Validity, the Squeezing Argument and Alternative Semantic Systems: the Case of Aristotelian Syllogistic

We investigate the philosophical significance of the existence of different semantic systems with respect to which a given deductive system is sound and complete. Our case study will be Corcoran’s deductive system D for Aristotelian syllogistic and some of the different semantic systems for syllogistic that have been proposed in the literature. We shall prove that they are not equivalent, in spite of D being sound and complete with respect to each of them. Beyond the specific case of syllogistic, the goal is to offer a general discussion of the relations between informal notions—in this case, an informal notion of deductive validity—and logical apparatuses such as deductive systems and (model-theoretic or other) semantic systems that aim at offering technical, formal accounts of informal notions. Specifically, we will be interested in Kreisel’s famous ‘squeezing argument’; we shall ask ourselves what a plurality of semantic systems (understood as classes of mathematical structures) may entail for the cogency of specific applications of the squeezing argument. More generally, the analysis brings to the fore the need for criteria of adequacy for semantic systems based on mathematical structures. Without such criteria, the idea that the gap between informal and technical accounts of validity can be bridged is put under pressure.     

Many Concepts and Two Logics of Algorithmic Reduction

Within the program of finding axiomatizations for various parts of computability logic, it was proven earlier that the logic of interactive Turing reduction is exactly the implicative fragment of Heyting’s intuitionistic calculus. That sort of reduction permits unlimited reusage of the computational resource represented by the antecedent. An at least equally basic and natural sort of algorithmic reduction, however, is the one that does not allow such reusage. The present article shows that turning the logic of the first sort of reduction into the logic of the second sort of reduction takes nothing more than just deleting the contraction rule from its Gentzen-style axiomatization. The first (Turing) sort of interactive reduction is also shown to come in three natural versions. While those three versions are very different from each other, their logical behaviors (in isolation) turn out to be indistinguishable, with that common behavior being precisely captured by implicative intuitionistic logic. Among the other contributions of the present article is an informal introduction of a series of new — finite and bounded — versions of recurrence operations and the associated reduction operations. Presented by Robert Goldblatt     

Rebutting formally valid counterexamples to the Humean “is-ought” dictum

Various formally valid counterexamples have been adduced against the Humean dictum that one cannot derive an “ought” from an “is.” There are formal rebuttals—some very sophisticated now (e.g., Charles R. Pigden’s and Gerhard Schurz’s)—to such counterexamples. But what follows is an intuitive and informal argument against them. I maintain that it is better than these sophisticated formal defenses of the Humean dictum and that it also helps us see why it implausible to think that we can be as decisive about the truth or falsity of the dictum as both the formal counterexamples or formal barriers to them purport to be.     

How True It Is = Who Says It’s True

This is a largely expository paper in which the following simple idea is pursued. Take the truth value of a formula to be the set of agents that accept the formula as true. This means we work with an arbitrary (finite) Boolean algebra as the truth value space. When this is properly formalized, complete modal tableau systems exist, and there are natural versions of bisimulations that behave well from an algebraic point of view. There remain significant problems concerning the proper formalization, in this context, of natural language statements, particularly those involving negative knowledge and common knowledge. A case study is presented which brings these problems to the fore. None of the basic material presented here is new to this paper—all has appeared in several papers over many years, by the present author and by others. Much of the development in the literature is more general than here—we have confined things to the Boolean case for simplicity and clarity. Most proofs are omitted, but several of the examples are new. The main virtue of the present paper is its coherent presentation of a systematic point of view—identify the truth value of a formula with the set of those who say the formula is true.     

The greening of engineers: A cross-cultural experience

Experience with a group of mechanical engineering seniors at the University of Colorado led to an informal experiment with engineering students in India. An attempt was made to qualitatively gauge the students’ ability to appreciate a worldview different from the standard engineering worldview—that of a mechanical universe. Qualitative differences between organic and mechanical systems were used as a point of discussion. Both groups were found to exhibit distinct thought and behavior patterns which provide important clues for sensitizing engineers to environmental issues in future educational initiatives. Cross-cultural and global dimensions of these initiatives are discussed.     

