The nature of probability

The thesis of this article is that the nature of probability is centered on its formal properties, not on any of its standard interpretations. Section 2 is a survey of Bayesian applications. Section 3 focuses on two examples from physics that seem as completely objective as other physical concepts. Section 4 compares the conflict between subjective Bayesians and objectivists about probability to the earlier strident conflict in physics about the nature of force. Section 5 outlines a pragmatic approach to the various interpretations of probability. Finally, Sect. 6 argues that the essential formal nature of probability is expressed in the standard axioms, but more explicit attention should be given to the concept of randomness.     

Against definitions

Definitional accounts of language structure are explored in this paper. Several classes of arguments for definitions are reviewed; those which connect to: classical theories of reference, theories of informal validity, theories of sentence comprehension, and theories of concept learning. We suggest that, for each of these areas, accounts which rely upon definition are, in fact, not to be preferred on evidential grounds to plausible non-definitional alternatives. We also present a series of experimental observations bearing on one of these areas — that of sentence comprehension. We show that one widely cited class of examples of definitional structures — that of “causative verbs” — fails to affect subject judgements of those relations among the words of causative sentences which depend upon the putative definitional structures. Such subject judgements are independently demonstrated to be sensitive to structural relations of comparable type for other linguistically non-problematic types.     

The theory of nomic probability

This article sketches a theory of objective probability focusing on nomic probability, which is supposed to be the kind of probability figuring in statistical laws of nature. The theory is based upon a strengthened probability calculus and some epistemological principles that formulate a precise version of the statistical syllogism. It is shown that from this rather minimal basis it is possible to derive theorems comprising (1) a theory of direct inference, and (2) a theory of induction. The theory of induction is not of the familiar Bayesian variety, but consists of a precise version of the traditional Nicod Principle and its statistical analogues.     

The foundations of epistemological probability

Epistemological probability is the kind of probability relative to a body of evidence. Many philosophers, including Henry Kyburg and Roderick Chisholm, hold that all epistemological probabilities reflect a relation between an evidential body of propositions and other propositions. But this article argues that some epistemological probabilities for empirical propositions must be relative to non-propositional evidence, specifically the contents of non-propositional perceptual states. In doing so, the article distinguishes between internalism and externalism regarding epistemological probability, and argues for a version of awareness internalism. The article draws three main concluding lessons. First, epistemological probability is not to be identified with the sort of objective, experience-independent probability that is familiar from statistical and propensity interpretations of probability. Second, it is doubtful that epistemological probability is measurable, in any useful way, by real numbers, even if it admits of comparative assessments. Third, contrary to the familiar claim of C. I. Lewis, epistemological probability should not be viewed as requiring a basis of certainty.     

The probability of causal conditionals

Conditionals in natural language are central to reasoning and decision making. A theoretical proposal called the Ramsey test implies the conditional probability hypothesis: that the subjective probability of a natural language conditional, P(if p then q), is the conditional subjective probability, P(q/p). We report three experiments on causal indicative conditionals and related counterfactuals that support this hypothesis. We measured the probabilities people assigned to truth table cases, P(pq), P(p notq), P( notpq) and P( notp notq). From these ratings, we computed three independent predictors, P(p), P(q/p) and P(q/ notp), that we then entered into a regression equation with judged P(if p then q) as the dependent variable. In line with the conditional probability hypothesis, P(q/p) was by far the strongest predictor in our experiments. This result is inconsistent with the claim that causal conditionals are the material conditionals of elementary logic. Instead, it supports the Ramsey test hypothesis, implying that common processes underlie the use of conditionals in reasoning and judgments of conditional probability in decision making.     

Life without definitions

The question ‘what is life?’ has long been a source of philosophical debate and in recent years has taken on increasing scientific importance. The most popular approach among both philosophers and scientists for answering this question is to provide a “definition” of life. In this article I explore a variety of different definitional approaches, both traditional and non-traditional, that have been used to “define” life. I argue that all of them are deeply flawed. It is my contention that a scientifically compelling understanding of the nature of life presupposes an empirically adequate scientific theory (vs. definition) of life; as I argue, scientific theories are not the sort of thing that can be encapsulated in definitions. Unfortunately, as I also discuss, scientists are currently in no position to formulate even a tentative version of such a theory. Recent discoveries in biology and biochemistry have revealed that familiar Earth life represents a single example that may not be representative of life. If this is the case, life on Earth today provides an empirically inadequate foundation for theorizing about life considered generally. I sketch a strategy for procuring the needed additional examples of life without the guidance of a definition or theory of life, and close with an application to NASA’s fledgling search for extraterrestrial life.     

Arguing about definitions

What are the implications of taking seriously Chaïm Perelman's proposition that “definitions are rhetorical”? Efforts to find Real Definitions are dysfunctional to the extent they direct argumentation toward pseudo “is” claims and away from explicit “ought” claims about how words are to be used. Addressing definitional disputes explicitly as propositions ofought rather thanis could put on the agenda the pragmatic concerns of definitional choice that might otherwise remain tacit.     

The cognitive substrate of subjective probability

The prominent cognitive theories of probability judgment were primarily developed to explain cognitive biases rather than to account for the cognitive processes in probability judgment. In this article the authors compare 3 major theories of the processes and representations in probability judgment: the representativeness heuristic, implemented as prototype similarity, relative likelihood, or evidential support accumulation (ESAM; D. J. Koehler, C. M. White, & R. Grondin, 2003); cue-based relative frequency; and exemplar memory, implemented by probabilities from exemplars (PROBEX; P. Juslin & M. Persson, 2002). Three experiments with different task structures consistently demonstrate that exemplar memory is the best account of the data whereas the results are inconsistent with extant formulations of the representativeness heuristic and cue-based relative frequency.     

A perceptual account of definitions

The traditional definition per genus et differentiam is argued to be cognitively grounded in perception and in order to avoid needless argument, definitions are stipulated to assert boundaries. An analysis of the notion of perspective shows that a boundary is a composite of two distinctions: similarity that includes and difference that excludes. The concept is applied to the type-token distinction and percepts are shown to be the result of a comparison between a token as representing some phenomenon and a type as representing the kind of object the phenomenon might be. The Principle of Connection is proposed as the mental architecture that gives rise to percepts. The value of a percept is shown to be one of Identical, Similar, Different or Contrary and its perceptual aspects represent the cognitive schema of Essence, Quality, Quantity and Relation. The two notions of similarity and difference are claimed to constitute the necessary and sufficient conditions for definitions. Accordingly, the qualitative elements of a definition signify the genus as representing the similarity of the defined entity in terms of others of its kind and the quantitative elements signify the differentia as representing the difference it has from everything else. Paying proper attention to both qualitative and quantitative aspects will enable formulation of definitions that are ‘good’. This paper is based on my master’s thesis at Monash University (2003). I thank Keith Allan for commenting on an earlier draft—any remaining infelicities are mine only.