What is the ontological status of mathematical structures? Michael Resnic, Stewart Shapiro and Gianluigi Oliveri, are contemporaries of American philosophers on mathematics, they give Platonic answers on this question.

We reconsider the pragmatic interpretation of intuitionistic logic [21] regarded as a logic of assertions and their justi cations and its relations with classical logic. We recall an extension of this approach to a logic dealing with assertions and obligations, related by a notion of causal implication [14, 45]. We focus on the extension to co-intuitionistic logic, seen as a logic of hypotheses [8, 9, 13] and on polarized bi-intuitionistic logic as a logic of assertions and conjectures: looking at the (...) S4 modal translation, we give a de nition of a system AHL of bi-intuitionistic logic that correctly represents the duality between intuitionistic and co-intuitionistic logic, correcting a mistake in previous work [7, 10]. A computational interpretation of cointuitionism as a distributed calculus of coroutines is then used to give an operational interpretation of subtraction.Work on linear co-intuitionism is then recalled, a linear calculus of co-intuitionistic coroutines is de ned and a probabilistic interpretation of linear co-intuitionism is given as in [9]. Also we remark that by extending the language of intuitionistic logic we can express the notion of expectation, an assertion that in all situations the truth of p is possible and that in a logic of expectations the law of double negation holds. Similarly, extending co-intuitionistic logic, we can express the notion of conjecture that p, de ned as a hypothesis that in some situation the truth of p is epistemically necessary. (shrink)

The essay consists in the analysis of the problem of the evil in the man and in the analysis of the remedies which the man can find against the evil. Plato affirms the presence of an active principle of evil in the soul of every man, which coincides with some instincts of the appetitive soul; the opposite principle to the evil is the reason, which needs, though, a correct education in order to be able to fight efficiently against the evil (...) in us. The man can be seen as a battle field of these opposite forces. Plato describes the presence of the evil in us in some passages of Republic Book 9, where he compares the appetitive part of the soul with a monster. The destiny of every person in her earthly existence consists in the continuing control of the appetitive part of the soul, if the status of ethical education is to be reached and maintained. The man who remains in the realm of the opinion, that is, in the realm of the doxa is an individual who only disposes of unstable opinions and who as a consequence do not have authentic remedies against the appetitive part. On the contrary, the individual who can ascend to the realm of being through the hard education represented by arithmetic, geometry, stereometry, astronomy, harmony and, finally, dialectic is really able to contrast the force of the evil within the individual. Ethics is really possible only through the complete education which passes through these disciplines: the more the individuals is theoretically educated, the more the individual is ethically educated. The knowledge of ideas is the only authentic therapy against the evil in us. (shrink)

Through the reconstruction of Leibniz's theory of the degrees of knowledge, this e-book investigates and explores the intrinsic relationship of imagination with space and time. The inquiry into this relationship defines the logic of imagination that characterizes both human and non-human animals, albeit differently, making them two different species of imaginative animals. -/- Lucia Oliveri explains how the emergence of language in human animals goes hand in hand with the emergence of thought and a different form of rationality constituted (...) by logical inferences based on identity and contradiction, principles that are out of reach of the imagination. The e-book concludes that the presence of innate principles in human animals transforms the way in which they sense-perceive the world, thereby constantly increasing the distinction between human and non-human animals. -/- Keywords: human and non-human animals, Leibniz and Locke on ideas, Leibniz on bodies, Leibniz on conceivability, Leibniz on degrees of knowledge, Leibniz on degrees of perception, Leibniz on innate ideas, Leibniz on modality, Leibniz on similarity and congruence, Leibniz on space and time, Leibniz’s philosophy of language, theory of types. (shrink)

