. Philosopher-theologian Bernard J. F. Lonergan defines emergence as the process in which “otherwise coincidental manifolds of lower conjugate acts invite the higher integration effected by higher conjugate forms” (Insight, [1957] 1992, 477). The meaning and implications of Lonergan’s concept of emergence are considered in the context of the problem of reductionism in the natural sciences. Examples are taken primarily from physics, chemistry, and biology.

The status of risk factors and disease remains a disputed question in the theory and practice of medicine and healthcare, and so does the related question of delineating disease boundaries. I present a framework based on Bernard Lonergan’s account of emergent probability for differentiating (1) generically distinct levels of systematic function within organisms and between organisms and their environments and (2) the methods of functional, genetic, and statistical investigation. I then argue on this basis that it is possible (...) to understand disease in terms of biological or higher intra-level dysfunction, risk factors—including genetic risk factors—in terms of statistical inter-level conditioning of a given stage or developmental sequence of systematic functioning, and the empirical boundaries of disease in terms of the limits of both functional categorization (from an epistemic standpoint) and upper-level integration of lower-level processes and events (from an ontological standpoint). (shrink)

Historical records show that there was no real concept of probability in Europe before the mid-seventeenth century, although the use of dice and other randomizing objects was commonplace. Ian Hacking presents a philosophical critique of early ideas about probability, induction, and statistical inference and the growth of this new family of ideas in the fifteenth, sixteenth, and seventeenth centuries. Hacking invokes a wide intellectual framework involving the growth of science, economics, and the theology of the period. He argues (...) that the transformations that made it possible for probability concepts to emerge have constrained all subsequent development of probability theory and determine the space within which philosophical debate on the subject is still conducted. First published in 1975, this edition includes an introduction that contextualizes his book in light of developing philosophical trends. Ian Hacking is the winner of the Holberg International Memorial Prize 2009. (shrink)

Ian Hacking here presents a philosophical critique of early ideas about probability, induction and statistical inference and the growth of this new family of ...

Historical records show that there was no real concept of probability in Europe before the mid-seventeenth century, although the use of dice and other randomizing objects was commonplace. Ian Hacking presents a philosophical critique of early ideas about probability, induction, and statistical inference and the growth of this new family of ideas in the fifteenth, sixteenth, and seventeenth centuries. Hacking invokes a wide intellectual framework involving the growth of science, economics, and the theology of the period. He argues (...) that the transformations that made it possible for probability concepts to emerge have constrained all subsequent development of probability theory and determine the space within which philosophical debate on the subject is still conducted. First published in 1975, this edition includes an introduction that contextualizes his book in light of developing philosophical trends. Ian Hacking is the winner of the Holberg International Memorial Prize 2009. (shrink)

A persistent question about the deBroglie–Bohm interpretation of quantum mechanics concerns the understanding of Born’s rule in the theory. Where do the quantum mechanical probabilities come from? How are they to be interpreted? These are the problems of emergence and interpretation. In more than 50 years no consensus regarding the answers has been achieved. Indeed, mirroring the foundational disputes in statistical mechanics, the answers to each question are surprisingly diverse. This paper is an opinionated survey of this literature. While acknowledging (...) the pros and cons of various positions, it defends particular answers to how the probabilities emerge from Bohmian mechanics and how they ought to be interpreted. (shrink)

A persistent question about the deBroglie–Bohm interpretation of quantum mechanics concerns the understanding of Born’s rule in the theory. Where do the quantum mechanical probabilities come from? How are they to be interpreted? These are the problems of emergence and interpretation. In more than 50 years no consensus regarding the answers has been achieved. Indeed, mirroring the foundational disputes in statistical mechanics, the answers to each question are surprisingly diverse. This paper is an opinionated survey of this literature. While acknowledging (...) the pros and cons of various positions, it defends particular answers to how the probabilities emerge from Bohmian mechanics and how they ought to be interpreted. (shrink)

(1991). The emerging “wholeness” worldview and its probable impact on cooperation. World Futures: Vol. 31, Cooperation: Toward a Post-Modern Ethic, pp. 73-83.

