We analyze log-data generated by an experiment with Mathtutor, an intelligent tutoring system for fractions. The experiment compares the educational effectiveness of instruction with single and multiple graphical representations. We extract the error-making and hint-seeking behaviors of each student to characterize their learning strategy. Using an expectation-maximization approach, we cluster the students by their strategic profile. We find that a) experimental condition and learning outcome are clearly associated b) experimental condition and learning strategy are not, and c) almost all of (...) the association between experimental condition and learning outcome is found among students implementing just one of the learning strategies we identify. This class of students is characterized by relatively high rates of error as well as a marked reluctance to seek help. They also show the greatest educational gains from instruction with multiple rather than single representations. The behaviors that characterize this group illuminate the mechanism underlying the effectiveness of multiple representations and suggest strategies for tailoring instruction to individual students. Our methodology can be implemented in an on-line tutoring system to dynamically tailor individualized instruction. (shrink)

The target article offers an intriguing hypothesis relating the content of phenomenal experience to a qualitative characteristic of information processing. This hypothesis, however, offers only an explanation of the of consciousness, not the – the experiencing agent remains mysterious. Their hypothesis about the unity of consciousness can be linked to an informational account of the agency or subjectivity of consciousness.

Dienes & Perner's target article constitutes a significant advance in thinking about implicit knowledge. However, it largely neglects processing details and thus the time scale of mental states realizing propositional attitudes. Considering real-time processing raises questions about the possible brevity of implicit representation, the nature of processes that generate explicit knowledge, and the points of view from which knowledge may be represented. Understanding the propositional attitude analysis in terms of momentary mental states points the way toward answering these questions.

Glenberg 's rethinking of memory theory seems limited in its ability to handle abstract symbolic thought, the selective character of cognition, and the self. Glenberg 's framework can be elaborated by linking it with theoretical efforts concerned with cognitive development and ecological perception. These elaborations point to the role of memory in specifying the self as an active agent.

The target article addresses important empirical issues, but adopts a nonanalytic stance toward consciousness and presents the mentalistic view as a very radical position that rules out informational description of anything other than conscious mental states. A better mentalistic strategy is to show how the structure of some informational states is both constitutive of consciousness and necessary for psychological functions.

The ancient Taoist text that forms the central part of this book was discovered by Wilhelm, who recognized it as essentially a practical guide to the integration of personality. Foreword and Appendix by Carl Jung; illustrations. Translated by Cary F. Baynes.A Helen and Kurt Wolff Book.

This study reconstructs the relationship between philosophy and politics in the way in which Heidegger's failure as a politician influenced the redevelopment of philosophy in the 1930s. The author also explains how Heidegger's failure influenced the content and direction of his later work.

The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued first order (...) logics in a general way, and to present some of the more important results in this area. In Systems covered are the resolution calculus, sequent calculus, tableaux, and natural deduction. This report is actually a template, from which all results can be specialized to particular logics. (shrink)

Hilbert’s program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to “dispose of the foundational questions in mathematics once and for all,” Hilbert proposed a two-pronged approach in 1921: first, classical mathematics should be formalized in axiomatic systems; second, using only restricted, “finitary” means, one should give proofs of the consistency of these axiomatic systems. Although Gödel’s incompleteness theorems show that the program as originally conceived cannot be carried out, it had many partial (...) successes, and generated important advances in logical theory and metatheory, both at the time and since. The article discusses the historical background and development of Hilbert’s program, its philosophical underpinnings and consequences, and its subsequent development and influences since the 1930s. (shrink)

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, but have been (...) expanded by the development of sophisticated methods to study the properties of such systems using proof and model theory. In parallel with this evolution of logical formalisms as tools for articulating mathematical theories (broadly speaking), much progress has been made in the quest for a mechanization of logical inference and the investigation of its theoretical limits, culminating recently in the development of new foundational frameworks for mathematics with sophisticated computer-assisted proof systems. In addition, logical formalisms developed by logicians in mathematical and philosophical contexts have proved immensely useful in describing theories and systems of interest to computer scientists, and to some degree, vice versa. Three examples of the influence of logic in computer science are automated reasoning, computer verification, and type systems for programming languages. (shrink)

Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions of (...) the connectives in question. (shrink)

We will study patterns which occur when considering how Σ 1 -elementary substructures arise within hierarchies of structures. The order in which such patterns evolve will be seen to be independent of the hierarchy of structures provided the hierarchy satisfies some mild conditions. These patterns form the lowest level of what we call patterns of resemblance . They were originally used by the author to verify a conjecture of W. Reinhardt concerning epistemic theories 449–460; Ann. Pure Appl. Logic, to appear), (...) but their relationship to axioms of infinity and usefulness for ordinal analysis were manifest from the beginning. This paper is the first part of a series which provides an introduction to an extensive program including the ordinal analysis of set theories. Future papers will conclude the introduction and establish, among other things, that notations we will derive from the patterns considered here represent the proof-theoretic ordinal of the theory KPℓ 0 or, equivalently, Π 1 1 −CA 0. (shrink)

Textbook on Gödel’s incompleteness theorems and computability theory, based on the Open Logic Project. Covers recursive function theory, arithmetization of syntax, the first and second incompleteness theorem, models of arithmetic, second-order logic, and the lambda calculus.

