Philosophy Lexicon of Arguments

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Simons, Peter
 
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Terminology I 14
Product/mereology/Simons: ~ Average = greatest lower bound. - Total: "The individual that overlaps something if it at least overlaps one of x or y - not always = least upper bound (lub) - lattice theory: "smallest individual; which contains both". Definition difference: the largest individual that is in x contained, which has no part in common with y - exists only if x is not part of y - Definition fusion/general sum: is the sum of all objects which satisfies a specific predicate Fx, denoted by the variable-binding operator s: sx [Fx] - There may be several fusions - the sum is the largest fusion.
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I 226
Fusion: includes replacement of the former. E.g. a former F is replaced by two Fs - Definition nucleus/general product: product of the objects that meet a predicate px[Fx] - Universe: sum of all objects. - This corresponds to the unit element of the Boolean algebra. - Atom: an individual that does not have any parts. - Individual general: may have parts. - Universe with 3 atoms (atom) may have 7 individuals. - If there are c atoms, there are 2c- 1 combinations. - It follows that there cannot be even numbers. - Combinations of individuals are individuals themselves again.
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I 32
Definition upper bound/mereology/Simons: the individuals which fulfill a predicate fx are bound up if there is an individual from which they are all a part. - Sum: "the individual that overlaps something if it at least overlaps one of x or y". - ((S) Hasse diagram: the upper point is part of the bottom.) - Universe: upper bound for everything. - The existence of an upper bound does not imply the existence of sums or least upper bounds. - E.g. the set of subsets of natural numbers which are either non-empty or finite or infinite and have a finite complement-. Each collection is upwardly limited by the entire set of natural numbers without a least upper bound. E.g.: collection of all finite sets of even numbers. - E.g. open intervals on the real number strand: here each two open intervals have at least an upper bound, namely the interval whose endpoints.
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I 33
Their outer extreme points are, however, separate intervals with a gap between them and they do not have a sum - if a sum exists, then also a least upper bound but not vice versa. - Being part of a wider whole means: having an upper bound.
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I 60
Definition prosthetics/Lesniewski/Simons: ("first principles"), Lesniewskis counterpart to propositional calculus, which it contains as a fragment. In addition, it includes variables for each type of statements and quantifiers - equivalent with systems of proposition types (statements types) by Church or Henkin.
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I 112
Definition upperbound/mereology/Simons: the individuals who are fulfilling a predicate fx are bound up if there is an individual from which they are all a part. - Sum: "the individual that overlaps something if it overlaps at least one of x or y".
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I 211
Coincidence/Simons: equality of the elements is not sufficient for equality of the parts. - (s) E.g. member-like bodies may have different chairpersons) - coincidence: = temporarily indistinguishable. - The class {Tib + Tail]} has only three parts. - Tibbles can have a lot more.
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I 225
Permanent coincidence of F1 and F2: indistinguishable in the real world. - At most by modal property.
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I 228
Coincidence principle/Simons: coincidence (all parts have in common) is necessary for superposition (two things at the same time in the same place).
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I 228
Composition/Composition/mereology/Simons: E.g. the ship, but not the wood is composed of planks. - A human has parts that are not shared by the collection of atoms.
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I 334
Topology/mereology/Simons topological concepts that go beyond the mereology: adjacency and connectivity - are used for the definition of "whole".

Si I
P. Simons
Parts Oxford New York 1987


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Ed. Martin Schulz, access date 2017-04-24