Aleoa
In the first Volume of his lectures (cap. 6 first Paragraph), Feynman cites Maxwell :

"The true logic of this world is in the calculus of probabilities".

Considering the formal and rigorous definition of probability, very often misunderstood by not-scientists, what do you think is the deep meaning of this aphorism ?
Often, during the day, we take decisions based on the "probability" of the outcome, but if probability is formally referred to a repeatible event in unchanging conditions, is still useful to use this surrogate of probability in every-day decisions ?

Aufbauwerk 2045, nuuskur and Charles Link

nuuskur
Measure theory teaches us that an impossible event and events with probability 0 are not the same. Allelujah! That is certainly intuitively clear! (not)

Maybe there is some hidden reference to quantum mechanics for which everything is probabilistic and so to grasp the true nature (or logic) of this world, one must understand measure theory and Lebesgue integrals etc etc.

...bah what do I know

Homework Helper
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Measure theory teaches us that an impossible event and events with probability 0 are not the same.

That is a misinterpretation of measure theory If you apply it to events in the real world.

I think we still do not understand what is the true logic of the world.

Obviously we use probability and statistics in both classical and modern physics. In quantum theory class we learn about probability waves and uncertainty. But I have never heard a satisfactory explanation of the basic issue of truly random vs pseudo-random. Of course if what we call "truly random" is actually pseudo-random, then it is deterministic, just like a sequence of numbers from a random number generator. If we apply Occam's razor to this discussion, we may be led to conclude that there is no observable basis for our belief in what we call "truly random."

In any event, I just happened to be organizing some of my old books today and I came across this passage from Born's Atomic Physics.

"As Neils Bohr first pointed out, the new views with regard to causality and determinism, which have arisen as a result of the quantum theory, are also of great significance for the biological sciences and for psychology. If even in inanimate nature the physicist comes up against absolute limits, at which strict causal connexion ceases and must be replaced by statistics, we should be prepared, in the realm of living things, and emphatically so in the processes connected with consciousness and will, to meet insurmountable barriers, where mechanistic explanation, the goal of the older natural philosophy, becomes entirely meaningless."