UNIVERSALS

PLATO

1. The idea of F, the universal F, is all and only what any F, insofar as an F, is

2. Any F, insofar as an F, is either G or not G.

3. No F, insofar as an F, is G.

4. No F, insofar as an F, is not G.

5. The idea of F is either G or not G, and is neither G nor not G.

ARISTOTLE

1. An F, in general, is thought to be all and only what any F, insofar as an F, is thought to be

2. Any F, insofar as an F, is thought to be either G or not G.

3. No F, insofar as an F, is thought to be G

4. No F, insofar as an F, is thought to be not G

5. an F, in general, is thought to be either G or not G, but is not thought to be G and is not thought to be not G either.

Abstraction: separating in thought that are inseparable in reality

(IÚS)x → Ix Ú Sx

(Triangle x is isosceles-or-scalene implies x is isosceles or x is scalene)

T[(IÚS)x] ~→ T[Ix] Ú T[Sx]

(Thinking that triangle x is isosceles-or-scalene does not imply thinking that x is isosceles or thinking that x is scalene)

Abstrahentium non est mendacium (Those who abstract do not lie)

Any act of thought [thinking (a thing otherwise] than the thing is) is false

Two senses:

(1) Any act of thought that thinks a thing to be otherwise than it is is false

[2] Any act of thought that thinks differently than the thing is is false

But a universal concept is an act of thought thinking the thing universally, while the thing exists “particularly” (i.e., as a particular thing), therefore, even if (1) is true, [2] is false.