Бөліктер мен тұтастар: Mereологияның философиялық зерттеуі

Study of parts and the wholes they form
Mereology (from Greek μέρος 'part' (root: μερε , mere , 'part') and the suffix logy, 'study, discussion, science') is the philosophical study of part whole relationships, also called parthood relationships. As a branch of metaphysics, mereology examines the connections between parts and their wholes, exploring how components interact within a system. This theory has roots in ancient philosophy, with significant contributions from Plato, Aristotle, and later, medieval and Renaissance thinkers like Thomas Aquinas and John Duns Scotus. Mereology gained formal recognition in the 20th century through the pioneering works of Polish logician Stanisław Leśniewski, who introduced it as part of a comprehensive framework for logic and mathematics, and coined the word "mereology". the theoretical framework continues to be influential. For a long time, nearly all philosophers and mathematicians avoided mereology, seeing it as tantamount to a rejection of set theory. Goodman too was a nominalist, and his fellow nominalist Richard Milton Martin employed a version of the calculus of individuals throughout his career, starting in 1941. Much early work on mereology was motivated by a suspicion that set theory was ontologically suspect, and that Occam's razor requires that one minimise the number of posits in one's theory of the world and of mathematics. Mereology replaces talk of "sets" of objects with talk of "sums" of objects, objects being no more than the various things that make up wholes. Many logicians and philosophers reject these motivations, on such grounds as:
They deny that sets are in any way ontologically suspect
Occam's razor, when applied to abstract objects like sets, is either a dubious principle or simply false
Mereology itself is guilty of proliferating new and ontologically suspect entities such as fusions. For a survey of attempts to found mathematics without using set theory, see Burgess and Rosen (1997). In the 1970s, thanks in part to Eberle (1970), it gradually came to be understood that one can employ mereology regardless of one's ontological stance regarding sets. This understanding is called the "ontological innocence" of mereology. This innocence stems from mereology being formalizable in either of two equivalent ways:
Quantified variables ranging over a universe of sets
Schematic predicates with a single free variable. Once it became clear that mereology is not tantamount to a denial of set theory, mereology became largely accepted as a useful tool for formal ontology and metaphysics. In set theory, singletons are "atoms" that have no (non empty) proper parts; many consider set theory useless or incoherent (not "well founded") if sets cannot be built up from unit sets. The calculus of individuals was thought to require that an object either have no proper parts, in which case it is an "atom", or be the mereological sum of atoms. Eberle (1970), however, showed how to construct a calculus of individuals lacking "atoms", i. e., one where every object has a "proper part" (defined below) so that the universe is infinite. There are analogies between the axioms of mereology and those of standard Zermelo–Fraenkel set theory (ZF), if Parthood is taken as analogous to subset in set theory. On the relation of mereology and ZF, also see Bunt (1985). One of the very few contemporary set theorists to discuss mereology is Potter (2004). Lewis (1991) went further, showing informally that mereology, augmented by a few ontological assumptions and plural quantification, and some novel reasoning about singletons, yields a system in which a given individual can be both a part and a subset of another individual. Various sorts of set theory can be interpreted in the resulting systems. For example, the axioms of ZFC can be proven given some additional mereological assumptions. Forrest (2002) revises Lewis's analysis by first formulating a generalization of CEM, called "Heyting mereology", whose sole nonlogical primitive is Proper Part, assumed transitive and antireflexive. There exists a "fictitious" null individual that is a proper part of every individual. Two schemas assert that every lattice join exists (lattices are complete) and that meet distributes over join. On this Heyting mereology, Forrest erects a theory of pseudosets, adequate for all purposes to which sets have been put.

Husserl never claimed that mathematics could or should be grounded in part whole rather than set theory. Lesniewski consciously derived his mereology as an alternative to set theory as a foundation of mathematics, but did not work out the details. Goodman and Quine (1947) tried to develop the natural and real numbers using the calculus of individuals, but were mostly unsuccessful; Quine did not reprint that article in his Selected Logic Papers. In a series of chapters in the books he published in the last decade of his life, Richard Milton Martin set out to do what Goodman and Quine had abandoned 30 years prior. A recurring problem with attempts to ground mathematics in mereology is how to build up the theory of relations while abstaining from set theoretic definitions of the ordered pair. Martin argued that Eberle's (1970) theory of relational individuals solved this problem. Topological notions of boundaries and connection can be married to mereology, resulting in mereotopology; see Casati and Varzi (1999: ch. 4,5). Whitehead's 1929 Process and Reality contains a good deal of informal mereotopology.

