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Single Idea 12833

[filed under theme 9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts ]

Full Idea

In classical mereology, if there are c atoms, where c is any cardinal number, there are 2^c - 1 individuals, so the cardinality of models is restricted. There are no models with cardinality 2, 12 or aleph-0, for example.

Gist of Idea

If there are c atoms, this gives 2^c - 1 individuals, so there can't be just 2 or 12 individuals

Source

Peter Simons (Parts [1987], 1.2)

Book Ref

Simons,Peter: 'Parts: a Study in Ontology' [OUP 1987], p.17

A Reaction

The news that there is no possible world containing just 2 or just 12 individuals ought to worry fans of extensional mereology. A nice challenge for God - create a world containing just 12 individuals.

The 69 ideas from 'Parts'

12819 A 'part' has different meanings for individuals, classes, and masses [Simons]
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]
12815 Classical mereology doesn't apply well to the objects around us [Simons]
12820 Without extensional mereology two objects can occupy the same position [Simons]
12814 Classical mereology says there are 'sums', for whose existence there is no other evidence [Simons]
12817 'Mereological extensionality' says objects with the same parts are identical [Simons]
12822 Proper or improper part: x < y, 'x is (a) part of y' [Simons]
12823 Overlap: two parts overlap iff they have a part in common, expressed as 'x o y' [Simons]
12824 Disjoint: two individuals are disjoint iff they do not overlap, written 'x | y' [Simons]
12825 Product: the product of two individuals is the sum of all of their overlaps, written 'x · y' [Simons]
12826 Sum: the sum of individuals is what is overlapped if either of them are, written 'x + y' [Simons]
12827 Difference: the difference of individuals is the remainder of an overlap, written 'x - y' [Simons]
12828 General sum: the sum of objects satisfying some predicate, written σx(Fx) [Simons]
12829 General product: the nucleus of all objects satisfying a predicate, written πx(Fx) [Simons]
12830 Universe: the mereological sum of all objects whatever, written 'U' [Simons]
12821 The part-relation is transitive and asymmetric (and thus irreflexive) [Simons]
12832 Complement: the rest of the Universe apart from some individual, written x-bar [Simons]
12831 Atom: an individual with no proper parts, written 'At x' [Simons]
12833 If there are c atoms, this gives 2^c - 1 individuals, so there can't be just 2 or 12 individuals [Simons]
12834 Criticisms of mereology: parts? transitivity? sums? identity? four-dimensional? [Simons]
12835 Does Tibbles remain the same cat when it loses its tail? [Simons]
12837 Four dimensional-objects are stranger than most people think [Simons]
12838 Four-dimensional ontology has no change, since that needs an object, and time to pass [Simons]
12836 Fans of process ontology cheat, since river-stages refer to 'rivers' [Simons]
12839 Relativity has an ontology of things and events, not on space-time diagrams [Simons]
12842 There are real relational changes, as well as bogus 'Cambridge changes' [Simons]
12840 I do not think there is a general identity condition for events [Simons]
12841 I don't believe in processes [Simons]
12844 Dissective: stuff is dissective if parts of the stuff are always the stuff [Simons]
12843 With activities if you are doing it you've done it, with performances you must finish to have done it [Simons]
12845 Some natural languages don't distinguish between singular and plural [Simons]
12846 A 'group' is a collection with a condition which constitutes their being united [Simons]
18847 Each wheel is part of a car, but the four wheels are not a further part [Simons]
12847 Mass nouns admit 'much' and 'a little', and resist 'many' and 'few'. [Simons]
12848 The same members may form two groups [Simons]
12850 To individuate something we must pick it out, but also know its limits of variation [Simons]
12849 Sums are more plausible for pluralities and masses than they are for individuals [Simons]
12854 An entrepreneur and a museum curator would each be happy with their ship at the end [Simons]
12855 The 'best candidate' theories mistakenly assume there is one answer to 'Which is the real ship?' [Simons]
12856 Intermittent objects would be respectable if they occurred in nature, as well as in artefacts [Simons]
12857 Tibbles isn't Tib-plus-tail, because Tibbles can survive its loss, but the sum can't [Simons]
12859 A mixture can have different qualities from its ingredients. [Simons]
12858 Mixtures disappear if nearly all of the mixture is one ingredient [Simons]
12860 Sortal nouns for continuants tell you their continuance- and cessation-conditions [Simons]
12862 Gold is not its atoms, because the atoms must be all gold, but gold contains neutrons [Simons]
12863 Mass terms (unlike plurals) are used with indifference to whether they can exist in units [Simons]
12864 We say 'b is part of a', 'b is a part of a', 'b are a part of a', or 'b are parts of a'. [Simons]
12865 Analytic philosophers may prefer formal systems because natural language is such mess [Simons]
12861 'The wolves' are the matter of 'the pack'; the latter is a group, with different identity conditions [Simons]
12866 Composition is asymmetric and transitive [Simons]
12867 A hand constitutes a fist (when clenched), but a fist is not composed of an augmented hand [Simons]
12871 Objects have their essential properties because of the kind of objects they are [Simons]
12870 We must distinguish the de dicto 'must' of propositions from the de re 'must' of essence [Simons]
12872 The zygote is an essential initial part, for a sexually reproduced organism [Simons]
12873 Original parts are the best candidates for being essential to artefacts [Simons]
12874 An essential part of an essential part is an essential part of the whole [Simons]
12875 One false note doesn't make it a performance of a different work [Simons]
12877 Sums of things in different categories are found within philosophy. [Simons]
12876 Philosophy is stuck on the Fregean view that an individual is anything with a proper name [Simons]
12879 Independent objects can exist apart, and maybe even entirely alone [Simons]
12880 Moments are things like smiles or skids, which are founded on other things [Simons]
12883 Moving disturbances are are moments which continuously change their basis [Simons]
12882 A wave is maintained by a process, but it isn't a process [Simons]
12881 A smiling is an event with causes, but the smile is a continuant without causes [Simons]
12886 A whole requires some unique relation which binds together all of the parts [Simons]
12885 Objects like chess games, with gaps in them, are thereby less unified [Simons]
12889 The limits of change for an individual depend on the kind of individual [Simons]
12888 The wholeness of a melody seems conventional, but of an explosion it seems natural [Simons]