Determinism
and Causality

 L
ogical concepts are 'fixed' relative to one another in this manner.
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)

Examples:

1.) A bar of metal of unit length (state A) is cooled (>) and now possesses unknown length (state B).
In the absence of a standard of measure (context or state C) it cannot be known if the bar has increased in length, decreased or stayed the same.
Placing the bar next to an uncooled bar (C) logically 'fixes' (validates) the state B.

2.) In the absence of an absolute reference frame the outcome of an event in 3-space is unspecified.
If two objects approach one another (A) whether x or y will collide with one another (B) cannot be predicted. No such prediction is possible because each either (x or y) may be rotating at such a rate as to keep the same face to the other. In this case they may appear to approach, stop instantaneously, reverse direction and move away without colliding. Or they may move ever more slowly never reaching a collision.
Without an absolute reference to standards of space and time the outcome of such an event cannot be specified.

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.
To be logically valid, events must be absolutely determined ; but no method of such determination is possible in principle.

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 brief definition of existence is 'consistency of interaction'. To understand this and its ramifications observe the following thought experiment.

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?"
Clearly, it could be said that each ball is an independent existent which just by chance follows a trajectory which corresponds to altered direction just at the instant it 'seems' to touch another independent existent (giving the illusion of a causal relationship).

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 roll of a die may be called determinate chance (there are physical reasons why a particular number comes up). 'Absolute chance' is however a non-mechanical concept, i.e. an action without cause 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.
Therefore, the universe must exist in two mutually contradictory states at once.

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).