Responding to potential hazards is likely to require precaution-related recalibration, the extensive integration of complex variables related to inferred risk and fitness. By swamping working memory with goal-demoted actions and focusing recalibration on the inferred threat, ritualized behaviors may serve to increase the efficacy of precaution-related recalibration. This benefit may be an important mechanism maintaining non-pathological ritualized behavior. (Published Online February 8 2007).

Pollock describes an exciting theory of rationality and its partial implementation in OSCAR, a computer system whose descendants will literally be persons.

Princeton University Press, 984. This book is out of print, but can be downloaded as a pdf file (3.9 MB).

There was a long tradition in philosophy according to which good reasoning had to be deductively valid. However, that tradition began to be questioned in the 1960’s, and is now thoroughly discredited. What caused its downfall was the recognition that many familiar kinds of reasoning are not deductively valid, but clearly confer justification on their conclusions. Here are some simple examples.

Imagine yourself sitting on your front porch, sipping your morning coffee and admiring the scene before you. You see trees, houses, people, automobiles; you see a cat running across the road, and a bee buzzing among the flowers. You see that the flowers are yellow, and blowing in the wind. You see that the people are moving about, many of them on bicycles. You see that the houses are painted different colors, mostly earth tones, and most are one-story but a (...) few are two-story. It is a beautiful morning. Thus the world interfaces with your mind through your senses. There is a strong intuition that we are not disconnected from the world. We and the other things we see around us are part of a continuous whole, and we have direct access to them through vision, touch, etc. However, the philosophical tradition tries to drive a wedge between us and the world by insisting that the information we get from perception is the result of inference from indirect evidence that is about how things look and feel to us. The philosophical problem of perception is then to explain what justifies these inferences. We will focus on visual perception. Figure one presents a crude diagram of the cognitive system of an agent capable of forming beliefs on the basis of visual perception. Cognition begins with the stimulation of the rods and cones on the retina. From that physical input, some kind of visual processing produces an introspectible visual image. In response to the production of the visual image, the cognizer forms beliefs about his or her surroundings. Some beliefs the perceptual beliefs are formed as direct responses to the visual input, and other beliefs are inferred from the perceptual beliefs. The perceptual beliefs are, at the very least, caused or causally influenced by having the image. This is signified by the dashed arrow marked with a large question mark. We will refer to this as the mystery link. Figure one makes it apparent that in order to fully understand how knowledge is based on perception, we need three different theories.. (shrink)

Counterexamples are constructed for the theory of rational choice that results from a direct application of classical decision theory to ordinary actions. These counterexamples turn on the fact that an agent may be unable to perform an action, and may even be unable to try to perform an action. An alternative theory of rational choice is proposed that evaluates actions using a more complex measure, and then it is shown that this is equivalent to applying classical decision theory to "conditional (...) policies" rather than ordinary actions. (shrink)

An argument is self-defeating when it contains defeaters for some of its own defeasible lines. It is shown that the obvious rules for defeat among arguments do not handle self-defeating arguments correctly. It turns out that they constitute a pervasive phenomenon that threatens to cripple defeasible reasoning, leading to almost all defeasible reasoning being defeated by unexpected interactions with self-defeating arguments. This leads to some important changes in the general theory of defeasible reasoning.

Human beings think of themselves in terms of a privileged non-descriptive designator — a mental “I”. Such thoughts are called “_de se_” thoughts. The mind/body problem is the problem of deciding what kind of thing I am, and it can be regarded as arising from the fact that we think of ourselves non-descriptively. Why do we think of ourselves in this way? We investigate the functional role of “I” (and also “here” and “now”) in cognition, arguing that the use of (...) such non-descriptive “reflexive” designators is essential for making sophisticated cognition work in a general-purpose cognitive agent. If we were to build a robot capable of similar cognitive tasks as humans, it would have to be equipped with such designators. (shrink)

Reporting peers’ counterproductive work behaviors (CWBs) is important for maintaining an ethical organization, but is a significant and potentially risky action. In Bandura’s Theory of Moral Thought and Action (Bandura, 1991) he states that such acts require significant moral agency, which is generated when an individual possesses adequate moral self-regulatory capacities to address the issue and is in a context that activates and reinforces those capacities. Guided by this theory, we assess moral potency (i.e., moral courage, moral efficacy, and moral (...) ownership) as key capacities predicting peer reporting intentions and assess three contextual factors influencing the generation and effects of moral potency: whether a potential informant (1) works for an ethical leader, (2) is embedded in a psychologically safe climate promoting interpersonal risk-taking, and (3) operates in a more normal or extreme context. We assess the proposed model across three field studies entailing both normal and extreme (i.e., firefighting units) contexts. Results show that ethical leaders raise employees’ moral potency, promoting greater willingness to report their peers’ CWBs. In normal work contexts, psychological safety positively moderated both the relationship between ethical leadership and moral potency and between moral potency and peer reporting intentions. However, psychological safety had the opposite effects in more extreme work contexts. Whereas psychological safety strengthens the positive association between moral potency and peer reporting intentions in normal work contexts, in contexts where individuals are more frequently exposed to extreme events, psychological safety weakens this relationship, thus highlighting the unforeseen downsides of psychological safety in extreme contexts. (shrink)

