Alberto Peruzzi

The main motivation of the paper lies in an argument which shows the relevance of the topological notion of lifting for semantic theory. After a brief examination of aspects of knowledge which are described by means of concepts of algebraic geometry, the development of a functorial connection between topology and group theory is related to aspects of logical analysis. In categorical terms, lifting is, with extension, a form of division. As such it is investigated here, starting from simple examples in general topology up to fiber spaces and topoi, in order to appreciate the recurrent pattern, which is finally used to explain the understanding of sentences about abstract domains.

The development of Artificial Intelligence has led to many controversies of philosophical interest involving issues of logic, computer science, software engeneering. The paper goes through the main steps of this development, deals with their philosophical relevance and sketches the unsolved problems, with special emphasis on the AI models of semantic competence. Some criticisms raised to such models in AI, either in its “classical” or “neural networks” format, are examined. On the ground of the discussion of these criticisms, a view is proposed which avoids the inherited gap between the project of AI and naturalistic philosophy and suggests that filling the gap also provides a filter in order to select a definite form of naturalism

The paper addresses the following questions: Which aspects of ‘critical ontology’ can provide effective orientation when confronted by the difficulties inherent to the opposition of logic- inspired philosophy vs phenomenology? Given the cyclical swing between the metaphysical realism of all-embracing Systems and the anti-realistic biases of relativism, does Hartmann offer a really satisfactory equilibrium- point? Is it still possible to construct a philosophical cosmology consistent with the natural sciences, while avoiding positivistic reduction of philosophy to analysis of language? How can we assign philosophy a task that goes beyond the meta-theoretical and the epistemological, while re- nouncing the temptation to adopt the view-from-nowhere? What about the project of a ‘new’ realism that refrains from positing Absolutes and yet admits the existence of perennially open problems, on which the advances of scientific knowledge seem to have little or no effect at all? How to anchor categorial analysis, if not by connecting it to the advances of social, cognitive and natural sciences? Starting from Hartmann’s characterisation of the objective spirit, some of the main motivations behind ontological strat- ification are examined. Its basic principles are formulated in a semi-axiomatic way, followed by a brief scholium in which both the consistency and the indeterminacy of the resulting system are discussed. Then, problems inherent in the hierarchy of strata are approached in terms of category theory. (More specifically, it is argued that the notion of adjointness, central to category theory, is effective in formally representing the constrained emergence of one stratum from another.) A few critical remarks about Hartmann’s treatment of modalities close the paper.