The work of which this is an English translation appeared originally in French as Precis de logique mathematique. In 1954 Dr. Albert Menne brought out a revised and somewhat enlarged edition in German. In making my translation I have used both editions. For the most part I have followed the original French edition, since I thought there was some advantage in keeping the work as short as possible. However, I have included the more extensive historical notes of Dr. (...) class='Hi'>Menne, his bibliography, and the two sections on modal logic and the syntactical categories, which were not in the original. I have endeavored to correct the typo graphical errors that appeared in the original editions and have made a few additions to the bibliography. In making the translation I have profited more than words can tell from the ever-generous help of Fr. Bochenski while he was teaching at the University of Notre Dame during 1955-56. OTTO BIRD Notre Dame, 1959 I GENERAL PRINCIPLES § O. INTRODUCTION 0. 1. Notion and history. Mathematical logic, also called 'logistic', ·symbolic logic', the 'algebra of logic', and, more recently, simply 'formal logic', is the set of logical theories elaborated in the course of the last century with the aid of an artificial notation and a rigorously deductive method. (shrink)

This is the collection of essays presented to Bochenski on his 60th birthday, and it contains, as a mirror of Bochenski's own work, a broad spectrum of studies ranging from formal logic and history of logic, to the philosophy of logic and language, and to the methodology of explanation in Greek philosophy. Of the seventeen articles, these are some of the more important to the reviewer: "Betrachtungen zum Sequenzen Kalkül" by Paul Bernays, which is an extensive study of (...) Gentzen-type formulations of logic; "Remarks on Formal Deduction," H. B. Curry, a further discussion of sequenzen-logics; "Marginalia on Gentzen's Sequenzen Kalkül" by Hughes Leblanc; "Method and Logic in Presocratic Explanation," Jerry Stannard; "On the Logic of Preference and Choice," H. S. Houthakker, a suggestive presentation of decision and utility theory in logical form; "Leibniz's Law in Belief Contexts," Chisholm; "On Ontology and the Province of Logic," R. M. Martin; and "N. A. Vasilev and the Development of Many-valued Logics," G. L. Kline, an important addition to the history of logic. Other contributors are: Storrs McCall, Albert Menne, E. W. Beth, Benson Mates, Ivo Thomas, J. F. Staal, F. R. Barbò, A.-T. Tymieniecka, and N. M. Luyten. There is a bibliography of Bochenski's writings through 1962.—P. J. M. (shrink)

Gyorgy Tamas works in the philosophy of logic, that difficult interdisciplin ary region wherein the notion of categories is both basic and subtle. To understand ways of thinking, to understand patterns of whatever is real, to recognize what is possible and to reject the nonsensical and the impossible is to comprehend the categories. This was a in thought and in fact, recurring motive of European thought from the earliest self-aware beginnings, and Tamas knows that history well, as his critical respect (...) demonstrates. Ancient, medieval, and modern thinkers appear in this book, set forth in their own words; and likewise we see that Tamas has built upon the historians and commentators, upon the pioneering historical investigation of the categories by Trendelenburg a century ago and by Bochenski in our days. Tamas has two principal goals here: to investigate the logic, which is to say the structure and the relations, of the philosophical categories; and to set forth the logic of thought which may then be based upon the critically established system of categories obtained by that investigation. Ancillary but of striking value is his style of historical relevance which enables the reader to engage in a discussion that is both analytically sharp and developmentally insightful. Furthermore, Tamas draws upon his contem porary colleagues with similar critical respect: Lukasiewicz, Quine, Patzig, Menne, Tavanets and others. (shrink)

