Interpretations of Probability

If you check the weather prediction on your phone, you might read that there is a 30 percent chance of rain at 4:00 in the afternoon. What does this mean? More precisely, what is the fraction 30/100 a measure of? Probability is a concept that is widespread both in everyday life and in science. Ordinary speakers of English utter and have some understanding of sentences such as “I will probably be late for the meeting,” or “it’s unlikely that Luxembourg will win the next World Cup.” Various sciences make explicit probabilistic claims: “the probability that a radium atom will decay in 1620 years is 0.5”; “the probability that a house mouse whose father is heterozygous for the t haplotype will inherit that trait is 0.9.” Other claims implicitly invoke probability: “the life expectancy of a child born in Japan today is 85.3 years.” Probability theory is also a major branch of mathematics, and it was given its modern formulation by Kolmogorov in 1933. Kolmogorov’s formalism presents a function P that satisfies a set of axioms: it is non-negative, normalized, and additive. These axioms entail a rich set of theorems concerning the behavior of P; together they make up the probability calculus. While the resulting theory is a formal theory in its own right, it is also natural to interpret P—to attach meanings, or truth conditions to claims involving it. ‘What is P?’, one may ask. This may be understood as a metaphysical question about what kinds of things are probabilities, or more generally as a question about what makes probability statements true or false. The various interpretations of probability attempt to answer this question, one way or another. This article surveys the literature on the interpretations of probability, due to mathematicians and especially philosophers. It divides the interpretations into two broad categories. Epistemological interpretations understand probability in terms of an agent’s beliefs, the strength of evidence in support of a statement, or other epistemological categories. Physical interpretations view probability as a feature of the world that would exist regardless of what evidence exists or what agents believe. This is a natural taxonomy, but others could be adopted, and its sub-categories are also somewhat pliable. The authors would like to thank Kim Border, Chris Bottomley, Kenny Easwaran, Hanti Lin, Charles Sebens, Glenn Shafer, Julia Staffel, Jeremy Strasser, and an anonymous referee for many helpful suggestions.

Mary Midgley

Mary Beatrice Midgley (née Scrutton; b. 13 September 1919–d. 10 October 2018) wrote twenty philosophical books that use an engaging style and surprisingly domestic metaphors to convey profound thought about a diverse range of topics, including human nature, animals, environmentalism, ethics, science, gender, and the practice of philosophy itself. Her first book was the influential Beast and Man, published in 1978, and her last was What Is Philosophy For?, a defense of the need for philosophical thinking, published just before her death at the age of ninety-nine. Midgley has recently garnered more philosophical attention and is now widely recognized as an original and incisive voice in philosophy. The daughter of a pacifist curate, Midgley was born in Dulwich, London, before moving to Cambridge, Greenford, and Kingston. A nature-loving child, with passions for drama and poetry, she was educated at Downe House School near Newbury, before reading Classics and Greats at Somerville College, Oxford, between 1938 and 1942. Here she met her fellow members of the wartime Quartet of women philosophers (see the separate Oxford Bibliographies in Philosophy articles on “G. E. M. Anscombe,” “Philippa Foot,” and “Iris Murdoch”). The four became great friends and influenced each other throughout their working lives. Their connections include a frustration with the narrowness of the systematic philosophy that was in vogue during their formative years, and the revival of virtue in moral philosophy. Unlike her contemporaries, Midgley published little work until her fifties, after she had raised children and left academic philosophy. As Midgley said, “I wrote no books until I was a good 50, and I’m jolly glad because I didn’t know what I thought before then.” For this reason, Midgley’s writing is striking in its consistency. Articles of this kind often chart changes of mind and theoretical revisions. While Midgley’s thought undoubtedly developed and expanded, there are no early or late periods, marked by stark differences of view. One of Midgley’s criticisms of her predecessors concerned their neglect of the history of ideas. Midgley holds that to understand a philosophical system, we must understand the context in which it arose. Philosophy and culture are interconnected: the great thinkers of any era are influenced by their historical circumstances, and the patterns of thought within a culture are, whether we realize it or not, profoundly philosophical. Philosophy, she argues, is indispensable, because it allows us to make sense of our current predicaments and—where necessary—make changes to our patterns of thought.