Bunt (1985), a study of the semantics of natural language, shows how mereology can help understand such phenomena as the mass–count distinction and verb aspect. But Nicolas (2008) argues that a different logical framework, called plural logic, should be used for that purpose. Also, natural language often employs "part of" in ambiguous ways (Simons 1987 discusses this at length). Hence, it is unclear how, if at all, one can translate certain natural language expressions into mereological predicates. Steering clear of such difficulties may require limiting the interpretation of mereology to mathematics and natural science. Casati and Varzi (1999), for example, limit the scope of mereology to physical objects.

In metaphysics there are many troubling questions pertaining to parts and wholes. One question addresses constitution and persistence, another asks about composition.

In metaphysics, there are several puzzles concerning cases of mereological constitution, that is, what makes up a whole. There is still a concern with parts and wholes, but instead of looking at what parts make up a whole, the emphasis is on what a thing is made of, such as its materials, e. g., the bronze in a bronze statue. Below are two of the main puzzles that philosophers use to discuss constitution. Ship of Theseus: Briefly, the puzzle goes something like this. There is a ship called the Ship of Theseus. Over time, the boards start to rot, so we remove the boards and place them in a pile. First question, is the ship made of the new boards the same as the ship that had all the old boards? Second, if we reconstruct a ship using all of the old planks, etc. from the Ship of Theseus, and we also have a ship that was built out of new boards (each added one by one over time to replace old decaying boards), which ship is the real Ship of Theseus? Statue and Lump of Clay: Roughly, a sculptor decides to mold a statue out of a lump of clay. At time t1 the sculptor has a lump of clay. After many manipulations at time t2 there is a statue. The question asked is, is the lump of clay and the statue (numerically) identical? If so, how and why? Constitution typically has implications for views on persistence: how does an object persist over time if any of its parts (materials) change or are removed, as is the case with humans who lose cells, change height, hair color, memories, and yet we are said to be the same person today as we were when we were first born. For example, Ted Sider is the same today as he was when he was born—he just changed. But how can this be if many parts of Ted today did not exist when Ted was just born? Is it possible for things, such as organisms to persist? And if so, how? There are several views that attempt to answer this question. Some of the views are as follows (note, there are several other views):

(a) Constitution view. This view accepts cohabitation. That is, two objects share exactly the same matter. Here, it follows, that there are no temporal parts. (b) Mereological essentialism, which states that the only objects that exist are quantities of matter, which are things defined by their parts. The object persists if matter is removed (or the form changes); but the object ceases to exist if any matter is destroyed. (c) Dominant Sorts. This is the view that tracing is determined by which sort is dominant; they reject cohabitation. For example, lump does not equal statue because they're different "sorts". (d) Nihilism—which makes the claim that no objects exist, except simples, so there is no persistence problem. (e) 4 dimensionalism or temporal parts (may also go by the names perdurantism or exdurantism), which roughly states that aggregates of temporal parts are intimately related. For example, two roads merging, momentarily and spatially, are still one road, because they share a part. (f) 3 dimensionalism (may also go by the name endurantism), where the object is wholly present. That is, the persisting object retains numerical identity.

One question that is addressed by philosophers is which is more fundamental: parts, wholes, or neither? Another pressing question is called the special composition question (SCQ): For any Xs, when is it the case that there is a Y such that the Xs compose Y? This question has caused philosophers to run in three different directions: nihilism, universal composition (UC), or a moderate view (restricted composition). The first two views are considered extreme since the first denies composition, and the second allows any and all non spatially overlapping objects to compose another object. The moderate view encompasses several theories that try to make sense of SCQ without saying 'no' to composition or 'yes' to unrestricted composition.

There are philosophers who are concerned with the question of fundamentality. That is, which is more ontologically fundamental the parts or their wholes. There are several responses to this question, though one of the default assumptions is that the parts are more fundamental. That is, the whole is grounded in its parts. This is the mainstream view. Another view, explored by Schaffer (2010) is monism, where the parts are grounded in the whole. Schaffer does not just mean that, say, the parts that make up my body are grounded in my body. Rather, Schaffer argues that the whole cosmos is more fundamental and everything else is a part of the cosmos. Then, there is the identity theory which claims that there is no hierarchy or fundamentality to parts and wholes. Instead wholes are just (or equivalent to) their parts. There can also be a two object view which says that the wholes are not equal to the parts—they are numerically distinct from one another. Each of these theories has benefits and costs associated with them. This theory, though well explored, has its own problems: it seems to contradict experience and common sense, to be incompatible with atomless gunk, and to be unsupported by space time physics. Many more hypotheses continue to be explored. A common problem with these theories is that they are vague. It remains unclear what "fastened" or "life" mean, for example. And there are other problems with the restricted composition responses, many of them which depend on which theory is being discussed.