Cumulative and divisive reference
Marcin Wągiel
OJ591
1 Cumulative reference
(1) ∀x[P(x) → ∀y[P(y) → P(x ⊕ y)]]
A property P is cumulative iff whenever it holds of two things, it also
holds of their sum.
2 Divisive reference
(2) ∀x[P(x) → ∀y[y x → P(y)]]
A property P is divisive iff whenever it holds of something, it also holds
of each of its proper parts.
3 Symbols
P – predicate variable ≈ ‘some property’
x, y – individual variable ≈ ‘some entity’
∀ – universal quantifier ≈ ‘for all’
→ – material implication ≈ ‘if. . . then’
⊕ – sum operation ≈ ‘sum of entities’
– parthood relation ≈ ‘part of an entity’
1