Bayesian Epistemology

Everyone agrees that it is good to know. We however believe many more things than we know, which has made the notion of belief a target of recent work in epistemology. Not only do we believe propositions, we also believe them to different degrees. That beliefs come in degrees is often taken as a psychological fact and as a normative principle of rationality. The most prominent normative approach to beliefs which come in degrees is Bayesian epistemology. Bayesian degrees of belief are postulated to be represented by numbers in the unit interval [0, 1] obeying the axioms of probability. The convention is that a greater number expresses a stronger belief. The second postulate of Bayesian epistemology governs the change of beliefs whenever new evidence becomes available via updating procedures, Bayesian updating for categorical evidence and the more general Jeffrey updating for uncertain evidence.

Anselm of Canterbury

Anselm of Canterbury (b. 1033–d. 1109) is the most enduringly influential philosopher-theologian of the Latin West between Augustine and the 13th century. Best known among philosophers for his “ontological” argument for the existence of God in the Proslogion and among theologians for his account of the Atonement in Cur Deus Homo, he is regarded as the quintessential “classical theist,” and his accounts of the divine nature and attributes, of freedom and the fall, and of human redemption continue to attract attention. This article provides an annotated list of Anselm’s complete works as well as selected English translations and secondary literature.

Internalism and Externalism in Epistemology

The internalism/externalism distinction in epistemology applies to both theories of justification and theories of knowledge. The distinction is most clearly defined for theories of justification. An internalist theory of epistemic justification is any theory that maintains that epistemic justifiedness is exclusively a function of states internal to the cognizer. Externalism is the denial of internalism. Thus, an externalist theory is any theory that maintains that epistemic justifiedness is at least partly a function of states or factors external to the cognizer, i.e., states or factors outside the cognizer’s ken. There is no unified agreement among internalists as to which internal states are epistemically relevant, and different internalisms emerge based on the subset of internal states deemed relevant. (See Internalism and Justification for details.) Internalists typically maintain that justification is a normative notion in the belief-guiding/regulative sense. Internalists also typically maintain that one can tell whether one is justified in believing p simply by reflecting on one’s internal evidence for p. The central internalist intuition, as highlighted by the New Evil Demon Problem is this: There can be no difference in justification without a difference in epistemically relevant internal states. Externalism is motivated by the intuition that epistemic justification must be conceptually connected to truth such that the conditions that make a belief justified also make it objectively probable. Externalists are also typically motivated by the view that children and animals can form justified beliefs, while failing to satisfy the internalist’s intellectualist requirements for justification. The dominant externalist theory of justification is process reliabilism, a simplified version of which holds that a belief is justified iff it’s produced by a reliable process. There is less canonical agreement when it comes to applying the internalist/externalist distinction to theories of knowledge. In one sense, every plausible epistemology is an externalist theory because every plausible epistemology requires an externalist truth condition and an externalist Gettier-blocking fillip. However, in another widely used sense, “externalist” theories of knowledge are theories that replace the internalist justification condition with either an externalist justification condition or some other externalist constraint (such as a causal or modal constraint); while “internalist” theories of knowledge hold that internalist justification is necessary for knowledge and also typically hold that no other kind of justification is needed for knowledge, though they do incorporate some sort of externalist constraint to handle the Gettier problem.

