This paper is a response to Tyler Wunder’s ‘The modality of theism and probabilistic natural theology: a tension in Alvin Plantinga's philosophy’ (this journal). In his article, Wunder argues that if the proponent of the Evolutionary Argument Against Naturalism (EAAN) holds theism to be non-contingent and frames the argument in terms of objective probability, that the EAAN is either unsound or theism is necessarily false. I argue that a modest revision of the EAAN renders Wunder’s objection irrelevant, and (...) that this revision actually widens the scope of the argument. (shrink)

Rollback arguments focus on long sequences of actions with identical initial conditions in order to explicate the luck problem that indeterminism poses for libertarian free will theories (i.e. the problem that indeterministic actions appear arbitrary in a free-will undermining way). In this paper, I propose a rollback argument for probability incompatibilism, i.e. for the thesis that free will is incompatible with all world-states being governed by objective probabilities. Other than the most prominently discussed rollback arguments, this argument explicitly (...) focusses on the ability to act otherwise. It argues that the negligible probability of the relative frequencies in overall rollback patterns being relevantly different indicates that even the ability to act otherwise with regard to individual actions is not free-will enabling. My proposed argument provides probability incompatibilists with a tool to argue against a classical event-causal response to the luck problem, while it can still motivate an agent-causal response to it. (shrink)

A probability distribution is regular if no possible event is assigned probability zero. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson (2017) and Benci et al. (2016) have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s (2007) “isomorphic” events are not in fact isomorphic, but Howson (...) is speaking of set-theoretic representations of events in a probability model. While those sets are not isomorphic, Williamson’s physical events are, in the relevant sense. Benci et al. claim that all three arguments rest on a conflation of different models, but they do not. They are founded on the premise that similar events should have the same probability in the same model, or in one case, on the assumption that a single rotation-invariant distribution is possible. Having failed to refute the symmetry arguments on such technical grounds, one could deny their implicit premises, which is a heavy cost, or adopt varying degrees of instrumentalism or pluralism about regularity, but that would not serve the project of accurately modelling chances. (shrink)

Given a few assumptions, the probability of a conjunction is raised, and the probability of its negation is lowered, by conditionalising upon one of the conjuncts. This simple result appears to bring Bayesian confirmation theory into tension with the prominent dogmatist view of perceptual justification – a tension often portrayed as a kind of ‘Bayesian objection’ to dogmatism. In a recent paper, David Jehle and Brian Weatherson observe that, while this crucial result holds within classical probability theory, (...) it fails within intuitionistic probability theory. They conclude that the dogmatist who is willing to take intuitionistic logic seriously can make a convincing reply to the Bayesian objection. In this paper, I argue that this conclusion is premature – the Bayesian objection can survive the transition from classical to intuitionistic probability, albeit in a slightly altered form. I shall conclude with some general thoughts about what the Bayesian objection to dogmatism does and doesn’t show. (shrink)

A probability distribution is regular if it does not assign probability zero to any possible event. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson and Benci et al. have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s “isomorphic” events are not in fact isomorphic, but Howson (...) is speaking of set-theoretic representations of events in a probability model. While those sets are not isomorphic, Williamson’s physical events are, in the relevant sense. Benci et al. claim that all three arguments rest on a conflation of different models, but they do not. They are founded on the premise that similar events should have the same probability in the same model, or in one case, on the assumption that a single rotation-invariant distribution is possible. Having failed to refute the symmetry arguments on such technical grounds, one could deny their implicit premises, which is a heavy cost, or adopt varying degrees of instrumentalism or pluralism about regularity, but that would not serve the project of accurately modelling chances. (shrink)

This article analyzes the role of entropy in Bayesian statistics, focusing on its use as a tool for detection, recognition and validation of eigen-solutions. “Objects as eigen-solutions” is a key metaphor of the cognitive constructivism epistemological framework developed by the philosopher Heinz von Foerster. Special attention is given to some objections to the concepts of probability, statistics and randomization posed by George Spencer-Brown, a figure of great influence in the field of radical constructivism.

The problem of probabilities of conditionals is one of the long-standing puzzles in philosophy of language. We defend and update Adams' solution to the puzzle: the probability of an epistemic conditional is not the probability of a proposition, but a probability under a supposition. -/- Close inspection of how a triviality result unfolds in a concrete scenario does not provide counterexamples to the view that probabilities of conditionals are conditional probabilities: instead, it supports the conclusion that probabilities (...) of conditionals violate standard probability theory. -/- This does not call into question probability theory per se; rather, it calls for a more careful understanding of its role: probability theory is a theory of probabilities of propositions; but as conditionals do not express propositions, their probabilities are not subject to the standard laws. -/- We argue that both conditional probabilities and probabilities of conditionals are best understood in terms of the dynamics of supposing, modeled as a restriction operation on a probability space. This version of the suppositionalist view allows us to connect Adams' Thesis to the widely held restrictor view of the semantics of conditionals. -/- We address two common objections to Adams' view: that the relevant probabilities are ‘probabilities only in name’, and that giving up conditional propositions puts us at a disadvantage when it comes to interpreting compounds. -/- Finally, we argue that some putative counterexamples to Adams' Thesis can be diagnosed as fallacies of probabilistic reasoning: they arise from applying to conditionals laws of standard probability theory which are invalid for them. (shrink)

