Abstract
An ontology of continuants and occurrents to be developed in the course of the book within a framework of regions of space and intervals of time is initially outlined in this chapter. First and foremost, quantities of matter, to which the principles of classical mereology are held to apply, are distinguished from material objects, here called individuals, that change their constitutive matter over time and to which mereological principles don’t apply. The motivation for this and detailed development of the features of the constitutes relation (as distinct from mereological parthood) comes in Chaps. 2 and 3. On this understanding, certain lines of objection to classical principles of mereology are put aside. Rehearsing reasons for rejecting some other suggestions for modifying classical principles mereology serves further to illustrate how the mereological concepts are understood here. But the main thrust of the chapter is to emphasise what the mereological principles say and what they leave open concerning the relations of part, overlap, separation and identity and the operations of sum, product and difference. Classical mereology is an incomplete theory whose axioms can be supplemented in various ways to characterise the kind of objects to which they apply. It is shown how this can be done for a theory reasonably called a theory of temporal intervals and again, when supplemented with an additional, nonmereological, primitive, to develop a theory of spatial regions. Both theories are complete first order theories (i.e., no further independent axioms can be added without contradiction). An analogous development doesn’t seem possible for a pure mereological theory of quantities of matter. Develo** a theory of quantities of matter requires introducing times and spaces, as well as other entities, along with predicates relating these various kinds of entities—a project pursued in the following chapters. Readers who are not interested in the technical details may like to skim quickly over the presentations of the theories of times and spaces, together with the proof of completeness, in Sects. 1.3 and 1.4 and their corresponding subsections, and proceed directly to the final section of the chapter which outlines the strategy for the remainder of the book.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Following Chappell (1973) in the use of the term “individual” for what he distinguishes from “matter”.
- 2.
The reference to Duhem reminds us that concern with the macroscopic realm is not equivalently expressed as a concern with the observable as opposed to the theoretical. Two points about his fundamental argument against a rigid distinction between the two (1954, pp. 144–64) are noteworthy here. His holistic argument applies to the macroscopic domain, and the holism is restricted. It is not the global holism of Quine’s “Two Dogmas” which has confused Duhem’s point with the so-called “Duhem-Quine” thesis which sanctions the underdetermination thesis.
- 3.
Philosophers with a special agenda may seek to circumvent the requirement of providing the details of a successful reduction by handwaving generalisation from a simple case that in no way justifies the general eliminative claim. This is not to deny that it may provide motivation for the proponent to pursue the line of enquiry and seek to flesh out the view. But it is in no way adequate to block the pursuit of alternative views not sharing the same vision. Thus, as a step in the presentation of his ontological structuralism, French (2014, Ch. 7) suggests that the general notion of the solidity of material objects is to be understood in terms of, and so eliminated in favour of, the way the Pauli exclusion principle (the antisymmetry requirement) governs the electronic structure of molecules. This leaves untouched the detailed problem of reducing to the properties of elementary particles the melting point of water, the point of maximum density of liquid water, and so on for virtually all the specific properties characterising macroscopic objects. In a later chapter he trades on the difficulties of characterising individual biological organisms (see e.g. Dupré and O’Malley 2009) to indicate how the structuralist viewpoint he advocates might be applicable outside the narrow confines of quantum physics, but without offering any definitive proposal of comparable detail.
In this connection it is interesting to note that the concept of an organism has once more become central to biology, having been denigrated in the twentieth century by population statistics and molecule biochemistry to “nothing more than an epiphenomenon of its genes”. Now, organisms are taken to be the primary agents of evolutionary change and the reductionist tenets of the central dogma, with its excessive reliance on molecular-level explanations, have given way to the view that DNA replication, protein synthesis, etc. proceeds “by virtue of the enabling conditions afforded by the pre-existing fundamental organization of the cell as a whole” (Nicholson 2014, pp. 348, 353).
- 4.