Why do Mathematicians Need Different Ways of Presenting Mathematical Objects? The Case of Cayley Graphs

This paper investigates the role of pictures in mathematics in the particular case of Cayley graphs—the graphic representations of groups. I shall argue that their principal function in that theory—to provide insight into the abstract structure of groups—is performed employing their visual aspect. I suggest that the application of a visual graph theory in the purely non-visual theory of groups resulted in a new effective approach in which pictures have an essential role. Cayley graphs were initially developed as exact mathematical constructions. Therefore, they are legitimate components of the theory (combinatorial and geometric group theory) and the pictures of Cayley graphs are a part of practical mathematical procedures.     

Physico-mathematics and the search for causes in Descartes’ optics—1619–1637

One of the chief concerns of the young Descartes was with what he, and others, termed “physico-mathematics”. This signalled a questioning of the Scholastic Aristotelian view of the mixed mathematical sciences as subordinate to natural philosophy, non explanatory, and merely instrumental. Somehow, the mixed mathematical disciplines were now to become intimately related to natural philosophical issues of matter and cause. That is, they were to become more ’physicalised’, more closely intertwined with natural philosophising, regardless of which species of natural philosophy one advocated. A curious, short-lived yet portentous epistemological conceit lay at the core of Descartes’ physico-mathematics—the belief that solid geometrical results in the mixed mathematical sciences literally offered windows into the realm of natural philosophical causation—that in such cases one could literally “see the causes”. Optics took pride of place within Descartes’ physico-mathematics project, because he believed it offered unique possibilities for the successful vision of causes. This paper traces Descartes’ early physico-mathematical program in optics, its origins, pitfalls and its successes, which were crucial in providing Descartes resources for his later work in systematic natural philosophy. It explores how Descartes exploited his discovery of the law of refraction of light—an achievement well within the bounds of traditional mixed mathematical optics—in order to derive—in the manner of physico-mathematics—causal knowledge about light, and indeed insight about the principles of a “dynamics” that would provide the laws of corpuscular motion and tendency to motion in his natural philosophical system.     

University Support for Student Volunteering in England: Historical Development and Contemporary Value

This article draws on a major study of student volunteering based on case studies of six Higher Education Institutions (HEIs) selected to represent the diversity of the higher education sector in England. The study finds that students contribute significantly to university life and to the wider community through both formal and informal volunteering. However in this paper we consider the challenges and problems with the organisation of student volunteering. Our research finds that students who were supported by their university to volunteer reported better experiences of volunteering and identified greater impacts on their personal development, soft skills, employability and community awareness. In this paper we challenge the tendency of some policy makers and practitioners to view student volunteering as an automatic ‘win, win, win’—for students, for universities and for communities. Rather we explore how without adequate support, management and opportunities for reflection and placing volunteering in wider social context, student volunteering can fail to benefit any of these groups. The paper outlines the development of institutional support for volunteering by students before assessing the value such support has for student volunteers today.     

The early Russell on the metaphysics of substance in Leibniz and Bradley

While considerable ink has been spilt over the rejection of idealism by Bertrand Russell and G.E. Moore at the end of the 19th Century, relatively little attention has been directed at Russell’s A Critical Exposition of the Philosophy of Leibniz, a work written in the early stages of Russell’s philosophical struggles with the metaphysics of Bradley, Bosanquet, and others. Though a sustained investigation of that work would be one of considerable scope, here I reconstruct and develop a two-pronged argument from the Philosophy of Leibniz that Russell fancied—as late as 1907—to be the downfall of the traditional category of substance. Here, I suggest, one can begin to see Russell’s own reasons—arguments largely independent of Moore—for the abandonment of idealism. Leibniz, no less than Bradley, adhered to an antiquated variety of logic: what Russell refers to as the subject-predicate doctrine of logic. Uniting this doctrine with a metaphysical principle of independence—that a substance is prior to and distinct from its properties—Russell is able to demonstrate that neither a substance pluralism nor a substance monism can be consistently maintained. As a result, Russell alleges that the metaphysics of both Leibniz and Bradley has been undermined as ultimately incoherent. Russell’s remedy for this incoherence is the postulation of a bundle theory of substance, such that the category of “substance” reduces to the most basic entities—properties.     