The emergence of mathematical probability has something to do with dice games: all the early discussions (Cardano, Galileo, Pascal) suggest as much. Although this has long been recognized, the problem is that gambling at dice has been a popular pastime since antiquity. Why, then, did gamblers wait until the sixteenth century ce to calculate the math of dicing? Many theories have been offerred, but there may be a simple solution: early-modern gamblers played different sorts of dice games than in (...) antiquity. While ancients diced at communal risk, early-moderns diced at individualized risk. These individual wager-games, for example, the game “hazard”, incentivized solving questions like “how likely is it to roll a triple-six?”. Before the early modern period there was no gambling game to which working out mathematical probability would have brought an advantage. (shrink)

David Wallace argues that we should take quantum theory seriously as an account of what the world is like--which means accepting the idea that the universe is constantly branching into new universes. He presents an accessible but rigorous account of the 'Everett interpretation', the best way to make coherent sense of quantum physics.

Proteins with nearly the same structure and function (homologous proteins) are found in increasing numbers in phylogenetically different, even very distant taxa (e.g. hemoglobins in vertebrates, in some invertebrates, and even in certain plants). In discussing the origin of those proteins biologists hardly at all consider convergent evolution because the origin of proteins is held to be a random process, at least ultimately, since selection can work only what the random process delivers as having a minimum adaptive value. The repetition (...) of a random process with the same result is considered to be extremely unlikely. The supposed (un)likelihood, however, is almost never determined quantitatively. This paper attempts such a quantitative determination. It appears that the probability for the random origin of a definite protein is greater than what one would expect in view of the enormous number of equally possible nucleotide sequences in the corresponding gene since what is equally possible is not always equally likely. The probability, however, of the convergent evolution of two proteins with approximately the same structure and function is too low to be plausible, even when all possible circumstances are present which seem to heighten the likelihood of such a convergence. If this is so, then the plausibility of a random evolution of two or more different but functionally related proteins seems hardly greater. (shrink)

Probability theory promises to deliver an exact and unified foundation for inquiry in epistemology and philosophy of science. But philosophy of religion is also fertile ground for the application of probabilistic thinking. This volume presents original contributions from twelve contemporary researchers, both established and emerging, to offer a representative sample of the work currently being carried out in this potentially rich field of inquiry. Grouped into five parts, the chapters span a broad range of traditional issues in religious epistemology. (...) The first three parts discuss the evidential impact of various considerations that have been brought to bear on the question of the existence of God. These include witness reports of the occurrence of miraculous events, the existence of complex biological adaptations, the apparent 'fine-tuning' for life of various physical constants and the existence of seemingly unnecessary evil. The fourth part addresses a number of issues raised by Pascal's famous pragmatic argument for theistic belief. A final part offers probabilistic perspectives on the rationality of faith and the epistemic significance of religious disagreement. (shrink)

Bacon’s project suggests in theory that the obtaining of absolute certain knowledge is possible but in fact such knowledge is revealed to be impossible. Th e description of the human mind on which Bacon’s account is based seems to imply that the impossibility of obtaining absolute certainty does not depend on the contingent historical situation of a preliminary stage of the scientifi c endeavor. Consequently, a gap emerges between the proposed goal of science and the ways to reach it: Bacon (...) tried to obtain absolute certainty but he only could arrive at degrees of certainty and probability both in theories and in facts. Malgrè lui, Bacon shows himself developing in fact a kind of probabilistic science instead of surpassing the limits to knowledge posed by the skeptical arguments. Th at is the reason why many of his followers could develop a mitigated skepticism in the framework of a Baconian science. (shrink)

