The notion of potential infinity dominated in mathematical thinking about infinity from Aristotle until Cantor. The coherence and philosophical importance of the notion are defended. Particular attention is paid to the question of whether potential infinity is compatible with classical logic or requires a weaker logic, perhaps intuitionistic.

This page is dedicated to an analysis of the first section of Parmenides' Poem, the Way of Truth, with a selection of critical judgments by the most important commentators and critics. In the Annotated Bibliography I list the main critical editions (from the first printed edition of 1573 to present days) and the translations in English, French, German, Italian and Spanish, with a selection of studies on Parmenides; in future, a section will be dedicated to an examination of some critical (...) variants of the Greek text, with particular attention to corrections to the Diels-Kranz (abbreviated DK) edition of the Fragmente der Vorsokratiker. The fragments of Parmenides' Poem are cited according to Diels-Kranz numbering system as adopted in the 6th edition, Berlin 1952; the Poem is divided into three parts: the Proem fr. I, 1-32; the Way of Truth (Alethéia) from fr. II to VIII, 49, and the Way of Mortal Opinion (Doxa) fr. VIII, 50 to XIX, 3. (shrink)

Terms for consciousness, used with a cognitive meaning, emerged as count nouns in the 17th century. This transformation repeats an evolution that had taken place in late antiquity, when related vocabulary, used in the sense of conscience, went from being mass nouns designating states to count nouns designating faculties possessed by every individual. The reified concept of consciousness resulted from the rejection of the Scholastic-Aristotelian theory of mind according to which the mind is not a countable thing, but a pure (...) potentiality. This rejection was motivated by an acute sense of the mind’s fallible subjectivity. While conditioned by recent historical events, the 17th century’s pervasive sense of subjectivity also reveals a heavy debt to Hellenistic philosophy, which had been recently rediscovered. But whereas Hellenistic thought, mistrustful of theoria, only reifies conscience, early modern thinking, more mistrustful of praxis and seeking its grounding in theoria, goes a step further and reifies consciousness. Partly modeled on theological ideas, the resulting concept of consciousness is plagued by paradoxes that have becomes notorious for their intractability. But essentially the same model of consciousness underwrites contemporary theory, embroiling contemporary debates in the same controversies that dominated the 17th century. Sidestepping these difficulties by returning to the Scholastic-Aristotelian theory of mind would be a tall order, but it is not impossible. Alfred North Whitehead's theory of consciousness offers an example. His novel theory of time enables Whitehead to rehabilitate the Aristotelian concept of passive mind in a wholly naturalistic way. (shrink)

In our recent book (Abraham and Roy 2010) we have repurposed a mathematical model for the quantum vacuum as a model of consciousness. In this model, discrete space and time are derived from a discrete cellular dynamical network. As our model is essentially atomistic, we included in our book a short support chapter on atomism. In this aticle we expand on the few pages of that chapter devoted to the history of atomism, to place the current revival of atomism in (...) a larger context. (shrink)

Cet article étudie la notion platonicienne d’instant. Je soutiens que dans leParménide, «maintenant» (nun) et «soudain» (exaiphnês) renvoient à la même entité, envisagée à partir des perspectives distinctes de l’Être éternel et du Devenir temporel. Cette interprétation complète et éclaire les notions platoniciennes de temps et d’éternité présentées dans leTimée. L’article met enfin en évidence le rôle décisif de la troisième déduction — où apparaît la notion d’instant — dans la compréhension de l’exercice dialectique duParménidedans son ensemble.

The article analyses the explication of the infinity in the philosophical courses taught at Kyiv-Mohyla Academy at the 17th and 18th centuries. It examines 12 philosophical courses – since 1645 (the course by Inokentii Gizel) until 1751 (the course by Georgii Konyskyi). It shows how the infinity was defined and in which kinds it was divided in different courses. In general, all the professors, as well as other scholastic philosophers, agree that categorematic infinity exists only in God, but syncategorematic is (...) present in the created world. Regarding the question whether God, being omnipotent, can create a categorematic infinity in the world, the Mogilyans are divided into several camps: (1) Inokentii Gizel, Stefan Yavorskyi, Inokentii Popovskyi, Sylvestr Pinovskyi, Platon Malynovskyi gave a positive answer to the question; (2) Yosyf Volchanskyi, Ilarion Levytskyi, Amvrosii Dubnevych, Sylvestr Kulabka believed that this kind of infinity is in principle impossible, hence God cannot create it; (3) Teofan Prokopovych and Georgii Konyskyi took a sceptical stand and consider that the human mind as such could not solve this problem. The article analyses which arguments were offered by each camp, and gives suggestions what influenced the position of certain Mohylian professors. Most probably, Mohylian philosophers who supported the possibility of actual infinity in the created world were influenced by nominalistically oriented Jesuit philosophers, like Pedro Hurtando de Mendoza and Rodrigo Arriaga. The other Mohylians backed a more traditional idea, supported by Thomas Aquinas, that only one actual infinity can exist and it is God. (shrink)