Teaching ethics and technology with <Emphasis Type="Italic">Agora</Emphasis>, an electronic tool

Courses on ethics and technology have become compulsory for many students at the three Dutch technical universities during the past few years. During this time, teachers have faced a number of didactic problems, which are partly due to a growing number of students. In order to deal with these challenges, teachers in ethics at the three technical universities in the Netherlands — in Delft, Eindhoven and Twente — have developed a web-based computer program called Agora (see www.ethicsandtechnology.com). This program enables students to exercise their ethical understanding and skills extensively. The program makes it possible for students to participate actively in moral reflection and reasoning, and to develop the moral competencies that are needed in their later professional practice. The developers of the program have tried to avoid two traps. Firstly, they rejected, from the outset, a cookbook style of dealing with ethical problems that applied ethics is often taken to be and, secondly, they wanted to design a flexible program that respects the student’s as well as the teacher’s creativity, and that tries to engage students in moral reflection. Agora meets these requirements. The program offers possibilities that extend beyond the requirements that are usually accepted for case-exercises in applied ethics, and that have been realised in several other computer models for teaching ethics. In this article, we describe the main considerations in the development of Agora and the features of the resulting program.     

ONE TRUE LOGIC?

This is a paper about the constituents of arguments. It argues that several different kinds of truth-bearer may be taken to compose arguments, but that none of the obvious candidates—sentences, propositions, sentence/truth-value pairs etc.—make sense of logic as it is actually practiced. The paper goes on to argue that by answering the question in different ways, we can generate different logics, thus ensuring a kind of logical pluralism that is different from that of J. C. Beall and Greg Restall.     

The dynamics of insight: Mathematical discovery as a phase transition

In recent work in cognitive science, it has been proposed that cognition is a self-organizing, dynamical system. However, capturing the real-time dynamics of cognition has been a formidable challenge. Furthermore, it has been unclear whether dynamics could effectively address the emergence of abstract concepts (e.g., language, mathematics). Here, we provide evidence that a quintessentially cognitive phenomenon—the spontaneous discovery of a mathematical relation—emerges through self-organization. Participants solved a series of gear-system problems while we tracked their eye movements. They initially solved the problems by manually simulating the forces of the gears but then spontaneously discovered a mathematical solution. We show that the discovery of the mathematical relation was predicted by changes in entropy and changes in power-law behavior, two hallmarks of phase transitions. Thus, the present study demonstrates the emergence of higher order cognitive phenomena through the nonlinear dynamics of self-organization.     

An Impossibility Theorem on Beliefs in Games

A paradox of self-reference in beliefs in games is identified, which yields a game-theoretic impossibility theorem akin to Russell’s Paradox. An informal version of the paradox is that the following configuration of beliefs is impossible:Ann believes that Bob assumes thatAnn believes that Bob’s assumption is wrongThis is formalized to show that any belief model of a certain kind must have a ‘hole.’ An interpretation of the result is that if the analyst’s tools are available to the players in a game, then there are statements that the players can think about but cannot assume. Connections are made to some questions in the foundations of game theory.Special Issue Ways of Worlds II. On Possible Worlds and Related Notions Edited by Vincent F. Hendricks and Stig Andur Pedersen     

Computer simulations of global memory models

Computer simulation models of memory—including the so-called global memory models—have had and continue to have a profound impact on current memory research and theory. Unfortunately, no memory textbooks published before 1998 present these models to students. The arguments for and against these types of models are summarized along with reasons why the models should be taught at both the undergraduate and graduate levels. A set of freely available computer programs that can facilitate classroom presentation is then briefly described.     