This paper deals with the strategy of defence that Aristotle dedicates to the principle of contradiction; the analysis is concentrated on passages of Metaphysics Gamma 4. The main thesis of the paper is that Aristotle’s strategy is an ontological, and therefore not only a logical, one: the principle is defended on the basis of the, from an ontological point of view, unacceptable consequences which would arise in case of the absence of the principle itself. These consequences are, for instance, the (...) disappearance of properties, of essences, of individual entities and of the plurality of essentially distinguishable entities, since the contents of the properties, the role of properties as essences and the constitution of the individual entities cannot hold, if the principle of contradiction does not hold. The principle of contradiction is, therefore, not only a logical principle: it is the ontological presupposition of the whole reality; without it there is no entity. (shrink)

This essay is the first part of an analysis on the form and matter in the works of Aristotle. Within the whole analysis, I shall examine passages taken from different works of Aristotle that are relevant to the investigation on form and matter. In this essay, I shall focus exclusively on the chapter Metaphysics Zeta 3. The concepts of substance, matter, ontological subject, form, composite substance, this something and separated, which are consistently used by Aristotle within the development of the (...) mentioned chapter, will be part of my survey of the contents of the chapter. The central argument of Metaphysics Zeta 3, which maintains the equivalence between substance and the feature represented by ontological subject, and which leads, through this first equivalence and through the equivalence between matter and ontological subject, to the result that matter is (the only) substance, will be investigated step by step so that all presuppositions, entailments, and consequences of the argument itself can be clearly shown. The problems which are caused by the mentioned equivalence of substance and ontological subject will be pointed out during my look at the chapter’s contents. In particular, Aristotle cannot accept that, in spite of the ontological subject being a correct feature of substance qua substance, substance is therewith reduced to matter. Being the ontological subject does not represent the only ontological feature of substance qua substance; the ontological features too of substance qua substance that are represented by being a this something and being separated belong to the concept of substance: they can never be forgotten within a right interpretation of substance. The identification of substance only with matter can never be accepted. Only the ontological values of substance represented by the form and by the composite substance possess the ontological features “being a this something” and “being separated”. Therefore, the ontological values of substance as form and as a composite substance must always be reckoned with in a correctly interpreted ontology. Neither of these values can be forgotten within an accurate inquiry of ontology. Hence, regardless of whether matter is substance and is correctly interpreted as substance, the values of substance as form and as composite substance must belong, in Aristotle’s view, to any right ontological system whatsoever. The plurality of values for substance, which I personally advocate, finds confirmation thanks to chapter Metaphysics Zeta 3: Matter, form, and composite substance all represent values for substance, despite the differences which they have as regards their own ontological features. (shrink)

The study deals with the main aspects of substance in the works of Aristotle. The presence of a plurality of values for substance is the central idea of the study; in particular, substance has 1) the value of living biological entity and 2) the value of form of the biological entity; both values are fundamental components of Aristotle's theory of substance. The prevalence, in the works of Aristotle, of the first or of the second of the two values depends on (...) the prevailing research interest of Aristotle in each work. The idea of a continuity in Aristotle's interpretation of substance in Aristotle's works is endorsed. This research treats, moreover, of the role of form as actuality, of the relations between form and matter in the material entities, and of the problem of the unity of definition. (shrink)

This study is dedicated to the chapter Metaphysics My 10, which, in my opinion, represents an example of basic research as regards Aristotle’s ontological investigations. The aim of my analysis is to point out that the chapter constitutes a manifesto for a new ontology: this new ontology is Aristotle’s typological ontology. The main entities of the typological ontology are universals, on the one hand, and instantiations of universals, on the other hand. The ontological levels, to which these two kinds of (...) entities belong, are different from each other: therefore they must be kept rigorously separated from each other. The new ontology constitutes a clear opposition to the ontology of ideas. In my opinion Aristotle does not aim at eliminating universals from the range of the existing entities: At least the universals which correspond to biological kinds (such as „man“ or „animal“) and to all the properties connected to these biological kinds are real entities, even though they do not exist at the same level at which the level of the instantiations do. Aristotle’s aim is thus to assign universals and individuals to different realms of reality. The reality consists both of individuals and of universals: these kinds of entities occupy different realms of reality. (shrink)

