On the Way to a Postmodern Curriculum Theory -- Moving from the Question of Unity to the Question of Difference

This article will examine the consequences of highlighting subject and difference in one of the curriculum theories that has been inspired by postmodernism. The term postmodernism is here first and foremost meant to signify the attempt to combine politics and morality with epistemology in accordance with Levinas, Lyotard and Bauman. The article will highlight some themes that need to be developed further for a postmodernism-inspired curriculum theory. A starting-point is a critique of the type of curriculum theory which has its base in the new sociology of education. From this critique, focused on universal claims, the Habermasian-inspired universalism is quickly and critically dropped and left behind, and another form of reasoning is embarked upon. The latter is inspired by a minotarian politics concept and tries to dissolve universalism as a prerequisite for critical conversations. With this background and with the help of Levinas, the article sets out to talk about difference without reduction to the Same and finally suggest a direction for a postmodern curriculum theory with a normative focus on knowledge.     

Beyond verisimilitude: A linguistically invariant basis for scientific progress

This paper proposes a solution to David Miller's Minnesotan-Arizonan demonstration of the language dependence of truthlikeness (Miller 1974), along with Miller's first-order demonstration of the same (Miller 1978). It is assumed, with Peter Urbach, that the implication of these demonstrations is that the very notion of truthlikeness is intrinsically language dependent and thus non-objective. As such, truthlikeness cannot supply a basis for an objective account of scientific progress. I argue that, while Miller is correct in arguing that the number of true atomic sentences of a false theory is language dependent, the number of known sentences (under certain straightforward assumptions) is conserved by translation; degree of knowledge, unlike truthlikeness, is thus a linguistically invariant notion. It is concluded that the objectivity of scientific progress must be grounded on the fact (noted in Cohen 1980) that knowledge, not mere truth, is the aim of science.For criticism and comments I am indebted to Noretta Koertge, David Miller, and an anonymous Synthese referee.     

A semantical investigation into Leśniewski's axiom of his ontology

A structure A for the language L, which is the first-order language (without equality) whose only nonlogical symbol is the binary predicate symbol , is called a quasi -struoture iff (a) the universe A of A consists of sets and (b) a b is true in A ([p) a = {p } & p b] for every a and b in A, where a(b) is the name of a (b). A quasi -structure A is called an -structure iff (c) {p } A whenever p a A. Then a closed formula in L is derivable from Leniewski's axiom x, y[x y u (u x) u; v(u, v x u v) u(u x u y)] (from the axiom x, y(x y x x) x, y, z(x y z y x z)) iff is true in every -structure (in every quasi -structure).     

A Translation of Intuitionistic Predicate Logic into Basic Predicate Logic

Basic Predicate Logic, BQC, is a proper subsystem of Intuitionistic Predicate Logic, IQC. For every formula in the language {, , , , , , }, we associate two sequences of formulas 0,1,... and 0,1,... in the same language. We prove that for every sequent , there are natural numbers m, n, such that IQC , iff BQC n m. Some applications of this translation are mentioned.     

Three prepositional calculi of probability

Attempts are made to transform the basis of elementary probability theory into the logical calculus.We obtain the propositional calculus NP by a naive approach. As rules of transformation, NP has rules of the classical propositional logic (for events), rules of the ukasiewicz logic ₀ (for probabilities) and axioms of probability theory, in the form of rules of inference. We prove equivalence of NP with a fragmentary probability theory, in which one may only add and subtract probabilities.The second calculus MP is a usual modal propositional calculus. It has the modal rules x x, x y x y, x x, x y (y x), (y x), in addition to the rules of classical propositional logic. One may read x as x is probable. Imbeddings of NP and of ₀ into MP are given.The third calculus P is a modal extension of ₀. It may be obtained by adding the rule ((xy)y) xy to the modal logic of quantum mechanics Q [5]. One may read x in P as x is observed. An imbedding of NP into P is given.     

