Matías Osta-Vélez

Category-based induction is an inferential mechanism that uses knowledge of conceptual relations in order to estimate how likely is for a property to be projected from one category to another. During the last decades, psychologists have identified several features of this mechanism, and they have proposed different formal models of it. In this article; we propose a new mathematical model for category-based induction based on distances on conceptual spaces. We show how this model can predict most of the properties of this kind of reasoning while providing a solid theoretical foundation for it. We also show that it subsumes some of the previous models proposed in the literature and that it generates new predictions.

Over the past few decades, cognitive science has identified several forms of reasoning that make essential use of conceptual knowledge. Despite significant theoretical and empirical progress, there is still no unified framework for understanding how concepts are used in reasoning. This paper argues that the theory of conceptual spaces is capable of filling this gap. Our strategy is to demonstrate how various inference mechanisms which clearly rely on conceptual information—including similarity, typicality, and diagnosticity-based reasoning—can be modeled using principles derived from conceptual spaces. Our first topic analyzes the role of expectations in inductive reasoning and their relation to the structure of our concepts. We examine the relationship between using generic expressions in natural language and common-sense reasoning as a second topic. We propose that the strength of a generic can be described by distances between properties and prototypes in conceptual spaces. Our third topic is category-based induction. We demonstrate that the theory of conceptual spaces can serve as a comprehensive model for this type of reasoning. The final topic is analogy. We review some proposals in this area, present a taxonomy of analogical relations, and show how to model them in terms of distances in conceptual spaces. We also briefly discuss the implications of the model for reasoning with concepts in artificial systems.

This thesis studies the role of conceptual content in inference and reasoning. The first two chapters offer a theoretical and historical overview of the relation between inference and meaning in philosophy and psychology. In particular, a critical analysis of the formality thesis, i.e., the idea that rational inference is a rule-based and topic-neutral mechanism, is advanced. The origins of this idea in logic and its influence in philosophy and cognitive psychology are discussed. Chapter 3 consists of an analysis of the relationship between inference and representation. It is argued that inference has to be studied from a pluralistic per- spective due to its dependence on different formats of representing information. The following four chapters apply conceptual spaces, a formal theory of concepts within cognitive semantics, to three concept-based inference-types. First, an explication of Sellars notion of material inference is advanced. Later, the model is extended to account for nonmonotonic inference by studying the role expectations in reasoning. Finally, a conceptual space-model of category-based induction is presented. This model predicts most of the empirical properties of this psychological phenomenon and subsumes some of the previous theories in psychology. It is stated that the explanatory fruitfulness of this new approach is evidence for the failure of the formality thesis and calls for a unified model of rational inference that puts semantics at center stage. The last chapter of the thesis discusses how inference and concepts interact in scientific reasoning, which makes constant use of hybrid symbolic structures for representing conceptual information. Stephen Toulmin’s notions of method of representation and inferential technique are developed and applied in a case study about the emergence of the notion of instantaneous speed during the passage from geometrical physics to analytical mechanics. It is claimed that this analysis provides support to the pluralistic perspective for theorizing about reasoning.

In this article I am going to reconstruct Stephen Toulmin’s procedural theory of concepts and explanations in order to develop two overlooked ideas from his philosophy of science: methods of representations and inferential techniques. I argue that these notions, when properly articulated, could be useful for shedding some light on how scientific reasoning is related to representational structures, concepts, and explanation within scientific practices. I will explore and illustrate these ideas by studying the development of the notion of instantaneous speed during the passage from Galileo’s geometrical physics to analytical mechanics. At the end, I will argue that methods of representations could be considered as constitutive of scientific inference; and I will show how these notions could connect with other similar ideas from contemporary philosophy of science like those of models and model-based reasoning.

In Gärdenfors and Makinson :197–245, 1994) and Gärdenfors it was shown that it is possible to model nonmonotonic inference using a classical consequence relation plus an expectation-based ordering of formulas. In this article, we argue that this framework can be significantly enriched by adopting a conceptual spaces-based analysis of the role of expectations in reasoning. In particular, we show that this can solve various epistemological issues that surround nonmonotonic and default logics. We propose some formal criteria for constructing and updating expectation orderings based on conceptual spaces, and we explain how to apply them to nonmonotonic reasoning about objects and properties.