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Definition Propensitiy/Popper/Fraassen: Thesis: according to this, probability is itself a physical quantity, the strength or intensity of the real chance of an occurrence or event that cannot be reduced by reference to actual classes of actual occurrences.
I 165
Probability/Fraassen: a) epistemic: e.g.
1. 75% of the recruits of 44 have survived.
2. Jones is recruit 44 - 1 and 2 are objective.
But the probability is subjective for me, because I have no further information about Jones.
N.B.: the information that I sum up has not the word "probability" in itself.
Information: that Jones belongs to a certain class. Thus, statistical mechanics has nothing to do with ignorance either.
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Objective Probability/Fraassen: For example, information about the time a system spends in a state is objective information. To call a probability function a measure for something is neither subjective nor objective.
It can also be a measure of ignorance.
Objective and subjective (epistemic) probability cannot always be kept apart in practice.
I 167
Statistics/probability/infinite/Fraassen: because subregions can be subdivided into even smaller parts ((s) why? - Because they end up as points) one needs infinite classes. -> Kolmogoroff axioms (countable additivity). - In order to map probability onto real numbers. - Still there is an extrapolation of finite proportions.
I 169
Probability/Quantum mechanics/Fraassen: Problem: Meaningless: half-life of a single atom. - Also for odd numbers of atoms (due to the decay of a half atom). - Solution: subjective probability. I have no further information on this atom. - Problem: objectively accurate ½, subjective: about 1/2 - Problem: there is no relation between exact and approximate!
Solution: in quantum mechanics there is no classic probability.
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Mixture/Quantum mechanics: Contrary to pure state: - analog in statistical mechanics: Difference between micro- and macro-state. - Ignorance: to say that the system is in one of e.g. three pure states. - (Ignorance interpretation) - Problem: mixed state: can be decomposed in more than one way.
I 174
Probability/Double Slit/Quantum mechanics/Fraassem: must not be equated with the proportions, to find the electron in a certain place. >
Quantum mechanics.
I 177
Infinite/Probability-Theory/Quantum Mechanics/Fraassen: problem: there are so many pure states and maximal observables as there are real numbers. >
Observation, >
Experiment, >
Method.
Probability-Theory: Theorem: if each of a class of mutually exclusive events has a probability > 0, there are only countable many.
Problem: then modality comes into play; the probabilities are about what would be the case if ...
I 178
Epistemic probability/subjective/Fraassen: can be left to the epistemology.
Objective probability: is a philosophical problem. - What does a probabilistic theory say? - To what are we bound to with this? >
Theories.
I 179
Probability Space:
1.K: sample space, event-R,
2.F: family of events,
3.P: Probability measure. - Significance: Problem when too fine-grained.
Definition field: family of subsets of K, completed under the operations average, union, complement formation.
Probability Space: if Field = Borel-Field (Sigma-Field): completed under countable infinitely many unions. - + + Propensity, strict frequency. >
Propensity.
