Let H be an infinite-dimensional (real or complex) Hilbert space, viewed as a metric structure in its natural signature. We characterize the definable linear operators on H as exactly the "scalar plus compact" operators.
Paul Churchland has recently offered a novel argument for the “objective reality” of color. The strategy he employs to make this argument is an instance of a more general research program for interpreting perceptual content, “domain‐portrayal semantics.” In the first half of the article, I point out some features of color vision that complicate Churchland's conclusion, in particular, the context‐sensitive and inferential nature of color perception. In the second half, I examine and defend the general research program, (...) concluding it is naturalistic in a minimal sense and should be of interest to naturalists and nonnaturalists alike. †To contact the author, please write to: Department of Philosophy, Stanford University, Stanford, CA 94305; e‐mail: firstname.lastname@example.org. (shrink)
Diachronic uncertainty, uncertainty about where an agent falls in time, poses interesting conceptual difficulties. Although the agent is uncertain about where she falls in time, this uncertainty can only obtain at a particular moment in time. We resolve this conceptual tension by providing a transformation from models with diachronic uncertainty relations into “equivalent” models with only synchronic uncertainty relations. The former are interpreted as capturing the causal structure of a situation, while the latter are interpreted as capturing its epistemic structure (...) . The models are equivalent in the sense that agents pass through the same information sets in the same order, In this paper, we investigate how such a transformation may be used to define an appropriate notion of equivalence, which we call epistemic equivalence . Although our project is motivated by problems which have arisen in a variety of disciplines, especially philosophy and game theory, our formal development takes place within the general and flexible framework provided by epistemic temporal logic. (shrink)
This paper surveys applications of logical methods in the cognitive sciences. Special attention is paid to non-monotonic logics and complexity theory. We argue that these particular tools have been useful in clarifying the debate between symbolic and connectionist models of cognition.
The claim that similarity plays a role in representation has been philosophically discredited. Psychologists, however, routinely analyse the success of mental representations for guiding behaviour in terms of a similarity between representation and the world. I provide a foundation for this practice by developing a philosophically responsible account of the relationship between similarity and representation in natural systems. I analyse similarity in terms of the existence of a suitable homomorphism between two structures. The key insight is that by restricting attention (...) to only those homomorphisms induced by causal processes, we can solve two philosophical problems with a single assumption. First, causal structure provides an adequate source for the bias required to ensure the similarity relation is non-trivial; second, it provides an adequate source for the directionality required to move from similarity to representation. I defend this account against objections by Goodman and van Fraassen and demonstrate that it is indeed the account of similarity's role in representation assumed by psychological practice. (shrink)
According to John Macmurray, action is the starting-point for an analysis of persons, who exist only in relation. This paper re-examines Macmurray’s argument from action and finds it lacking. However, rather than implying an obstacle to a relational definition of persons, the failure to arrive at this definition provides the opening or space wherein God, who is fully relational, can be revealed. The implications for human persons are mirrored in the dual concept of the person found in a social trinitarianism, (...) which lends support to an unexpected affirmation. Persons are found within community, but only by granting priority to the individual does this relational unity, which is the unity of the person, spring to life. (shrink)
This exploratory study examines awareness of the other party''s instrumental, terminal, and work values by members of supervisor and employee dyads. Subjective estimates of value congruence, provided by either member of the dyad, correlated with actual value congruence scores determine conscious awareness levels in all cases. Results demonstrate supervisory awareness of employee terminal values, but not work values or instrumental values, even though these latter value types probably possess the greatest relevance to achieving organizational goals. Further, employees possess awareness of (...) supervisor work values but not instrumental or terminal values. These findings challenge traditional assumptions underlying the functionalism position on organizational culture that appears in the literature most frequently read by practicing managers. (shrink)
A hippocampal patient is described who shows preserved item recognition and simple recognition-based recollection but impaired recall and associative recognition. These data and other evidence suggest that contrary to Aggleton & Brown's target article, Papez circuit damage impairs only complex item-item-context recollection. A patient with perirhinal cortex damage and a delayed global memory deficit, apparently inconsistent with A&B's framework, is also described.