Frege,Boolos, and Logical Objects

In this paper, the authors discuss Frege's theory of logical objects (extensions, numbers, truth-values) and the recent attempts to rehabilitate it. We show that the eta relation George Boolos deployed on Frege's behalf is similar, if not identical, to the encoding mode of predication that underlies the theory of abstract objects. Whereas Boolos accepted unrestricted Comprehension for Properties and used the eta relation to assert the existence of logical objects under certain highly restricted conditions, the theory of abstract objects uses unrestricted Comprehension for Logical Objects and banishes encoding (eta) formulas from Comprehension for Properties. The relative mathematical and philosophical strengths of the two theories are discussed. Along the way, new results in the theory of abstract objects are described, involving: (a) the theory of extensions, (b) the theory of directions and shapes, and (c) the theory of truth values.     

Metaphysics and the interpretation of persons: Davidson on thinking and Conceptual Schemes

Certain metaphysical and epistemological presuppositions are shown to play a role in the defense of Davidson's claims that an empirically constructed theory of truth provides an adequate theory of meaning for any natural language. Dadivson puts forward demonstrative arguments in favor of these presuppositions in On the Very Idea of a Conceptual Scheme, Thought and Talk, and The Method of Truth in Metaphysics. These arguments are examined and found to include controversial and dubitable assumptions as premises. It is then suggested that both these controversial assumptions and Davidson's metaphysical and epistemological presuppositions can be partially defended, however, by dialectical, interpretive, and historical arguments that elucidate the nature of persons.     

Religious Parties, Religious Political Identity, and the Cold Shoulder of Liberal Democratic Thought

Elements of the relation between religion and politics are standard themes in political theory: toleration and free exercise rights; the parameters of separation of church and state; arguments for and against constraints imposed on religious discourse by philosophic norms of public reason. But religious parties and partisanship are no part of political theory, despite contemporary interest in value pluralism and in liberal democratic theory's capacity to address multicultural, religious, and ethnic group claims. This essay argues that religious parties are missing elements in discussions of identity politics. They play an important role not just in expressing but also in constructing and mobilizing religious political identity. Political activity linked to parties is a principal way of bringing diffuse, politically unorganized groups, whose leaders are self-appointed and not regularly accountable for the way they represent co-religionists in political life, into the democratic mainstream. With political organization and especially partisanship, the fact of pluralism is made concrete for democratic purposes.     

O liczbach kardynalnych

Tre: Wstp. I. Niektóre pojcia i prawa teorii klas stosunków. II. O klasach abstrakcji. III. O równoskadnikowoci. IV. O kardynalnych liczbach skadników. V. O. stosowanej teorii równoskadnikowoci. VI. O relacji równej liczby elementów. VII. Stosunek obu poj liczb kardynalnych. Zakoczenie.Allatum est die 30 Augusti 1961     

Suppositions in argumentation

The atheist who begins to argue his case by saying, Suppose there is an omniscient Being of the sort in which Christians believe ... is employing a very familiar move in argumentation. However, most books on argumentation theory ignore suppositions completely. Searle omits suppositions entirely from his taxonomy of speech acts and this appears to lead to a similar omission in Speech Acts in Argumentative Discussions by van Eemeren and Grootendorst.This paper argues that suppositional argument is elegant, powerful and extremely common, that the correct way to understand it is based on Gottlob Frege's distinction between asserted and unasserted propositions and hence that suppositions are neither assertions nor (and this is more important) assertives. The paper discusses the connections between suppositions and conditionals; it argues that argumentation theory which ignores suppositions is systematically misleading; and it concludes by indicating some possible developments in argumentation theory.Revised version of a paper delivered at the University of Amsterdam, April 3, 1987.     

Независимость одной системы аксиом и правила вывода пропозиционального исчисления

- Allatum est die 5 Martii 1970     

THE MEDIA AND POLITICAL VIOLENCE

The meanings of violence, political violence, and terrorism are briefly discussed. I then consider the responsibilities of the media, especially television, with respect to political violence, including such questions as how violence should be described, and whether the media should cover terrorism. I argue that the media should contribute to decreasing political violence through better coverage of arguments for and against political dissidents' views, and especially through more and better treatment of nonviolent means of influencing political processes. Since commercial pressures routinely conflict with media responsibility, I argue that society should liberate substantial amounts of culture from such pressures.     

