Medieval Theories of the Categories (SEP)

This entry is intended as a brief and general introduction to the development of category theory from the beginning of the Middle Ages, in the sixth century, to the Silver Age of Scholasticism, in the sixteenth. This development is fascinating but extraordinarily complex. Scholars are just beginning to take note of the major differences in the understanding of categories and of how these differences are related to the discussion of other major philosophical topics in the Middle Ages. Much work remains to be done, even regarding the views of towering figures, so necessarily we have had to restrict our discussion to only a few major figures and topics. Still, we hope that the discussion will serve as a good starting point for anyone interested in category theory and its history.

1. Issues

Philosophers speak about categories in many different ways. There is one initial, and rather substantial, difference between philosophers who allow a very large number of categories and those who allow only a very small number. The first include among categories such different things as human, green, animal, thought, and justice; the second speak only of very general things such as substance, quality, relation, and the like, as categories. Among twentieth-century authors who allow many categories is Gilbert Ryle (b. 1900, d. 1976). Roderick Chisholm (b. 1916, d. 1999) is an example of those who have only very few. Medieval authors follow Aristotle’s narrow understanding.

The disagreement concerning categories in the history of philosophy does not end there. Even if we restrict the discussion to a small number of items of the sort that Aristotle regards as categories, many issues remain to be settled about them, and philosophers frequently disagree about how to settle them. These issues may be gathered into roughly ten groups.

The first group comprises what may be described roughly as extensional issues; they have to do with the number of categories. The extension of a term is comprised by the things of which the term can be truthfully predicated. Thus the extension of ‘cat’ consists of all the animals of which it is true to say that they are cats. Philosophers in general frequently disagree on how many categories there are. For example, Aristotle lists up to ten, but gives the impression that the ultimate number is not settled at all. Plotinus (204/5–270) and Baruch Spinoza (1632–77) reduce the number radically, but their views do not by any means establish themselves as definitive. In the Middle Ages the number of categories is always small (ten or less) but it nonetheless varies.

Read the rest here: https://plato.stanford.edu/entries/medieval-categories/

Bounded Rationality (SEP)

Herbert Simon introduced the term ‘bounded rationality’ (Simon 1957b: 198; see also Klaes & Sent 2005) as shorthand for his proposal to replace the perfect rationality assumptions of homo economicus with a concept of rationality better suited to cognitively limited agents:

Broadly stated, the task is to replace the global rationality of economic man with the kind of rational behavior that is compatible with the access to information and the computational capacities that are actually possessed by organisms, including man, in the kinds of environments in which such organisms exist. (Simon 1955a: 99)

Bounded rationality now describes a wide range of descriptive, normative, and prescriptive accounts of effective behavior which depart from the assumptions of perfect rationality. This entry aims to highlight key contributions—from the decision sciences, economics, cognitive- and neuropsychology, biology, physics, computer science, and philosophy—to our current understanding of bounded rationality.

1. Homo Economicus and Expected Utility Theory

Bounded rationality has come to encompass models of effective behavior that weaken, or reject altogether, the idealized conditions of perfect rationality assumed by models of economic man. In this section we state what models of economic man are committed to and their relationship to expected utility theory. In later sections we review proposals for departing from expected utility theory.

The perfect rationality of homo economicus imagines a hypothetical agent who has complete information about the options available for choice, perfect foresight of the consequences from choosing those options, and the wherewithal to solve an optimization problem (typically of considerable complexity) that identifies an option which maximizes the agent’s personal utility.

Read the rest here: https://plato.stanford.edu/entries/bounded-rationality/

Boundary (SEP)

We think of a boundary whenever we think of an entity demarcated from its surroundings. There is a boundary (a line) separating Maryland and Pennsylvania. There is a boundary (a circle) isolating the interior of a disc from its exterior. There is a boundary (a surface) enclosing the bulk of this apple. Sometimes the exact location of a boundary is unclear or otherwise controversial (as when you try to trace out the borders of a desert, the edges of a mountain, or even the boundary of your own body). Sometimes the boundary lies skew to any physical discontinuity or qualitative differentiation (as with the border of Wyoming, or the boundary between the upper and the lower halves of a homogeneous sphere). But whether sharp or blurry, natural or artificial, for every object there appears to be a boundary that marks it off from the rest of the world. Events, too, have boundaries — at least temporal boundaries. Our lives are bounded by our births and by our deaths; the soccer game began at 3pm sharp and ended with the referee’s final whistle at 4:45pm. It is sometimes suggested that even abstract entities, such as concepts or sets, have boundaries of their own (witness the popular method for representing the latter by means of simple closed curves encompassing their contents, as in Euler circles and Venn diagrams), and Wittgenstein could emphatically proclaim that the boundaries of our language are the boundaries of our world (1921: prop. 5.6). Whether all this boundary talk is coherent, however, and whether it reflects the structure of the world or simply the organizing activity of our mind, or of our collective practices and conventions, are matters of deep philosophical controversy.

