrine about the relation between mathematics and physics. The article shows that Ockham's account influenced William of Heytesbury, John Dumbleton, and Nicholas Oresme to re-interpret disciplinary relations and disciplinary boundaries. They did so, however, in ways compatible with other basic principles of Aristotelian philosophy of nature; nevertheless, their modifications of the Aristotelian account of mathematics stimulated later philosophers to construct (...) robust theories of mathematics compatible with modern mathematical physics. (shrink)

I argue in the essay that the fourteenth-century logicians William Heytesbury and Albert of Saxony developed an argument I call the Socrates-Minus Argument. Their analysis and rejection of it indicates a direction towards a pragmatic resolution to the contemporary Descartes-Minus Argument. Their resolution is similar to the view adopted today by Peter van Inwagen, namely, that “arbitrary undetached parts of physical objects,” like 'all of Socrates except his finger' simply do not exist. I conclude the fourteenth-century approach does not run (...) afoul of Leibniz's law of the Indiscernibility of Identicals, but utilizes a form of Leibniz's Identity of Indiscernibles that, when combined with a weak “anthropic principle,” yield a pragmatic resolution to the Descartes-Minus Argument. (shrink)

: Following Aristotle, medieval natural philosophers believed that knowledge was ultimately based on perception and observation; and like Aristotle, they also believed that observation could not explain the "why" of any perception. To arrive at the "why," natural philosophers offered theoretical explanations that required the use of the imagination. This was, however, only the starting point. Not only did they apply their imaginations to real phenomena, but expended even more intellectual energy on counterfactual phenomena, both extracosmic and intracosmic, extensively discussing, (...) among other themes, the possible existence of other worlds and the possibility of an infinite extracosmic space. The application of the imagination to scientific problems during the Middle Ages was not an empty exercise, but, as I shall show, played a significant role in the development of early modern science. (shrink)

Tout au long de la période médiévale, la logique est un instrument privilégié d'acquisition et d'exposition des autres savoirs. Dans cet article, on se propose d'évaluer la portée de son investissement dans le champ de la philosophie naturelle, à partir d'un exemple: celui d'Albert de Saxe . A travers l'étude de la quantité et du mouvement, on voit se mettre en place une approche originale du corps naturel. All along the Medieval period, logic is an instrument for acquisition and exposition (...) of the other fiels of knowing. In this article is proposed an evaluation of the results of its use in natural philosophy, through an example: that of Albert of Saxony . By studing quantity and mouvement, we can see the emergence of an original approach of the natural body. (shrink)

Some fourteenth-century treatises on paradoxes of the liar family offer a promising starting-point for the formulation of full-fledged theories of truth with systematic relevance in their own right. In particular, Bradwardine's thesis that sentences typically say more than one thing gives rise to a quantificational approach to truth, and Buridan's theory of truth based on the notion of suppositio allows for remarkable metaphysical parsimony. Bradwardine's and Buridan's theories both have theoretical advantages, but fail to provide a satisfactory account of truth (...) because both are committed to the thesis, fatal for both, that every sentence signifies/implies its own truth. I close with remarks on Greg Restall's recent model-theoretic formalization of Bradwardine's theory of truth. (shrink)

As the title indicates the author presents a contemporary theory of consequence. In so doing he establishes a terminology that enables a description, interpretation and evaluation of medieval theory independently of medieval vocabulary. In the interest of better understanding the medieval writers the author puts himself in the position of the medieval scholar in Erfurt. The reader learns about the Erfurt schools and the controversal debate on the so-called modi significandi, using only texts that are known to have been available (...) in Erfurt in the first half of the 14th century. The two tracts, a short epitome of Thomas Maulfelt and a comprehensive volume of Albert of Saxony represent the two most common tracts of this discipline, and are discussed on the basis of questions arising in the introduction. New conclusions can be reached about the scope and the goal of medieval consequence theory which is an original accomplishment of the high Middle Ages and its place in the history of logic. Der Ankündigung im Titel gehorchend stellt der Autor eine zeitgenössische Theorie zu Schlußfolgerung dar. Somit wird eine Terminologie erstellt, in der — unabhängig von der Fachsprache des Mittelalters – die verschiedenen Ausführungen zur Schlußfolgerungslehre des Spätmittelalters beschreiben, interpretiert und bewertet werden können. Um die mittelalterlichen Autoren Thomas Maulfelt und Albert von Sachsen zu verstehen, versetzt sich der Autor in die Perspektive eines Scholars im Erfurt der Mitte des 14. Jahrhunderts. Der Leser wird über die Schulsituation in Erfurt unterrichtet, er erfährt von der hitzigen Debatte um die modi significandi und blickt zur weiteren Erläuterung lediglich in solche Schriften, deren Vorkommen für die Mitte des 14. Jahrhunderts in Erfurt belegbar sind. Anhand von Fragestellungen, die sich aus dem Einleitungsteil ableiten, werden die zwei Traktate, die in Form, Inhalt und Umfang die zwei häufigsten Schrifttypen zur Schlußfolgerungslehre repräsentieren, untersucht. So ergeben sich zur Anwendungreichweite, zur Zielsetzung dieser Disziplin, die eine originäre Leistung des hohen Mittelalters ist, sowie zu ihrem Stellenwert in der Logikgeschichte neue Erkenntnisse. (shrink)

