Reflexivity: From Paradox to Consciousness

Notre Dame Journal of Formal Logic, 1983

It has been widely recognized that Thomson's "small theorem" [5] is of central importance in understanding the reflexive paradoxes. Several authors (e.g., Herzberger [2], Martin [3], and Goldstein [1]) have exploited it and variations in it in different ways. The purpose of this paper, however, is to show that the formal and philosophical consequences of the theorem are so extensive that they force a general reappraisal of the paradoxes as such. The concern here is to bring out some of these consequences. In Part I there is no intention to promote a particular solution, though in Part II a generalization of Frege's solution is developed. Here, however, the interest is in the general conditions which must be satisfied by any reflexive paradox and any proposed solution. Some of the results which are arrived at are already well known, but they are presented here as interconnected conclusions within a general theory of paradoxicality which arises naturally from Thomson's theorem. The analysis is carried out entirely in terms of classical two-valued logic since part of the purpose is to discover what can and cannot be done to block the occurrence of reflexive contradictions in a language based on standard quantification theory. We do not want to deny that there are other and perhaps better ways of handling the paradoxes than those which are available in standard two-valued logic, and nothing we say is incompatible with, say, *An early version of this article (Part I), entitled "What paradoxes?," was read to the Australasian Association of Philosophy (Victorian Branch) in July 1980. For many helpful comments on that version and successive drafts, we are much indebted to

SHS Web of Conferences

The article describes semantics and pragmatics of reflexive constructions. Common notes on the semantics of reflexivity are given. Reflexivity reflects specific subject-object relationships demonstrated in explicitly and implicitly reflexive constructions. Implicit reflexivity is discussed of a relatively small class of verbs in English. It is stated that the full referent identity of an anaphora pronoun and personal antecedent in the position of the subject is not obligatory. Different standpoints on the nature of reflexivity are distinguished. The existence of a special type of referential identity of a reflexive anaphora and an antecedent word is substantiated, when one and the same referent is interpreted by these linguistic units in a different way carrying out different semantic and syntactic functions in a sentence. Moreover, an antecedent and an anaphora turn out to be united at the level of the semantic structure. In the syntactic structure, the anaphora and an antecedent w...

2000

Toward an Integrated Account of Reflexive and Reflective Reasoning John E. Hummel ([email protected]) Department of Psychology University of California Los Angeles 405 Hilgard Ave. Los Angeles, CA 90095-1563 Jesse M. Choplin ([email protected]) Department of Psychology University of California Los Angeles 405 Hilgard Ave. Los Angeles, CA 90095-1563 Abstract Some inferences are seemingly automatic (reflexive; Shastri & Ajjanagadde, 1993), whereas others require more effort (i.e., are reflective). We present the beginnings of an integrated account of reflexive and reflective reasoning, based on the LISA model of analogical reasoning (Hummel & Holyoak, 1997). The account holds that reflexive inferences are those that can be generated automatically based on existing knowledge in long-term memory, whereas reflective inferences require explicit structure- mapping and therefore demand greater attention and working memory. According to this account, reflexive inferences manife...

Nordlyd, 2011

To a young child, it may not be immediately obvious that Bill's selling Mary his car implies that she now owns the car; but after a sufficient number of examples, the child will eventually induce a schema that makes the relationship between buying and owning reflexive (if evidenced only by the fact that the inference is reflexive for an adult).

2019

This article aims to critically examine three approaches to reflexiv-ity in philosophical texts, specifically the case when the textuality becomes its own topic. The first approach is when there is no re-flexivity at all. It is just describing how-according to the author-things are. As an example of this approach I take German media philosophy. This tradition is specific because reflexivity is supposed to be its very topic. However, the media philosophers succeeded in touching the indefinability of mediality itself. Another method is to question one's own and possibly also the reader's position. I have chosen Annemarie Mol's empirical philosophy as the example here. The problem is that despite following the "ontological turn", the author remains (probably inevitably) also to a large extent trapped in the fact that he/she describes the world, that is, in sub-ject/object dichotomy and therefore, in epistemology. The third way to write aims to make readers feel what the author tells. My example here is the varied work of Walter Benjamin whom I for the purpose of this article consider more as a prophet rather than the precise thinker who he (also) by all means was. While using the second approach myself, I discuss advantages and challenges of the three and find their points of touch.

1989

2003

Reflexive research can be grouped into five clusters with circular relations between two elements x ↔ x, namely circular relations between observers, between scientific building blocks like concepts, theories or models, between systemic levels, between rules and rule systems or as circular relations or x ↔ y between these four components. By far the most important cluster is the second cluster which becomes reflexive through a re-entry operation RE into a scientific element x and which establishes its circular formation as x(x). Many of the research problems in these five clusters in reflexivity research are still unexplored and pose grand challenges for future research.

This chapter discusses the paradoxes of reflexivity from a new perspective according to which such paradoxes could be inconsistencies derived from the hypothesis of the actual infinity that legitimizes Dedekind's definition of the infinite sets.