Die Logik, einst Grundbestand der Philosophie, hat sich in unserem J ahrhundert zu einer selbstandigen Wissenschaft ent 1 wickelt. Sie wird zur Abgrenzung gegeniiber friiheren Gestalten "neue Logik" oder "moderne Logik" genannt; auch sind Be zeichnungen wie "theoretische Logik", "mathematische Logik", "symbolische Logik", "formale Logik", "Logistik" gebrauch 2 lich, urn die Eigenart der grundlegenden Methoden anzudeuten. Die genannten Benennungen werden in dieser Arbeit gleichbe rechtigt gebraucht. Mit 1. M. BOCHENSKI und A. MENNE kann man unter Logistik in weiterem (...) Sinne "die Lehre vom Logikkalkiil, seinen Voraus 3 setzungen und Anwendungen" verstehen. Die Absicht dieser Arbeit ist eine philosophische; sie fragt nach dem, was die Aussage als Aussage zum Element positiver Logik werden laBt. In Frage ist daher die Aussagen- und (ele mentare) Pradikatenlogik, die in formaler Hinsicht "durch den Vollstandigkeitssatz (Go DEL I930) und den Unentscheidbarkeits- 1 Texte zur Geschichte der modernen Logik: I.M. BOCHENSKI, Formale Logik, Freiburg-Miinchen I956, S. 3II-477. 2 s. z.B.: B. JUH6s, Elemente der neuen Logik, Wien I954. G. HASEN]AEGER, Einfuhrung in die Grundbegritfe und Probleme der modernen Logik, Freiburg-Miinchen I962. D. HILBERT und W. ACKERMANN, Grundzi~ge der theoretischm Logik, 3. Aufl., B- lin-Gi:ittingen-Heidelberg I949. H. SCHOLZ und G. HASEN]AEGER, Grundzuge der mathematischen Logik, Berlin 1961. H. HERMES, Einfuhrung in die mathematische Logik, Stuttgart 1963. R. CARNAP, Symbolische Logik, Wien 1954. P. LORENZEN, Formale Logik. I.M. BOCHENSKI, GrundrifJ der Logistik, aus dem Franzi:isischen iibers., neubearb. und erweitert von A. MENNE, 2. erweiterte Auf I., Paderborn 1962. (shrink)

"Anton Wilhelm Amo is the first modern African philosopher to study and teach in a European university and write in the European philosophical tradition. We give an extensive historical and philosophical introduction to Amo's life and work, and provide Latin texts, with facing translations and explanatory notes, of Amo's two philosophical dissertations, On the Impassivity of the Human Mind and the Philosophical Disputation containing a Distinct Idea of those Things that Pertain either to the Mind or to our Living and (...) Organic Body, both published in 1734. The Impassivity is an extended argument that the mind cannot be acted on, that sensation is a being-acted-on by the sensed object, and therefore that sensation does not belong to the mind, and must belong instead to the body The Distinct Idea works out the implications for the mind's actions, and tries to show how the mind understands, wills, and effects things through the body by 'intentions' which direct motions in our body intentionally toward external things. Both dissertations try to show how far each type of human act belongs to the mind, how far to the body, and expose and resolve earlier philosophers' self-contradictions on these questions"--. (shrink)

The dominant theory of cross-disciplinarity represents multidisciplinarity as ‘lower’ or ‘less interesting’ than interdisciplinarity. In this paper, it is argued that this unfavorable representation of multidisciplinarity is ungrounded because it is an effect of the theory being incomplete. It is also explained that the unfavorable, ungrounded representation of multidisciplinarity is problematic: when someone adopts the dominant theory of cross-disciplinarity, the unfavorable representation supports the development of a preference for interdisciplinarity over multidisciplinarity. However, being ungrounded, the support the representation provides for (...) a preference for interdisciplinarity, is invalid. The issue is even more pressing because research policy makers and funding bodies are among the adopters of the theory, which means that there is a risk of policies reflecting an unjustified preference for interdisciplinarity over multidisciplinarity. This paper presents an improved version of the dominant theory of cross-disciplinarity, obtained by completing the original version with the information it was missing. Because the improved version is more neutral regarding the value of different types of cross-disciplinarity, it is better suited for use by research policy makers and funding bodies. (shrink)

Late ancient Platonists and Aristotelians describe the method of reasoning to first principles as "analysis." This is a metaphor from geometrical practice. How far back were philosophers taking geometric analysis as a model for philosophy, and what work did they mean this model to do? After giving a logical description of analysis in geometry, and arguing that the standard (not entirely accurate) late ancient logical description of analysis was already familiar in the time of Plato and Aristotle, I argue that (...) Plato, in the second geometrical passage of the "Meno" (86e4-87b2), is taking analysis as a model for one kind of philosophical reasoning, and I explore the advantages and limits of this model for philosophical discovery, and in particular for how first principles can be discovered, without circularity, by argument. (shrink)

This book is a systematic study of Descartes' relation to Augustine. It offers a complete reevaluation of Descartes' thought and as such will be of major importance to all historians of medieval, neo-Platonic, or early modern philosophy. Stephen Menn demonstrates that Descartes uses Augustine's central ideas as a point of departure for a critique of medieval Aristotelian physics, which he replaces with a new, mechanistic anti-Aristotelian physics. Special features of the book include a reading of the Meditations, a comprehensive historical (...) and philosophical introduction to Augustine's thought, a detailed account of Plotinus, and a contextualization of Descartes' mature philosophical project which explores both the framework within which it evolved and the early writings, to show how the collapse of the early project drove Descartes to the writings of Augustine. (shrink)

