The authors explicate Aquinas's conception of mathematics. They show that in his work the Aristotelian conception is prevalent, according to which this discipline is—together with physics and metaphysics—a theoretical science, whose subject is the study of real quantity and its necessary properties. But, alongside this dominant and prevalent conception, Aquinas's work contains a number of indications that cast doubt. These sparse and rather marginal reflections lead the authors to conclude that Aquinas's texts contain a "constructivist" conception of mathematics in rudimentary (...) form. According to this approach, mathematics is not a theoretical science examining real quantity but, rather, a special kind of "art" by means of which mathematical objects are "created." From a constructivist point of view the authors then attempt to formulate a conception of mathematics that would accord with the basic Aristotelian assumptions of Aquinas's thought. (shrink)

We deal with the concept of man and woman, as well as with the problem of their equality, in the two great ancient thinkers Plato and Aristotle. The discussion of Plato leads to the conclusion that there is no substantial difference between man and woman. We find Plato’s view close or similar to today’s widely held doctrine of “unisexism”. Aristotle on the other hand believes that there are important differences between man and woman and we find in his texts two (...) approaches to the problem. In his first view the sex difference is due to the lesser perfection of woman, according to the second view both sexes are equally perfect, nevertheless each in its own way. Both conceptions have their supporters in contemporary thought (so-called theories of „polarism“ and „compatibilism“). From a systematic point of view we suggest that Aristotle´s second approach should be further developed as it is most in accord with our Christian worldview. (shrink)

Formal abstraction is a key instrument Aquinas employs to secure the possibility of mathematics conceived as a theoretical Aristotelian science. In this concept, mathematics investigates quantitative beings, which are grasped by means of formal abstraction in their necessary, universal, and changeless properties. Based on this, the paper divides into two main parts. In the first part (section II) I explicate Aquinas’s conception of (formal) abstraction against the background of the Aristotelian theory of science and mathematics. In the second part (section (...) III) I present and critically assess the problems associated with formal abstraction in mathematics. With all due respect to Aquinas’s genius, I find his conception of formal abstraction (as well as mathematics) unsatisfactory and list the main reasons for its failure in the conclusion. (shrink)

The paper deals with the problem of the ratio of unity in the work of Thomas Aquinas. More specifically, it tries to answer the question wherein the ratio of unity consists: whether it is a “positive entity of being” or rather the “negative aspect of being undivided.” In order to answer the question properly the paper is divided into four main parts. In the first two parts the constitutive characteristics of unity are explained and attention is focused on the concepts (...) division and negationof division. In the third part Aquinas’s statements that seem to reflect a negative conception of unity are expounded and the relationship of unity and goodness tothe “entitative principles” of being (essence and existence) are elucidated. Finally, in the fourth part the answer to the fundamental question of the article is givenand arguments for the “positive” conception of unity are presented. (shrink)

The paper deals with the problem of the ratio of unity in the work of Thomas Aquinas. More specifically, it tries to answer the question wherein the ratio of unity consists: whether it is a “positive entity of being” or rather the “negative aspect of being undivided.” In order to answer the question properly the paper is divided into four main parts. In the first two parts the constitutive characteristics of unity are explained and attention is focused on the concepts (...) division and negationof division. In the third part Aquinas’s statements that seem to reflect a negative conception of unity are expounded and the relationship of unity and goodness tothe “entitative principles” of being (essence and existence) are elucidated. Finally, in the fourth part the answer to the fundamental question of the article is givenand arguments for the “positive” conception of unity are presented. (shrink)

Throughout the greater part of the twentieth century, both in the analytic and continental traditions, metaphysics was deemed to be passé. The last few decades, however, have witnessed a remarkable growth of interest among analytic philosophers in various traditional metaphysical topics, such as modality, truth, causality, etc. which resulted in the emergence of various forms of analytic metaphysics. The new forms of metaphysics differ from its traditional forms mostly in their methodology and in the range of proposed solutions to particular (...) problems. Besides these and other differences, however, there are also many similarities and there are even some who intentionally develop traditional metaphysical themes using the contemporary analytical methods. All these developments call for detailed exploration, which is the general goal of the present publication Metaphysics: Aristotelian, Scholastic, Analytic. The publication is the fruit of the conference which took place in Prague in 2010 and which had for its aim to bring together those willing to explore relations between the traditional and contemporary concerns, both from among the leading analytic philosophers working in metaphysics and the historians of philosophy devoted to the study of the metaphysical tradition. The specific focus of the conference was a re-examination of topics such as categories, metaphysical structure, substance and accident, existence, modalities, and predication. (shrink)

