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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.
Gist of Idea
Two standard formalisations of part-whole theory are the Calculus of Individuals, and Mereology
Source
Peter Simons (Parts [1987], Intro)
Book Ref
Simons,Peter: 'Parts: a Study in Ontology' [OUP 1987], p.1
A Reaction
Simons catalogues several other modern attempts at axiomatisation in his chapter 2.
| 17245 | A part of a part is a part of a whole [Hobbes] |
| 18999 | y is only a proper part of x if there is a z which 'makes up the difference' between them [Yablo] |
| 10564 | We might combine the axioms of set theory with the axioms of mereology [Fine,K] |
| 14984 | Which should be primitive in mereology - part, or overlap? [Sider] |
| 12813 | Two standard formalisations of part-whole theory are the Calculus of Individuals, and Mereology [Simons] |
| 12816 | Classical mereology doesn't handle temporal or modal notions very well [Simons] |
| 12821 | The part-relation is transitive and asymmetric (and thus irreflexive) [Simons] |
| 18847 | Each wheel is part of a car, but the four wheels are not a further part [Simons] |
| 10677 | Extensional mereology needs two definitions and two axioms [Hossack] |