Matteo D’Angelo (University of Chieti-Pescara) - Logical Rules and Human Rationality

Looking for a more exhaustive definition of the term "logic", which renders justice of its many nuances, one comes across the reductionist tendency to identify this science -- in its general sense -- with its only deductive part. We can ear the echo of this tendency also in non-specialistic dictionaries, in which the definition of logic, as "science of the correct reasoning", implicitly or explicitly refers to features  only typical of the deductive logic.

A critique of this standard and incorrect definition is the basis to  introduce the notion of "context-situated reasoning": a notion formally introduced by Piazza and Pulcini, whose philosophical consequences are:

1. A different general definition of logic closer to the concept of human rationality;
2. An alternative to the old and stale debate between monists and pluralists;

A total rethinking of the relationship between classical and non-classical logics (especially non monotonic, paraconsistent and relevance logics).

Matias Osta Velez (Université de Paris 1 Panthéon-Sorbonne/IHPST - Ludwig-Maximilians-Universität München/Munich Center for Mathematical Philosophy) - Modeling categorical inferences with conceptual spaces

Reasoning and concepts are two central research areas in philosophy and cognitive psychology. Surprisingly enough, they have traditionally been understood as independent topics and they rarely intersect in the literature. This is probably due to the fact that reasoning studies have been dominated by a logicist approach that conceives inference as a purely formal-syntactic processes (i.e. non semantical), that builds on some set of domain general and topic-neutral rules of inference. In that view, lexical concepts are seen as inferentially inert, that is, not playing any crucial role the very process of inference and reasoning.

However, as some have already argued (see Evans 1989; Thagard 1984; Gärdenfors 2000), if we look beyond deductive reasoning the relationship between concepts and everyday inference is much more intimate than it was traditionally thought. For instance, inferential processes that deal with uncertainty seem to strongly rely on background knowledge of the agent. These mechanisms are hardly formal since they exploit semantic information that is not codified at the symbolic-propositional level (see Gärdenfors & Stephens 2018). Explaining how they work would require a theory about how such conceptual information is structured and then exploited in inferential procedures.

One of these semantic-based inferential mechanisms is category-based induction (Rips 1975), a kind of inductive reasoning that exploits information about individual categories (and about relations among categories) for estimating the probability of property projection among members of them. For instance, the inference “Dogs have sesamoid bones, then wolves have sesamoid bones” relies on the conceptual similarities among the categories DOG and WOLVES, and not on the logical form of the argument or some other propositionally codified property.

In this presentation, I will discuss the main features of category-based induction, and I will propose conceptual spaces (Gärdenfors 2000, 2014) as an explanatory framework for it. Conceptual spaces is a theory about the structure and organization of conceptual knowledge, which includes a formal apparatus for modeling conceptual relations by using geometrical and topological tools. Building on some of these tools, I’ll propose a formal model capable of predicting a good deal of the phenomena that characterize category-based inferences according to the empirical literature in cognitive psychology (Rips 1975; Osherson et al. 1990; Sloman 1998). More specifically, I use the built-in distance function of conceptual spaces, and the fact that they can capture the prototypical structure of categories by using Voronoi tessellations (Gärdenfors 2000), for modeling the two main factors contributing to argumentstrength: similarity and typicality relations among categories within a particular conceptual structure.

At the end, I will compare the above proposal with other two classical models of category-based induction: the similarity-coverage model (Osherson et al. 1990) and the featurebased model (Sloman 1998). And I will discuss how to extend this approach to more sophisticated semantic-based inferences, like interpolative reasoning and analogical inferences.

References

Evans, J. S. B. T. (1989). Concepts and Inference. Mind & Language, 4(1‐2), 29–34.
Gärdenfors, P. (2000). Conceptual Spaces. MIT Press.
Gärdenfors, P. (2011). Semantics Based on Conceptual Spaces. In X. He, J. Horty, & E.
Pacuit (Eds.), Logic, Rationality, and Interaction (Vol. 6521, pp. 1–11). Berlin,
Heidelberg: Springer.
Gärdenfors, P., & Stephens, A. (2018). Induction and knowledge-what. European Journal
for Philosophy of Science, 8(3), 471–491.
Osherson, D., Smith, E. E., Wilkie, O., López, A., & Shafir, E. (1990). Category-Based
Induction. Psychological Review, 97(2), 185–200.
Rips, L. J. (1975). Inductive Judgments about Natural Categories. Journal of Verbal
Learning and Verbal Behavior , 14, 665–681.
Sloman, S. A. (1998). Categorical Inference Is Not a Tree: The Myth of Inheritance
Hierarchies. Cognitive Psychology, 35(1), 1–33.
Thagard, P. (1984). Frames, knowledge, and inference. Synthese, 61(2), 233–259.