Al-Fbb al-f, is apparently the first person to maintain that existence, in one of its senses, is a second-order concept [mal th]. As he interprets Metaphysics d] has two meanings, second-order being as truth'' (including existence as well as propositional truth), and first-order being as divided into the categories.'' The paronymous form of the Arabic word mawjd] distinct from their essences: for al-Kindd of all things. Against this, al-Fburr thinks that Greek more appropriately expressed many such concepts, including being, by (...) particles rather than nouns or verbs; he takes Metaphysics r's title can mean both Book of Particles'' and Aristotle's Metaphysics.''. (shrink)

This book is the first sustained modern investigation of Plato’s theology. A central thesis of the book is that Plato _had _a theology—not just a mythology for the ideal city, not just the theory of forms or the theory of cosmic souls, but also, irreducible to any of these, an account of God as _Nous _, the source of rational order both to souls and the world of bodies. The understanding of God as Reason, and of the world as governed (...) directly or indirectly by Reason, is worked out in the dialogues of Plato’s last period, the _Statesman, Philebus, Timaeus, _and _Laws. _These dialogues offer a strategy for explaining the physical world that goes beyond anything in the middle dialogues, and gives the best starting point for understanding the cosmologies and theologies of Aristotle, the Stoics, and later ancient thinkers. Menn focuses on the _Timaeus _as Plato’s most sustained effort to provide what _Anaxagoras had failed to deliver: an explanation of the world through Reason, showing that things are as they are because it is best, or because it best serves the order of the world as a whole. Anaxagoras was disappointed because he explained things through their material constituents, without explaining why the constituents are ordered as they are; but the theory of forms has the same defect, since it_ _cannot explain why different parts of the universe participate in different forms according to a particular order. The _Timaeus _and other late dialogues attempt to supply the missing explanation of the ordering of the physical world. These dialogues do not retreat from the middle dialogue theory of forms, nor do they escape into an esoteric theory of numbers; but they add to the middle dialogues an analysis of the principles necessary to account for the existence and partial intelligibility of the sensible world—not only forms and a material substance but also _Nous _and souls. Although the demiurge of the _Timaeus _ _is represented as a cause both to souls and bodies, most scholars have been reluctant to identify the demiurge as a being separate from and superior to souls, because they think that both the meaning of the Greek word _nous _and Plato’s own statements require that _Nous _is_ _either a kind of soul or something inseparable from souls. Reexamining the linguistic evidence and the Platonic texts, Menn argues that _nous _can mean something separate from souls, namely the virtue of rationality or intelligence that souls participate in. Menn argues that Anaxagoras’ _Nous _should be construed as such a virtue; then he examines what status this virtue has in the context of the Platonic theory of forms, and how it_ _is a cause both to souls and to bodies. Soul plays a crucial role in mediating the causality of _Nous _and introducing rational order into the world of bodies, but neither soul in general nor the world-soul in particular can be identified with _Nous. _ Menn stresses the pre-Socratic context for the cosmology and theology of Plato’s late dialogues; he argues for the importance of Diogenes of Appolonia in particular, and he reconstructs a possible new fragment of Diogenes from the _Timaeus _and from the Hippocratic treatise _On Breaths. _In the _Timaeus _and other late dialogues Plato attempts to do better than his predecessors by standards implicit in Socrates’ critique of Anaxagoras in the _Phaedo, _but what Plato offers remains consciously provisional. Aristotle argues that the _Timaeus _remains liable to some of the same criticisms that Socrates had leveled against Anaxagoras, and Aristotle’s own cosmology and theology take up Plato’s challenge to carry out Anaxagoras’ promise of an explanation of the world through _Nous, _and attempt to improve on the _Timaeus _as_ _Plato had improved on Anaxagoras. In this way the _Timaeus _serves as an essential starting point, not only_ _for those later ancient philosophers who took it as an authoritative statement on the world and on God but also for those who took it as a challenge to do better. (shrink)

J'examine le statut et la fonction des Catégories dans la philosophie d'Aristote.Le traité n'appartient ni à la philosophie première, ni même à la philosophie tout court, mais à la dialectique. Il ne s'agit pas d'une « discussion dialectique » de l'être, mais plutôt de dialectique en tant que tel : ce traité forme un ensemble avec les Topiques, qui a pour but d'aider le questionneur dans un débat dialectique à décider si le terme donné peut tomber sous la définition proposée (...) ou sous le genre proposé. Bien qu'il y ait un emploi philosophique des Catégories, tout comme de la dialectique en général, l'opposition prétendue entre la théorie de la substance des Catégories et celle de la Métaphysique est fondée sur une méconnaissance des buts différents des deux traités. I examine the status and function of the Categories in Aristotle's philosophy.The work does not belong to « first philosophy, » or indeed to philosophy at all, but to dialectic; not as a « dialectical discussion » of being, but in the strict sense that it is intended, together with the Topics, to help the dialectical disputant to decide whether a given term can fall under a proposed definition or a proposed genus. Although the Categories, like dialectic in general, has uses in philosophical argument, the supposed opposition between the accounts of substance in the Categories and in the Metaphysics depends on a misunderstanding of the different aims of the two works. (shrink)

