This volume of essays brings together leading commentators from both sides of the Atlantic to provide an introduction to Badiou's work through critical studies ...

Scientists and philosophers frequently speak about levels of description, levels of explanation, and ontological levels. In this paper, I propose a unified framework for modelling levels. I give a general definition of a system of levels and show that it can accommodate descriptive, explanatory, and ontological notions of levels. I further illustrate the usefulness of this framework by applying it to some salient philosophical questions: (1) Is there a linear hierarchy of levels, with a fundamental level at the bottom? And (...) what does the answer to this question imply for physicalism, the thesis that everything supervenes on the physical? (2) Are there emergent properties? (3) Are higher-level descriptions reducible to lower-level ones? (4) Can the relationship between normative and non-normative domains be viewed as one involving levels? Although I use the terminology of “levels”, the proposed framework can also represent “scales”, “domains”, or “subject matters”, where these are not linearly but only partially ordered by relations of supervenience or inclusion. (shrink)

This paper considers the nature and role of axioms from the point of view of the current debates about the status of category theory and, in particular, in relation to the "algebraic" approach to mathematical structuralism. My aim is to show that category theory has as much to say about an algebraic consideration of meta-mathematical analyses of logical structure as it does about mathematical analyses of mathematical structure, without either requiring an assertory mathematical or meta-mathematical background theory as a "foundation", (...) or turning meta-mathematical analyses of logical concepts into "philosophical" ones. Thus, we can use category theory to frame an interpretation of mathematics according to which we can be structuralists all the way down. (shrink)

Structure–activity relationship and quantitative SAR are modeling methods largely used in assessing biological properties of chemical substances. QSAR is based on the hypothesis that the chemical structure is responsible for the activity; it follows that similar molecules are expected to have similar properties. Similarity plays an important role in read across, which categorizes molecules primarily on the basis of similarity. Similarity, and chemical similarity too, is a property differently perceived by humans. The various proposed metrics often disagree with human judgment, (...) and no a unique metric for chemical similarity is universally adopted. Researchers argued that categorization is not only explained by similarity but depends as well on abstract knowledge and the task to accomplish. Moreover, similarity cannot be the unique explanation of a categorization, as different perceptual processes take place in category formation. Assuming that similarity judgments are deeply rooted in human knowledge and perception, cognitive sciences contributions are as important as the mathematical considerations of the classical theories. After an excursus in the many views of similarity in philosophy, mathematics, and cognitive science, the paper explores how connectionist systems, which loosely mimic the human cognitive system, could improve similarity-based choices. A case study on building SARs using connectionism and deep neural networks shows the role of similarity in building and explaining those models. A discussion about deep learning for QSAR and as a modeling tool for science concludes the presentation. (shrink)

Decision-making typically requires judgments about causal relations: we need to know the causal effects of our actions and the causal relevance of various environmental factors. We investigate how several individuals' causal judgments can be aggregated into collective causal judgments. First, we consider the aggregation of causal judgments via the aggregation of probabilistic judgments, and identify the limitations of this approach. We then explore the possibility of aggregating causal judgments independently of probabilistic ones. Formally, we introduce the problem of causal-network aggregation. (...) Finally, we revisit the aggregation of probabilistic judgments when this is constrained by prior aggregation of qualitative causal judgments. (shrink)

Scientists and philosophers frequently speak about levels of description, levels of explanation, and ontological levels. This paper presents a framework for studying levels. I give a general definition of a system of levels and discuss several applications, some of which refer to descriptive or explanatory levels while others refer to ontological levels. I illustrate the usefulness of this framework by bringing it to bear on some familiar philosophical questions. Is there a hierarchy of levels, with a fundamental level at the (...) bottom? And what does the answer to this question imply for physicalism, the thesis that everything supervenes on the physical? Are there emergent higher-level properties? Are higher-level descriptions reducible to lower-level ones? Can the relationship between normative and non-normative domains be viewed as one involving levels? And might a levelled framework shed light on the relationship between third-personal and first-personal phenomena? (shrink)

This expository paper presents a general framework for representing levels and inter-level relations. The framework is intended to capture both epistemic and ontological notions of levels and to clarify the sense in which levels of explanation might or might not be related to a levelled ontology. The framework also allows us to study and compare different kinds of inter-level relations, especially supervenience and reduction but also grounding and mereological constitution. This, in turn, enables us to explore questions such as whether (...) supervenience implies explanatory reducibility and whether there can be irreducible higher-level explanations or even “emergent” higher-level properties. The paper finally discusses some further philosophical applications: to the free-will debate, the determinism-indeterminism distinction, indexicality and consciousness, and the relationship between positive and normative facts. (shrink)

[The paper is in Polish, an English abstract is given only for information.] This article is intended for philosophers and logicians as a short partial introduction to category theory and its peculiar connection with logic. First, we consider CT itself. We give a brief insight into its history, introduce some basic definitions and present examples. In the second part, we focus on categorical topos semantics for propositional logic. We give some properties of logic in toposes, which, in general, is an (...) intuitionistic logic. We next present two families of toposes whose tautologies are identical with those of classical propositional logic. The relatively extensive bibliography is given in order to support further studies. (shrink)

The Integrated Information Theory (IIT) formulated for the first time in 2004 by the neuroscientist Giulio Tononi, is a theoretical framework aiming to scientifically explain phenomenal consciousness. The IIT is presented in the first part of this work. Broadly speaking, integrated information is an abstract quantitative measure of the causal power a system has on itself. The main claim of IIT is the identity between informational structures and experience. The nature of this identity will be the subject of the second (...) part. One can interpret the IIT as a fundamental law of nature connecting the physical domain to the mental domain. The philosophical implications of such a claim are numerous and they are subject to criticism. This will be the main concern of the third and last part. (shrink)