There is a state A, an operation is performed > resulting in a change of state B.
But such a change, to be valid, must occur in the presence of a standard of measure C which is not functionally attached to the state change A > B.
A = C ; A becomes B ; B does not = C
The reason for this is clear. Since A becomes B, there is no record of A to compare with B. C is necessary to validate the embodied changes of state if logic is internalized.(see LP #14)
1.) A bar of metal of unit length (state A) is cooled (>) and now possesses unknown length (state B).
2.) In the absence of an absolute reference frame the outcome of an event in 3-space is unspecified.
The reference required is that which has already been given, i.e. unit space coupled with unit time. The unit space/time validates state A and thus defines as necessary state B by being a functionally disconnected standard.
The previous discussion of an absolute standard reference cannot be completely correct, for to exist relative to something is to interact with it. To interact with means to change state. Thus, for A>B to be validated by C requires a change in C which contradicts the defined absolutism of C.
Hence, there must be some element of the unspecified in any interaction whatsoever.
There are then two contradictory requirements to existence.
Interaction is the embodiment of logical operations.
Therefore, just as any abstract unit is embodied in some form, the fact of its existence relative to other units is embodied in the manner of an interaction, i.e. causal change in the form of the unit or in its relationship to other forms.
Thus, a 'ghost' passing through other forms without the capacity to influence them is simply a variant non-existent.
To exist is to interact with others.
A number of elastic spheres are held in a finite box. They move and in so doing bounce off one another
and the sides of the box. The question is "How is it that they exist relative to one another?"
The probability against this is large and therefore causality is accepted implicitly. But the explicit proof of causality lies in infinite faultless demonstration.
Returning to the box of spheres, if consistent rules of collision are observed, recorded and deduced, what would be the consequence of an inappropriate bounce or of two spheres simply passing through one another? Such a causeless occurence would serve to undercut the valididty of all the consistent bounces.
Existence consists of logic embodying itself, interacting with itself, and validating itself by infinite causal demonstration. Conversely, acausality would consist of logic invalidating itself by acausal demonstration.
The acausal is that which occurs by means unaccountable in principle.
The question then is "Is absolute chance present in what is observed as existence?". The answer must be yes and the reason for its necessary inclusion is symmetry.
If the universe were totally determinate it could be run in reverse back to the starting position. Such a starting position could not be a perfect crystaline lattice formation in principle, for the random set presently observed could not be arrived at without injecting some bit of absolute chance to take it out of perfect symmetry.
Interactive changes validate existence but no change is possible in a state of perfect symmetry because any change is always cancelled by its symmetric inverse. Therefore, existence is impossible without absolute chance (acausality).
Clearly the world cannot be determinate (causal) else it could not appear as it does. Neither can it be indeterminate for this would invalidate logic.
A model of existence will be constructed as a ray (with a beginning and no end in the manner of a number line). At the beginning it will be wholly indeterminate. After an infinite duration it will be wholly determinate. In between (any finite time) it will be part determinate and part indeterminate.
The contradiction is sustained because the universe as a whole does not exist in time or space (LP #14a) so that causality and acausality are logically congruent with respect to the entirety of existence (qua logic).