The paper deals with the ontological status of number. The authors are convinced that it is useful to discuss the concept of number within the framework of the Aristotelian division of being into substance and accident. Number can thus be taken as ens in se or ens in alio. Aristotle and Thomas Aquinas believed that number is an accident and their concept is explained in the first part of the paper. In the second part it is shown that the Aristotelian (...) concept is not correct. However, if number is not an accident then it seems that it must be identified with a Platonic entity. In the third part the authors reject this Platonic conclusion that Frege seems to have defended. In the final part, a possible solution is shown: From the logical point of view number is an object but from the ontological point of view it is an entity that depends on linguistic structure. (shrink)

Responsione nostra disputationem cum L. Novák prosequimur, qui tractationem nostram, cui titulus “Různá pojetí matematiky u vybraných autorů od antiky po raný novověk”, impugnavit. Impugnatio a L. Novák sub titulo “Tomáš Akvinský instrumentalistou v matematice?” conscripta ansam praebuit nobis ad nonnulla, quae dixeramus, non solum clarius, sed etiam latius ac profundius explananda. Qua in re inprimis ad hoc attendimus, quomodo S. Thomas mathematicam, scientiasque medias necnon philosophiam intellexerit. Adhuc in nostra sententia sistimus, duplicem scil. ac valde diversam interpretationem harum disciplinarum (...) proponi posse. Quamquam multi textus testantur, S. Thomam mathematicam scientiasque medias realistice intellexisse, inveniuntur tamen apud eum dicta nonnulla, quae interpretationi favent instrumentalisticae. Hanc duplicem interpretationem prae oculis ponere multum iuvat, nostro iudicio, ad subsequentem intellectualem historiam, praecipue modernae aetatis, adaequate intelligendam.In our contribution we continue our discussion with L. Novák, who criticised our paper “Různá pojetí matematiky u vybraných autorů od antiky po raný novověk.” Novák’s critique titled “Tomáš Akvinský instrumentalistou v matematice?” served as an incentive for us not only to clarify certain points, but also to deepen our original exposition. We focused on Aquinas’s understanding of mathematics, the middle sciences and philosophy. We still insist that two substantially different interpretations of these disciplines are possible. On the one hand, there is much evidence for Aquinas’s realistic approach to mathematics and the middle sciences. On the other hand, ideas can also be found in Aquinas’s texts supporting an instrumentalist reading. In our opinion, it is important to point out these two approaches to the mathematical sciences in order to adequately understand the subsequent evolution of the history of ideas, especially in the modern period. (shrink)

[Physical premotion and self-determination].

Suárez’s solution to the problem of the conceptual Addition of the One to being follows firstly the Aristotelian-Averroistic tradition mediated by Aquinas. According to this tradition, the One adds to being only a negative determination. Suárez claims that the One does not signify any positive perfection either really or conceptually distinct from being as such. Suárez’s own solution to the problem is presented in a critical discussion with many different conceptions, but Suárez pays most attention to the theory of certain, (...) mainly Franciscan, authors who hold that the One adds to being a positive perfection which is only conceptually distinct from being as such. The main argument for this thesis is based on the assumption that indivision is to be taken as a double negation, by which an affirmation is expressed. This concept of indivision was, according to Suárez, also defended by Aquinas, who holds that the negation which is expressed by the One negates the division of one being from another. Suárez rejects this solution and proposes his own conception, according to which the One does not negate the negative moment of the division of one being from another, but the positive moment of an essential division of a being in itself. The One thus negates a real positive division of being in itself. On the basis of this theory, Suárez further rejected Aquinas’s (and the Thomistic) conception of a conceptual priority of the One over the Many, which was put forth as an answer to the old Aristotelian problem of a privative opposition between the One and the Many. Suárez defends the real priority of an indivision over a division as well as a real and conceptual priority of the One over the Many. Suárez’s conception seems to us to be compatible with his concept of a negative Addition of the One to being. (shrink)

The paper deals with Aquinas’s concept of participation. Its goal is to introduce the reader to the problem, since no significant attention has been paid to it in Czech literature so far. The article is divided into three main parts: first a general description and division of participation is given, second the mutually opposite properties “to be through essence” and “to be through participation” are explained and finally the other general characteristics of participation are put forth.