Stalnaker's Thesis about indicative conditionals is, roughly, that the probability one ought to assign to an indicative conditional equals the probability that one ought to assign to its consequent conditional on its antecedent. The thesis seems right. If you draw a card from a standard 52-card deck, how confident are you that the card is a diamond if it's a red card? To answer this, you calculate the proportion of red cards that are diamonds -- that is, you (...) calculate the probability of drawing a diamond conditional on drawing a red card. Skyrms' Thesis about counterfactual conditionals is, roughly, that the probability that one ought to assign to a counterfactual equals one's rational expectation of the chance, at a relevant past time, of its consequent conditional on its antecedent. This thesis also seems right. If you decide not to enter a 100-ticket lottery, how confident are you that you would have won had you bought a ticket? To answer this, you calculate the prior chance--that is, the chance just before your decision not to buy a ticket---of winning conditional on entering the lottery. The central project of this article is to develop a new uniform theory of conditionals that allows us to derive a version of Skyrms' Thesis from a version of Stalnaker's Thesis, together with a chance-deference norm relating rational credence to beliefs about objective chance. (shrink)

The role of probability is one of the most contested issues in the interpretation of contemporary physics. In this paper, I’ll be reevaluating some widely held assumptions about where and how probabilities arise. Larry Sklar voices the conventional wisdom about probability in classical physics in a piece in the Stanford Online Encyclopedia of Philosophy, when he writes that “Statistical mechanics was the first foundational physical theory in which probabilistic concepts and probabilistic explanation played a fundamental role.” And the (...) conventional wisdom about quantum probabilities is that they are basic, not reducible to the types of probabilities we see in statistical mechanics. In the first section of this paper, I’ll argue that in fact classical physics was steeped in probability long before statistical mechanics came on the scene, specifically, that an objective measure over phase space is an indispensable component of any informative physical theory. In the next section, I’ll argue that this objective measure is the fundamental form of physical probability and that quantum probabilities can be defined in terms of it. In the last, I’ll raise some questions about the metaphysical status of the fundamental measure. (shrink)

In the Bayesian approach to quantum mechanics, probabilities—and thus quantum states—represent an agent’s degrees of belief, rather than corresponding to objective properties of physical systems. In this paper we investigate the concept of certainty in quantum mechanics. Particularly, we show how the probability-1 predictions derived from pure quantum states highlight a fundamental difference between our Bayesian approach, on the one hand, and Copenhagen and similar interpretations on the other. We first review the main arguments for the general claim (...) that probabilities always represent degrees of belief. We then argue that a quantum state prepared by some physical device always depends on an agent’s prior beliefs, implying that the probability-1 predictions derived from that state also depend on the agent’s prior beliefs. Quantum certainty is therefore always some agent’s certainty. Conversely, if facts about an experimental setup could imply agent-independent certainty for a measurement outcome, as in many Copenhagen-like interpretations, that outcome would effectively correspond to a preexisting system property. The idea that measurement outcomes occurring with certainty correspond to preexisting system properties is, however, in conflict with locality. We emphasize this by giving a version of an argument of Stairs [(1983). Quantum logic, realism, and value-definiteness. Philosophy of Science, 50, 578], which applies the Kochen–Specker theorem to an entangled bipartite system. (shrink)

Probability can be used to measure degree of belief in two ways: objectively and subjectively. The objective measure is a measure of the rational degree of belief in a proposition given a set of evidential propositions. The subjective measure is the measure of a particular subject’s dispositions to decide between options. In both measures, certainty is a degree of belief 1. I will show, however, that there can be cases where one belief is stronger than another yet both (...) beliefs are plausibly measurable as objectively and subjectively certain. In ordinary language, we can say that while both beliefs are certain, one belief is more certain than the other. I will then propose second, non probabilistic dimension of measurement, which tracks this variation in certainty in such cases where the probability is 1. A general principle of rationality is that one’s subjective degree of belief should match the rational degree of belief given the evidence available. In this paper I hope to show that it is also a rational principle that the maximum stake size at which one should remain certain should match the rational weight of certainty given the evidence available. Neither objective nor subjective measures of certainty conform to the axioms of probability, but instead are measured in utility. This has the consequence that, although it is often rational to be certain to some degree, there is no such thing as absolute certainty. (shrink)

Non-Archimedean probability functions allow us to combine regularity with perfect additivity. We discuss the philosophical motivation for a particular choice of axioms for a non-Archimedean probability theory and answer some philosophical objections that have been raised against infinitesimal probabilities in general.

Credences are beliefs about evidential probabilities. We give the view an assessment-sensitive formulation, show how it evades the standard objections, and give several arguments in support.

