Abstract
Randomness was one of Mario Bunge’s earliest philosophical interests, and remains as one of his most persistent. Bunge’s view of the nature of randomness has been largely consistent over many decades, despite some evolution. For a long time now, he has seen chance as a purely ontological matter of contingency, something that does not result from either psychological uncertainty or epistemological indeterminacy, and that disappears once the die is cast. He considers the Bayesian school of probability and statistics to be pseudoscientific. Bunge upholds a fairly conventional view that chance is not any part of the purely mathematical theory of probability, and a thoroughly unconventional view that ontologically contingent processes are deterministic, though not classically so. This chapter examines Bunge’s views on probability by investigating what any of the following have to do with each other: chance or randomness, likelihood, the mathematical theory of probability, determinism, independence, belief, psychological uncertainty, and epistemological indeterminacy.
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Notes
- 1.
In his Foundations of Physics, Bunge says “Kolmogoroff himself did employ a misleading terminology but it is as supernumerary as the observer and the ideal experiment in [quantum mechanics]... random samplings will occur in informal inferences and in applications of [the calculus of probability] not in its foundations.” (Bunge 1967, p. 90)
- 2.
Those who insist that equiprobability is all that is needed have two options: explain why the probabilities should be equal; or offer no explanation. The former is the same as explaining why the respective events should be considered equivalent, while the latter is the same as assigning their equivalence arbitrarily. Thus, there is no escaping the concept of equal (or else proportional) likelihood, whether arising naturally or assigned arbitrarily.
- 3.
The concept of likelihood (of events) in classical probability is not the same as the technical concept of likelihood (of model parameters) introduced by Fisher and as used in modern statistics, both Bayesian and non-Bayesian (see e.g. Reid 2013).
- 4.
That is, stopped at a time drawn from a probability distribution whose values are proportional to the radii of the circles of latitude crossed at the corresponding times, and so to the surface areas between corresponding differentially (infinitesimally) separated lines of latitude.
- 5.
Transition probabilities are instead modelled using sequences of random variables indexed by a set used to represent time values. This extends the basic theory to the theory of stochastic processes (see Sect. 34.6).
- 6.
In purely mathematical problems, there is no reason for the conditional probability P(A | B) to be read as “the probability of A, given that B has occurred”. Instead it should be read as “the probability of B, given that A is the case”; or in other words, the probability of A renormalized to B as the sample space.
- 7.
Bunge says something similar in e.g. volume 5 of his Treatise, where he held that “A sequence of events can be said to be random if every event in it has a definite probability; otherwise the sequence is either chaotic or causal. This is not the standard definition of randomness—but then there is no standard definition.” (Bunge 1983, pp. 365–366)
- 8.
This is a change from the view Bunge expressed in volume 3 of his Treatise, where he said “Randomness, being a special case of stochasticity, is a type of order” (Bunge 1977, p. 209).
- 9.
A series is a sum of (finitely or infinitely many) terms, a sequence (or string) is a list of them.
- 10.
- 11.
In Chasing Reality, Bunge says there are three: event, probability space, and probability measure (Bunge 2006, p. 100). By “probability space” Bunge refers to the σ-algebra (field) of measurable subsets.
- 12.
In Evaluating Philosophies, Bunge says “objective indeterminacy implies subjective uncertainty—though not conversely” (Bunge 2012, p. 108). Yet the former implication is also false. It is so easy and common to be certain about outcomes which are not fixed in advance that the corresponding vocabulary is part of everyday life, to include overconfidence, hubris, and counting chickens before they are hatched.
- 13.
Bunge has it instead as a random individual who tests positive for HIV, but this complicates the problem over his subsequent discussions, because positive tests have a probability of being false.
- 14.
Bunge may have eventually realized this, as later he objected for different reasons:
...what is the use of this exercise? None, because what we need to know is the mechanisms of infection and immunity, and this is a matter for scientific research, not for logic. And if these mechanisms turn out to be causal rather than stochastic, we will not need the probability calculus either. We may call this objection the argument from barrenness. (Bunge 2010, p. 25)
- 15.
Bunge has mentioned this problem by name (Bunge 2012, p. 107), but without the second step that makes it interesting. He has also often commented on what sounds like it should be an equivalent problem, phrased in terms of three of the Apostles. It is inequivalent because the contestant does not make any selection, let alone two, only the “host” does. The paradox can be resolved similarly though. Bunge holds that problem to be effectively the same as the Monty Hall problem, and that in both cases no chance is involved and it makes no sense to talk about the probability of winning (e.g. Bunge 2003, pp. 229–230).
- 16.
At one time Bunge explicitly claimed it possible to go from non-probabilistic premises to probabilistic ones using the method of arbitrary functions (Bunge 1969, p. 445), but that was incorrect and in his writings since then he has consistently asserted the contrary.
- 17.
Bunge has also objected to the propensity label, preferring to call his own version the objectivist or realist interpretation (Bunge 2006, p. 103).
- 18.
“Propensity methods” is sometimes used as a description for propensity score matching methods as invented by Rubin, but they are not a reconceptualization of statistics in propensity terms, and include a Bayesian aspect. See Rubin (2007).
- 19.
Likelihoods as used in the technical statistical sense do not obey the laws of probability (see e.g. Cox and Mayo 2010).
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Acknowledgement
I thank Michael Matthews and Paul McColl for their respective contributions in shepherding the manuscript through its various stages.
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Kary, M. (2019). On Leaving as Little to Chance as Possible. In: Matthews, M.R. (eds) Mario Bunge: A Centenary Festschrift. Springer, Cham. https://doi.org/10.1007/978-3-030-16673-1_34
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