Tense and Truth Conditions

The B-theory of time holds that McTaggart’s A-series of past, present, and future is reducible to the B-series of events running from earlier to later. According to the date-theory—originally put forth by J.J.C. Smart and later endorsed by by D.H. Mellor—the truth conditions of tensed or Asentence-tokens can be given in terms of tenseless or B-sentences and, therefore, A-sentence-tokens do not ascribe any A-determinations of pastness, presentness, or futurity. However, as Nathan Oaklander has argued, the date-theory does not provide an adequate analysis of the ontological truth conditions of irreducible A-propositions. I show that the co-reporting theory—which holds that for every A-sentence-token there is a B-sentence that differs in sense but reports the same event or state of affairs—escapes the objections Oaklander has addressed against the date-theory.     

Public and private communication are different: results on relative expressivity

Dynamic Epistemic Logic (DEL) is the study of how to reason about knowledge, belief, and communication. This paper studies the relative expressivity of certain fragments of the DEL language for public and private communication. It is shown that the language of public communication with common knowledge and the language of private communication with common knowledge are expressively incomparable for the class of all pointed Kripke models, which provides a formal proof that public and private communication are fundamentally different in the presence of common knowledge. It is also shown that single-recipient private communication does not add expressive power to the language of modal logic with common knowledge for any class of transitive pointed Kripke models. The latter result provides a sense in which positive introspection—believing our own beliefs—induces a kind of self-dialog.     

Connecting Information with Scientific Method: Darwin’s Significance for Epistemology

Theories of epistemology make reference—via the perspective of an observer—to the structure of information transfer, which generates reality, of which the observer himself forms a part. It can be shown that any epistemological approach which implies the participation of tautological structural elements in the information transfer necessarily leads to an antinomy. Nevertheless, since the time of Aristotle the paradigm of mathematics—and thus tautological structure—has always been a hidden ingredient in the various concepts of knowledge acquisition or general theories of information transfer. We hold that Darwin’s Evolutionary Theory is the first scientific theory which consistently presupposes a non-tautological structure for the information transfer and, at the same time, keeps it strictly distinct from the tautological metric of scientific observation. The consequences of this technique—namely the dissociation of information from intentionality—have not yet been fully drawn.     

Iona College Community Centered Family Health History Project: Lessons Learned from Student Focus Groups

The Community Centered Family Health History project was initiated to create accessible family health history tools produced by and for the community. The project goal was to promote increased community engagement in health education by encouraging conversations among family members that would translate knowledge of family health history into healthy lifestyle choices. As one of seven community partners, Iona College participated in customizing and beta-testing the Does It Run in the Family? toolkit. Twenty-nine college students were engaged to recruit three relatives related by blood to provide feedback on the utility of the toolkit. The toolkit consists of two booklets—“A Guide to Family Health History” and “A Guide to Understanding Genetics and Health”—explaining the importance of knowing and talking about health within the family as well as basics about how conditions are passed down through generations. Twenty-two of the twenty-nine students participated in focus groups to discuss their reactions to participation in the project. Students in the focus group reported that the study participants—students and their family members—found the toolkit to be user friendly and the experience a valuable one that prompted many to take positive steps toward good health.     

Corruption and Representations of Scholarly Output

In this paper I analyze representations of scholarly output for the purpose of identifying corrupt practices. Accordingly, the components of output—price, quantity, and time—are examined. A key part of the analysis is recognizing the unique role that the scholarly community plays in scholarship and the implications this has for the roles of groups other than the scholarly community. Finally, a survey of students indicates that particular representations of scholarly output are viewed by students as unethical.