0. The ancient and honorable role of philosophy as a servant to the learning, development and use of scientific knowledge, though sadly underdeveloped since Grassmann, has been re-emerging from within the particular science of mathematics due to the latter's internal need; making this relationship more explicit (as well as further investigating the reasons for the decline) will, it is hoped, help to germinate the seeds of a brighter future for philosophy as well as help to guide the much wider learning (...) of mathematics and hence of all the sciences. 1. The unity of interacting opposites "space vs. quantity", with the accompanying "general vs. particular" and the resulting division of variable quantity into the interacting opposites "extensive vs. intensive", is susceptible, with the aid of categories, functors, and natural transformations, of a formulation which is on the one hand precise enough to admit proved theorems and considerable technical development and yet is on the other hand general enough to admit incorporation of almost any specialized hypothesis. Readers armed with the mathematical definitions of basic category theory should be able to translate the discussion in this section into symbols and diagrams for calculations. 2. The role of space as an arena for quantitative "becoming" underlies the qualitative transformation of a spatial category into a homotopy category, on which extensive and intensive quantities reappear as homology and cohomology. 3. The understanding of an object in a spatial category can be approached through definite Moore-Postnikov levels; each of these levels constitutes a mathematically precise "unity and identity of opposites", and their ensemble bears features strongly reminiscent of Hegel's Science of Logic. This resemblance suggests many mathematical and philosophical problems which now seem susceptible of exact solution. (shrink)

Foundations and Applications depend ultimately for their existence on each other. The main links between them are education and the axiomatic method. Those links can be strengthened with the help of a categorical method which was concentrated forty years ago by Cartier, Grothendieck, Isbell, Kan, and Yoneda. I extended that method to extract some essential features of the category of categories in 1965, and I apply it here in section 3 to sketch a similar foundation within the smooth categories which (...) provide the setting for the mathematics of change. The possibility that other methods may be needed to clarify a contradiction introduced by Cantor, now embedded in mathematical practice, is discussed in section 5. (shrink)

Explicit concepts and sufficiently precise definitions are the basis for further advance of a science beyond a given level. To move toward a situation where the whole population has access to the authentic results of science (italics mine) requires making explicit some general philosophical principles which can help to guide the learning, development, and use of mathematics, a science which clearly plays a pivotal role regarding the learning, development and use of all the sciences. Such philosophical principles have not come (...) from speculation but from studying and concentrating the development of actual mathematical subjects such as algebraic geometry, functional analysis, continuum mechanics, combinatorics, etc. The simplifications in the conceptual relations revealed by such philosophical/mathematical advances are of great value, not only in: (1) clarifying and guiding further research in the mathematical sciences, but also in (2) reforming pedagogy and popularization in ways that will not prove deceptive. (shrink)

: The Convention on Human Rights and Biomedicine developed by the Council of Europe, now undergoing ratification, is the first international treaty focused on bioethics. This article describes the background of the Convention's development and its general provisions and provides a comparison of its requirements with those of federal regulations governing research with human subjects. Although most provisions are comparable, there are significant differences in scope and applicability, for example, in the areas of compensation for injury, research participation by persons (...) with limited capacity to consent, assisted reproduction, organ transplantation, and research in emergency situations. The Convention represents a milestone in international bioethics and protection of human rights that will probably be referred to with increasing frequency. (shrink)

Hannah Arendt's approach to politics focuses on action and conduct, rather than institutions, constitutions, and states. In light of Arendtian conceptions of politics, essays in this book challenge conventional IR theories. The contributions on agency explore concepts and categories of political action that enable individuals to act politically and to re-make the world in new, unpredictable ways. The contributions on structure explore how Arendt provides new critical purchase upon often reified structures and categories.

Various laws and theories in the natural and social sciences are presented with a view to discerning the syntactic and semantic characteristics of many idealizations in science. Three different kinds of idealizations are discussed: ideal conditions, ideal cases, and idealized theories. An ideal condition is a formula in which state variables occur, whose existential closure is false, and for which there is another formula that can be constructed out of the original formula such that the existential closure of the new (...) formula is true. An ideal case is a statement which is logically equivalent to a universal conditional which has an ideal condition as its antecedent. And an idealized theory is a set of false universal conditional statements. Alternative syntactic and semantic analyses are viewed and criticized. (shrink)

We use evidence from cognitive psychology and the history of science to examine the issue of the theory-ladenness of perceptual observation. This evidence shows that perception is theory-laden, but that it is only strongly theory-laden when the perceptual evidence is ambiguous or degraded, or when it requires a difficult perceptual judgment. We argue that debates about the theory-ladenness issue have focused too narrowly on the issue of perceptual experience, and that a full account of the scientific process requires an examination (...) of theory-ladenness in attention, perception, data interpretation, data production, memory, and scientific communication. We conclude that the evidence for theory-ladenness does not lead to a relativist account of scientific knowledge. (shrink)

The pedagogical technique of the playful Plato, especially his ability to create living discourses that directly address the student, is the subject of Plato the Teacher. “The crisis of the Republic” refers to the decisive moment in his central dialogue when philosopher-readers realize that Plato’s is challenging them to choose justice by going back down into the dangerous Cave of political life for the sake of the greater Good, as both Socrates and Cicero did.

The goal of this chapter is to describe recollective memory and give an account of some of the characteristics of this form of human memory. I take recollective memory to be the type of memory that occurs when an individual recalls a specific episode from their past experience. I start with this very loose definition because a large part of this chapter consists of an attempt to work out a more detailed and analytic description of this form of memory.