This study shows that Aristotle’s introduction of the concept of substance represents a caesura in the history of ontology. The study takes two values for substance into consideration, which are a) substance as an organism (as a biological entity) and b) substance as essence, nature, form of an organism. Substances as organisms are biological concretized properties. Substance as form is the soul directing the organism and the development of the organism; the soul is both the principle of life of the (...) organism and the program which is realized in the organism. The substance as an organism is assigned the central position in Aristotle’s ontology: the organism is not reduced to forces or factors which should have an ontological primacy over the organism; the principle of life and activity of every organism is put into the biological entity and it is not identified with factors that lie outside the organism. (shrink)

In my analysis I deal with some causes and origins of evil and of moral degeneration in the human dimension. My analysis focuses on Plato’s Republic. The origins and causes of the presence of injustice and of vice lie in the very structure of the human soul. The division of the soul into parts which are at least reciprocally independent of each other implies that there is the possibility that they are in conflict with each other. This is the origin (...) of injustice and the root of every form of evil. The correct equilibrium among the parts of the soul, which, in my opinion, are to be interpreted as authentic potencies, can be achieved only by developing the rational part. This development requires a thorough education in philosophy. Throughout my analysis I quote passages in which Plato points out the presence of bad instincts and, in general, of a morally difficult component in our soul. The kind of soul considered in my analysis is the embodied soul. (shrink)

The present essay is the first part of an analysis regarding aspects of Aristotle’s ontology. Aristotle’s ontology is, in my opinion, a formal ontology that examines the fundamental structures of reality and that investigates the features belonging to entities such as substance, quantity, quality, universals. Aristotle’s ontology investigates, moreover, the reciprocal relations existing between these entities. Aristotle’s interpretation of universals is not, in my opinion, a nominalist interpretation of universals: I do not think Aristotle regards universals as being only mental (...) entities. Aristotle, rather, aims at the differentiation between the realms of reality to which individuals and universals belong. In this part of my investigation, I first expose my interpretation of the fundaments of Aristotle’s ontology. Thereafter, I concentrate my attention on chapter Metaphysics Zeta 13: I comment on Aristotle’s investigation regarding the ontological features belonging to the universal qua universal and to the substance qua substance. I analyse the ontological laws that Aristotle finds about universal and substance: substance and universals are considered by Aristotle as mutually incompatible entities. The analysis shows that a false interpretation of the features of the universals endangers the whole ontology. Moreover, the Third-Man-Regress, which is one of the consequences of the misunderstanding of the position of universals in the reality, is regarded as the key to the interpretation of one of Aristotle’s aims: Aristotle aims at the foundation of a typological ontology putting individual entities and universal entities on different levels of reality. The danger of the Third-Man-Regress is avoided through the introduction of a new ontology, that is, through the introduction of the typological ontology of the entities. (shrink)

My essay is a first analysis of the fundaments of the animal ethics. Reflections contained in the studies of Tom Regan, of Peter Singer, of Gary Francione are examined in order to present positions which – despite the differences existing between each other – are in favour of the extension of (at least) some rights to (at least) some kinds of animals. I have chosen the positions of Peter Carruthers in order to present positions being strongly against any extension of (...) rights to whichever kind of animals. This essay will be followed by further investigations. (shrink)

This study deals with the ontological position of predicated entities in comparison with the entities of which they are predicated of. Aristotle strongly criticizes, in some passages of his works, the interpretation that the predicated entities are entities which independently exist of the entities of which they are predicated. Aristotle opposes his interpretation of the universals as entities which does not independently exist, against Plato's ideas, which he interprets as independently existing entities. Aristotle's criticism of Plato's ideas is radical: he (...) does not accept any characteristic of ideas and want them to be expelled from a sane ontology. Aristotle's ontology of instantiation, therefore, completely refuses Plato's ontology of participation. (shrink)