John Pollock aims to construct a theory of rational decision making for real agents--not ideal agents. Pollock argues that theories of ideal rationality are largely irrelevant to the decision making of real agents. Thinking about Acting aims to provide a theory of "real rationality.".

Epistemology is about how we can know the various things we claim to know. Epistemology is driven by attempts to answer the question, “How do you know?” This gives rise to investigations on several different levels. At the lowest level, philosophers investigate particular kinds of knowledge claims. Thus we find theories of perceptual knowledge (“How do you know the things you claim to know directly on the basis of perception?”), theories of induction and abduction (“How do you know the general (...) truths you infer from observation of particular cases?”), theories of our knowledge of other minds, theories of mathematical knowledge, and so forth. At an intermediate level, topics are investigated that pertain to all or most of the specific kinds of knowledge discussed at the lowest level. Theories of reasoning, both deductive and defeasible, occur at this level. At the highest level we find general epistemological theories that attempt to explain how knowledge in general is possible. At this level we encounter versions of foundationalism, coherentism, probabilism, reliabilism, and direct realism. One can be doing epistemology by working at any of these levels. The levels cannot be isolated from each other, however. Work at any level tends to presuppose something about the other levels. For example, work on inductive reasoning at least presupposes that reasoning plays a role in the acquisition or justification of beliefs and normally presupposes something about the structure of defeasible reasoning. (shrink)

When your word processor or email program is running on your computer, this creates a "virtual machine” that manipulates windows, files, text, etc. What is this virtual machine, and what are the virtual objects it manipulates? Many standard arguments in the philosophy of mind have exact analogues for virtual machines and virtual objects, but we do not want to draw the wild metaphysical conclusions that have sometimes tempted philosophers in the philosophy of mind. A computer file is not made of (...) epiphenomenal ectoplasm. I argue instead that virtual objects are "supervenient objects". The stereotypical example of supervenient objects is the statue and the lump of clay. To this end I propose a theory of supervenient objects. Then I turn to persons and mental states. I argue that my mental states are virtual states of a cognitive virtual machine implemented on my body, and a person is a supervenient object supervening on his cognitive virtual machine. (shrink)

Logical Options introduces the extensions and alternatives to classical logic which are most discussed in the philosophical literature: many-sorted logic, second-order logic, modal logics, intuitionistic logic, three-valued logic, fuzzy logic, and free logic. Each logic is introduced with a brief description of some aspect of its philosophical significance, and wherever possible semantic and proof methods are employed to facilitate comparison of the various systems. The book is designed to be useful for philosophy students and professional philosophers who have learned some (...) classical first-order logic and would like to learn about other logics important to their philosophical work. (shrink)

5.5. Every topos is linguistic: the equivalence theorem.

IN THEIR WELL-KNOWN PAPER, Kochen and Specker (1967) introduce the concept of partial Boolean algebra (pBa) and show that certain (finitely generated) partial Boolean algebras arising in quantum theory fail to possess morphisms to any Boolean algebra (we call such pBa's intractable in the sequel). In this note we begin by discussing partial..

We investigate Hilbert’s varepsilon -calculus in the context of intuitionistic type theories, that is, within certain systems of intuitionistic higher-order logic. We determine the additional deductive strength conferred on an intuitionistic type theory by the adjunction of closed varepsilon -terms. We extend the usual topos semantics for type theories to the varepsilon -operator and prove a completeness theorem. The paper also contains a discussion of the concept of “partially defined‘ varepsilon -term. MSC: 03B15, 03B20, 03G30.