The philosophy of probability has been alive and well for several decades in Australia and New Zealand. Some distinctive lines of thought have emerged, resonating with broader themes that have come to be associated with Australasian philosophers: realist/objectivist accounts of various theoretical entities; an ongoing concern with logic, including the development of non­classical logics; and enthusiasm for conceptual analysis, rooted in commonsense but informed by science. In this article I concentrate on work by philosophers on the interpretation of (...) class='Hi'>probability, its logical foundations, and its philosophical applications.1 My nomination for the earliest major Australasian philosopher of probability may surprise some readers: Karl Popper. He counts as Australasian by dint of his employment at the University of Canterbury from 1937 until the end of World War II; he counts as a major philosopher of probability by any estimation. Two of his contributions have initiated research programs in the foundations of probability that are still thriving: his (1959a) axiomatization of primitive conditional probability functions (so­called ‘Popper functions’), and his ‘propensity’ interpretation of probability (1959b), intended to illuminate single­case attributions of objective probabilities, as are putatively found in quantum mechanics. (shrink)

The Everett interpretation of quantum mechanics divides naturally into two parts: first, the interpretation of the structure of the quantum state, in terms of branching, and second, the interpretation of this branching structure in terms of probability. This is the second of two reviews of the Everett interpretation, and focuses on probability. Branching processes are identified as chance processes, and the squares of branch amplitudes are chances. Since branching is emergent, physical probability is emergent as (...) well. (shrink)

We offer a new argument for the claim that there can be non-degenerate objective chance (“true randomness”) in a deterministic world. Using a formal model of the relationship between different levels of description of a system, we show how objective chance at a higher level can coexist with its absence at a lower level. Unlike previous arguments for the level-specificity of chance, our argument shows, in a precise sense, that higher-level chance does not collapse into epistemic probability, despite higher-level (...) properties supervening on lower-level ones. We show that the distinction between objective chance and epistemic probability can be drawn, and operationalized, at every level of description. There is, therefore, not a single distinction between objective and epistemic probability, but a family of such distinctions. (shrink)

Everettian quantum mechanics results in ‘multiple, emergent, branching quasi-classical realities’ . The possible outcomes of measurement as per ‘orthodox’ quantum mechanics are, in EQM, all instantiated. Given this metaphysics, Everettians face the ‘probability problem’—how to make sense of probabilities and recover the Born rule. To solve the probability problem, Wallace, following Deutsch , has derived a quantum representation theorem. I argue that Wallace’s solution to the probability problem is unsuccessful, as follows. First, I examine one of (...) the axioms of rationality used to derive the theorem, ‘branching indifference’ . I argue that Wallace is not successful in showing that BI is rational. While I think it is correct to put the burden of proof on Wallace to motivate BI as an axiom of rationality, it does not follow from his failing to do so that BI is not rational. Thus, second, I show that there is an alternative strategy for setting one’s credences in the face of branching which is rational and which violates BI. This is ‘branch counting’ . Wallace is aware of BC and has proffered various arguments against it. However, third, I argue that Wallace’s arguments against BC are unpersuasive. I conclude that the probability problem in EQM persists. 1 Introduction2 Branching Indifference2.1 The positive argument for branching indifference2.2 The negative argument for branching indifference2.3 Branching indifference section summary3 Branch Counting3.1 Branch counting is rational under the subjective-uncertainty viewpoint3.2 Branch counting is rational under the objective-determinism viewpoint3.3 Branch counting section summary4 Number of Branches4.1 Veracity of the framework4.2 No such thing as the number of branches4.2.1 The number of branches is indeterminate4.2.2 The number of branches is indeterminable4.3 Rationality and weight5 Conclusion. (shrink)