1. Issues

Euclid defined a boundary as “that which is an extremity of anything” (Elements, I, def. 13). Aristotle defined the extremity of a thing as “the first thing beyond which it is not possible to find any part [of the given thing], and the first within which every part is” (Metaphysics, V, 1022a4–5). Together, these two definitions deliver the classic account of boundaries, an account that is both intuitive and comprehensive and offers the natural starting point for any further investigation into the boundary concept. Indeed, although Aristotle’s definition concerned primarily the extremities of spatial entities, it applies equally well in the temporal domain. Just as the Mason-Dixon line marks the boundary between Maryland and Pennsylvania insofar as no part of Maryland can be found on the northern side of the line, and no part of Pennsylvania on its southern side, so “the now is an extremity of the past (no part of the future being on this side of it), and again of the future (no part of the past being on that side of it)” (Physics, VI, 233b35–234a2). Similarly for concrete objects and events: just as the surface of an apple marks its spatial boundary insofar as the apple extends only up to it, so the referee’s whistle marks the temporal boundary of the game insofar as the game protracts only up to it. In the case of abstract entities, such as concepts and sets, the account is perhaps adequate only figuratively. Still, it is telling that one of the Greek words for ‘boundary’, ὅρος, is also a word for ‘definition’: as John of Damascus nicely put it, “definition is the term for the setting of land boundaries taken in a metaphorical sense” (The Fount of Knowledge, I, 8). Likewise, it is telling that in point-set topology the standard definition of a set’s boundary (from Hausdorff 1914, §7.2) reflects essentially the same intuition: the boundary, or frontier, of a set A is the set of those points all of whose neighborhoods intersect both A and the complement of A (where a neighborhood of a point p is, intuitively, a set of points that entirely “surround” p). It is not an exaggeration, therefore, to say that the Euclidean-Aristotelian characterization captures a general intuition about boundaries that applies across the board. Nonetheless, precisely this intuitive characterization gives rise to several puzzles that justify philosophical concern.

Read the rest here: https://plato.stanford.edu/entries/boundary/

The Principle of Beneficence in Applied Ethics (SEP)

Beneficent actions and motives have traditionally occupied a central place in morality. Common examples today are found in social welfare programs, scholarships for needy and meritorious students, communal support of health-related research, policies to improve the welfare of animals, philanthropy, disaster relief, programs to benefit children and the incompetent, and preferential hiring and admission policies. What makes these diverse acts beneficent? Are such beneficent acts and policies obligatory or merely the pursuit of optional moral ideals?

These questions have generated a substantial literature on beneficence in both theoretical ethics and applied ethics. In theoretical ethics, the dominant issue in recent years has been how to place limits on the scope of beneficence. In applied and professional ethics, a number of issues have been treated in the fields of biomedical ethics and business ethics.

1. The Concepts of Beneficence and Benevolence

The term beneficence connotes acts or personal qualities of mercy, kindness, generosity, and charity. It is suggestive of altruism, love, humanity, and promoting the good of others. In ordinary language, the notion is broad, but it is understood even more broadly in ethical theory to include effectively all norms, dispositions, and actions with the goal of benefiting or promoting the good of other persons. The language of a principle or rule of beneficence refers to a normative statement of a moral obligation to act for the others’ benefit, helping them to further their important and legitimate interests, often by preventing or removing possible harms. Many dimensions of applied ethics appear to incorporate such appeals to obligatory beneficence, even if only implicitly. For example, when apparel manufacturers are criticized for not having good labor practices in factories, the ultimate goal of the criticisms is usually to obtain better working conditions, wages, and other benefits for workers.

