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mereology In logic, philosophy and related fields, mereology ( (root: , ''mere-'', 'part') and the suffix ''-logy'', 'study, discussion, science') is the study of parts and the wholes they form. Whereas set theory is founded on the membership relation bet ...
, an area of
philosophical logic Understood in a narrow sense, philosophical logic is the area of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. Some theorists conceive philosophical ...
, the term gunk applies to any whole whose parts all have further proper parts. That is, a gunky object is not made of indivisible ''atoms'' or '' simples''. Because parthood is transitive, any part of gunk is itself gunk. If point-sized objects are always simple, then a gunky object does not have any point-sized parts. By usual accounts of gunk, such as
Alfred Tarski Alfred Tarski (, born Alfred Teitelbaum;School of Mathematics and Statistics, University of St Andrews ''School of Mathematics and Statistics, University of St Andrews''. January 14, 1901 – October 26, 1983) was a Polish-American logician a ...
's in 1929, three-dimensional gunky objects also do not have other degenerate parts shaped like one-dimensional curves or two-dimensional surfaces. (See also ''
Whitehead's point-free geometry In mathematics, point-free geometry is a geometry whose primitive ontological notion is ''region'' rather than point. Two axiomatic systems are set out below, one grounded in mereology, the other in mereotopology and known as ''connection theor ...
''.) Gunk is an important test case for accounts of the composition of material objects: for instance, Ted Sider has challenged
Peter van Inwagen Peter van Inwagen (; born September 21, 1942) is an American analytic philosopher and the John Cardinal O'Hara Professor of Philosophy at the University of Notre Dame. He is also a Research Professor of Philosophy at Duke University each sprin ...
's account of composition because it is inconsistent with the possibility of gunk. Sider's argument also applies to a simpler view than van Inwagen's: mereological ''nihilism'', the view that only material simples exist. If nihilism is
necessarily true Logical truth is one of the most fundamental concepts in logic. Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity of its constituent propositions. In other words, a logical truth is a statement whic ...
, then gunk is impossible. But, as Sider argues, because gunk is both conceivable and possible, nihilism is false, or at best a contingent truth. Gunk has also played an important role in the history of
topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing h ...
in recent debates concerning change, contact, and the structure of physical
space Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually consider ...
. The composition of space and the composition of material objects are related by ''receptacles''—regions of space that could harbour a material object. (The term receptacles was coined by Richard Cartwright (Cartwright 1975).) It seems reasonable to assume that if space is gunky, a receptacle is gunky and then a material object is possibly gunky. The term was first used by David Lewis in his work ''Parts of Classes'' (1991). Dean W. Zimmerman defends the possibility of atomless gunk (1996b). See also Hud Hudson (2007).


History

Arguably, discussions of material gunk run all the way back to at least Aristotle and possibly as far back as
Anaxagoras Anaxagoras (; grc-gre, Ἀναξαγόρας, ''Anaxagóras'', "lord of the assembly";  500 –  428 BC) was a Pre-Socratic Greek philosopher. Born in Clazomenae at a time when Asia Minor was under the control of the Persian Empire, ...
, and include such thinkers as
William of Ockham William of Ockham, OFM (; also Occam, from la, Gulielmus Occamus; 1287 – 10 April 1347) was an English Franciscan friar, scholastic philosopher, apologist, and Catholic theologian, who is believed to have been born in Ockham, a small vill ...
,
René Descartes René Descartes ( or ; ; Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science. Mathem ...
, and Alfred Tarski. However, the first contemporary mentionings of gunk is found in the writings of
A. N. Whitehead Alfred North Whitehead (15 February 1861 – 30 December 1947) was an English mathematician and philosopher. He is best known as the defining figure of the philosophical school known as process philosophy, which today has found applicat ...
and
Bertrand Russell Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, ar ...
, and later in the writings of David Lewis. Elements of gunk thought are present in
Zeno Zeno ( grc, Ζήνων) may refer to: People * Zeno (name), including a list of people and characters with the name Philosophers * Zeno of Elea (), philosopher, follower of Parmenides, known for his paradoxes * Zeno of Citium (333 – 264 BC), ...
's famous paradoxes of plurality. Zeno argued that if there were such things as discrete instants of time, then objects can never move through time. Aristotle's solution to Zeno's paradoxes involves the idea that time is not made out of durationless instants, but ever smaller temporal intervals. Every interval of time can be divided into smaller and smaller intervals, without ever terminating in some privileged set of durationless instants. In other words, motion is possible because time is gunky. Despite having been a relatively common position in
metaphysics Metaphysics is the branch of philosophy that studies the fundamental nature of reality, the first principles of being, identity and change, space and time, causality, necessity, and possibility. It includes questions about the nature of consci ...
, after
Cantor A cantor or chanter is a person who leads people in singing or sometimes in prayer. In formal Jewish worship, a cantor is a person who sings solo verses or passages to which the choir or congregation responds. In Judaism, a cantor sings and lead ...
's discovery of the distinction between denumerable and non-denumerable infinite
cardinalities In mathematics, the cardinality of a set is a measure of the number of elements of the set. For example, the set A = \ contains 3 elements, and therefore A has a cardinality of 3. Beginning in the late 19th century, this concept was generalized ...
, and mathematical work by Adolf Grünbaum, gunk theory was no longer seen as a necessary alternative to a topology of space made out of points. Recent mathematical work in the topology of spacetime by scholars such as Peter Roeper and Frank Arntzenius have reopened the question of whether a gunky spacetime is a feasible framework for doing
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relat ...
. Possibly the most influential formulation of a theory of gunky spacetime comes from A. N. Whitehead in his seminal work ''Process and Reality''. Whitehead argues that there are no point regions of space and that every region of space has some three-dimensional extension. Under a Whiteheadian conception of spacetime, points, lines, planes, and other less-than-three-dimensional objects are constructed out of a method of "extensive abstraction", in which points, lines, and planes are identified with infinitely converging abstract sets of nested extended regions.


