[BNP/E3, 13A – 23-24]

1.

Charles Robert Anon    Book II.

Proposition I.

Two opposite things are identical.

For two things to be perfectly opposite they must both be absolute, relative only in regard to each other. For ex., to oppose good and evil properly we must take absolute good and evil; as relatives they would be degrees of one of themselves, as, for instance, more or less good, more or less evil and so forth.

       Now, to prove this by mathematics, there are 2 absolutes: zero (absolute nothing) and infinity, all (absolute thing). Here is the proof:

       Take anything say a which is, by human reason infinitely multipliable and divisible

       Multiplying, by mathematics:

           a × ∞ = ∞        (i)

Dividing, also by mathematics,

            = 0           (ii)

Substituting in (i) the value of a, we have

           (0 × ∞) ∞ = ∞

               0 × ∞ = ∞

           whence    0 = ∞

Q. E. D.

[23^v]

Proposition II.

Any two unlike things are identical.

Let a and b be two unlike things.

Divide each by infinity, since each is (by reason) so divisible

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Proof

Idea of infinity the only true “idea” in the human mind. (reason)

Proof  a) According to Idealism = There being no exterior world, there is no limit, limit being suggested only by the object.

          b) According to Realism = Attributes of objects such as extension, duration are only limited in the object. By themselves they are without end.

[24^r]

Human Reason claims in things infinite divisibility.

For if anything be not infinitely divisible, it is not divisible at all; to be divisible it cannot be so finitely. If it be not divisible, then the universe is not divisible and the existence of this thing is a pure illusion. But since infinite = 0, to be infinitely divisible is not to be divisible.

If it be infinitely divisible then its quotient by infinity is zero (Mathematics).

Then it is equal to zero multiplied by infinity, which gives zero for zero multiplied by infinity is zero and no more.

If a thing be infinitely divisible call one of these ultimate facts or atoms a

Then we have{…}

(But what is indivisible is not multipliable).

[24^v]

Negation of:   Extension.

              Relation.

Being is:     One (?)

              Infinite (+ zero)?

              External (+ zero?)

              Immutable

              There is no Past nor Future

_______

Since each part of the infinite is O and since zero is equal to the infinite (Proposition I) then, infinity is divisible into itself, i.e. is indivisible. Therefore All plurality is an illusion. For if infinite be divisible each of its parts = 0.