Those who argue that constitution is identity will complain that this is moving the goalposts. But I reply that they set up their discussion by imposing their construal from the outset, and only consider compliant examples.
- 5.
- 6.
An appropriate order relation for circular time (or time in an incomplete theory which leaves the question of linearity or circularity open) would be a 4-place relation of separation closure, which could be defined on the basis of the same mereological resources but will not be pursued here (see Needham 1981, p. 57).
- 7.
What Lowe (1998, p. 96) calls existing in time distinguishing material from abstract objects calls for specific predicates like “occupies”. It is not sufficient to have some property at a time, or as Lowe would have it, to have had, to have now or to be going to have a property. Although I wouldn’t say that 2 + 2 = 4 is ever, and certainly not always, true (nor as Arthur Prior would have it, that it always was, is and always will be that 2 + 2 = 4), numbers do nevertheless stand in relations to times. For example, 4 could well be the present volume of a quantity of gas in cubic meters, or the length in seconds of an interval of time, or the factor by which one interval is longer than another, or the factor by which the length of an interval in seconds is greater than the weight of a quantity of matter in grammes. A time-dependent existence predicate E(π, t) expressing existence in time could be defined in terms of a specific predicate like “occupies” as ∃p Occ(π, p, t). But I wouldn’t call the relation between 4 and t defined by “There is a quantity π whose volume in m3 at t is 4” time-dependent existence expressing the existence of the number 4 in time. The difference regarding existence in time is not merely a matter of being related to times, but specifically that quantities of matter occupy a region of space at a time whereas numbers don’t. Other features that presuppose occupying a region of space, such as participating in a process of reacting chemically with another substance, are also marks of existence in time.
- 8.
“Substance”, here and throughout this book, is used in its ordinary English sense of “chemical substance”.
- 9.
Or van Inwagen’s richer notion of a mereological partition (mutually separate parts whose sum is identical with the whole). In Sect. 9.2 it is argued that a quantity of water cannot be mereologically partitioned into hydrogen and oxygen, nor substances in general into atoms.
References
Clarke, B. L. (1981). A calculus of individuals based on ‘Connection’. Notre Dame Journal of Formal Logic, 22, 204–218.
Clarke, B. L. (1985). Individuals and points. Notre Dame Journal of Formal Logic, 26, 204–218.
Chappell, V. (1973). Matter. Journal of Philosophy, 70, 679–696.
Denbigh, K. G., & Denbigh, J. S. (1985). Entropy in relation to incomplete knowledge. Cambridge: Cambridge University Press.
Duhem, P. (1954). The aim and structure of physical theories. Translated by Philip Wiener of La théorie physique: son objet – Sa structure (Paris, 1914). Princeton: Princeton University Press.
Faye, J. (1997). Is the mark method time dependent? In J. Fay, U. Scheffler, & M. Urchs (Eds.), Perspectives on time (pp. 215–236). Dordrecht: Kluwer.
Frege, G. (1895). Kritische Beleuchtung einiger Punkter in E. Schröders Vorlesungen über die Algebra der Logik. Archiv für systematische Philosophie, 1, 433–456. Translated in P. Geach, & M. Black (1966). Translations from the philosophical writings of gottlob frege. Oxford: Blackwell.
Frigg, R. (2008). A field guide to recent work on the foundations of statistical mechanics. In D. Rickles (Ed.), The Ashgate companion to contemporary philosophy of physics. London: Ashgate.
Hamblin, C. L. (1969). Starting and stop**. The Monist, 53, 410–425.
Hamblin, C. L. (1971). Instants and intervals. Studium Generale, 24, 127–134.
Hawley, K. (2002). How things persist. Oxford: Oxford University Press.
Heller, M. (1990). The ontology of physical objects: Four-dimensional hunks of matter. Cambridge: Cambridge University Press.
Hilgevoord, J. (2002). Time in quantum mechanics. American Journal of Physics, 70, 301–306.
