Propensity probability

The propensity theory of probability is one interpretation of the concept of probability.

The two main kinds of theory of physical probability are frequentist accounts (such as those of Venn, Reichenbach and von Mises ) and propensity accounts (such as those of Popper, Miller, Giere and Fetzer).

The propensity theory of probability is one interpretation of the concept of probability.

A propensity theory of probability was given by Charles Sanders Peirce. A later propensity theory was proposed by philosopher Karl Popper, who had only slight acquaintance with the writings of Charles S. Peirce, however.

Though Peirce was largely a frequentist, his possible world semantics introduced the "propensity" theory of probability before Karl Popper.

Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief.

Frequentists are unable to take this approach, since relative frequencies do not exist for single tosses of a coin, but only for large ensembles or collectives.

A central aspect of this explanation is the law of large numbers.

This law, which is a consequence of the axioms of probability, says that if (for example) a coin is tossed repeatedly many times, in such a way that its probability of landing heads is the same on each toss, and the outcomes are probabilistically independent, then the relative frequency of heads will (with high probability) be close to the probability of heads on each single toss.

In addition to explaining the emergence of stable relative frequencies, the idea of propensity is motivated by the desire to make sense of single-case probability attributions in quantum mechanics, such as the probability of decay of a particular atom at a particular time.

In addition to explaining the emergence of stable relative frequencies, the idea of propensity is motivated by the desire to make sense of single-case probability attributions in quantum mechanics, such as the probability of decay of a particular atom at a particular time.

In addition to explaining the emergence of stable relative frequencies, the idea of propensity is motivated by the desire to make sense of single-case probability attributions in quantum mechanics, such as the probability of decay of a particular atom at a particular time.

A later propensity theory was proposed by philosopher Karl Popper, who had only slight acquaintance with the writings of Charles S. Peirce, however.

First, propensities cannot be empirically ascertained, on this account, since the limit of a sequence is a tail event, and is thus independent of its finite initial segments.

A number of other philosophers, including David Miller and Donald A. Gillies, have proposed propensity theories somewhat similar to Popper's, in that propensities are defined in terms of either long-run or infinitely long-run relative frequencies.

A number of other philosophers, including David Miller and Donald A. Gillies, have proposed propensity theories somewhat similar to Popper's, in that propensities are defined in terms of either long-run or infinitely long-run relative frequencies.

Other propensity theorists (e.g. Ronald Giere ) do not explicitly define propensities at all, but rather see propensity as defined by the theoretical role it plays in science.

They argue, for example, that physical magnitudes such as electrical charge cannot be explicitly defined either, in terms of more basic things, but only in terms of what they do (such as attracting and repelling other electrical charges).

Other theories have been offered by D. H. Mellor, and Ian Hacking

Other theories have been offered by D. H. Mellor, and Ian Hacking

David Lewis called this the Principal Principle, a term that philosophers have mostly adopted.

(Propensity probability is an analogous idea, according to which probabilities have an objective existence and are not just limitations in a subject's knowledge).