The so-called ‘Third Axiom of Probability’ is false — Dr. Işık Barış Fidaner

(TR)

1. There are factors that contribute both to the actualization & non-actualization of a possible outcome.

For the throw of a die, here are some of the factors that contribute both to the actualization and non-actualization of the number six turning up:

i) The actual throw. Without the throw itself, the number six may neither turn up nor non-turn up.

ii) The time passing after the throw. Without sufficient time passing after the throw, the number six may neither turn up nor non-turn up.

iii) The non-occlusion of view. Without a clear view of the die for an observer, the number six may neither turn up nor non-turn up.

iv) A trustworthy observer. Without at least one trustworthy observer (oneself or another) the number six may neither turn up nor non-turn up.

v) A flat ground. Without a flat ground, the number six may neither turn up nor non-turn up.

vi) Gravity on the Earth. Without the gravity on the Earth, the number six may neither turn up nor non-turn up.

vii) A common language that includes symbols for numbers. Without the ability to register it via a common language, the number six may neither turn up nor non-turn up.

I’ll call these factors, shared factors of a possible outcome.

2. To indicate such factors, there must be some common terms between the summation that computes the probability of the possible outcome being actualized, and the summation that computes the probability of the same possible outcome not being actualized.

The shared factors of a possible outcome are vital for that outcome and other outcomes related to it: The initial impulse, the time passing, the visibility, the trust, the ground, the gravity and the symbols to express the outcome. Any algorithm that computes outcomes related to that possible outcome must take these factors into account.

The actualization and non-actualization of the possible outcome must be articulated in a way to include the shared factors that occur on both sides of the possible outcome.

3. The set of terms that signal the actualization of a possibility cannot be mutually disjoint with the set of terms that signal the non-actualization of the same possibility.

If the terms that express the actualization and the non-actualization of an outcome satisfied mutual exclusivity, if any one of the terms that articulate an outcome appeared only on one side of the possibility in question, they would simply amount to a failure in articulation that ignores the vital shared factors that determine the outcome.

4. The so-called ‘Third Law of Probability’ or ‘Third Axiom of Probability’ is false.

Dr. Işık Barış Fidaner