In finite probability theory, events are subsets S⊆U of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events." Probabilities are introduced for classical events, superposition events, and their mixtures by using density matrices. Then probabilities for experiments or `measurements' of all these events can be determined in a manner exactly like in quantum mechanics (QM) using density matrices. Moreover the transformation of the (...) density matrices induced by the experiments or `measurements' is the Lüders mixture operation as in QM. And finally by moving the machinery into the n-dimensional vector space over ℤ₂, different basis sets become different outcome sets. That `non-commutative' extension of finite probability theory yields the pedagogical model of quantum mechanics over ℤ₂ that can model many characteristic non-classical results of QM. (shrink)

The epistemic probability of A given B is the degree to which B evidentially supports A, or makes A plausible. This paper is a first step in answering the question of what determines the values of epistemic probabilities. I break this question into two parts: the structural question and the substantive question. Just as an object’s weight is determined by its mass and gravitational acceleration, some probabilities are determined by other, more basic ones. The structural question asks what probabilities (...) are not determined in this way—these are the basic probabilities which determine values for all other probabilities. The substantive question asks how the values of these basic probabilities are determined. I defend an answer to the structural question on which basic probabilities are the probabilities of atomic propositions conditional on potential direct explanations. I defend this against the view, implicit in orthodox mathematical treatments of probability, that basic probabilities are the unconditional probabilities of complete worlds. I then apply my answer to the structural question to clear up common confusions in expositions of Bayesianism and shed light on the “problem of the priors.”. (shrink)

One popular approach to statistical mechanics understands statistical mechanical probabilities as measures of rational indifference. Naive formulations of this ``indifference approach'' face reversibility worries - while they yield the right prescriptions regarding future events, they yield the wrong prescriptions regarding past events. This paper begins by showing how the indifference approach can overcome the standard reversibility worries by appealing to the Past Hypothesis. But, the paper argues, positing a Past Hypothesis doesn't free the indifference approach from all reversibility worries. For (...) while appealing to the Past Hypothesis allows it to escape one kind of reversibility worry, it makes it susceptible to another - the Meta-Reversibility Objection. And there is no easy way for the indifference approach to escape the Meta-Reversibility Objection. As a result, reversibility worries pose a steep challenge to the viability of the indifference approach. (shrink)

The major competing statistical paradigms share a common remarkable but unremarked thread: in many of their inferential applications, different probability interpretations are combined. How this plays out in different theories of inference depends on the type of question asked. We distinguish four question types: confirmation, evidence, decision, and prediction. We show that Bayesian confirmation theory mixes what are intuitively “subjective” and “objective” interpretations of probability, whereas the likelihood-based account of evidence melds three conceptions of what constitutes an (...) “objective” probability. (shrink)

The objective Bayesian view of proof (or logical probability, or evidential support) is explained and defended: that the relation of evidence to hypothesis (in legal trials, science etc) is a strictly logical one, comparable to deductive logic. This view is distinguished from the thesis, which had some popularity in law in the 1980s, that legal evidence ought to be evaluated using numerical probabilities and formulas. While numbers are not always useful, a central role is played in uncertain reasoning (...) by the ‘proportional syllogism’, or argument from frequencies, such as ‘nearly all aeroplane flights arrive safely, so my flight is very likely to arrive safely’. Such arguments raise the ‘problem of the reference class’, arising from the fact that an individual case may be a member of many different classes in which frequencies differ. For example, if 15 per cent of swans are black and 60 per cent of fauna in the zoo is black, what should I think about the likelihood of a swan in the zoo being black? The nature of the problem is explained, and legal cases where it arises are given. It is explained how recent work in data mining on the relevance of features for prediction provides a solution to the reference class problem. (shrink)

We generalize the Kolmogorov axioms for probability calculus to obtain conditions defining, for any given logic, a class of probability functions relative to that logic, coinciding with the standard probability functions in the special case of classical logic but allowing consideration of other classes of "essentially Kolmogorovian" probability functions relative to other logics. We take a broad view of the Bayesian approach as dictating inter alia that from the perspective of a given logic, rational degrees of (...) belief are those representable by probability functions from the class appropriate to that logic. Classical Bayesianism, which fixes the logic as classical logic, is only one version of this general approach. Another, which we call Intuitionistic Bayesianism, selects intuitionistic logic as the preferred logic and the associated class of probability functions as the right class of candidate representions of epistemic states (rational allocations of degrees of belief). Various objections to classical Bayesianism are, we argue, best met by passing to intuitionistic Bayesianism—in which the probability functions are taken relative to intuitionistic logic—rather than by adopting a radically non-Kolmogorovian, for example, nonadditive, conception of (or substitute for) probability functions, in spite of the popularity of the latter response among those who have raised these objections. The interest of intuitionistic Bayesianism is further enhanced by the availability of a Dutch Book argument justifying the selection of intuitionistic probability functions as guides to rational betting behavior when due consideration is paid to the fact that bets are settled only when/if the outcome bet on becomes known. (shrink)