Studies the politics of Heidegger in terms of "thrownness" or "existential contingency". Attempts to think through Heidegger's philosophy in a manner that parallels his own dialogue with other key western thinkers.

A principal aim of the branch of ethics called ‘population theory’ or ‘population ethics’ is to find a plausible welfarist axiology, capable of comparing total outcomes with respect to value. This has proved an exceedingly difficult task. In this paper I shall state and discuss two ‘trilemmas’, or choices between three unappealing alternatives, which the population ethicist must face. The first trilemma is not new. It originates with Derek Parfit's well-known ‘Mere Addition Paradox’, and was first explicitly stated by Yew-Kwang (...) Ng. I shall argue that one horn of this trilemma is less unattractive than Parfit and others have claimed. The second trilemma, which is a kind of mirror image of the first, appears hitherto to have gone unnoticed. Apart from attempting to resolve the two trilemmas, I shall suggest certain features which I believe a plausible welfarist axiology should possess. The details of this projected axiology will, however, be left open. (shrink)

"This is an excellent textbook on Neoplatonism which gives the reader a very concise and lucid overview of the basic doctrines and leading thinkers of the last great philosophy to emerge before the Christianization of the Roman Empire. I’ve no doubt that my students next semester will benefit from the analyses contained in the book. The contents of the chapters are very informative and adequately place developments in their socio-cultural context." --Michael B. Simmons, Auburn University at Montgomery.

Despite their differences in origin, the three influential schools of twentieth-century continental cultural criticism--the Frankfurt School, existentialism, and poststructuralism--have long been treated as an ensemble and with critical hesitancy. Examining these schools as responses to the apparent collapse of Western civilization in the twentieth-century and as formidable intellectual challenges to the cultural legacies of the Enlightenment, this book provides a productive base for criticism and broadens our understanding of their histories and reception.

In Section 1, I rehearse some arguments for the claim that morality should be ``action-guiding'', and try to state the conditions under which a moral theory is in fact action-guiding. I conclude that only agents who are cognitively and conatively ``ideal'' are in general able to use a moral theory as a guide to action. In Sections 2 and 3, I discuss whether moral ``actualism'' implies that morality cannot be action-guiding even for ideal agents. If actualism is true, an ideal (...) agent will know about her own future actions. Since such foreknowledge is often thought to be incompatible with deliberation, and since action-guidance presupposes the possibility of deliberation, there is an apparent difficulty in combining actualism with the requirement of action-guidance. In opposition to an argument by Jan Österberg, I try to show that actualism and action-guidance are in fact compatible. (shrink)

This paper criticizes the consequentialist theory recently put forward by Fred Feldman. I argue that this theory violates two crucial requirements. Another theory, proposed by Peter Vallentyne, is similarly flawed. Feldman's basic ideas could, however, be developed into a more plausible theory. I suggest one possible way of doing this.

In a recent article in this journal, John Martin Fischer defends the view that death harms its victim after she dies. More specifically, he develops a “truthmaking” account in order to solve what he calls the Problem of Predication for this view. In this reply, we argue that Fischer’s proposed solution to this problem is unsuccessful.

This book is the complete story of the creation of the universe, as it was understood by the ancient Egyptians. It is a collection of harmonic and radical 'Black Thoughts' and the pursuit of equality for all of this planet's inhabitants"--P. vii.

Having visited Ireland regularly during the 1930s, Ludwig Wittgenstein resigned his Cambridge philosophy professorship in 1947 and moved there, living in a fishing village on the Atlantic coast and hotels in Dublin and the Wicklow Mountains. Although Wittgenstein spent some time out of the country, Ireland was effectively his base for three very productive years during which he worked on what would become one of his key books, the posthumously published Philosophical Investigations. Wittgenstein in Ireland represents the first sustained account (...) of Wittgenstein's time in Ireland, placing it in its historical context. Wall pays a good deal of attention to the representation of the Irish landscape in which the Austrian philosopher found himself able to work; a large part of his writings were produced in the bleak landscapes of Ireland and Norway. (shrink)