| 17245 | A part of a part is a part of a whole [Hobbes] |
| Full Idea: A part of a part is a part of a whole. | |
| From: Thomas Hobbes (De Corpore (Elements, First Section) [1655], 2.07.09) |
| 18999 | y is only a proper part of x if there is a z which 'makes up the difference' between them [Yablo] |
| Full Idea: The principle of Supplementation says that y is properly part of x, only if a z exists that 'makes up the difference' between them. [note: that is, z is disjoint from y and sums with y to form x] | |
| From: Stephen Yablo (Aboutness [2014], 03.2) |
| 10564 | We might combine the axioms of set theory with the axioms of mereology [Fine,K] |
| Full Idea: We might combine the standard axioms of set theory with the standard axioms of mereology. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 14984 | Which should be primitive in mereology - part, or overlap? [Sider] |
| Full Idea: Should our fundamental theory of part and whole take 'part' or 'overlap' as primitive? | |
| From: Theodore Sider (Writing the Book of the World [2011], 02.3) |
| 12816 | Classical mereology doesn't handle temporal or modal notions very well [Simons] |
| Full Idea: The underlying logic of classical extensional mereology does not have the resources to deal with temporal and modal notions such as temporary part, temporal part, essential part, or essential permanent part. | |
| From: Peter Simons (Parts [1987], Intro) | |
| A reaction: Simons tries to rectify this in the later chapters of his book, with modifications rather than extensions. Since everyone struggles with temporal and modal issues of identity, we shouldn't judge too harshly. |
| 12813 | Two standard formalisations of part-whole theory are the Calculus of Individuals, and Mereology [Simons] |
| Full Idea: The standardly accepted formal theory of part-whole is classical extensional mereology, which is known in two logical guises, the Calculus of Individuals of Leonard and Goodman, and the Mereology of Lesniewski. | |
| From: Peter Simons (Parts [1987], Intro) | |
| A reaction: Simons catalogues several other modern attempts at axiomatisation in his chapter 2. |
| 12821 | The part-relation is transitive and asymmetric (and thus irreflexive) [Simons] |
| Full Idea: Formally, the part-relation is transitive and asymmetric (and thus irreflexive). Hence nothing is a proper part of itself, things aren't proper parts of one another, and if one is part of two which is part of three then one is part of three. | |
| From: Peter Simons (Parts [1987], 1.1.1) |
| 18847 | Each wheel is part of a car, but the four wheels are not a further part [Simons] |
| Full Idea: The four wheels of a car are parts of it (each is part of it), but there is not a fifth part consisting of the four wheels. | |
| From: Peter Simons (Parts [1987], 4.6) | |
| A reaction: This raises questions about the transitivity of parthood. If there are parts of parts of wholes, the basic parts are OK, and the whole is OK, but how can there also be an intermediate part? Try counting the parts of this whole! |
| 10677 | Extensional mereology needs two definitions and two axioms [Hossack] |
| Full Idea: Extensional mereology defs: 'distinct' things have no parts in common; a 'fusion' has some things all of which are parts, with no further parts. Axioms: (transitivity) a part of a part is part of the whole; (sums) any things have a unique fusion. | |
| From: Keith Hossack (Plurals and Complexes [2000], 5) |