Intellectual Virtues

Intellectual virtues are qualities that make us excellent thinkers. There are different analyses of exactly which qualities count as intellectual virtues: virtue responsibilists have emphasized praiseworthy character traits, such as open-mindedness and intellectual humility, while virtue reliabilists have emphasized reliable skills and faculties, such as vision, memory, and skills of logic. Importantly, all agree that intellectual virtues are (i) excellences, as opposed to defects; and (ii) distinctively intellectual and not, or not simply, moral. In other words, intellectual virtues are qualities that make us excellent (and not defective) as thinkers, not (or not simply) as people in general. This bibliography provides an overview of philosophical work on the intellectual virtues. It includes articles and books addressing responsibilist and reliabilist analyses of the structure of intellectual virtue; analyses of individual intellectual virtues; the application of intellectual virtue to education and other professional fields; the role of intellectual virtues in epistemology; and, finally, the structure of intellectual vice. It also includes some historical sources on intellectual virtue, though its focus is contemporary. Analyses of intellectual virtue (and of individual intellectual virtues) have developed in tandem with the epistemological subfield of virtue epistemology, which employs the notion of intellectual virtue in an account of knowledge. These analyses also frequently draw on virtue ethics, especially in the Aristotelian tradition. Some of the sources cited touch upon connections between intellectual virtue and these fields, though a fuller treatment of these topics can be found in the corresponding bibliographies on Virtue Epistemology and Virtue Ethics.

Images

Natural languages, numerals, formal languages, maps, diagrams, graphs, and pictures are all representations. Traditionally, philosophical discussion has divided these representations into two groups: imagistic and linguistic. Just as there are many natural and formal languages that fit on the linguistic side of this divide, there are many kinds of images. In what follows, then, “image” is meant to refer to the broad class of nonlinguistic representations that all seem to have much in common. There might be representations that are neither imagistic nor linguistic, and many representations are hybrids that partake of more than one kind. Focusing on images is not the same thing as focusing on pictures. (See the separate Oxford Bibliographies in Philosophy entry on “Depiction.”) Pictures are images, but so are maps, graphs, radar images, and the like. So an account of pictures can be consistent with many accounts of images, just as an account of images can be consistent with more than one theory of pictures. There are very few accounts of images in this general sense, so the following does not include a section devoted to that topic. Instead, this entry traces the evolving interest in images and looks at the most prominent topics that have occupied philosophers over the last half century or so. One topic not covered here is the use of images in science. For that topic, see the separate Oxford Bibliographies in Philosophy entry on “Scientific Representation.”

Collective Intentionality

Collective intentionality concerns the intentionality of groups or collectives. Intentionality is the property of being about, directed at, oriented toward, or representing objects, events, properties, and states of affairs. Examples of intentional states (states with intentionality, not just intentions) are belief, desire, hope, intention, admiration, perception, guilt, love, grief, fear, and so on. Collective intentionality involves joint, shared, or group intentionality and the intentionality of members (qua members) of groups that have joint or shared attitudes. More broadly, the study of collective intentionality concerns forms of intentionality that underpin social reality. What is distinctive about the study of collective intentionality within the broader study of social interactions and structures is its focus on the conceptual, ontological, and psychological features of joint or shared actions and attitudes, that is, actions and attitudes of (or apparent attributions of such to) groups or collectives, their relations to individual actions and attitudes, and their implications for the nature of social groups and their functioning. It subsumes collective action, intention, thought, reasoning, emotion, phenomenology, decision-making, responsibility, knowledge, trust, rationality, cooperation, competition, and related issues, and how these underpin social practices, conventions, institutions, and social ontology. The two main theoretical questions in the study of collective intentionality concern the ontology and psychology of collective agency and collective attitudes. The main ontological question is whether we should admit into our ontology group subjects of intentional states or attribute intentionality only to their members. The main psychological questions are, if we admit group subjects of intentional states, first, how to understand what they come to, whether they are the same or different than the intentional states we attribute to individuals and if different exactly how, and, second, what is special about the attitudes of individuals who participate in group action or whose attitudes underpin attributions of intentionality to groups? More specifically, can we understand what is special about the attitudes of individuals who participate in group agency or sustain the potential for group agency in terms of concepts already available in our understanding of individual agency, or must we introduce new concepts either of the modes of intending, believing, etc., or in the contents of such attitudes? Both questions concern the debate between methodological individualists and holists about the social, the first with respect to its ontology, the second with respect to its ideology.