This paper compares the epistemological conception of Isaac Levi with mine. We are joined in both giving a constructive answer to the relation of belief and probability, without reducing one to the other. However, our constructions differ in at least nine more or less important ways, all discussed in the paper. In particular, the paper explains the similarities and differences of Shackle's functions of potential surprise, as used by Levi, and my ranking functions in formal as well as in (...) philosophical respects. The appendix explains how ranking and probability theory can be combined in the notion of a ranked probability measure (or probabilified ranking function). (shrink)
All of the ingredients for what has become known as Anselmian perfect being theology were present already in the thought of St. Augustine. This paper develops that thesis by calling attention to various claims Augustine makes. It then asks whether there are principled reasons for determining which properties the greatest possible being has and whether an account of what contributes to greatness can settle the question whether the greatest possible being is the same as the God of Abraham, Isaac, (...) and Jacob. The paper develops Augustine’s answer to the first question by extracting several principles he endorses that generate a hierarchy of greatness. It addresses the second question by discussing the requirements of worship and of creation. (shrink)
The first edition of Isaac Newton's famous Principia mathematica (1687) contains only one reference to the Scriptures and one mention of God and natural theology. Thus, there is superficial evidence to suggest that this pivotal work of physics is a mostly secular book that is not fundamentally associated with theology and natural theology. The fact that the General Scholium – with its overt theological and natural theological themes – was only added to the Principia a quarter-century later with the (...) second edition of 1713 may also suggest that this theology came as an afterthought and is therefore not integral to the conceptual structure of the Principia . Moreover, the relative paucity of theology in the first edition, combined with the evidence of the appended General Scholium of 1713, could be used as evidence of a ‘theological turn’ in Newton's thought after 1687. This article uses evidence from Newton's private manuscripts to argue that there is more theology in all three editions of the Principia than a simple reading of the published text would imply. This article also demonstrates that the seeds of Newton's theological conception of Nature and the cosmos – conceptions that can be found in manuscripts beginning in the early 1690s, and that are acknowledged in the General Scholium of 1713 – are already present in Newton's private papers prior to 1687. Newton engaged in a great deal of theological writing after 1687, but the period of the composition of the Principia only marks the end of the first third of Newton's six-decade intellectual career and thus it should not be surprising to find more theology after the Principia than before. Nevertheless, there are important theological writings going back to the 1660s that show that Newton's strongly biblical and providentialist theology pre-dates the Principia and, crucially, that his theological conception of the cosmos does as well. The first edition of the Principia , therefore, was composed after Newton had begun to formulate his theology and theological understanding of the cosmos. (shrink)
IsaacLevi, currently John Dewey Professor of Philosophy at Columbia University, has explored the principles of American pragmatism in greater depth and more consistency than others before him. The result is a sophisticated and powerful philosophical system whose key elements stand in stark opposition not only to current mainstream epistemology, but also to the positions of other contemporary authors writing in the same pragmatist tradition. The essays in this timely volume, written by some of philosophy's finest scholars, contribute (...) substantially to the understanding and appraisal of Levi's work. (shrink)
The branch of philosophical logic which has become known as “belief change” has, in the course of its development, become alienated from its epistemological origins. However, as formal criteria do not suffice to defend a principled choice between competing systems for belief change, we do need to take their epistemological embedding into account. Here, on the basis of a detailed examination of Isaac Levi's epistemology, we argue for a new direction of belief change research and propose to construct systems (...) for belief change that can do without, but do not rule out, selection functions, in order to enable an *empirical* assessment of the relative merits of competing belief change systems. (shrink)
