This paper studies the notions of conceptual grounding and conceptual explanation (which includes the notion of mathematical explanation), with an aim of clarifying the links between them. On the one hand, it analyses complex examples of these two notions that bring to the fore features that are easily overlooked otherwise. On the other hand, it provides a formal framework for modeling both conceptual grounding and conceptual explanation, based on the concept of proof. Inspiration and analogies are drawn with the recent (...) research in metaphysics on the pair metaphysical grounding–metaphysical explanation, and especially with the literature in philosophy of science on the pair causality-causal explanation. (shrink)

In this short paper we consider Linnebo's thin/thick dichotomy: first, we show that it does not overlap with the very common one between abstract/concrete objects; second, on the basis of some difficulties with the distinction, we propose, as a possible way out, to move from thin/thick objects to thin/thick concepts.

Hume’s Principle states that the cardinal number of the concept F is identical with the cardinal number of G if and only if F and G can be put into one-to-one correspondence. The Schwartzkopff-Rosen Principle is a modification of HP in terms of metaphysical grounding: it states that if the number of F is identical with the number of G, then this identity is grounded by the fact that F and G can be paired one-to-one, 353–373, 2011, 362). HP is (...) central to the neo-logicist program in the philosophy of mathematics ; in this paper we submit that, even if the neo-logicists wish to venture into the metaphysics of grounding, they can avoid the SR Principle. In Section 1 we introduce neo-logicism. In Sections 2 and 3 we examine the SR Principle. We then formulate an account of arithmetical facts which does not rest on the SR Principle; we finally argue that the neo-logicists should avoid the SR Principle in favour of this alternative proposal. (shrink)

In Thin objects: an abstractionist account (Oxford University Press, 2018), Øystein Linnebo claims that ‘mathematical objects are thin in the sense that very little is required for their existence’. Linnebo articulates his view in an abstractionist manner: according to Linnebo, the truth of the right‐hand side of a Fregean abstraction principle, which states that two items stand in a given equivalence relation, is sufficient for the truth of its left‐hand side, which states that the same abstract object is associated to (...) both items. This special issue contains nine articles discussing different aspects of Linnebo's book. In this introduction, we provide an opinionated introduction to the Special Issue and an overview of the contributions. (shrink)

A popular stance amongst philosophers is one according to which, in Lewis’ words, “identity is utterly simple and unproblematic”. Building from Lewis’ famous passage on the matter, we reconstruct, and then criticize, an argument to the conclusion that identities cannot be grounded. With the help of relatively uncontroversial assumption concerning identity facts, we show that not all identities are equi-fundamental, and, on the contrary, some appear to be provided potential grounding bases using two-level identity criteria. Further potential grounding bases for (...) identities are presented. Identity might be utterly simple and unproblematic, but this is not sufficient to conclude that identities are ungrounded, or fundamental. (shrink)

In this paper we reconstruct an argument, based on the observations of David Lewis and Jaegwon Kim, according to which, given that identities are necessary, they cannot be grounded; and given that they cannot be grounded, they cannot be explained either. We argue against two key premises of this argument. Furthermore, we present two counterexamples, in the form of two alleged sets of cases of explanation of identities. This argument against the explanation of identities is instrumental for a wider discussion (...) about the nature of explanation itself, in relation with other notions of recent philosophical interest such as grounding. (shrink)

In this paper we introduce some logical and philosophical refinements to OntoClean, first by developing some formal constraints on identity criteria, secondly by specifying a kind of identity criteria, two level identity criteria, whose role is to explain an identity among some entities referring to some other, more basic, entities. Using such refinement we add a formal constraint to the stock of OntoClean meta-constraints (OC+). We, then, observe that two level identity criteria have an intuitive reading in terms of dependence (...) of a kind of entities on some other entities, possibly specified in terms of a grounding relation. Are identity criteria grounding principles? In the second part of the paper we discuss this option. (shrink)