Perfectionism

The term perfectionism in philosophy, unlike its more common usage in popular psychology, denotes a range of theoretical positions. There are perfectionist accounts of ethics, perfectionist accounts of well-being, and perfectionist accounts of politics. These positions are often mutually supportive, but one can accept some of them while rejecting others. Perfectionist views purport to be objective in that they characterize states of affairs, character traits, activities, and/or relationships as good in themselves and not good in virtue of the fact that they are desired or enjoyed by human beings. In the history of philosophy, perfectionism has a long and impressive pedigree. It is often associated with ethical theories that characterize the human good in terms of the development and exercise of capacities that are taken to be central to human nature. Aristotle is the foundational figure in this tradition, but perfectionist arguments of this kind can be found in writers as diverse as Aquinas, Kant, (arguably) Mill, Marx, Nietzsche, G. E. Moore, and T. H. Green, among others. Perfectionism also has been associated with ethical theories that, while not tying the human good specifically to the development of human nature, accept some alternative objective account of the human good. Typically, such views have a teleological structure, holding that we have duties to promote the good. More recently, perfectionism has been used to refer to political theories that reject the liberal principle of state neutrality and hold that it is permissible for states to favor, actively and intentionally, objectively valuable conceptions of the good over base ones. Perfectionism, in both moral and political philosophy, has often been charged with being anti-egalitarian and hostile to individual liberty. This charge is encouraged and sustained by a selective focus on the elitist ideas of certain influential perfectionist writers, such as Nietzsche. For these writers, what matters is the excellence of the few, not the mediocrity of the many. It is a mistake, however, to identify perfectionism with any specific articulation of it. Contemporary defenses of perfectionism have attempted to show how its central ideas are compatible with, and indeed supportive of, human equality and individual autonomy.

Theoretical Virtues in Science

A theoretical virtue in science is a property of a scientific theory that is considered desirable. Standard theoretical virtues include testability, empirical accuracy, simplicity, unification, consistency, coherence, and fertility. First highlighted by Thomas S. Kuhn in a seminal paper in 1977, theoretical virtues have come to play an important role in a number of philosophical debates. A central bone of contention in many of these debates is whether theoretical virtues are epistemic, i.e., whether they are indicative of a theory’s correctness, or whether they are just pragmatic, concerning only the convenient use of a theory. Particularly contested virtues are simplicity and unifying power. In the scientific realism debate, in which philosophers argue about whether or not scientific theories allow us to uncover the reality behind the phenomena, scientific realists have argued that virtuous theories are more likely to be correct than a less virtuous ones, even when they accommodate the same data. In the closely related debate about the so-called Inference to the Best Explanation, realists have argued that not only can we determine the best explanation on the basis of its virtues, but we can also determine which explanation is the true one. In discussions about “theory choice” or “theory appraisal,” philosophers discuss which virtues might be most decisive in scientists’ deliberations about which theory they should adopt. Here a theory’s successful novel predictions, or novel successes for short, have been a particular focus. Philosophers have also discussed possible trade-offs between various virtues and the difficulties which these may pose for theory choice. Samir Okasha has argued recently that there cannot be any rational algorithm for theory choice. Theoretical virtues also play a role in philosophical accounts of the laws of nature. One extremely prominent account, namely David Lewis’ Best System Analysis, appeals to simplicity and unifying power to determine what generalizations qualify as genuine laws of nature (rather than just accidentally true generalizations). Even in philosophical theorizing about science, theoretical virtues have been appealed to: Rudolf Carnap believed that simplicity and fruitfulness were important desiderata guiding the explication of scientific concepts. Finally, psychologists have started to investigate the role of theoretical virtues in picking explanations. There is work that appears to show that children and adults have preferences for simple and broad theories.