A common objection to probabilistic theories of causation is that there are prima facie causes that lower the probability of their effects. Among the many replies to this objection, little attention has been given to Mellor's (1995) indirect strategy to deny that probability-lowering factors are bona fide causes. According to Mellor, such factors do not satisfy the evidential, explanatory, and instrumental connotations of causation. The paper argues that the evidential connotation only entails an epistemically relativized form of causal (...) attribution, not causation itself, and that there are clear cases of explanation and instrumental reasoning that must appeal to negatively relevant factors. In the end, it suggests a more liberal interpretation of causation that restores its connotations. Una objeción común a las teorías probabilísticas de la causalidad es que aparentemente existen causas que disminuyen la probabilidad de sus efectos. Entre las muchas respuestas a esta objeción, se le ha dado poca atención a la estrategia indirecta de D. H. Mellor (1995) para negar que un factor que disminuya la probabilidad de un efecto sea una causa legítima. Según Mellor, tales factores no satisfacen las connotaciones evidenciales, explicativas e instrumentales de la causalidad. El artículo argumenta que la connotación evidencial sólo implica una forma epistémicamente relativizada de atribución causal y no la causalidad misma, y que hay casos claros de explicación y razonamiento instrumental que deben apelar a factores negativamente relevantes. Se sugiere una interpretación más liberal de la causalidad que reinstaura sus connotaciones. (shrink)

Reasoning from inconclusive evidence, or ‘induction’, is central to science and any applications we make of it. For that reason alone it demands the attention of philosophers of science. This Element explores the prospects of using probability theory to provide an inductive logic, a framework for representing evidential support. Constraints on the ideal evaluation of hypotheses suggest that overall support for a hypothesis is represented by its probability in light of the total evidence, and incremental support, or confirmation, (...) indicated by an increased probability given the evidence than otherwise. This proposal is shown to have the capacity to reconstruct many canons of the scientific method and inductive inference. Along the way, significant objections are discussed, such as the challenge from inductive scepticism and the objection that the probabilistic approach makes evidential support arbitrary. (shrink)

In this paper, I will claim that fictional works apparently about utterly immigrant objects, i.e., real individuals imported in fiction from reality, are instead about fictional individuals that intentionally resemble those real individuals in a significant manner: fictional surrogates of such individuals. Since I also share the realists’ conviction that the remaining fictional works concern native characters, i.e., full-fledged fictional individuals that originate in fiction itself, I will here defend a hyperrealist position according to which fictional works only concern fictional (...) individuals. (shrink)

Several scholars have recently entertained proposals for "epistocracy," a political regime in which decision-making power is concentrated in the hands of a society's most informed and competent citizens. These proposals rest on the claim that we can expect better political outcomes if we exclude incompetent citizens from participating in political decisions because competent voters are more likely to vote "correctly" than incompetent voters. We develop what we call the objection from selection bias to epistocracy: a procedure that selects voters on (...) the basis of their observed competence---as epistocracy does---will often be "biased" in the sense that competent voters will be, on average, more likely than incompetent voters to possess certain attributes that reduce the probability of voting correctly. Our objection generalizes the "demographic objection" discussed in previous literature, showing that the range of realistic scenarios in which epistocracy is vulnerable to selection bias is substantially broader than previous discussions appreciate. Our discussion also shows that previous discussions have obscured the force of the threat of selection bias. Since we lack reasons to believe that epistocratic proposals can avoid selection bias, we have no reason to seriously entertain epistocracy as a practical proposal. (shrink)

There is widespread excitement in the literature about the method of arbitrary functions: many take it to show that it is from the dynamics of systems that the objectivity of probabilities emerge. In this paper, I differentiate three ways in which a probability function might be objective, and I argue that the method of arbitrary functions cannot help us show that dynamics objectivise probabilities in any of these senses.

“Negative probability” in practice. Quantum Communication: Very small phase space regions turn out to be thermodynamically analogical to those of superconductors. Macro-bodies or signals might exist in coherent or entangled state. Such physical objects having unusual properties could be the basis of quantum communication channels or even normal physical ones … Questions and a few answers about negative probability: Why does it appear in quantum mechanics? It appears in phase-space formulated quantum mechanics; next, in quantum correlations … and (...) for wave-particle dualism. Its meaning:- mathematically: a ratio of two measures (of sets), which are not collinear; physically: the ratio of the measurements of two physical quantities, which are not simultaneously measurable. The main innovation is in the mapping between phase and Hilbert space, since both are sums. Phase space is a sum of cells, and Hilbert space is a sum of qubits. The mapping is reduced to the mapping of a cell into a qubit and vice versa. Negative probability helps quantum mechanics to be represented quasi-statistically by quasi-probabilistic distributions. Pure states of negative probability cannot exist, but they, where the conditions for their expression exists, decrease the sum probability of the integrally positive regions of the distributions. They reflect the immediate interaction (interference) of probabilities common in quantum mechanics. (shrink)

The logical interpretation of probability, or "objective Bayesianism'' – the theory that (some) probabilities are strictly logical degrees of partial implication – is defended. The main argument against it is that it requires the assignment of prior probabilities, and that any attempt to determine them by symmetry via a "principle of insufficient reason" inevitably leads to paradox. Three replies are advanced: that priors are imprecise or of little weight, so that disagreement about them does not matter, within limits; (...) that it is possible to distinguish reasonable from unreasonable priors on logical grounds; and that in real cases disagreement about priors can usually be explained by differences in the background information. It is argued also that proponents of alternative conceptions of probability, such as frequentists, Bayesians and Popperians, are unable to avoid committing themselves to the basic principles of logical probability. (shrink)