Paradoxical consequences of Balzer''s and G?hde''s criteria of theoreticity. Results of an application to ten scientific theories

It is shown that the criteria of T-theoreticity proposed by Balzer and Gähde lead to strongly counterintuitive and in this sense paradoxical results: most of the obviously empirical or at least nontheoretical terms come out as theoretical. This is demonstrated for a lot of theories in different areas. On the way, some improved and some new structuralist theory-reconstructions are given. The conclusion is drawn that the T-theoreticity of a term cannot possibly be proved on the basis of the mathematical structure of theory T alone (as Gähde and Balzer suggest). Rather, an independent notion of pre-T-theoreticity and-more importantly-of empiricity is needed; i.e., not empirical and not pre-T-theoretical are independent, necessary but not sufficient conditions for T-theoretical (this is also a necessary complement of Sneed's original criterion). Finally it is asked whether the structuralist criterion of T-theoreticity complemented by such independent conditions would be a satisfactory answer to Putnam's challenge, and the answer again is negative: the criterion is not able to distinguish between empirically contentful and completely contentless (superfluous) theoretical terms.     

On superintuitionistic logics as fragments of proof logic extensions

Coming fromI andCl, i.e. from intuitionistic and classical propositional calculi with the substitution rule postulated, and using the sign to add a new connective there have been considered here: Grzegorozyk's logicGrz, the proof logicG and the proof-intuitionistic logicI set up correspondingly by the calculiFor any calculus we denote by the set of all formulae of the calculus and by the lattice of all logics that are the extensions of the logic of the calculus, i.e. sets of formulae containing the axioms of and closed with respect to its rules of inference. In the logiclG the sign is decoded as follows: A = (A & A). The result of placing in the formulaA before each of its subformula is denoted byTrA. The maps are defined (in the definitions of x and the decoding of is meant), by virtue of which the diagram is constructedIn this diagram the maps, x and are isomorphisms, thereforex ^–1 = ; and the maps and are the semilattice epimorphisms that are not commutative with lattice operation +. Besides, the given diagram is commutative, and the next equalities take place: ^–1 = ^–1 and = ^–1 x. The latter implies in particular that any superintuitionistic logic is a superintuitionistic fragment of some proof logic extension.     

Ecocentrism and argumentative competence: Roots of a postmodern argument theory from the brazilian deforestation debate

This essay examines the Brazilian deforestation debate to explicate the beginnings of a post-modern theory of argumentation. Modernist argumentation reflects two distinct approaches, found in the deforestation controversy. The first approach, universal minimilization, presumes that the survival of humanity is sufficient grounds upon which to base argument. The alternative, strategic manipulation, results in argument being employed as a technical device to advance one's interest. In place of the modernist approach, we offer an ecocentric theory of argumentation. This conception calls for individuals to set aside differences in values to sustain humanity but at the same time to be sensitive to differences in costs and benefits that accrue from common efforts to persons differently situated. Additionally, this view operates with a tacit working assumption that environmental questions are not discrete entities to be evaluated separately. Rather, people must act collectively on a range of interconnected issues to ensure survival.     

Cooperation,Knowledge, and Time: Alternating-time Temporal Epistemic Logic and its Applications