In the scholarship on medieval logic and semantics of the last decades, Ockham’s theory of supposition is probably the most extensively studied version of such theories; yet, it seems that we still do not fully understand all its intricacies. In this paper, I focus on a phrase that occurs countless times throughout Ockham’s writings, but in particular in the sections dedicated to supposition in the Summa logicae: the phrase ‘denotatur’. I claim that an adequate understanding of the role of the (...) concept of denotatur within Ockham’s supposition theory shall yield a deeper understanding of the theory as a whole. Here, I first examine a few uses of the term ‘denotatur’ and its variants by other authors. I then turn to Ockham: first I briefly mention some uses of the term in contexts other than his theory of supposition. Following that, I focus on his supposition theory, in particular on how ‘denotatur’ allows him to deal with two crucial puzzles, namely the supposition of empty terms and the supposition of terms in false affirmative propositions. The treatment of these two puzzles suggests that Ockham’s theory of supposition must be understood as a theory chiefly intended for the generation of the meanings of propositions. (shrink)

The 'Perutilis logica' is both by its content and its didactic value the most paradigmatic logical compendium of the 14th century. The study presented here tries to show on the basis of an interpretative analysis of the second treatise that the doctrine of the properties of terms is stated in a unusually developed form in the 'Perutilis logica' and that suggestions that it lacks originality must be revised.

For John Buridan, truth-bearers are assertions. This fact explains why the inference ‘p is true, therefore p’ may fail. On the one hand, the tense of the verb plus the time of utterance do not determine the time about which a sentence is intended to be true: the intention of the speaker is needed. On the other hand, since the meaning of vocal and written words is conventional, it may seem that they can be used with different meanings on each (...) side of the inference. While the antecedent may talk about a situation different from the present one, this doesn’t make it the actual situation of utterance, and the words have meanings only in the actual situation of use. Although such situations are different, in both of them we are asked to see the importance of identifying features of which the disquotational schema doesn’t keep track and that can only be specified in the context of use. (shrink)

The essay develops two major arguments. First, if John Buridan's 'first argument' for the reintroduction of natural supposition is only that the "eternal truth" of a scientific proposition is preserved because subject terms in scientific propositions supposit for all the term's past, present, and future significata indifferently; then Albert of Saxony thinks it is simply ineffective. Only the 'second argument', i.e. the argument for the existence of an 'atemporal copula', adequately performs this task; but is rejected by Albert. Second, later (...) fourteenth-century criticisms of Buridan's natural supposition, given in certain Notabilia from the anonymous author in, Paris, BnF, lat. 14.716, ff. 40va-41rb, are nothing but an interpolated hodge-podge of criticisms given earlier in the century against various views of Buridan's by Albert of Saxony. It is this fact that makes Albert the real source of late fourteenth-century criticisms of Buridan's view of natural supposition. (shrink)

This work is an exegetical account of the modal logic of Albert of Saxony, a 14th century logician and scientist. The text used was the 1522 Venice edition of the Perutilis logica. As there is no critical edition of the text, a "working edition" of the pertinent sections accompanies the dissertation as an appendix. ;Aristotle's modal logic which served as a basis for modal logic in the Middle Ages is briefly reviewed. Albert's non-modal propositional logic, onto which the modal logic (...) is grafted, is then presented informally. ;Albert's chapter on the semantic and syntactic considerations for a modal logic is analyzed in detail as are his chapters on modal consequences and his chapters on modal syllogisms . In these chapters, Albert makes the distinction between modal propositions in sensu composito and in sensu diviso, and gives the truth conditions for each type of modal proposition. He goes on to state the rules which govern what can be inferred from the two sorts of propositions and finally examines syllogisms constructed from modal propositions following the Aristotelian classification of figures and moods. While he mentions the modes of knowing, doubting, etc., he primarily is interested in the modes of possibility and necessity and, to a lesser extent, the mode of contingency. ;In the concluding chapter, Albert's system is briefly compared with modern systems and the ground-work for a semantic model is laid, i.e., considerations concerning the truth of modal propositions which the formal logician must take into account for the construction of such a model are put forward. Further, a brief comparison between Albert, Aristotle, and Ockham is made concerning certain aspects of necessity. ;For the purposes of clarity and convenience, standard quantified modal predicate calculus is used. ;Pertinent findings include the fact that Albert's system encompasses the modern T system and an argument can be made that it includes the S5 system as well. ;More importantly, Albert ultimately wishes to distinguish four different sorts of necessity: a necessity concerning how an attribute applies to an individual, a necessity concerning the relationship between the subject and predicate terms, an 'hypothetical' necessity concerning an event once it has occurred, and, finally, it is argued, a necessity concerning the relationship of the subject and predicate terms not on the basis of their denotata but on the basis of their signification, i.e., their meaning. ;Though Albert does not succeed in constructing an unambiguous formal logical system, he does bring to light some aspects of the nature of necessity and possibility and the ways in which the terms "necessary" and "possible" are used in natural language. (shrink)