Evolutionary theory (ET) is teeming with probabilities. Probabilities exist at all levels: the level of mutation, the level of microevolution, and the level of macroevolution. This uncontroversial claim raises a number of contentious issues. For example, is the evolutionary process (as opposed to the theory) indeterministic, or is it deterministic? Philosophers of biology have taken different sides on this issue. Millstein (1997) has argued that we are not currently able answer this question, and that even scientific realists ought to remain (...) agnostic concerning the determinism or indeterminism of evolutionary processes. If this argument is correct, it suggests that, whatever we take probabilities in ET to be, they must be consistent with either determinism or indeterminism. This raises some interesting philosophical questions: How should we understand the probabilities used in ET? In other words, what is meant by saying that a certain evolutionary change is more or less probable? Which interpretation of probability is the most appropriate for ET? I argue that the probabilities used in ET are objective in a realist sense, if not in an indeterministic sense. Furthermore, there are a number of interpretations of probability that are objective and would be consistent with ET under determinism or indeterminism. However, I argue that evolutionary probabilities are best understood as propensities of population-level kinds. (shrink)

In the following we will investigate whether von Mises’ frequency interpretation of probability can be modified to make it philosophically acceptable. We will reject certain elements of von Mises’ theory, but retain others. In the interpretation we propose we do not use von Mises’ often criticized ‘infinite collectives’ but we retain two essential claims of his interpretation, stating that probability can only be defined for events that can be repeated in similar conditions, and that exhibit frequency stabilization. The (...) central idea of the present article is that the mentioned ‘conditions’ should be well-defined and ‘partitioned’. More precisely, we will divide probabilistic systems into object, initializing, and probing subsystem, and show that such partitioning allows to solve problems. Moreover we will argue that a key idea of the Copenhagen interpretation of quantum mechanics (the determinant role of the observing system) can be seen as deriving from an analytic definition of probability as frequency. Thus a secondary aim of the article is to illustrate the virtues of analytic definition of concepts, consisting of making explicit what is implicit. (shrink)

This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or "toy" model of quantum mechanics over sets (QM/sets). There are two parts. The notion of an "event" is reinterpreted from being an epistemological state of indefiniteness to being an objective state of indefiniteness. And the mathematical framework of finite probability theory is recast as the quantum probability calculus for QM/sets. (...) The point is not to clarify finite probability theory but to elucidate quantum mechanics itself by seeing some of its quantum features in a classical setting. (shrink)

The problem of unconceived alternatives can be undermined, regardless of whether the possibility space of alternatives is bounded or unbounded. If it is bounded, pessimists need to justify their assumption that the probability that scientists have not yet eliminated enough false alternatives is higher than the probability that scientists have already eliminated enough false alternatives. If it is unbounded, pessimists need to justify their assumption that the probability that scientists have not yet moved from the possibility space (...) of false alternatives to the possibility space of true alternatives is higher than the probability that scientists have already moved from the former to the latter space. (shrink)

I introduce a formalization of probability which takes the concept of 'evidence' as primitive. In parallel to the intuitionistic conception of truth, in which 'proof' is primitive and an assertion A is judged to be true just in case there is a proof witnessing it, here 'evidence' is primitive and A is judged to be probable just in case there is evidence supporting it. I formalize this outlook by representing propositions as types in Martin-Lof type theory (MLTT) and defining (...) a 'probability type' on top of the existing machinery of MLTT, whose inhabitants represent pieces of evidence in favor of a proposition. One upshot of this approach is the potential for a mathematical formalism which treats 'conjectures' as mathematical objects in their own right. Other intuitive properties of evidence occur as theorems in this formalism. (shrink)

Some propositions are more epistemically important than others. Further, how important a proposition is is often a contingent matter—some propositions count more in some worlds than in others. Epistemic Utility Theory cannot accommodate this fact, at least not in any standard way. For EUT to be successful, legitimate measures of epistemic utility must be proper, i.e., every probability function must assign itself maximum expected utility. Once we vary the importance of propositions across worlds, however, normal measures of epistemic utility (...) become improper. I argue there isn’t any good way out for EUT. (shrink)

How were reliable predictions made before Pascal and Fermat's discovery of the mathematics of probability in 1654? What methods in law, science, commerce, philosophy, and logic helped us to get at the truth in cases where certainty was not attainable? The book examines how judges, witch inquisitors, and juries evaluated evidence; how scientists weighed reasons for and against scientific theories; and how merchants counted shipwrecks to determine insurance rates. Also included are the problem of induction before Hume, design arguments (...) for the existence of God, and theories on how to evaluate scientific and historical hypotheses. It is explained how Pascal and Fermat's work on chance arose out of legal thought on aleatory contracts. The book interprets pre-Pascalian unquantified probability in a generally objective Bayesian or logical probabilist sense. (shrink)

One of our most sophisticated accounts of objective chance in quantum mechanics involves the Deutsch-Wallace theorem, which uses state-space symmetries to justify agents’ use of the Born rule when the quantum state is known. But Wallace argues that this theorem requires an Everettian approach to measurement. I find that this argument is unsound. I demonstrate a counter-example by applying the Deutsch-Wallace theorem to the de Broglie-Bohm pilot-wave theory.