The possibility of gunk

Many, such as Ted Sider (1993) have argued that even the possibility of gunk undermines another position, that of
mereological nihilism In philosophy, mereological nihilism (also called compositional nihilism) is the metaphysical thesis that there are no objects with proper parts. Equivalently, mereological nihilism says that mereological simples, or objects without any proper ...
. Sider's argument is as follows: # Nihilism is either necessarily true, or necessarily false. # Gunk is metaphysically possible. # If gunk is metaphysically possible, then nihilism is not necessarily true. # Therefore, nihilism is necessarily false. This argument is interesting because all it turns upon is whether or not gunk is even possible, not whether or not the actual world is a gunky one. Sider defends 1) by appealing to the fact that since nihilism is a metaphysical thesis, it must be true or false of necessity. In defense of 2), Sider argues that since a gunk world is conceivable; that is, we can imagine a gunky world without any internal contradiction, the gunk must be possible. 3) Follows from an understanding of necessity and possibility that stems from an understanding of possible world semantics. Simply put, a proposition P is necessarily false if and only if it is false in all possible worlds, and if a proposition P is possible, it is true in at least one possible world. Thus, if a proposition is possible, then it is not necessarily false, as it is not false in all possible worlds. 4) Follows deductively from the other premises. Sider's argument is valid, so most strategies to resist the argument have focused on denying one or more of his premises. Strategies that deny 1) have been called the "contingency defense". Deniers of 1) say that the facts that determine the composition of objects are not necessary facts, but can differ in different possible worlds. As such, nihilism is a contingent matter of fact, and the possibility of gunk does not undermine the possibility of nihilism. This is the strategy endorsed by Cameron (2007) and Miller (2010). Alternatively, one could deny 2) and say that gunk is metaphysically impossible. Most strategies that take this route deny 2) in virtue of denying another relatively common intuition: that conceivability entails metaphysical possibility. Although this metaphysical principle dates back to at least the works of Descartes, recent work by philosophers such as Marcus (2004) and Roca-Royes (2010) have shed some doubt on the reliability of conceivability as a guide to metaphysical possibility. Furthermore, Sider's own arguments in defense of 1) seem to undermine the argument. Gunk is also a metaphysical thesis, thus, it seems that (like 1) it would also have to be either necessarily true or necessarily false. The argument would only work if gunk were necessarily true, but this would amount to question-begging.


See also

*
Mereology In logic, philosophy and related fields, mereology ( (root: , ''mere-'', 'part') and the suffix ''-logy'', 'study, discussion, science') is the study of parts and the wholes they form. Whereas set theory is founded on the membership relation bet ...
*
Mereological nihilism In philosophy, mereological nihilism (also called compositional nihilism) is the metaphysical thesis that there are no objects with proper parts. Equivalently, mereological nihilism says that mereological simples, or objects without any proper ...
*
Mereological essentialism In philosophy, mereological essentialism is a mereological thesis about the relationship between wholes, their parts, and the conditions of their persistence. According to mereological essentialism, objects have their parts necessarily. If an obj ...
*
Perdurantism Perdurantism or perdurance theory is a philosophical theory of persistence and identity.Temporal parts
*
Endurantism Endurantism or endurance theory is a philosophical theory of persistence and identity. According to the endurantist view, material objects are persisting three-dimensional individuals wholly present at every moment of their existence, which goes ...
*
Mereotopology In formal ontology, a branch of metaphysics, and in ontological computer science, mereotopology is a first-order theory, embodying mereological and topological concepts, of the relations among wholes, parts, parts of parts, and the boundaries bet ...


References

* Cartwright, Richard, 1975, "Scattered Objects", in
Keith Lehrer Keith Lehrer (born January 10, 1936) is Emeritus Regent's Professor of philosophy at the University of Arizona and a research professor of philosophy at the University of Miami, where he spends half of each academic year. Education and career L ...
, ed., ''Analysis and Metaphysics'' (Dordrecht: Reidel, 1975), pp. 153–171. Reprinted in ''Philosophical Essays'', pp. 171–186. * Hud Hudson, 2007. "Simples and Gunk", ''Philosophy Compass'' 2 (2), pp. 291–302. * Lewis, David, 1970. "Nominalistic Set Theory", ''Noûs'' 4, pp. 225–40. * Lewis, David, 1991. ''Parts of Classes'', Cambridge: Basil Blackwell. * Sider, Ted, 1993. "Van Inwagen and the Possibility of Gunk", ''Analysis''. 53(4): 285-289. , * Tarski, Alfred, 1929. "Foundations of the Geometry of Solids." * Zimmerman, Dean W., 1996a. "Indivisible Parts and Extended Objects: Some Philosophical Episodes from Topology’s Prehistory." ''Monist'' 79(1). 148–180. * Zimmerman, Dean W., 1996b. "Could Extended Objects Be Made Out of Simple Parts? An Argument for 'Atomless Gunk'", ''Philosophy and Phenomenological Research'' 56: 1-29. {{DEFAULTSORT:Gunk (Mereology) Mereology Metaphysics Materialism