When Aristotle speaks of theologikê, he means not the study of a single God, but the study of gods and divine things in general. He never uses the phrase “the unmoved mover” to pick out just one being, and that phrase would not express the essence of the beings it applies to. To see what sort of religious interest there might be in such a being, and how the words “god” and “divine” enter into Aristotle's philosophy, it is best to (...) start with what he says about gods and divine things in moral and political contexts. Guided by his criticisms of Plato on the soul's self-motion, Aristotle sets out, in Physics VIII, to give a revised version of Plato's cosmotheological argument in Laws X. This article focuses on Aristotle's theology and his views about gods, the soul, the cosmos, heavens and heavenly bodies, and the first principle or first cause. (shrink)

ARISTOTLE PRESENTS HIS DOCTRINE OF GOD as the first unmoved mover as the crown of his metaphysics, and thus of his entire theoretical philosophy. He obviously considers it an important achievement. Yet the doctrine has been peculiarly resistant to interpretation. It is difficult to know where to break in to Aristotle's theology: certainly not with his proof that the first mover must be unmoved. The proof has clearly been developed for the sake of the conclusion and not vice versa. How (...) did this conclusion occur to Aristotle, and why did he want it to be true? (shrink)

In this paper I reexamine Plato's method of collection and division, and specifically of collection. If collection and division are simply methods for mapping out genus-species trees, then it is hard to understand why Plato is so excited about them. But a close study of Plato's examples shows that these methods are something broader, and shows why Plato would regard collection as an important tool for coming to know "elements" in any domain of inquiry. In the first section I focus (...) on a notoriously problematic example of collection from the "Philebus," Theuth's discovery of the letters of the alphabet; I show how Plato interprets this discovery as a process of collection, and draw conclusions about what Plato takes collection to be. In the process, I try to bring out Plato's analysis of what is involved in learning to read and write a language, which he takes as paradigmatic for other knowledge. In the second section, stepping back from the "Philebus" passage and applying its lessons, I describe the function of collection and division, for the late Plato, in coming to know "elements," including the Forms, or the most basic Forms. Reflection on Plato's use of collection suggests a (relatively non-mystical) account of what it is to know non-complex intelligible entities, and of how we can come to know them. I also use Plato's descriptions of collection and division to suggest a Platonic context for the notion of the separation of the Forms, to which the late Plato remains firmly committed. (shrink)

Here I reexamine Duhem's question of the continuity between medieval dynamics and early modern conservation theories. I concentrate on the heavens. For Aristotle, the motions of the heavens are eternally constant (and thus mathematizable) because an eternally constant divine Reason is their mover. Duhem thought that impetus and conservation theories, by extending sublunar mechanics to the heavens, made a divine renewer of motion redundant. By contrast, I show how Descartes derives his law of conservation by extending Aristotelian celestial dynamics to (...) the earth. Descartes argues that motion is intrinsically linear, not circular. But he agrees that motion is mathematically intelligible only where divine Reason moves bodies in a constant and eternal motion. Descartes strips bodies of active powers, leaving God as the only natural mover; thus both celestial and sublunar motions are constant, and uniformly mathematizable. The law of conservation of the total quantity of motion is an attempt to harmonize the constancy derived a priori with the phenomenal inconstancy of sublunar motions. (shrink)

0.1 Logic, in particular the modern symbolic logic, is not accused of being deficient in precision and accuracy, but one does sometimes hear that it is unrealistic, that it cannot be applied to reality, that it is utopian.

With regard to scientific theory it is important to note that Kant in contrast to many later authors, believes that philosophy is a knowledge. To prove his argument, Kant found scientific examples for philosophical theses. According to his 12 categories of intellect he attempted to prove his view by the construction of 12 logical judgements. His scheme is considerably different to the Aristotelian devision of judgements despite his own view that the logic did make no progress since Aristotle. Kants categorisation (...) differs also from the devisions of all 18th century philosophers. It appears that his categorisation is a construction post factum according to his already accepted 12 categories of intellect. His devision is furthermore not supported from a modern view of logic. It would therefore appear that under the view of modern theory of science Kant did not give a proof for his scheme of categories. (shrink)