Problem: Can communication emerge from the interaction of “self-referentially closed systems,” conceived as operating solely on the base of the “internal” output of their onboard means? Or in terms of philosophical conceptions: can communication emerge without (“outward” directed) “intention” or “will to be understood”? Method: Multi-agent simulation based on a conceptual analysis of the theory of social systems as suggested by Niklas Luhmann. Results: Agents that co-evolutionarily aggregate probabilities on how to cope with their environment can structurally couple and generate (...) a form of “eigenbehavior” that retrospectively (i.e., by an observer) might be interpreted as communication. Implications: The “intention” or the “will to be understood,” as prominently claimed to be indispensable in communication by theoreticians such as Jürgen Habermas, can be seen as a retrospective ascription to an emergent property of complex interaction. Constructivist content: The paper attempts to base constructivist reasoning on data generated in simulations. (shrink)

Everettian quantum mechanics (EQM) results in ‘multiple, emergent, branching quasi-classical realities’ (Wallace [2012]). The possible outcomes of measurement as per ‘orthodox’ quantum mechanics are, in EQM, all instantiated. Given this metaphysics, Everettians face the ‘probability problem’—how to make sense of probabilities and recover the Born rule. To solve the probability problem, Wallace, following Deutsch ([1999]), has derived a quantum representation theorem. I argue that Wallace’s solution to the probability problem is unsuccessful, as follows. First, I examine (...) one of the axioms of rationality used to derive the theorem, ‘branching indifference’ (BI). I argue that Wallace is not successful in showing that BI is rational. While I think it is correct to put the burden of proof on Wallace to motivate BI as an axiom of rationality, it does not follow from his failing to do so that BI is not rational. Thus, second, I show that there is an alternative strategy for setting one’s credences in the face of branching which is rational and which violates BI. This is ‘branch counting’ (BC). Wallace is aware of BC and has proffered various arguments against it. However, third, I argue that Wallace’s arguments against BC are unpersuasive. I conclude that the probability problem in EQM persists. 1 Introduction2 Branching Indifference 2.1 The positive argument for branching indifference 2.2 The negative argument for branching indifference 2.3 Branching indifference section summary3 Branch Counting 3.1 Branch counting is rational under the subjective-uncertainty viewpoint 3.2 Branch counting is rational under the objective-determinism viewpoint 3.3 Branch counting section summary4 Number of Branches 4.1 Veracity of the framework 4.2 No such thing as the number of branches 4.2.1 The number of branches is indeterminate 4.2.2 The number of branches is indeterminable 4.3 Rationality and weight5 Conclusion. (shrink)

In order that a degree-of-belief function be coherent it is necessary and sufficient that it satisfy the axioms of probability theory. This theorem relies heavily for its proof on the two-valued sentential calculus, which emerges as a limiting case of a continuous scale of truth-values. In this "continuum of certainty" a theorem analogous to that instanced above is proved.

Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics: it is argued that neither Bohr's Copenhagen interpretation, nor the pilot-wave theory, nor stochastic state-reduction theories, give a satisfactory answer to the question of what objective probabilities are in quantum mechanics, or why they should satisfy the Born rule; nor do they give any reason why subjective probabilities should track objective (...) ones. But it is shown that if probability only arises with decoherence, then they must be given by the Born rule. That further, on the Everett interpretation, we have a clear statement of what probabilities are, in terms of purely categorical physical properties; and finally, along lines laid out by Deutsch and Wallace, that there is a clear basis in the axioms of decision theory as to why subjective probabilities should track these objective ones. These results hinge critically on the absence of hidden-variables or any other mechanism (such as state-reduction) from the physical interpretation of the theory. The account of probability has traditionally been considered the principal weakness of the Everett interpretation; on the contrary it emerges as one of its principal strengths. (shrink)

The prelims comprise: Introduction The Breakthrough with Expert Systems in the 1970s The Emergence of Bayesian Networks in the 1980s Philosophical Problems Connected with Probability in AI Appendix.

Historically the emergence of a precise technical meaning for probability, as distinct from its vague popular useage, has taken time; and confusion still arises from the concept of probability having different meanings in different flelds of discourse. Its technical meaning and appropriate rules are surveyed in the flelds of logic , mathematics , and science , and the relation between these three aspects of probability theory discussed. ‐. M. S. B.