(Joint work with Igor Douven.)

In the conceptual spaces framework, natural concepts are often modeled as convex regions within a similarity space—an assumption motivated by the principle of cognitive economy. Convexity is thought to enhance learnability, making such concepts easier to acquire than those that are represented by regions that satisfy topological criteria that are less stringent. In this talk, I critically examine this hypothesis by comparing the learnability of convex concepts to that of merely connected ones. I will present findings from both computational studies using neural networks that are supposed to approximate human concept learning and behavioral experiments with human participants. All studies were conducted within a shape-based similarity space designed to represent various types of containers

Most theories of concepts focus on first-order similarity—how individual instances share features or occupy nearby regions in multidimensional space. However, many conceptual phenomena hinge on detecting patterns of feature covariation rather than simple overlap (Richardson 2019; Solomon & Schapiro 2024). For example, two animal categories may differ in their average feature values yet share analogous internal covariation structures, supporting analogical reasoning and robust generalization. This talk explores the role of covariation in terms of higher-order similarity, arguing that structural similarity across covariational patterns is a crucial yet underappreciated dimension of conceptual organization. I argue that data analysis techniques such as principal component analysis can help formalize this kind of similarity. This perspective accounts for the formation of overhypotheses and structural phenomena such as consistent contrast and value systematicity (Billman & Davies 2005, Dewar & Xu 2010). By moving beyond first-order similarity to the structure of relations among features, we arrive at a two-tier model of conceptual knowledge: intra-concept coherence for local prediction and inter-concept covariational alignment for efficient generalization. This framework might help explain why some conceptual systems are easier to learn, transfer, and remember.

Johnson (1932) and Carnap (1950) independently derived formal versions of enumerative induction that allow for different initial priors and arbitrary sensitivity to new evidence. Though this achievement was monumental for inductive logic, the Johnson-Carnap system could not account for the effects of analogical influences on inductive inferences. The most notable criticism of the system with respect to analogical influences comes from Achinstein (1963). The contribution of my paper is twofold: first, I provide a conceptual mapping of the treatment of analogy in the inductive logic tradition, from Hosiasson-Lindenbaum (1941) and Carnap (1945; 1980) to modern commentators. In particular, I distinguish three kinds of extensions of Carnap’s inductive logic system with respect to analogies: axiomatic (e.g. Huttegger 2019), parametric (e.g. Romeijn 2006), and geometrical approaches (e.g. Sznajder 2021). The second contribution of this paper is to argue that the literature was operating on a productive but fundamental mistake: the extensions of the Johnson-Carnap system did not capture the analogical influence Achinstein had in mind. A recent paper by Huttegger (2019) captures this kind of influence but does not highlight it.

The contemporary debate on Carnapian conceptual engineering largely hinges on the late Carnap’s notion of explication. By contrast, the early Carnap’s notions of rational reconstruction and quasi-analysis have received comparatively little attention. Emphasis has been placed on the continuity (Dutilh-Novaes 2020) or discontinuity (Carus 2007) between rational reconstruction and explication. So far, the comparisons between rational reconstruction and explication have not taken into account the scientific revaluation of Carnap’s quasi-analysis, as developed by Mormann (2009) and Leitgeb (2007). In this contribution, I aim to bridge this gap by drawing a comparison between explication and rational reconstruction that takes into account the mathematical revaluation of Carnap’s quasi-analysis.

I will argue for a thesis of discontinuity between rational reconstruction and explication. Specifically, I contend that (1) rational reconstruction and explication are distinct kinds of conceptual constructions. Moreover, I contend that (2) rational reconstruction exhibits philosophical virtues in responding to objections commonly raised against Carnapian conceptual engineering. To demonstrate (1) and (2), I assume that explication is equivalent to Carnap’s (1950) performances of explication. I also assume that rational reconstruction is equivalent to Carnap’s performance of quasi-analysis in the Aufbau (1928).

Nelson Goodman formulated his general strictures against similarity as an explanatorily useful concept as a reaction to the usage of similarity as a fundament of cognitive development in empiricist philosophy and in Carnap’s Aufbau. His criticism influenced not only philosophers, but also cognitive scientists, who vividly debated on the role and nature of similarity since the 1970ies. One of the critical issues of the debate is the extent to which similarity itself is really fundamental or rather a result of reasoning, categorization and other cognitive processes. This talk aims to revisit the philosophical history of similarity as a foundational notion of explaining cognitive development. In this talk, I explore and cautiously defend the view that some variant of similarity should be considered as a fundamental notion, in line with Carnap’s original framework and the tradition of classical empiricism.