Would the Jewish tradition agree with Søren Kierkegaard's claim that the biblical episode of Abraham's near-sacrifice of Isaac represents a fearful "teleological suspension of the ethical"? After surveying a variety of classical Jewish sources, the author concludes that Kierkegaard's interpretation has almost no resonance within the Jewish tradition. Rather than involving a suspension of the ethical, this episode is viewed by Jewish writers as involving a moment of supreme moral responsibility on the part of both God and man. This (...) treatment of the biblical episode points up a central fact about the Jewish tradition: although Judaism is unquestionably an ethical tradition based on the divine command, it is also a tradition of human autonomy and reason. If Jews have regarded God's commands as absolute, they have also found it unthinkable that these commands should ultimately defy our human sense of right and wrong. (shrink)
It has long been considered that Arabic algebra scarcely left any traces in mathematical literature of Hebrew expression. Thanks to the unpublished sources we have discovered, and to an attentive examination of already-known texts, one can no longer subscribe to such a judgement. The evidence we examine in this first article sheds light on the circulation, in erudite Jewish circles, of Arabic algebraic knowledge in Spain, Italy, Provence, and Sicily, between the 12th and the 14th centuries. The Epistle on number (...) by the Castillian astronomer Isaac ben Salomon al-A[hudot]dab was written in Sicily at the end of the 14th century, and based on the Talkhi[sudot] a'mal al-[hudot]isab of Ibn al-Banna' (1256-1321). That part of the Epistle that is devoted to algebra follows the tradition of al-Karaji. It offers, for the first time in Hebrew, a rational presentation of arithmetical operations extended to algebraic expressions. (shrink)
The biblical story of the binding of Isaac may have originally been written without the figure of the angel. As such, it reads strongly as an account of Abraham disobeying God’s direct command for the sake of Isaac. Interestingly, then, many interpreters since the time of the text’s final redaction read the binding of Isaac as an account of ethical disobedience despite the presence of the angel. In what follows, I consider Levinas’s account of religion, revelation and (...) ethics for the way in which this can impact our reading of the biblical text. In this way, I hope to develop an account of the binding of Isaac which becomes an allegory for the need to mediate all modes of religious and/or political allegiance with concern for the well-being of other people. (shrink)
_René Descartes proposed an interactive dualism that posits an interaction between the_ _mind of a human being and some of the matter located in his or her brain. Isaac Newton_ _subsequently formulated a physical theory based exclusively on the material/physical_ _part of Descartes’ ontology. Newton’s theory enforced the principle of the causal closure_ _of the physical, and the classical physics that grew out of it enforces this same principle._ _This classical theory purports to give, in principle, a complete deterministic (...) account of the_ _physically described properties of nature, expressed exclusively in terms of these_ _physically described properties themselves. Orthodox contemporary physical theory_ _violates this principle in two separate ways. First, it injects random elements into the_ _dynamics. Second, it allows, and also requires, abrupt probing actions that disrupt the_ _mechanistically described evolution of the physically described systems. These probing_ _actions are called Process 1 interventions by von Neumann. They are psycho-physical_ _events. Neither the content nor the timing of these events is determined either by any_ _known law, or by the afore-mentioned random elements. Orthodox quantum mechanics_ _considers these events to be instigated by choices made by conscious agents. In von_ _Neumann’s formulation of quantum theory each such intervention acts upon the state of_ _the brain of some conscious agent. Thus orthodox von Neumann contemporary physics_ _posits an interactive dualism similar to that of Descartes. But in this quantum version the_ _effects of the conscious choices upon our brains are controlled, in part, by the known_ _basic rules of quantum physics. This theoretically specified mind-brain connection allows_ _many basic psychological and neuropsychological findings associated with the apparent_ _physical effectiveness of our conscious volitional efforts to be explained in a causal and_ _practically useful way.. (shrink)
Here, I shall argue that Van Helmont needs to be added to the list of sources on which Newton drew when formulating his doctrine of absolute time. This by no means implies that Van Helmont is the factual source of Newton's views on absolute time (I have found no clear-cut evidence in support of this claim). It is by no means my aim to debunk the importance of the other sources, but rather to broaden them. Different authors help to explain (...) different aspects of Newton's conception of absolute time. (shrink)