If science disputes the validity or authenticity of religious knowledge it is because both the scientist and the rational man assume that every object of knowledge there is or can be exists as a material percept in time and space. If we assume that knowledge of material objects is definite knowledge – an assumption itself suspect considering that the latest WMAP data indicates that 95.4% of the total matter in our universe is dark matter and dark energy – all scientific (...) knowledge (confined as it is to knowledge of 4.6% of the visible universe) is definite knowledge; but because it’s knowledge is confined to a miniscule fraction of all knowledge there is or can be had in our material universe, it can scarcely be said – as Sir Bertrand Russell claims – that all definite knowledge is scientific knowledge. There are other reasons why all definite knowledge is not in the domain of science. Parts of the universe are; the universe as a whole isn’t. The sentient body is; the Self that is clothed by that body isn’t. Analysis of both these wholes reveals the possibility of the existence of a third entity that is beyond scientific knowledge. This humanity calls God. A detailed investigation not conducted but outlined here reveals that (a) Russell’s claim that science holds a monopoly of definite knowledge is false: he probably meant that science has a monopoly of objectively verifiable knowledge; (b) as objective verifiability is contingent upon objectively real existence, science’s monopoly is over entities that are objectively real; (c) all objects of knowledge are not material objects in time and space: there are objects that, because they are not percepts, are not objectively verifiable. There is nothing indefinite about knowledge of such entities. There is nothing subjective about the knowledge of such entities either: so it is not open to science to dismiss knowledge of such entities as subjective, arising from the state of mind of the observer. Space and time are aspects of objective reality and not of subjective reality. The second part of this paper briefly examines the nature of dimensions. Space, time and Self consciousness are three types of dimensions considered. The third part of this paper speaks of a concept called immutable wholes. This is a logical culmination of the paper because dimensions are the state-giving norms of the wholes that these dimensions define and characterize. Spiritual seekers make these entities (sub specie aeternitatis) objects of their realization. Such entities as the Universe as a Whole, the Self, and God belong to this class of existents. If Universe as a Whole {not parts of it (study of which is in the domain of science), no matter how large those parts are, but the whole. Only a true seeker can tell science why the whole ≠ sum of all its parts – but that would be the subject of another paper}. (shrink)

This paper is concerned with representations of belief by means of nonadditive probabilities of the Dempster-Shafer (DS) type. After surveying some foundational issues and results in the D.S. theory, including Suppes's related contributions, the paper proceeds to analyze the connection of the D.S. theory with some of the work currently pursued in epistemic logic. A preliminary investigation of the modal logic of belief functions à la Shafer is made. There it is shown that the Alchourrron-Gärdenfors-Makinson (A.G.M.) logic of belief change (...) is closely related to the D.S. theory. The final section compares the critique of Bayesianism which underlies the present paper with some important objections raised by Suppes against this doctrine. -/- . (shrink)

The concept of a physical object has figured prominently in the history of philosophy, and is probably more important now than it has ever been before. Yet the question What are physical objects?, i.e., What is the correct analysis of the concept of a physical object?, has received surprisingly little attention. The purpose of this paper is to address this question. I consider several attempts at answering the question, and give my reasons for preferring one of them over its rivals. (...) The account of physical objects that I recommend---the Spatial Location Account---defines physical objects as objects with spatial locations. The intuitive idea behind the Spatial Location Account is this. Objects from all of the different ontological categories---physical objects; non-physical objects like souls, if there are any; propositions; universals; etc.---have this much in common: they all exist in time. But not all of them exist in space. The ones that exist in time and space, i.e., the ones that have spatial locations, are the ones that count as physical objects. (shrink)

The growing range of methods for statistical model selection is inspiring new debates about how to handle the potential for conflicting results when different methods are applied to the same data. While many factors enter into choosing a model selection method, we focus on the implications of disagreements among scientists about whether, and in what sense, the true probability distribution is included in the candidate set of models. While this question can be addressed empirically, the data often provide inconclusive (...) results in practice. In such cases, we argue that differences in prior metaphysical views about the local adequacy of the models can produce underdetermination of results, even for the same data and candidate models. As a result, data alone are sometimes insufficient to settle rational beliefs about nature. (shrink)

I defend external world realism. I assume that the principle of inference to the best explanation is justified: roughly, a hypothesis that provides a better explanation of the total evidence is more probable than one that does not. I argue that the existence of a world of spatial objects provides a systematic explanation of the spatial contents of visual experience, and that it provides a better explanation than traditional skeptical hypotheses. This paper thus pursues the explanationist strategy of Laurence BonJour (...) and Jonathan Vogel. It is an improved, more compelling defense, for at least two reasons. First, the attention to spatial properties, and in particular to what I call perspectival projections, makes the explanatory power of the realist hypothesis much more vivid and concrete. Second, the argument preserves and elucidates much that seems correct in the explanationist arguments others have offered while avoiding significant problems and shortcomings. (shrink)

