Probability

• Probability is a quantitative notion that can be understood in subjective terms, as it is connected to one's belief or expectation.
• Probability is connected with the degree of belief warranted by evidence.
• Probability is connected with the tendency to produce stable frequencies.
• Randomness has an ancient origin, as evidenced by gambling, which may be the first indication of human society.
• The birth time of probability was around 1660, when many people independently hit on the basic ideas of probabilities.
• Probability has a duality, being both statistical and epistemological.
• Koplik's spots are not the cause of the measles, but rather, both the spots and the measles are the joint effects of a common cause, the measles virus.
• Hempel's counter objection: the author admits that there are similar cases and that this sub-thesis is weaker than the former.
• Koplik's spots are symptoms of the measles virus, not the cause of the measles.
• The presence of Koplik's spots permits the prediction of the rise of the measles, but does not explain that the patient will contract the disease.
• Stochastic processes are characterized by the values taken by a set of random variables whose values change over time.
• The duality of probability is at the basis of the problem of its philosophical interpretation, with different positions favoring either the objective or subjective side of the notion.
• Frequency understanding of probability corresponds to the frequency of the occurrence of an event, as endorsed by Reichenbach.
• Propensities understanding of probability sees probability as a hidden property, like color shape weight, which can manifest as the frequency of that event.
• Propensities are not to be identified with frequencies; rather, they are the causes of observable frequencies.
• Statistical theories focus on the tendency, displayed by some experimental or natural arrangements, to deliver stable long term frequencies on repeated trials.
• Propensities are as real as any other feature, such as the movement of a needle.
• The statistical distribution of subjects who can read and write in the sample (of which John is an element) is not the fact that John can read and write.
• Reichenbach supported the notion of probability as frequency.
• The propensities of John to read and write is not the fact that John can read and write.
• The explanans makes highly liking the conclusion to occur in the I-S model of explanation.
• The expectation (equal to 90%) of a rational subject that John can read and write is not the fact that John can read and write.
• Propensities are an hidden feature and it is as real as any other feature.
• Statistical law in the premises and even if the premises are true we are not 100 percent sure that the conclusion will be true.
• Depending on the understanding of the notion of probability, the explanation of the same phenomenon can vary.
• Propensities are physical realities and not mere possibilities.
• Reichenbach is an empiricist, so his understanding of probability is a reaction (opposed) of a rational view of probability.
• Rationalisms position: Rationalism is the position that there are ways that we can gain knowledge independent of sense experience.
• Frequencies are a reaction to an understanding probability which is rationalistic character.
• Poppers objectivist theory of probability is in opposition to the subjective theory of probability.
• Probability can be expressed in terms of frequencies even if we are not considering equal possibilities.
• Propensity is a hidden property which is unobservable but it is in some conditions in at the case for a loaded dice frequencies are the propensities for the die to give 6.
• Epistemological theories are concerned with the credibility of propositions in the light of judgment or evidence.
• From 1927 to 1945, the world was mainly considered as a precise deterministic clockwork, characterized by absolute precision.
• In the case of loaded dice, there are still 6 possibilities but they are now not equal possibilities but loaded or weighted possibilities.
• Scientists adopted a subjective way of understanding probabilities, attributing indeterminacies to our ignorance.
• The degree of expectation of a, on the basis of b, is represented by the symbol r.
• Heisenberg’s discovery of objective indeterminacies led to a change in the understanding of the world as a deterministic clockwork.
• Poppers objectivists theory of probability is based on the notion that the probability of an event is the number of favorable possibilities divided by the number of equal possibilities.
• Statistical averages can be used to estimate the various weights of the various possibilities.