David Lewis (1980) proposed the Principal Principle (PP) and a “reformulation” which later on he called ‘OP’ (Old Principle). Reacting to his belief that these principles run into trouble, Lewis (1994) concluded that they should be replaced with the New Principle (NP). This conclusion left Lewis uneasy, because he thought that an inverse form of NP is “quite messy”, whereas an inverse form of OP, namely the simple and intuitive PP, is “the key to our concept of chance”. I argue (...) that, even if OP should be discarded, PP need not be. Moreover, far from being messy, an inverse form of NP is a simple and intuitive Conditional Principle (CP). Finally, both PP and CP are special cases of a General Principle (GP); it follows that so are PP and NP, which are thus compatible rather than competing. (shrink)

David Lewis (1980) proposed the Principal Principle (PP) and a “reformulation” which later on he called ‘OP’(Old Principle). Reacting to his belief that these principles run into trouble, Lewis (1994) concluded that they should be replaced with the New Principle (NP). This conclusion left Lewis uneasy, because he thought that an inverse form of NP is “quite messy”, whereas an inverse form of OP, namely the simple and intuitive PP, is “the key to our concept of chance”. I argue that, (...) even if OP should be discarded, PP need not be. Moreover, far from being messy, an inverse form of NP is a simple and intuitive Conditional Principle (CP). Finally, both PP and CP are special cases of a General Principle (GP); it follows that so are PP and NP, which are thus compatible rather than competing. (shrink)

I follow Hájek (Synthese 137:273–323, 2003c) by taking objective probability to be a function of two propositional arguments—that is, I take conditional probability as primitive. Writing the objective probability of q given r as P(q, r), I argue that r may be chosen to provide less than a complete and exact description of the world’s history or of its state at any time. It follows that nontrivial objective probabilities are possible in deterministic worlds and about the past. A very simple (...) chance–credence relation is also then natural, namely that reasonable credence equals objective probability. In other words, we should set our actual credence in a proposition equal to the proposition’s objective probability conditional on available background information. One advantage of that approach is that the background information is not subject to an admissibility requirement, as it is in standard formulations of the Principal Principle. Another advantage is that the “undermining” usually thought to follow from Humean supervenience can be avoided. Taking objective probability to be a two-argument function is not merely a technical matter, but provides us with vital flexibility in addressing significant philosophical issues. (shrink)

David Lewis's influential work on the epistemology and metaphysics of objective chance has convinced many philosophers of the central importance of the following two claims: First, it is a serious cost of reductionist positions about chance (such as that occupied by Lewis) that they are, apparently, forced to modify the Principal Principle--the central principle relating objective chance to rational subjective probability--in order to avoid contradiction. Second, it is a perhaps more serious cost of the rival non-reductionist position that, unlike reductionism, (...) it can give no coherent explanation for why the Principal Principle should hold. I argue that both of these claims are fundamentally mistaken. (shrink)

Whilst Bayesian epistemology is widely regarded nowadays as our best theory of knowledge, there are still a relatively large number of incompatible and competing approaches falling under that umbrella. Very recently, Wallmann and Williamson wrote an interesting article that aims at showing that a subjective Bayesian who accepts the principal principle and uses a known physical chance as her degree of belief for an event A could end up having incoherent or very implausible beliefs if she subjectively chooses the probability (...) of an event F for which she has much poorer evidence. They also argued that their own version of objective Bayesianism is completely immune to that challenge. In this article, after having presented the strongest version of Wallmann’s and Williamson’s argument, I will show that if successful, it has far-reaching consequences and would not only invalidate moderate subjective Bayesianism and imprecise probalism but also a form of objective Bayesianism that relies on conditionalisation, the principal principle, reference classes, and the principle of indifference applied to the most basic partitions. I then argue that their argument can be defeated by adding the rule that it is always irrational to choose a probability that can be computed from the known probabilities associated to one’s other beliefs. I finally argue that the authors’ main intuition that probabilities have different degrees of reliability favours imprecise Bayesianism over precise Bayesianism. (shrink)

We show a somewhat surprising result concerning the relationship between the Principal Principle and its allegedly generalized form. Then, we formulate a few desiderata concerning chance-credence norms and argue that none of the norms widely discussed in the literature satisfies all of them. We suggest that the New Principle comes out as the best contender.

The foundations of probability are viewed through the lens of the subjectivist interpretation. This article surveys conditional probability, arguments for probabilism, probability dynamics, and the evidential and subjective interpretations of probability.

It is widely thought that chance should be understood in reductionist terms: claims about chance should be understood as claims that certain patterns of events are instantiated. There are many possible reductionist theories of chance, differing as to which possible pattern of events they take to be chance-making. It is also widely taken to be a norm of rationality that credence should defer to chance: special cases aside, rationality requires that one's credence function, when conditionalized on the chance-making facts, should (...) coincide with the objective chance function. It is a shortcoming of a theory of chance if implies that this norm of rationality is unsatisfiable. The primary goal of this paper is to show, on the basis of considerations concerning computability and inductive learning, that this shortcoming is more common than one would have hoped. (shrink)

