I 14
Product/mereology/Simons: the average equals the greatest lower bound.
Total: "the individual that overlaps something if it at least overlaps one of x or y, is the total. It is not always equivalent to the least upper bound (lub).
Lattice theory: the lattice theory is about the "smallest individual which contains both".
Def difference: the largest individual that is contained in x, which has no part in common with y, exists only if x is not part of y.
Def fusion/general sum: a fusion or 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.
I 226
Fusion: fusion includes replacement of the former. E.g. a former F is replaced by two Fs.
Def nucleus/general product: the nucleus is the product of the objects that meet a predicate px[Fx].
Universe: the universe is the sum of all objects. This corresponds to the unit element of the Boolean algebra.
Atom: an individual that does not have any parts is an atom. An individual in general may have parts. A 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.
I 32
Def 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: here, the upper bound is for everything. The existence of an upper bound does not imply the existence of sums or least upper bound, 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 of its endpoints.
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.
I 60
Def prosthetics/Lesniewski/Simons: ("first principles"): prosthetics is Lesniewski's counterpart to the 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.
I 112
Definition upper bound/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".
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: the coincidence is temporarily indistinguishable. The class {Tib + Tail]} has only three parts. Tibbles can have a lot more.
I 225
Permanent coincidence of F1 and F2: F1 and F2 are indistinguishable in the real world. At most by modal property.
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).
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.
I 334
Topology/mereology/Simons topological concepts that go beyond the mereology: adjacency and connectivity are used for the definition of "whole".
