The Limits of Classical Extensional Mereology for the Formalization of Whole–Parts Relations in Quantum Chemical Systems

Marina Paola Banchetti-Robino

doi:10.3390/philosophies5030016

Abstract

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.

Highlights

This paper examines whether classical extensional mereology is adequate for formalizing the whole–parts relation in quantum chemical systems
Other philosophers have stressed that classical extensional and summative mereology does not adequately formalize whole–parts relation within the organic wholes and social wholes studied by biology and by the social sciences, such critiques often assume that summative mereology is appropriate for formalizing the whole–parts relation in inorganic wholes such as atoms and molecules
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

Summary

Introduction

This paper examines whether classical extensional mereology is adequate for formalizing the whole–parts relation in quantum chemical systems. This paper will contribute to this debate by establishing that standard extensional mereology cannot adequately describe the relations between atoms and molecules as they are conceptualized in quantum chemistry, since the properties and behavior of such systems are context-dependent and resist attempts at reductionist formalization. This context-dependence, includes dependence upon the environment in which the parts and the whole exist and, as in the case of chemistry, the kinds of procedures employed to analyze and synthesize such systems. This paper argues that such a summative mereology cannot adequately describe the whole–parts relation within higher-order wholes, in which the properties of the whole cannot be formalized as a simple summation of the properties of the individual parts

The Fundamental Principles of Standard Summative Extensional Mereology

Conclusions