A theory of cognitive systems individuation is presented and defended. The approach has some affinity with Leonard Talmy's Overlapping Systems Model of Cognitive Organization, and the paper's first section explores aspects of Talmy's view that are shared by the view developed herein. According to the view on offer -- the conditional probability of co-contribution account (CPC) -- a cognitive system is a collection of mechanisms that contribute, in overlapping subsets, to a wide variety of forms of intelligent behavior. Central (...) to this approach is the idea of an integrated system. A formal characterization of integration is laid out in the form of a conditional-probabilitybased measure of the clustering of causal contributors to the production of intelligent behavior. I relate the view to the debate over extended and embodied cognition and respond to objections that have been raised in print by Andy Clark, Colin Klein, and Felipe de Brigard. (shrink)

Classical physics and quantum physics suggest two meta-physical types of reality: the classical notion of a objectively definite reality with properties "all the way down," and the quantum notion of an objectively indefinite type of reality. The problem of interpreting quantum mechanics (QM) is essentially the problem of making sense out of an objectively indefinite reality. These two types of reality can be respectively associated with the two mathematical concepts of subsets and quotient sets (or partitions) which are category-theoretically dual (...) to one another and which are developed in two mathematical logics, the usual Boolean logic of subsets and the more recent logic of partitions. Our sense-making strategy is "follow the math" by showing how the logic and mathematics of set partitions can be transported in a natural way to Hilbert spaces where it yields the mathematical machinery of QM--which shows that the mathematical framework of QM is a type of logical system over ℂ. And then we show how the machinery of QM can be transported the other way down to the set-like vector spaces over ℤ₂ showing how the classical logical finite probability calculus (in a "non-commutative" version) is a type of "quantum mechanics" over ℤ₂, i.e., over sets. In this way, we try to make sense out of objective indefiniteness and thus to interpret quantum mechanics. (shrink)

What is the most general common set of attributes that characterises something as intrinsically valuable and hence as subject to some moral respect, and without which something would rightly be considered intrinsically worthless or even positively unworthy and therefore rightly to be disrespected in itself? This paper develops and supports the thesis that the minimal condition of possibility of an entity's least intrinsic value is to be identified with its ontological status as an information object. All entities, even when interpreted (...) as only clusters of information, still have a minimal moral worth qua information objects and so may deserve to be respected. The paper is organised into four main sections. Section 1 models moral action as an information system using the object-oriented programming methodology (OOP). Section 2 addresses the question of what role the several components constituting the moral system can have in an ethical analysis. If they can play only an instrumental role, then Computer Ethics (CE) is probably bound to remain at most a practical, field-dependent, applied or professional ethics. However, Computer Ethics can give rise to a macroethical approach, namely Information Ethics (IE), if one can show that ethical concern should be extended to include not only human, animal or biological entities, but also information objects. The following two sections show how this minimalist level of analysis can be achieved. Section 3 provides an axiological analysis of information objects. It criticises the Kantian approach to the concept of intrinsic value and shows that it can be improved by using the methodology introduced in the first section. The solution of the Kantian problem prompts the reformulation of the key question concerning the moral worth of an entity: what is the intrinsic value of x qua an object constituted by its inherited attributes? In answering this question, it is argued that entities can share different observable properties depending on the level of abstraction adopted,and that it is still possible to speak of moral value even at the highest level of ontological abstraction represented by the informational analysis. Section 4 develops a minimalist axiology based on the concept of information object. It further supports IE's position by addressing five objections that may undermine its acceptability. (shrink)

In the worlds of philosophy, linguistics, and communications theory, a view has developed which understands conscious experience as experience which is 'reflected' back upon itself through language. This indicates that the consciousness we experience is possible only because we have culturally invented language and subsequently evolved to accommodate it. This accords with the conclusions of Daniel Dennett (1991), but the 'hermeneutic objection' would go further and deny that the objective sciences themselves have escaped the hermeneutic circle. -/- The consciousness (...) we humans experience is developed only within the context of crossing the 'symbolic threshold' (Percy 1975; Deacon 1997) and one of the earliest and most important symbols we acquire is that of the self, or 'the subject of experience'. It is only when we achieve self-awareness that the world, as such, comes to exist for us as an object (which contains categories and sub-categories of objects). Any consciousness imputed to prelinguistic stages of development is based on projection and guesswork, since we can know nothing directly of it. It can be said that any experience which does not separate an inner subject from an outer world is probably a continuum of sensation in which environmental stimulus and instinctive response are experienced as a unity; it may be 'lived experience' but it is experience 'lived' non-consciously. -/- Speech requires assertion and by learning to speak we find ourselves asserting, in essence, our selves into the world. The narrative form of language allows us to develop life stories, self-knowledge, and, most important, narrative memory coincident with narrative time. All this is made possible with the intersubjective 'net' of language which allows us to know ourselves by first identifying with the viewpoint of others; and, later, such allows us to identify with other minds as we anticipate their reception our communication. These three, assertion, narrative, and intersubjectivity are the essence of what language is and are the keystones that make culture possible outside of nature. (shrink)

A fully developed sophisticated response-dependent account would fill in specifications for B (the beings) and C (the conditions), would probably replace the reference to disapproval with a reference to a more complex response, and might involve a more complex scheme.[ii] For simplicity, however, I shall focus my argument on the above simple scheme of moral wrongness, since added complexities will be irrelevant to my argument.

