This chapter explores a potential analogy between mereological principles and laws of nature. Against a backdrop of what Marmodoro has termed ‘power structuralism’ (and a rejection of a Humean worldview), the connection between parthood and modality may be richer than has hitherto been considered. Mereological principles delineate possibilities for parts and wholes, and putting powers at the centre of a discussion about parthood can furnish a novel conception of mereological laws, much as dispositionalism has done so for natural laws; namely, (...) these principles express connections between fundamental dispositional properties. By extending dispositionalism to comprehend mereology in this way, we can help fulfil its promise to provide a foundational, naturalistic metaphysics, as foundational mereological debates then begin to mirror those relating to dispositionalist views of laws of nature: we may treat natural and mereological laws in tandem, as holding either necessarily or contingently, with associated strategies for dealing with supposed counterexamples to one’s preferred set of mereological principles. We can thus bring new life to the debate over whether questions of composition admit of contingent or only necessary answers. (shrink)

Although mathematical philosophy is flourishing today, it remains subject to criticism, especially from non-analytical philosophers. The main concern is that even if formal tools serve to clarify reasoning, they themselves contribute nothing new or relevant to philosophy. We defend mathematical philosophy against such concerns here by appealing to its metaphysical foundations. Our thesis is that mathematical philosophy can be founded on the phenomenological theory of ideas as developed by Roman Ingarden. From this platonist perspective, the “unreasonable effectiveness of mathematics in (...) philosophy”—to adapt Wigner’s phrase—is analogous to that of mathematical explanations in science. As success-criteria for mathematical philosophy, we propose that it should be correct, responsive, illuminating, promising, relevant, and adequate. (shrink)

In the paper "Full development of Tarski's geometry of solids" Gruszczyński and Pietruszczak have obtained the full development of Tarski’s geometry of solids that was sketched in [14, 15]. In this paper 1 we introduce in Tarski’s theory the notion of congruence of mereological balls and then the notion of diameter of mereological ball. We prove many facts about these new concepts, e.g., we give a characterization of mereological balls in terms of its center and diameter and we prove that (...) the set of all diameters together with the relation of inequality of diameters is the dense linearly ordered set without the least and the greatest element. (shrink)

ABSTRACTHow did the traditional doctrine of parts and wholes evolve into contemporary formal mereology? This paper argues that a crucial missing link may lie in the early modern and especially Wolf...

The special composition question, which asks under which conditions objects compose a further object, establishes a central debate in modern metaphysics. Recent successes of inductive metaphysics, which studies the implications of the natural sciences for metaphysical problems, suggest that insights into the SCQ can be gained by investigating the physics of composite systems. In this work, I show that the minus first law of thermodynamics, which is concerned with the approach to equilibrium, leads to a new approach to the SCQ, (...) the thermodynamic composition principle : Multiple systems in thermal contact compose a single system. This principle, which is justified based on a systematic classification of possible mereological models for thermodynamic systems, might form the basis of an inductive argument for universalism. A formal analysis of the TCP is provided on the basis of mereotopology, which is a combination of mereology and topology. Here, “thermal contact” can be analyzed using the mereotopological predicate “self-connectedness”. Self-connectedness has to be defined in terms of mereological sums to ensure that scattered objects cannot be self-connected. (shrink)

In this paper, using a propositional modal language extended with the window modality, we capture the first-order properties of various mereological theories. In this setting,$\Box \varphi $readsall the parts(of the current object)are$\varphi $, interpreted on the models with awhole-partbinary relation under various constraints. We show that all the usual mereological theories can be captured by modal formulas in our language via frame correspondence. We also correct a mistake in the existing completeness proof for a basic system of mereology by providing (...) a new construction of the canonical model. (shrink)

This paper examines whether classical extensional mereology is adequate for formalizing the whole–parts relation in quantum chemical systems. Although other philosophers have argued that classical extensional and summative mereology does not adequately formalize whole–parts relation within organic wholes and social wholes, such critiques often assume that summative mereology is appropriate for formalizing the whole–parts relation in inorganic wholes such as atoms and molecules. However, my discussion of atoms and molecules as they are conceptualized in quantum chemistry will establish that standard (...) mereology cannot adequately fulfill this task, since the properties and behavior of such wholes are context-dependent and cannot simply be reduced to the summative properties of their parts. To the extent that philosophers of chemistry have called for the development of an alternative mereology for quantum chemical systems, this paper ends by proposing behavioral mereology as a promising step in that direction. According to behavioral mereology, considerations of what constitutes a part of a whole is dependent upon the observable behavior displayed by these entities. Thus, relationality and context-dependence are stipulated from the outset and this makes behavioral mereology particularly well-suited as a mereology of quantum chemical wholes. The question of which mereology is appropriate for formalizing the whole–parts relation in quantum chemical systems is relevant to contemporary philosophy of chemistry, since this issue is related to the more general questions of the reducibility of chemical wholes to their parts and of the reducibility of chemistry to physics, which have been of central importance within the philosophy of chemistry for several decades. More generally, this paper puts contemporary discussions of mereology within the philosophy of chemistry into a broader historical and philosophical context. In doing so, this paper also bridges the gap between formal mereology, conceived as a branch of formal ontology, and “applied” mereology, conceived as a branch of philosophy of science. (shrink)