Branching-time temporal logics have proved to be an extraordinarily successful tool in the formal specification and verification of distributed systems. Much of their success stems from the tractability of the model checking problem for the branching time logic CTL, which has made it possible to implement tools that allow designers to automatically verify that systems satisfy requirements expressed in CTL. Recently, CTL was generalised by Alur, Henzinger, and Kupferman in a logic known as Alternating-time Temporal Logic (ATL). The key insight in ATL is that the path quantifiers of CTL could be replaced by cooperation modalities, of the form , where is a set of agents. The intended interpretation of an ATL formula is that the agents can cooperate to ensure that holds (equivalently, that have a winning strategy for ). In this paper, we extend ATL with knowledge modalities, of the kind made popular in the work of Fagin, Halpern, Moses, Vardi and colleagues. Combining these knowledge modalities with ATL, it becomes possible to express such properties as group can cooperate to bring about iff it is common knowledge in that . The resulting logic — Alternating-time Temporal Epistemic Logic (ATEL) — shares the tractability of model checking with its ATL parent, and is a succinct and expressive language for reasoning about game-like multiagent systems.     

Three views of demonstrative reference

Three views of demonstrative reference are examined: contextual, intentional, and quasi-intentional. According to the first, such reference is determined entirely by certain publicly accessible features of the context. According to the second, speaker intentions are criterial in demonstrative reference. And according to the third, both contextual features and intentions come into play in the determination of demonstrative reference. The first two views (both of which enjoy current popularity) are rejected as implausible; the third (originally proposed by Kaplan in Dthat) is argued to be highly plausible.     

Kenneth Strike on Liberalism,Citizenship and the Private Interest in Schooling

After indicating a number of points of agreement with the argument 0eveloped by Kenneth Strike in his article Liberalism, Citizenship and the Private Interest in Schooling, this article identifies and explores a number of queries and criticisms which arise in relation to that argument. These queries and criticisms relate especially to the nature and extent of the expansiveness involved in Strike's conception of public or common educational influence, and to the implications and justification of the claim that private educational interests enjoy a greater salience and recognition on Strike's view of public or common educational influence than on some alternative views.     

Reformulation of the hidden variable problem using entropic measure of uncertainty

Using a recently introduced entropy-like measure of uncertainty of quantum mechanical states, the problem of hidden variables is redefined in operator algebraic framework of quantum mechanics in the following way: if A, , E(A), E() are von Neumann algebras and their state spaces respectively, (, E()) is said to be an entropic hidden theory of (A, E(A)) via a positive map L from onto A if for all states E(A) the composite state ° L E() can be obtained as an average over states in E() that have smaller entropic uncertainty than the entropic uncertainty of . It is shown that if L is a Jordan homomorphism then (, E()) is not an entropic hidden theory of (A, E(A)) via L.     

A new approach to the formulation and testing of learning models

It is argued that current attempts to model human learning behavior commonly fail on one of two counts: either the model assumptions are artificially restricted so as to permit the application of mathematical techniques in deriving their consequences, or else the required complex assumptions are imbedded in computer programs whose technical details obscure the theoretical content of the model. The first failing is characteristic of so-called mathematical models of learning, while the second is characteristic of computer simulation models. An approach to model building which avoids both these failings is presented under the title of a black-box theory of learning. This method permits the statement of assumptions of any desired complexity in a language which clearly exhibits their theoretical content.Section II of the paper is devoted to the problem of testing and comparing alternative learning theories. The policy advocated is to abandon attempts at hypothesis testing. It is argued that, in general, we not only lack sufficient data and sufficiently powerful techniques to test hypotheses, but that the truth of a model is not really the issue of basic interest. A given model may be true in the sense that on the basis of available evidence we cannot statistically reject it, but not interesting in the sense that it provides little information about the processes underlying behavior. Rather, we should accept or reject models on the basis of how much information they provide about the way in which subjects respond to environmental structure. This attitude toward model testing is made precise by introducing a formal measure of the information content of a model. Finally, it is argued that the statistical concept of degrees-of-freedom is misleading when used in the context of model testing and should be replaced by a measure of the information absorbed from the data in estimating parameters.I would like to express my indebtedness to Ernest W. Adams and Julian Feldman for their guidance and encouragement of the research reported here.Much of the research reported here was conducted at the University of California, Berkeley, and incorporated in a Ph.D. dissertation in Logic and the Methodology of Science [15]. The research was supported in part by the Computer Institute for Social Science Research, Michigan State University.