According to Agnosticism with a capital A, even if we don’t see how any reason we know of would justify God in permitting all the evil in the world and even if we lack evidential and non-evidential warrant for theism, we should not infer that there probably is no reason that would justify God. That’s because, under those conditions, we should be in doubt about whether the goods we know of constitute a representative sample of all the goods there are, (...) among relevantly similar things. In my "Epistemic Humility, Arguments from Evil, and Moral Skepticism" (2009), I defended Agnosticism against the charge that it leaves us in doubt about whether we are obligated to intervene to prevent horrific suffering we can prevent at no risk to ourselves. In his “Agnosticism, Skeptical Theism, and Moral Obligation” (2014), Stephen Maitzen argues that, in light of my defense, Agnosticism is at odds with commonsense morality’s insistence that we have an obligation to intervene in such cases. In the present essay, I argue that the moral principle Maitzen seems to impute to commonsense (it's hard to tell what principle he has in mind) is false and that a moral principle much more in keeping with commonsense is compatible with Agnosticism and my defense of it. Along the way, I mention multiple misrepresentations Maitzen makes of Agnosticism and my defense of it. (shrink)

Some recent work in philosophy of religion addresses what can be called the “axiological question,” i.e., regardless of whether God exists, would it be good or bad if God exists? Would the existence of God make the world a better or a worse place? Call the view that the existence of God would make the world a better place “Pro-Theism.” We argue that Pro-Theism is not implausible, and moreover, many Theists, at least, (often implicitly) think that it is true. That (...) is, many Theists think that various good outcomes would arise if Theism is true. We then discuss work in cognitive science concerning human cognitive bias, before discussing two noteworthy attempts to show that at least some religious beliefs arise because of cognitive bias: Hume’s, and Draper’s and Nichols’s. We then argue that, as a result of certain cognitive biases that result when good outcomes might be at stake, Pro-Theism causes many Theists to inflate the epistemic probability that God exists, and as a result, Theists should lower the probability they assign to God’s existence. Finally, based our arguments, we develop a novel objection to Pascal’s wager. (shrink)

In a recent paper, Eric Schwitzgebel argues that if materialism about consciousness is true, then the United States is likely to have its own stream of phenomenal consciousness, distinct from the streams of conscious experience of the people who compose it. Indeed, most plausible forms of materialism have to grant that a certain degree of functional and behavioral complexity constitutes a sufficient condition for the ascription of phenomenal consciousness – and Schwitzgebel makes a case to show that the United States (...) as a whole fulfills this condition. One way to avoid this counter-intuitive consequence of materialism about consciousness is to adopt what Schwitzgebel calls an “anti-nesting principle”: a principle that states that there can be no nested forms of phenomenal consciousness and that therefore a conscious whole cannot have parts that are themselves conscious. However, Schwitzgebel then proceeds in his paper to draw up various objections, notably based on thought experiments, in order to dismiss these kinds of “anti-nesting” principles. My aim in this paper is to present a version of a sophisticated anti-nesting principle that avoids Schwitzgebel’s objections. This principle is reasonable, intuitive, and as non-arbitrary as possible. Moreover, it can resist the objections mounted by Schwitzgebel against simple anti-nesting principles. This principle helps materialists avoid the implication that the United States has its own stream of consciousness, while granting consciousness to some entities which, in many cases, are intuitive instantiators of phenomenal consciousness. This principle therefore constitutes a way out for a materialist who wants to deny that the United States is conscious. (shrink)

Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such probability from the same notion in empirical science. Yet it is hard to see how there could be probabilistic relations between the necessary truths of pure mathematics. The existence of such logical relations, short of certainty, is defended using the theory of logical probability (or (...) objective Bayesianism or non-deductive logic), and some detailed examples of its use in mathematics surveyed. Examples of inductive reasoning in experimental mathematics are given and it is argued that the problem of induction is best appreciated in the mathematical case. (shrink)

I argue that riskier killings of innocent people are, other things equal, objectively worse than less risky killings. I ground these views in considerations of disrespect and security. Killing someone more riskily shows greater disrespect for him by more grievously undervaluing his standing and interests, and more seriously undermines his security by exposing a disposition to harm him across all counterfactual scenarios in which the probability of killing an innocent person is that high or less. I argue that the (...) salient probabilities are the agent’s sincere, sane, subjective probabilities, and that this thesis is relevant whether your risk-taking pertains to the probability of killing a person or to the probability that the person you kill is not liable to be killed. I then defend the view’s relevance to intentional killing; show how it differs from an account of blameworthiness; and explain its significance for all-things-considered justification and justification under uncertainty. (shrink)

Arguments from evil purport to show that some fact about evil makes it (at least) probable that God does not exist. Skeptical theism is held to undermine many versions of the argument from evil: it is thought to undermine a crucial inference that such arguments often rely on. Skeptical objections to skeptical theism claim that it (skeptical theism) entails an excessive amount of skepticism, and therefore should be rejected. In this article, I show that skeptical objections to skeptical theism have (...) a very limited scope: only those who reject certain (apparently) popular epistemological theories will be threatened by them. (shrink)