OSCAR is a fully implemented architecture for a cognitive agent, based largely on the author’s work in philosophy concerning epistemology and practical cognition. The seminal idea is that a generally intelligent agent must be able to function in an environment in which it is ignorant of most matters of fact. The architecture incorporates a general-purpose defeasible reasoner, built on top of an efficient natural deduction reasoner for first-order logic. It is based upon a detailed theory about how the various aspects (...) of epistemic and practical cognition should interact, and many of the details are driven by theoretical results concerning defeasible reasoning. The architecture is easily extensible by changing the set of inference schemes supplied to the reasoner. Existing inference schemes handle many kinds of epistemic cognition, including reasoning from perceptual input, causal reasoning and the frame problem, and reasoning defeasibly about probabilities. Work is underway to implement a system of defeasible decisiontheoretic planning. (shrink)

If we imagine a chess-board with alternate blue and red squares, then this is something in which the individual red and blue areas allow themselves to be distinguished from each other in juxtaposition, and something similar holds also if we imagine each of the squares divided into four smaller squares also alternating between these two colours. If, however, we were to continue with such divisions until we had exceeded the boundary of noticeability for the individual small squares which result, then (...) it would no longer be possible to apprehend the individual red and blue areas in their respective positions. But would we then see nothing at all? Not in the least; rather we would see the whole chessboard as violet, i.e. apprehend it as something that participates simultaneously in red and blue. (shrink)

In this paper we attempt to show how the goal of resolving moral problems in a patient's care can best be achieved by working at the bedside.We present and discuss three cases to illustrate the art and science of clinical ethics consultation. The sine qua non of the clinical ethics consultant is that he or she goes to the patient's bedside to obtain specific clinical and ethical information. Unlike ethics committees, which often depend on secondhand information from a physician or (...) nurse, clinical ethics consultants personally speak with and examine patients and review their laboratory data and medical records. The skills of the clinical ethics consultant include the ability to delineate and resolve ethical problems in a particular patient's case and to teach other health professionals to build their own frameworks for clinical ethical decision making. When the clinical situation requires it, clinical ethics consultants can and should assist primary physicians with case management. (shrink)

Since antiquity, opposed concepts such as the One and the Many, the Finite and the Infinite, and the Absolute and the Relative, have been a driving force in philosophical, scientific, and mathematical thought. Yet they have also given rise to perplexing problems and conceptual paradoxes which continue to haunt scientists and philosophers. In _Oppositions and Paradoxes_, John L. Bell explains and investigates the paradoxes and puzzles that arise out of conceptual oppositions in physics and mathematics. In the process, Bell (...) not only motivates abstract conceptual thinking about the paradoxes at issue, but he also offers a compelling introduction to central ideas in such otherwise-difficult topics as non-Euclidean geometry, relativity, and quantum physics. These paradoxes are often as fun as they are flabbergasting. Consider, for example, the famous Tristram Shandy paradox: an immortal man composing an autobiography so slowly as to require a year of writing to describe each day of his life — he would, if he had infinite time, presumably never complete the work, although no individual part of it would remain unwritten. Or think of an office mailbox labelled “mail for those with no mailbox”—if this is a person’s mailbox, how can they possibly have “no mailbox”? These and many other paradoxes straddle the boundary between physics and metaphysics, and demonstrate the hidden difficulty in many of our most basic concepts. (shrink)

Call a family F of subsets of a set E inductive if ∅ ∈ F and F is closed under unions with disjoint singletons, that is, if ∀X∈F ∀x∈E–X(X ∪ {x} ∈ F]. A Frege structure is a pair (E.

Containing 609 encyclopedic articles written by more than 200 prominent scholars, The Oxford Companion to the History of Modern Science presents an unparalleled history of the field invaluable to anyone with an interest in the technology, ideas, discoveries, and learned institutions that have shaped our world over the past five centuries. Focusing on the period from the Renaissance to the early twenty-first century, the articles cover all disciplines, historical periods, concepts, and methodologies and philosophies. Coverage is international, tracing the spread (...) of science from its traditional centers and explaining how the prevailing knowledge of non-Western societies has modified or contributed to the dominant global science as it is currently understood. Revealing the interplay between science and the wider culture, the Companion includes entries on topics such as minority groups, art, religion, and science's practical applications. One hundred biographies of the most iconic historic figures, chosen for their contributions to science and the interest of their lives, are also included. Above all The Oxford Companion to the History of Modern Science is a companion to world history: modern in coverage, generous in breadth, and cosmopolitan in scope. The volume's utility is enhanced by a thematic outline of the entire contents, a thorough system of cross-referencing, and a detailed index that enables the reader to follow a specific line of inquiry along various threads from multiple starting points. Each essay has numerous suggestions for further reading, all of which favor literature that is accessible to the general reader, and a bibliographical essay provides a general overview of the scholarship in the field. Lastly, as a contribution to the visual appeal of the Companion, over 100 black-and-white illustrations and an eight-page color section capture the eye and spark the imagination. (shrink)

