Mathematicians often consider Zermelo-Fraenkel Set Theory with Choice (ZFC) as the only foundation of Mathematics, and frequently don’t actually want to think much about foundations. We argue here that modern Type Theory, i.e. Homotopy Type Theory (HoTT), is a preferable and should be considered as an alternative.

The paper deals with Leibniz’s ontology and the metaphysics of the aggregate. Concerning the ontology of aggregates, the main aim is to provide _a new argument_ in favor of the claim that an aggregate and its constituents have the same ontological import. This argument takes the form of a weakening of a principle known in the contemporary literature of mereology as ‘composition as identity’ (CAI). The paper shows that Leibniz’s nominalism toward aggregates is a direct consequence of two elements: the (...) way in which he considers the relationship between aggregates and their constituents in his logical calculus; and his theory of identity (and more generally, equivalence relations) as providing us with the ground for substitution _salva veritate_. It is concluded that Leibniz is committed to a principle that the author dubs Ontological-CAI: the aggregate/whole is _ontologically identical_ (i.e. it has the same ontological import) as its constituents/parts. Concerning the metaphysics of aggregates, the paper outlines in what sense aggregates are grounded on their constituents: arguing that Leibniz is committed to a further principle that the author calls Metaphysical-CAI: the aggregate/whole is _metaphysically grounded_ on its constituents/parts. From this it can be understood in which sense Leibniz could be considered a mereological nihilist, and in which sense not. The paper also sets out two different and competing readings of Metaphysical-CAI, and argues that Leibniz accepted both of them by interpreting them as different levels of explanation of the nature of aggregates. (shrink)

This article presents a detailed, novel account of the emergence of (the meaning of) empirical concepts. Acquiring experience and empirical concepts is shown to be the result of multifaceted, cognitive processes, which require both material realization and conceptual interpretation. Generally speaking, the meaning of empirical concepts consists of several distinct components, but it includes at least a structuring and an abstracting component. These two meaning components are abstract entities, which can be justifiably interpreted as real objects. On this basis, I (...) address the subject of emergence. The primary claim is that the abstracting meaning component (but not the structuring one) emerges from its underlying empirical processes: it both depends on and transcends these processes. This claim is expounded by discussing relevant similarities and dissimilarities between the emergence of abstract meanings and a range of central features of emergence prominent in recent debates on this topic. The conception of empirical concepts with emergent abstracting meaning components involves an interpretation that avoids the problematic extremes of both empiricism and Platonism. (shrink)

In the current debate on the metaphysical grounding of semantic properties Donald Davidson is usually taken to represent interpretationism, a stance according to which the meaning of expressions is metaphysically grounded by the process of assigning them semantic values which maximize certain parameters such as truth or rationality of the speaker. This stance is often contrasted with productivism, which takes circumstances of expression’s production, not interpretation, to ground its meaning. In this article, I argue that this widespread understanding of Davidson’s (...) thought is false and that given such demarcation Davidson should be regarded as a productivist. To support my claim, I begin by briefly outlining the state of debate on metasemantics and main theses of Davidson’s program, and then I present three exegetical arguments against interpretationist reading of Davidson’s work. I conclude by reconstructing what I take to be the actual metaphysical picture of semantic properties emerging from Davidson’s work. (shrink)