Over the past 50 years, there has been a great deal of philosophical interest in laws of nature, perhaps because of the essential role that laws play in the formulation of, and proposed solutions to, a number of perennial philosophical problems. For example, many have thought that a satisfactory account of laws could be used to resolve thorny issues concerning explanation, causation, free-will, probability, and counterfactual truth. Moreover, interest in laws of nature is not constrained to metaphysics or philosophy of (...) science; claims about laws play essential roles in areas as diverse as the philosophy of religion (e.g., in the argument from design) and the philosophy of mind (e.g., in the formulation of Davidson’s anomalous monism). In my dissertation, I consider and reject the widely-held thesis that the facts concerning laws can be reduced to the facts concerning the particular entities that the laws “govern,” and that the laws thus have no independent existence. I instead defend a version of nomic primitivism, according to which the facts about laws cannot be reduced to facts that are themselves non-nomic – i.e., to facts that do not fundamentally involve laws, counterfactuals, causes, etc. Insofar as the truth or falsity of reductionism about laws has implications for many of the problems mentioned above, I think that this result should be of interest even to those who who do not work in metaphysics or the philosophy of science. My methodology, which I lay out and defend in Chapter One, is a version of Carnapian explication. This method emphasizes the importance of articulating and maintaining clear distinctions between (1) the vague concept (or concepts) law of nature inherent in ordinary language and scientific practice and (2) the precise analyses of “law of nature” that philosophers have proposed as potential replacements for this concept. I argue that metaphysics-as-explication has clear advantages over rival conceptions of metaphysical methodology; in particular, it allows us to formulate evaluative criteria for metaphysical claims. In Chapter Two, I offer an example of how careful attention to concepts already in use can help resolve philosophical debate. Specifically, I argue that much recent literature has mistakenly assumed that there is only one concept of “law of nature” in use, while there are in fact at least two. Strong laws are the principles pursued by fundamental physics: they are true, objective, and bear distinctive relationships to counterfactuals and explanation. Weak laws, by contrast, lack at least one of these distinctive characteristics but play central roles in both the “special sciences” and in everyday life. In Chapters Three and Four, I offer extended arguments against the two most prominent versions of reductionism about laws – Humeanism and law necessitarianism. According to philosophical Humeans, the laws of nature supervene upon the non-modal, non-nomic facts concerning the behavior of particular things at particular times and places. Law necessitarians, by contrast, argue that the laws are in fact metaphysically necessary, and that which laws there are is determined by a class of primitive, modally loaded facts concerning the essences, natures, or dispositions. I argue that both of these views are mistaken insofar as they disagree with well-entrenched scientific practices and those in favor of reductionism have failed to provided sufficient reason for thinking that these practices should be revised. Much of my argument is focused on the role played by a number of supposed methodological principles, including appeals to intuition, parsimony, and methodological naturalism. While the conclusions of this dissertation are explicitly constrained to laws, many of the arguments should be of interest to those who are concerned about philosophical methodology (especially in the role of intuition in philosophical argument) or the appropriate relation between metaphysics, science, and the philosophy of science. (shrink)

David Lewis' "Principal Principle" is a purported principle of rationality connecting credence and objective chance. Almost all of the discussion of the Principal Principle in the philosophical literature assumes classical probability theory, which is unfortunate since the theory of modern physics that, arguably, speaks most clearly of objective chance is the quantum theory, and quantum probabilities are not classical probabilities. Given the generally accepted updating rule for quantum probabilities, there is a straight forward sense in which the Principal Principle is (...) a theorem of quantum probability theory for any credence function satisfying a suitable additivity requirement. No additional principle of rationality is needed to bring credence into line with objective chance. (shrink)

The paper takes thePrincipal Principle to be a norm demanding that subjective degrees of belief of a Bayesian agent be equal to the objective probabilities once the agent has conditionalized his subjective degrees of beliefs on the values of the objective probabilities, where the objective probabilities can be not only chances but any other quantities determined objectively. Weak and strong consistency of the Abstract Principal Principle are defined in terms of classical probability measure spaces. It is proved that the Abstract (...) Principal Principle is weakly consistent and that it is strongly consistent in the category of probability measure spaces where the Boolean algebra representing the objective random events is finite. It is argued that it is desirable to strengthen the Abstract Principal Principle by adding a stability requirement to it. Weak and strong consistency of the resulting Stable Abstract Principal Principle are defined, and the strong consistency of the Abstract Principal Principle is interpreted as necessary for a non-omniscient Bayesian agent to be able to have rational degrees of belief in all epistemic situations. It is shown that the Stable Abstract Principal Principle is weakly consistent, but the strong consistency of the Stable Abstract Principal principle remains an open question. We conclude that we do not yet have proof that Bayesian agents can have rational degrees of belief in every epistemic situation. (shrink)

The discussion of different principles of additivity for probability functions has been largely focused on the personalist interpretation of probability. Very little attention has been given to additivity principles for physical probabilities. The form of additivity for quantum probabilities is determined by the algebra of observables that characterize a physical system and the type of quantum state that is realizable and preparable for that system. We assess arguments designed to show that only normal quantum states are realizable and preparable and, (...) therefore, quantum probabilities satisfy the principle of complete additivity. We underscore the little remarked fact that unless the dimension of the Hilbert space is incredibly large, complete additivity in ordinary non-relativistic quantum mechanics reduces to countable additivity. We then turn to ways in which knowledge of quantum probabilities may constrain rational credence about quantum events and, thereby, constrain the additivity principle satisfied by rational credence functions. (shrink)