Holden, T. (2004). The architecture of matter: Galileo to Kant. Oxford: Clarendon Press.
Huntington, E. V. (1904). Sets of independent postulates for the algebra of logic. Transactions of the American Mathematical Society, 5, 288–309.
Huntington, E. V. (1913). A set of postulates for abstract geometry, expressed in terms of the simple relation of inclusion. Mathematische Annalen, 73, 522–559.
Johnson, W. E. (1921). Logic (Vol. I). Cambridge: Cambridge University Press.
Lang, S. (1969). Analysis I. Reading: Addison-Wesley.
Leonard, H., & Goodman, N. (1940). The calculus of individuals and its uses. Journal of Symbolic Logic, 5, 45–55.
Lesniewski, S. (1916 [1992]). Foundations of the general theory of sets. I. Translated by D. I. Barnett in S. Lesniewski, Collected works (Vol. 1, pp. 129–73). S. J. Surma, J. Srzednicki, D. I. Barnett, & F. V. Rickey (Eds.). Dordrecht: Kluwer.
Lombard, B. (1986). Events: A metaphysical study. London: Routledge and Kegan Paul.
Lowe, E. J. (1998). The possibility of metaphysics. Oxford: Clarendon Press.
Lowe, E. J. (2006). The four-category ontology. Oxford: Clarendon Press.
Needham, P. (1981). Temporal intervals and temporal order. Logique et Analyse, 24, 49–61.
Needham, P. (1985). Would cause. Acta Philosophica Fennica, 38, 156–182.
Needham, P. (2009b). Reduction and emergence: A critique of Kim. Philosophical Studies, 146, 93–116.
Needham, P. (2010). Nagel’s analysis of reduction: Comments in defence as well as critique. Studies in History and Philosophy of Modern Physics, 41, 163–170.
Nicholson, D. (2014). The return of the organism as a fundamental explanatory concept in biology. Philosophy Compass, 9, 347–359.
Noonan, H. (1993). Constitution is identity. Mind, 102, 133–146.
Potter, M. (2004). Set theory and its philosophy. Oxford: Clarendon Press.
Randlee, D. A., Cui, Z., Cohn, A. G. (1992). A spatial logic based on regions and connection. In B. Nebel, et al. (Eds.), Principles of knowledge representation and reasoning, proceedings of the third international conference (pp. 165–176). Los Altos: Morgan Kaufmann.
Rescher, N. (1955). Axioms for the part relation. Philosophical Studies, 6, 8–11.
Ruben, D. -H. (1983). Social parts and wholes. Mind, 92, 219–238.
Seibt, J. (2000). The dynamic constitution of things. In J. Faye, U. Scheffler, & M. Urchs (Eds.), Facts, things, events (Poznan studies in the philosophy of the sciences and the humanities, Vol. 76, pp. 241–78). Amsterdam: Rodopi.
Sider, T. (2001). Four-dimensionalism: An ontology of persistence and time. Oxford: Oxford University Press.
Simons, P. (1987). Parts: A study in ontology. Oxford: Clarendon Press.
Sklar, L. (1993). Physics and chance: Philosophical issues in the foundations of statistical mechanics. Cambridge: Cambridge University Press.
Tarski, A. (1926) [1983]. Foundations of the geometry of solids. Translated of original 1926 article in Logic, semantics and metamathematics. Indianapolis: Hackett Publishing Company.
van Inwagen, P. (1987). When are objects parts? Philosophical Perspectives, 1(Metaphysics), 21–47.
Vendler, Z. (1967). Verbs and times. In Linguistics and philosophy. Ithica: Cornell University Press.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Needham, P. (2017). Mereology. In: Macroscopic Metaphysics. Synthese Library, vol 390. Springer, Cham. https://doi.org/10.1007/978-3-319-70999-4_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-70999-4_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-70998-7
Online ISBN: 978-3-319-70999-4
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)