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Ideas for 'Posthumous notes', 'Parts' and 'The Status of Content'

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22 ideas

4. Formal Logic / G. Formal Mereology / 1. Mereology
Classical mereology doesn't apply well to the objects around us [Simons]
Complement: the rest of the Universe apart from some individual, written x-bar [Simons]
Criticisms of mereology: parts? transitivity? sums? identity? four-dimensional? [Simons]
A 'part' has different meanings for individuals, classes, and masses [Simons]
4. Formal Logic / G. Formal Mereology / 2. Terminology of Mereology
Proper or improper part: x < y, 'x is (a) part of y' [Simons]
Overlap: two parts overlap iff they have a part in common, expressed as 'x o y' [Simons]
Disjoint: two individuals are disjoint iff they do not overlap, written 'x | y' [Simons]
Difference: the difference of individuals is the remainder of an overlap, written 'x - y' [Simons]
Product: the product of two individuals is the sum of all of their overlaps, written 'x y' [Simons]
General sum: the sum of objects satisfying some predicate, written σx(Fx) [Simons]
Sum: the sum of individuals is what is overlapped if either of them are, written 'x + y' [Simons]
General product: the nucleus of all objects satisfying a predicate, written πx(Fx) [Simons]
Universe: the mereological sum of all objects whatever, written 'U' [Simons]
Atom: an individual with no proper parts, written 'At x' [Simons]
Dissective: stuff is dissective if parts of the stuff are always the stuff [Simons]
4. Formal Logic / G. Formal Mereology / 3. Axioms of Mereology
Two standard formalisations of part-whole theory are the Calculus of Individuals, and Mereology [Simons]
Classical mereology doesn't handle temporal or modal notions very well [Simons]
The part-relation is transitive and asymmetric (and thus irreflexive) [Simons]
Each wheel is part of a car, but the four wheels are not a further part [Simons]
4. Formal Logic / G. Formal Mereology / 4. Groups
A 'group' is a collection with a condition which constitutes their being united [Simons]
The same members may form two groups [Simons]
'The wolves' are the matter of 'the pack'; the latter is a group, with different identity conditions [Simons]