Philosophy has long either dismissed or paid only minimal attention to creativity, and even with the rise of research on imagination, the creative imagination has largely been ignored as well. The aim of this volume is to correct this neglect. By bringing together existing research in various sub-disciplines, we also aim to open up new avenues of research. The chapters in Part I provide some framing and history on the philosophical study of imagination and creativity, along with an overview of (...) the empirical literature. Part II explores imagination and creativity as they manifest in, and in turn shape, the individual. Part III surveys the role of imagination and creativity across a wide variety of artistic domains, and the chapters of Part IV turn to societal domains. Part V focuses on the interplay of imagination and creativity with regard to particular features of creative subjects and different kinds of creative subjects. *** -/- Part I: Theories and Approaches 1. Theories of Imagination (Peter Kung) 2. Theories of Creativity (Julia Langkau) 3. Historical Treatments of Imagination in the Western Tradition (Lucia Oliveri) 4. Historical Treatments of Creativity in the Western Tradition (Elliot Paul) 5. Non-Western Treatments of Imagination (Reza Hadisi and Jing Iris Hu) 6. Non-Western Treatments of Creativity (Nicolas B. Verger and Vlad Glăveanu) 7. Empirical Treatments of Imagination and Creativity (Dustin Stokes) 8. Experimental Philosophy of Imagination and Creativity (Michael T. Stuart) 9. The Relationship between Imagination and Creativity (Margherita Arcangeli) -/- Part II: Imagination and Creativity in Mind and Action 10. Imagination, Creativity, and Skill (Amy Kind) 11. Imagination, Creativity, and Attention (Bence Nanay) 12. Imagination, Creativity, and Agency (Caterina Moruzzi) 13. Imagination, Creativity, and Emotion (Julien Deonna and Fabrice Teroni) 14. Imagination, Creativity, and Embodiment (Adriana Clavel-Vázquez and María Jimena Clavel Vázquez) 15. Imagination, Creativity, and Gender (Luke Roelofs) 16. Imagination, Creativity, and Race (Nicholas Whittaker) 17. Imagination, Creativity, and Child Development (Thalia Goldstein, Anna Sofia Caruso, Darian Stapleton, and Lamin Fatty) -/- Part III: Imagination and Creativity in the Arts 18. Imagination, Creativity, and the Visual Arts (Claire Anscomb) 19. Imagination, Creativity, and Music (Matteo Ravasio) 20. Imagination, Creativity, and Fiction (Hannah H. Kim) 21. Imagination, Creativity, and Dance (David Davies and Anna Pakes) 22. Imagination, Creativity, and the Culinary Arts (Patrik Engisch) 23. Imagination, Creativity, and Film (Murray Smith) 24. Imagination, Creativity, and Acting (Tzachi Zamir) 25. Imagination, creativity, and fashion (Laura T. Di Summa) -/- Part IV: Imagination and Creativity in Society 26. Imagination and Creativity in the Scientific Realm (Alice Murphy) 27. Imagination and Creativity in the Moral Realm (Tim Mulgan) 28. Imagination and Creativity in the Political Realm (Avshalom Schwartz) 29. Imagination and Creativity in the Law (Maksymilian Del Mar) 30. Imagination and Creativity in the Religious Realm (Neil Van Leeuwen) 31. Imagination and Creativity in Business (Eric Peterson) 32. Imagination and Creativity in Times of Crisis (Jennifer Fraser and Noah Stemeroff) Part V: Emerging Issues in Imagination and Creativity Research 33. Imagination, Creativity, and Aphantasia (Andrea Blomkvist) 34. Imagination, Creativity, and Neurodivergence (Sofia Ortiz-Hinojosa) 35. Imagination, Creativity, and Non-Human Animals (Henry Shevlin) 36. Imagination, Creativity, and Artificial Intelligence (Peter Langland-Hassan) 37. Collective Imagination and Collective Creativity (Nick Wiltsher) . (shrink)