Disposition

φ. For each υ in Γ, υx and γt in Γ, if both (γ, υx) and (γ, γt) are elements of some functor Fu, then υx = γt.

f (γ, γt) ∙ (γ, υx) = φ (γ, γt) ∙ (γ, υx)

ψ. For each υ in Γ, υx and γt in Γ, if either or both (γ, υx) and (γ, γt) are not elements of some functor Fu, then υx ≠ γt.
f (γ, γt) ∙ (γ, υx) = ψ (γ, γt) ∙ (γ, υx)

3.333. ‘The reason a function cannot be its own argument is that the sign for a function is already contains the prototype of its argument, and it cannot contain itself.

‘For let us suppose that the function F(fx) could be its be its own argument: in that case there would be a function ‘F(F(f x))’, in which the outer function F and the inner function F must have different meanings, since the inner one has the form φ(f x) and the outer one has the form ψ(φ(f x)). Only the letter ‘F’ is common to the two functions, but the letter by itself signifies nothing.’

Wittgenstein is clear: 3.333. ‘This immediately becomes clear if instead of F(Fu) we write ‘(φ): F(φu) . φu = Fu’. That disposes of Russell’s paradox.’

It also disposes of the paradox of special relativity and declares that the very possibility of a situation ψ is eliminated. There is another way of writing this:

F: φ (γ, γt) ∙ (γ, υx) ↔ ((φ): F(φu) . φu = Fu)
F: ψ (γ, γt) ∙ (γ, υx) ↔ ¬ ((φ): F(φu) . φu = Fu)

And further. If i is an imaginary aggregate, or if it is merely and indicator, then:

F: φ (γ, γt) ∙ (γ, υx) ↔ ((φ): F(φu) . φu = Fu) = F (φ) ↔ i
F: ψ (γ, γt) ∙ (γ, υx) ↔ ¬ ((φ): F(φu) . φu = Fu) = F (ψ) ↔ ¬ i

This indicator has full forensic authority over the whole matter of a confused physics - both i and its negation ¬ i. The ultimate reduction.

One thing it demonstrates is the ultimate absurdity of Baez’s claim that functors should not have elements (he means, in the sense that sets do) simply because a functor is not strictly a set but enhances categories; this would be much too simplistic.

I personally tend to think that the indicator is representative and not procedural and that it represents the logical canvassing of physical reasoning – or, the logical indication of a metaphysics, although not the metaphysics itself.

I want to dispose of metaphysics actually by means of reducing physics to a logical indicator.