This paper sketches a concept of higher-level objective probability (“short-run mechanistic probability”, SRMP) inspired partly by a style of explanation of relative frequencies known as the “method of arbitrary functions”. SRMP has the potential to fill the need for a theory of objective probability which has wide application at higher levels and which gives probability causal connections to observed relative frequency (without making it equivalent to relative frequency). Though this approach provides probabilities on a space of event types, it does (...) not provide probabilities for outcomes on particular trials. This allows SRMP to coexist with lower-level probabilities which do govern individual trials. (shrink)

This is the sequel to my "Fifteen Arguments Against Finite Frequentism" (Erkenntnis 1997), the second half of a long paper that attacks the two main forms of frequentism about probability. Hypothetical frequentism asserts: The probability of an attribute A in a reference class B is p iff the limit of the relative frequency of A's among the B's would be p if there were an infinite sequence of B's. I offer fifteen arguments against this analysis. I consider various frequentist responses, (...) which I argue ultimately fail. I end with a positive proposal of my own, 'hyper-hypothetical frequentism', which I argue avoids several of the problems with hypothetical frequentism. It identifies probability with relative frequency in a hyperfinite sequence of trials. However, I argue that this account also fails, and that the prospects for frequentism are dim. (shrink)

Reichenbach’s use of ‘posits’ to defend his frequentistic theory of probability has been criticized on the grounds that it makes unfalsifiable predictions. The justice of this criticism has blinded many to Reichenbach’s second use of a posit, one that can fruitfully be applied to current debates within epistemology. We show first that Reichenbach’s alternative type of posit creates a difficulty for epistemic foundationalists, and then that its use is equivalent to a particular kind of Jeffrey conditionalization. We conclude that, under (...) particular circumstances, Reichenbach’s approach and that of the Bayesians amount to the same thing, thereby presenting us with a new instance in which chance and credence coincide. (shrink)

A common line of argument for the impossibility of closed causal loops is that they would involve causal paradoxes. The usual reply is that such loops impose heavy consistency constraints on the nature of causal connections in them; constraints that are overlooked by the impossibility arguments. Hugh Mellor has maintained that arguments for the possibility of causal loops also overlook some constraints, which are related to the chances (single-case, objective probabilities) that causes give to their effects. And he argues that (...) a consideration of these constraints demonstrates that causal loops are impossible. I consider Mellor's argument and more generally the nature of chance in causal loops. I argue that Mellor's line of reasoning is unwarranted since it is based on untenable premisses about the relation between chances and long-run frequencies in causal loops. Yet, this line of reasoning may still be of interest to those who maintain that causes determine the chances of their effects; for it raises some unresolved questions about the nature of chance in causal loops. (shrink)

We propose a new interpretation of objective deterministic chances in statistical physics based on physical computational complexity. This notion applies to a single physical system (be it an experimental set--up in the lab, or a subsystem of the universe), and quantifies (1) the difficulty to realize a physical state given another, (2) the 'distance' (in terms of physical resources) from a physical state to another, and (3) the size of the set of time--complexity functions that are compatible with the physical (...) resources required to reach a physical state from another. (shrink)

According to finite frequentism, the probability of an attribute A in a finite reference class B is the relative frequency of actual occurrences of A within B. I present fifteen arguments against this position.

This is the sequel to my “Fifteen Arguments Against Finite Frequentism” ( Erkenntnis 1997), the second half of a long paper that attacks the two main forms of frequentism about probability. Hypothetical frequentism asserts: The probability of an attribute A in a reference class B is p iff the limit of the relative frequency of A ’s among the B ’s would be p if there were an infinite sequence of B ’s. I offer fifteen arguments against this analysis. I (...) consider various frequentist responses, which I argue ultimately fail. I end with a positive proposal of my own, ‘hyper-hypothetical frequentism’, which I argue avoids several of the problems with hypothetical frequentism. It identifies probability with relative frequency in a hyperfinite sequence of trials. However, I argue that this account also fails, and that the prospects for frequentism are dim. (shrink)

According to finite frequentism, the probability of an attribute A in a finite reference class B is the relative frequency of actual occurrences of A within B. I present fifteen arguments against this position.

Wesley Salmon provided three classic criteria of adequacy for satisfactory interpretations of probability. A fourth criterion is suggested here. A distinction is drawn between frequency‐driven probability models and theory‐driven probability models and it is argued that single case accounts of chance are superior to frequency accounts at least for the latter. Finally it is suggested that theories of chance should be required only to be contingently true, a position which is a natural extension of Salmon's ontic account of probabilistic causality (...) and his own later views on propensities. (shrink)

This paper offers a metaphysics of physical probability in (or if you prefer, truth conditions for probabilistic claims about) deterministic systems based on an approach to the explanation of probabilistic patterns in deterministic systems called the method of arbitrary functions. Much of the appeal of the method is its promise to provide an account of physical probability on which probability assignments have the ability to support counterfactuals about frequencies. It is argued that the eponymous arbitrary functions are of little philosophical (...) use, but that they can be substituted for facts about frequencies without losing the ability to provide counterfactual support. The result is an account of probability in deterministic systems that has a “propensity-like” look and feel, yet which requires no supplement to the standard modern empiricist tool kit of particular matters of fact and principles of physical dynamics. (shrink)