In this book, William H. F. Altman argues that it is not order of composition but reading order that makes Euthyphro, Apology of Socrates, Crito, and Phaedo “late dialogues,” and shows why Plato’s decision to interpolate the notoriously “late” Sophist and Statesman between Euthyphro and Apology deserves more respect from interpreters.

In his Critique of Pure Reason, Kant makes the interesting, but obscure claim that the normative constraints that constitute the objectivity of our representations have their source ultimately in transcendental apperception. Keller focuses on this claim. He interprets Kant’s condition of transcendental apperception as the claim that I must represent myself in an impersonal way, and he argues that impersonal self-consciousness is a necessary condition under which I can distinguish my particular take on things from the way things are independently (...) of my own perspective on them. He elaborates his interpretation and defense of the condition of transcendental self-consciousness by discussing its role in each of the central arguments in the Critique in which the notion importantly figures: the transcendental deduction in both the first edition and in the second, the Analogies of Experience, the Paralogisms, and the second-edition refutation of idealism. (shrink)

Hegel's objection -- Is Kant's idealism subjective? -- An ambiguity in 'subjectivism' -- The epistemological problem -- The transcendental deduction of the categories and subjectivism -- Are Kant's categories subjective? -- Hegel's suspicion : Kantian critique and subjectivism -- What is kantian philosophical criticism? -- Hegel's suspicion : initial formulation -- A shallow suspicion? -- Deepening the suspicion : criticism, autonomy, and subjectivism -- Directions of response -- Critique and suspicion : unmasking the critical philosophy -- Hegel's transformation of critique (...) -- The rejection of Kantian critique : philosophy, skepticism, and the recovery of the ancient idea -- Hegel's epistemology in the shadow of Schelling -- Schulze's skepticism contra the critical philosophy -- Ancient versus modern skepticism : Hegel's difference -- Against the modern conception of rational cognition -- Against modern self-certainty -- The history of skepticism: decline into dogmatism -- Philosophy counter culture and time -- The return to Kantian critique : recognizing the rights of ordinary consciousness -- Two conceptions of philosophical critique -- The return to critique and the relation of philosophy to its history -- The rights of ordinary consciousness and the need for critique -- Critique as the realization of the science of metaphysics -- Hegel's self-transformational criticism -- Presuppositionless philosophy -- The problem of the criterion -- Self-transformational criticism -- The problem of the we' -- Our transformation -- Hegel's alternative model : critical transformation as self-realization. (shrink)

In this book, William H. F. Altman considers the pedagogical connections behind the post-Republic dialogues from Timaeus to Theaetetus in the context of their Reading Order.

A brief discussion is offered of what it means to say that a set of statements provides D-N explanation with special emphasis given to approximative D-N explanation. An idealized theory is seen to provide approximative D-N explanation. An ideal case provides explanation only if postulates are offered which connect the ideal antecedent condition with actual conditions. Such postulates will help in accounting for deviations between what the consequent of the ideal case entails and what actually occurs. Three ways are presented (...) for deciding on the acceptability of idealizations: (i) as actual conditions more closely approximate the ideal antecedent conditions specified in an ideal case, the more closely actual cases ought to approximate the consequent of the ideal case; (ii) the additional postulates connecting ideal antecedent conditions with actual conditions ought to account for deviations between what is entailed by an idealized theory and what actually occurs; and (iii) an idealized theory is explained by a more general theory when certain state variables in the more general theory are given extreme values. It is argued that (iii) is not a necessary condition for the acceptability of idealizations. (shrink)

In this paper we provide a psychological account of the nature and development of explanation. We propose that an explanation is an account that provides a conceptual framework for a phenomenon that leads to a feeling of understanding in the reader/hearer. The explanatory conceptual framework goes beyond the original phenomenon, integrates diverse aspects of the world, and shows how the original phenomenon follows from the framework. We propose that explanations in everyday life are judged on the criteria of empirical accuracy, (...) scope, consistency, simplicity, and plausibility. We conclude that explanations in science are evaluated by the same criteria, plus those of precision, formalisms, and fruitfulness. We discuss several types of explanation that are used in everyday life – causal/mechanical, functional, and intentional. We present evidence to show that young children produce explanations that have the same essential form as those used by adults. We also provide evidence that children use the same evaluation criteria as adults, but may not apply those additional criteria for the evaluation of explanations that are used by scientists. (shrink)

The German Stranger provides a guide to Leo Strauss that situates his thought in the context of National Socialism; by destroying any middle ground between 'Athens' and 'Jerusalem, ' Strauss undermined modernity's secular bulwark against political theology. Once National Socialism is understood as an atheistic religion re-enacted by post-Revelation 'philosophers, ' the German avatar of Plato's Athenian Stranger can be recognized as its principal theoreticia.

This book is a study of Plato’s most elementary dialogues, arranged in relation to Reading Order as opposed to order of composition. Beginning with the theatrical Protagoras and reaching a mountaintop in Symposium, the dialogues between them—Alcibiades, Lovers, Hippias, Ion, and Menexenus—introduce the student to both philosophy and Platonism.

Phenomenal reports were obtained immediately after participants retrieved information from long-term memory. Data were gathered for six basic forms of memory and for three forms of memory that asked for declarative information about procedural tasks . The data show consistent reports of mental imagery during retrieval of information from the generic perceptual, recollective, motor—declarative, rote—declarative, and cognitive—declarative categories; much less imagery was reported for the semantic, motor, rote, and cognitive categories. Overall, the data provide support for the theoretical framework outlined (...) in Brewer and Pani. (shrink)