Read the rest here: https://plato.stanford.edu/entries/principle-beneficence/

Belief (SEP)

Bayes’ Theorem (SEP)

Bayes’ Theorem is a simple mathematical formula used for calculating conditional probabilities. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes’ Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem’s central insight — that a hypothesis is confirmed by any body of data that its truth renders probable — is the cornerstone of all subjectivist methodology.

Read the rest here: https://plato.stanford.edu/entries/bayes-theorem/

The Epistemic Basing Relation

The epistemic basing relation is the relation which holds between a reason and a belief if and only if the reason is a reason for which the belief is held. It is generally thought to be a necessary, but not sufficient, condition for a belief’s being justified that the belief be based on a reason. The basing relation is what distinguishes good reasons which a person possesses that contribute to the personal justification of a given belief from good reasons which the person possesses but that do not contribute to the personal justification of the belief.

Basing relations may be involved in both inferential and non-inferential justification. For example, one may hold that sensory states count as reasons, and thus require that a sensory belief be based on a reason if it is to be justified by that reason. In addition, one might understand at least some self-evident beliefs to be based on the meanings of the various terms of the sentence expressing the proposition believed. For example, one’s belief that all bachelors are unmarried men may be understood to be based on the meanings of ‘all’, ‘bachelors’, ‘are’, etc.

The basing relation is most frequently analyzed in terms of a reason’s causing a belief.^[1] In such analyses, the reason and the belief are understood to be mental states of a person. The cause may be a contributing cause or a sufficient cause. However, the basing relation has also been analyzed as an appropriate counterfactual cause of a belief and also as depending on an appropriate meta-belief to the effect that a reason is a good reason to hold the belief.

Analysis of the basing relation is relevant to a variety of fundamental epistemological issues. It is relevant to the nature of epistemic rationalization and to questions regarding the internalism/externalism debate. In addition, it has been argued that reliabilist theories of justification are incompatible with the correct analysis of the basing relation.

Read the rest here: https://plato.stanford.edu/entries/basing-epistemic/

Bodily Awareness (SEP)

At the sensory level we continuously receive a flow of information about our own body through external and internal perceptions. Not only can we see our body and touch it, but we also have several inner receptors that convey information about the position of our limbs, the balance of our body, and its physiological condition. Unlike external perception, the inner sensory flow never stops and cannot be voluntarily controlled. Thus, an important amount of information is constantly available whether we want it or not, whether we pay attention to it or not. In that respect, our body qualifies as the object that we know best. Yet, despite numerous sources of information, the phenomenology of bodily awareness is limited. In painful and learning situations, our body appears at the core of our interest, but when we walk in the street, we are rarely aware of the precise position of our legs and of the contact of the floor on our feet. Schwitzgebel (2007), for instance, asked how frequently participants wearing a device beeping at random intervals had tactile experiences in their left foot just before the beeping sound. He found a high variability in the answers, but one participant reported tactile sensations only 16% of the time. Our conscious field is primarily occupied by our environment, instead of the bodily medium that allows us to perceive it and to move through it. Hence, the most permanent and preponderant object in life may also be the most elusive one (Leder 1990; Merleau-Ponty 1945; O’Shaughnessy 1980).

One may then question whether we are completely unaware of it. Except in rare illusory or pathological cases, we never feel fully disembodied. James (1890: 242), for instance, claims that we are constantly conscious of the presence of our body, although at the margin of the stream of our consciousness:

Our own bodily position, attitude, condition, is one of the things of which some awareness, however inattentive, invariably accompanies the knowledge of whatever else we know.

What is the content of this marginal body consciousness? James (1890: 242) alludes to a “feeling of the same old body always there” or a mere “feeling of warmth and intimacy” but can we go beyond this rough and metaphorical description?

Read the rest here: https://plato.stanford.edu/entries/bodily-awareness/

Personal Autonomy

Autonomous agents are self-governing agents. But what is a self-governing agent? Governing oneself is no guarantee that one will have a greater range of options in the future, or the sort of opportunities one most wants to have. Since, moreover, a person can govern herself without being able to appreciate the difference between right and wrong, it seems that an autonomous agent can do something wrong without being to blame for her action. What, then, are the necessary and sufficient features of this self-relation? Philosophers have offered a wide range of competing answers to this question.

Read the rest here: https://plato.stanford.edu/entries/personal-autonomy/