The "Natural" and the "Formal"

The paper presents an argument against a metaphysical conception of logic according to which logic spells out a specific kind of mathematical structure that is somehow inherently related to our factual reasoning. In contrast, it is argued that it is always an empirical question as to whether a given mathematical structure really does captures a principle of reasoning. (More generally, it is argued that it is not meaningful to replace an empirical investigation of a thing by an investigation of its a priori analyzable structure without paying due attention to the question of whether it really is the structure of the thing in question.) It is proposed to elucidate the situation by distinguishing two essentially different realms with which our reason must deal: the realm of the natural, constituted by the things of our empirical world, and the realm of the formal, constituted by the structures that we use as prisms to view, to make sense of, and to reconstruct the world. It is suggested that this vantage point may throw light on many foundational problems of logic.     

Meaning and Circular Definitions

Gupta"s and Belnap"s Revision Theory of Truth defends the legitimacy of circular definitions. Circularity, however, forces us to reconsider our conception of meaning. A readjustment of some standard theses about meaning is here proposed, by relying on a novel version of the sense–reference distinction.     

A Revenge-Immune Solution to the Semantic Paradoxes

The paper offers a solution to the semantic paradoxes, one in which (1) we keep the unrestricted truth schema True(A)A, and (2) the object language can include its own metalanguage. Because of the first feature, classical logic must be restricted, but full classical reasoning applies in ordinary contexts, including standard set theory. The more general logic that replaces classical logic includes a principle of substitutivity of equivalents, which with the truth schema leads to the general intersubstitutivity of True(A) with A within the language.The logic is also shown to have the resources required to represent the way in which sentences (like the Liar sentence and the Curry sentence) that lead to paradox in classical logic are defective. We can in fact define a hierarchy of defectiveness predicates within the language. Contrary to claims that any solution to the paradoxes just breeds further paradoxes (revenge problems) involving defectiveness predicates, there is a general consistency/conservativeness proof that shows that talk of truth and the various levels of defectiveness can all be made coherent together within a single object language.     

Conservative Theories of Classical Truth

Some axiomatic theories of truth and related subsystems of second-order arithmetic are surveyed and shown to be conservative over their respective base theory. In particular, it is shown by purely finitistically means that the theory PA ÷ "there is a satisfaction class" and the theory FS of [2] are conservative over PA.     

Logical Pluralism from a Pragmatic Perspective

This paper presents a new view of logical pluralism. This pluralism takes into account how the logical connectives shift, depending on the context in which they occur. Using the Question-Under-Discussion Framework as formulated by Craige Roberts, I identify the contextual factor that is responsible for this shift. I then provide an account of the meanings of the logical connectives which can accommodate this factor. Finally, I suggest that this new pluralism has a certain Carnapian flavour. Questions about the meanings of the connectives or the best logic outside of a specified context are not legitimate questions.     

Robust Improvements on Reasoning Performance Following Discussion in Japan

Group discussion significantly improves performance on intellective problems. However, most experiments have been conducted in Western cultures. Cross‐cultural psychology suggests that members of Eastern cultures might be less likely to benefit from group discussion. One experiment in Japan suggested that this was not the case, but this experiment suffered from some limitations. To address these limitations, Japanese participants were asked to solve an intellective task four times: individually (pre‐test), in small discussion groups (test), individually again (transfer task, post‐test), and individually after a delay (delayed post‐test). The results revealed a robust improvement during group discussion. Groups in which at least one member had found the correct answer individually agreed on it during the discussion. Moreover, and in contrast with results obtained in Western cultures, most groups with no such member also found the correct answer. The gains obtained during discussion were maintained in the transfer tasks. This result provides further evidence that the improvement of reasoning performance in group discussion is a universal phenomenon, and provides support for the practice of collaborative learning in Japan.     

John Cage and W. R. Bion: an exercise in interdisciplinary dialogue

The author discusses some striking convergences which appear in the thought of two unsettling and powerfully stimulating personalities of the 20th century: John Cage in music and art, and W.R. Bion in psychoanalysis. Both foster openness to the unknown and the need to tolerate 'uncertainties, mysteries, doubts', arguing for an attitude requiring negative valence and receptive emptiness. In their search for fresh personal awareness of reality aimed at allowing mental transformation and growth, both strive to disturb intellectual comfort and do not hesitate to use pro(e)vocative and even shocking means. They both propose an attitude towards tradition which demands the freedom to use and recreate inherited knowledge in a personal and innovative way. Finally, both Cage and Bion maintained a highly auto-reflective attitude, carefully considering the artist's/psychoanalyst's contribution to the process of art and psychoanalysis. These convergences probably represent important and wider contemporary cultural trends which permeate in their different realizations.     

Modeling,Truth, and Philosophy

Knowledge requires truth, and truth, we suppose, involves unflawed representation. Science does not provide knowledge in this sense but rather provides models, representations that are limited in their accuracy, precision, or, most often, both. Truth as we usually think of it is an idealization, one that serves wonderfully in most ordinary applications, but one that can terribly mislead for certain issues in philosophy. This article sketches how this happens for five important issues, thereby showing how philosophical method must take into account the idealized nature of our familiar conception of truth.     

Two Key Differences between Science and Philosophy

C. S. Peirce made the following claim: If science reveals truth, then consensus among scientists can be expected in the limit. This article does not dispute this claim; it simply assumes it. On the basis of this assumption, the following question is asked: Is it possible to extend Peirce's claim to philosophy in a natural way? It is argued that two important differences between science and philosophy strongly militate against such an extension. Does this mean that there is no truth to be found in philosophy? Are there, perhaps, different kinds of truth (scientific, philosophical, religious, and so on)? But such questions, though related to the present investigation, are nevertheless well beyond the scope of this article.     

Observing a client's grieving process: bringing logical positivism into qualitative grief counselling research

This positional paper originates from our need as researcher/practitioners to establish a meaningful epistemological framework for research into bereaved people's journey through loss and grief over time. We describe how the field of grief research has a long and established biological basis, in keeping with a positivist epistemology. However, there has been a diminution of the influence of logical positivism in twenty-first-century counselling research. We argue that in grief counselling research, naturalistic observation of the grieving process within a logical positivist paradigm, remains a valid and valuable construct. We posit an observational protocol for the grief counselling process which minimises the intrusion of research method into the therapeutic process. We offer this as a means of conducting qualitative research within a bereavement counselling service. Further, we suggest that the development of an observational protocol for a client's grieving process has potential implications for developing good practice in grief work.