The article deals with the problem of the future contingents from the logical point of view, i.e. whether the propositions about (conditional) future contingents have a determinate truth-value. The author attemps to show how the problem was discussed both in the 17. century between a Prague’s Jesuit M. Větrovský and a French Dominican A. Goudin, as well as how the discussion has progressed through contemporary analytical philosophy. Firstly the history of the problem is explored to provide the sources for the (...) discussion. Secondly the polemic of Větrovský with Goudin is examined and finally how A. J. Freddoso and W. L. Craig discuss the problem in contemporary analytical philosophy. The essential aspect of the argument is whether the propositions about (conditional) future contingents might have a determinate truth-value if the causal grounding (futuritio causalis) is being detached. (shrink)

The paper deals with the conception of transcendental and categorial concepts in the work of Thomas Aquinas. As a starting point of the exposition the discussion of this matter in De veritate 1, 1 has been chosen, where Aquinas, drawing on Aristotle and Avicenna, determines which are the first concepts of intellect. The absolutly first concept, the terminus of conceptual analysis, is the concept of being (ens). All other concepts, both categorial and transcendental, result from conceptual addition to being. Aquinas’s (...) conception of conceptual addition is explained in detail and used to illustrate Aquinas’s explication of individual transcendentals and categories. Finally it is shown, how Aquinas derives transcendental and categorial concepts as general and special modes of being (modi essendi) of being as such. Translation: Lukáš Novák. (shrink)

According to formalism, a mathematician is not concerned with mysterious metaphysical entities but with mathematical symbols. As a result, mathematical entities become simply sensible signs. However, the price that has to be paid for this move seems to be too high, for mathematics, at present considered to be the queen of sciences, turns out to be a to a contentless game. That is why it seems absurd to regard numbers and all mathematical entities as mere symbols. The aim of our (...) paper is to show the reasons that have led some philosophers and mathematicians to adopt the view that mathematical terms in the proper sense refer to nothing and mathematical propositions have no real content. At the same time we want to explain how formalism helped to overcome the traditional concept of science. (shrink)

Huius recensione subiectum liber est, qui ab Ulrico G. Leinsle sub titulo Einführung in die scholastische Theologie Germanice conscriptus, a M. J. Miller magna cum sollertia Anglice redditus est. In hoc libro Leinsle materiae historicae copiam diligentissime collegit ac ordine disposuit, contributionem faciens singularem et novam ad philosophiae historiam cognoscendam. Scholaribus et viris scientificis, qui hisce legatis intellectualiis studeant, liber dictus conspectum offerit latum et valde comprehensivum principaliorum problematum ac methodorum theologiae scholasticae, rebus tamen minutis non neglectis. Leinsle demonstravit, locupletem (...) ac multiformem traditionem scholasticam partem principalem habuisse in civilizatione occidentali constituenda.The subject of this review is the book Introduction to Scholastic Theology by Ulrich G. Leinsle which was originally published in Germany as Einführung in die scholastische Theologie (the English translation of the book was very well rendered by M. J. Miller). Leinsle gathered rich historical material which he organized into an original, impressive contribution to our knowledge of the history of philosophy. It offers students and scholars interested in this intellectual legacy a comprehensive, panoramic overview of the main problems and methods of Scholastic theology and provides a quick glimpse of many sub-topicsas well. Leinsle has shown that the rich and varied Scholastic tradition played a key role in constituting our Western civilization. (shrink)

The paper deals with a type of whole and part that can be found in Aquinas’ work and to which no attention has been paid so far. This type of whole and part can be called metaphysical whole and metaphysical part, respectively. In the paper, metaphysical whole and part are put forth on the problem of the logical and metaphysical structure of a common nature.