A productive way to think about imagistic mental models of physical systems is as though they were sources of quasi‐empirical evidence. People depict or imagine events at those points in time when they would experiment with the world if possible. Moreover, just as they would do when observing the world, people induce patterns of behavior from the results depicted in their imaginations. These resulting patterns of behavior can then be cast into symbolic rules to simplify thinking about future problems and (...) to reveal higher order relationships. Using simple gear problems, three experiments explored the occasions of use for, and the inductive transitions between, depictive models and number‐based rules. The first two experiments used the convergent evidence of problem‐solving latencies, hand motions, referential language and error data to document the initial use of a model, the induction of rules from the modeling results, and the fallback to a model when a rule fails. The third experiment explored the intermediate representations that facilitate the induction of rules from depictive models. The strengths and weaknesses of depictive modeling and more analytic systems of reasoning are delineated to motivate the reasons for these transitions. (shrink)

Axioms for the continuum, or smooth real line R. These include the usual axioms for a commutative ring with unit expressed in terms of two operations + and i , and two distinguished elements 0 ≠ 1. In addition we stipulate that R is a local ring, i.e., the following axiom: ∃y x i y = 1 ∨ ∃y (1 – x) i y = 1. Axioms for the strict order relation < on R. These are: 1. a < b (...) and b < c implies a < c. 2. ¬(a < a) 3. a < b implies a + c < b + c for any c. ≤ 4. a < b and 0 < c implies acbc.. (shrink)

Full proofs of the Gödel incompleteness theorems are highly intricate affairs. Much of the intricacy lies in the details of setting up and checking the properties of a coding system representing the syntax of an object language (typically, that of arithmetic) within that same language. These details are seldom illuminating and tend to obscure the core of the argument. For this reason a number of efforts have been made to present the essentials of the proofs of Gödel’s theorems without getting (...) mired in syntactic or computational details. One of the most important of these efforts was made by Löb [8] in connection with his analysis of sentences asserting their own provability. Löb formulated three conditions (now known as the Hilbert-Bernays-Löb derivability conditions), on the provability predicate in a formal system which are jointly sufficient to yield the Gödel’s second incompleteness theorem for it. A key role in Löb’s analysis is played by (a special case of) what later became known as the diagonalization or fixed point property of formal systems, a property which had already, in essence, been exploited by Gödel in his original proofs of the incompleteness theorems. The fixed point property plays a central role in Lawvere’s [7] category-theoretic account of incompleteness phenomena (see also [10]). Incompleteness theorems have also been subjected to intensive investigation within the framework of modal logic (see, e.g.[4], [5]). In this formulation the modal operator takes up the role previously played by the provability predicate, and the derivability conditions on the latter are translated into algebraic conditions (the so-called GL, i.e., Gödel–Löb, conditions) on the former. My purpose here is to present a framework for incompleteness phenomena, fully compatible with intuitionistic or constructive principles, in which the idea of a coding system is retained, only in a 2 simple, but very general form, a form wholly free of syntactical notions. As codes we shall take the elements of an arbitrary given nonempty set, possibly, but not necessarily, the set of natural numbers.. (shrink)

This book is written for those who are in sympathy with its spirit. This spirit is different from the one which informs the vast stream of European and American civilization in which all of us stand. That spirit expresses itself in an onwards movement, in building ever larger and more complicated structures; the other in striving in clarity and perspicuity in no matter what structure. The first tries to grasp the world by way of its periphery—in its variety; the second (...) at its centre—in its essence. And so the first adds one construction to another, moving on and up, as it were, from one thing to the next, while the other remains where it is and what it tries to grasp is always the same. (shrink)

In this paper a number of oppositions which have haunted mathematics and philosophy are described and analyzed. These include the Continuous and the Discrete, the One and the Many, the Finite and the Infinite, the Whole and the Part, and the Constant and the Variable.

A polymodal lattice is a distributive lattice carrying an n-place operator preserving top elements and certain finite meets. After exploring some of the basic properties of such structures, we investigate their freely generated instances and apply the results to the corresponding logical systems — polymodal logics — which constitute natural generalizations of the usual systems of modal logic familiar from the literature. We conclude by formulating an extension of Kripke semantics to classical polymodal logic and proving soundness and completeness theorems.

In this paper we develop the notion of formal precover in a topos by defining a relation between elements and sets in a local set theory. We show that such relations are equivalent to modalities and to universal closure operators. Finally we prove that these relations are well characterized by a convenient restriction to a particular set.