Combining Texts
Ideas for
'A Dictionary of Political Thought', 'A Structural Account of Mathematics' and 'Parts'
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30 ideas
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
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9550
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We only know relational facts about the empty set, but nothing intrinsic [Chihara]
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9562
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In simple type theory there is a hierarchy of null sets [Chihara]
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9572
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Realists about sets say there exists a null set in the real world, with no members [Chihara]
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9573
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The null set is a structural position which has no other position in membership relation [Chihara]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
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9551
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What is special about Bill Clinton's unit set, in comparison with all the others? [Chihara]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing
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9549
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The set theorist cannot tell us what 'membership' is [Chihara]
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4. Formal Logic / F. Set Theory ST / 7. Natural Sets
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9571
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ZFU refers to the physical world, when it talks of 'urelements' [Chihara]
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4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
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9563
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A pack of wolves doesn't cease when one member dies [Chihara]
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4. Formal Logic / G. Formal Mereology / 1. Mereology
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12815
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Classical mereology doesn't apply well to the objects around us [Simons]
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12819
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A 'part' has different meanings for individuals, classes, and masses [Simons]
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12832
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Complement: the rest of the Universe apart from some individual, written x-bar [Simons]
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12834
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Criticisms of mereology: parts? transitivity? sums? identity? four-dimensional? [Simons]
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4. Formal Logic / G. Formal Mereology / 2. Terminology of Mereology
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12827
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Difference: the difference of individuals is the remainder of an overlap, written 'x - y' [Simons]
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12828
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General sum: the sum of objects satisfying some predicate, written σx(Fx) [Simons]
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12822
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Proper or improper part: x < y, 'x is (a) part of y' [Simons]
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12823
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Overlap: two parts overlap iff they have a part in common, expressed as 'x o y' [Simons]
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12824
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Disjoint: two individuals are disjoint iff they do not overlap, written 'x | y' [Simons]
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12825
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Product: the product of two individuals is the sum of all of their overlaps, written 'x · y' [Simons]
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12826
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Sum: the sum of individuals is what is overlapped if either of them are, written 'x + y' [Simons]
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12829
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General product: the nucleus of all objects satisfying a predicate, written πx(Fx) [Simons]
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12830
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Universe: the mereological sum of all objects whatever, written 'U' [Simons]
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12831
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Atom: an individual with no proper parts, written 'At x' [Simons]
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12844
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Dissective: stuff is dissective if parts of the stuff are always the stuff [Simons]
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4. Formal Logic / G. Formal Mereology / 3. Axioms of Mereology
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12816
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Classical mereology doesn't handle temporal or modal notions very well [Simons]
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12821
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The part-relation is transitive and asymmetric (and thus irreflexive) [Simons]
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18847
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Each wheel is part of a car, but the four wheels are not a further part [Simons]
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12813
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Two standard formalisations of part-whole theory are the Calculus of Individuals, and Mereology [Simons]
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4. Formal Logic / G. Formal Mereology / 4. Groups
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12848
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The same members may form two groups [Simons]
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12846
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A 'group' is a collection with a condition which constitutes their being united [Simons]
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12861
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'The wolves' are the matter of 'the pack'; the latter is a group, with different identity conditions [Simons]
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