On paradoxes and the experience of duality

Abstract

Opposing attitudes, emotions, or perceptions of self and other that set the stage for experiences of duality influence our interactions and self–other schemas. The experience of duality that has been conceptualised as “conflict,” “self state,” and “paradox" in psychoanalytic theory has been extensively considered, particularly in terms of its manifestation in transference–countertransference relations and in the analytic material from patients' experiences. They have not, however, been compared and contrasted as entities that lead to similar kinds of experience. Scant attention has been paid, moreover, to paradox as a mental organisation that underlies certain experiences of duality. The concept of paradox has thus been emphasised and developed in this paper.     

The paradoxes

Conclusion The paradoxes act as restraints on undisciplined or erroneous reasoning and so perform a valuable role. The fact that they have resisted solution for so long suggests that the current systems of logic are defective. The paradoxes of set theory, in my opinion, completely condemn all the current forms of set theory and their associated definitions of the natural numbers. Nothing short of a complete review of the whole area seems capable of remedying the situation.     

Model-theoretic semantics and revenge paradoxes

Philosophical Studies - Revenge arguments purport to show that any proposed solution to the semantic paradoxes generates new paradoxes that prove that solution to be inadequate. In this paper, I...     

Reference, paradoxes and truth

We introduce a variant of pointer structures with denotational semantics and show its equivalence to systems of boolean equations: both have the same solutions. Taking paradoxes to be statements represented by systems of equations (or pointer structures) having no solutions, we thus obtain two alternative means of deciding paradoxical character of statements, one of which is the standard theory of solving boolean equations. To analyze more adequately statements involving semantic predicates, we extend propositional logic with the assertion operator and give its complete axiomatization. This logic is a sub-logic of statements in which the semantic predicates become internalized (for instance, counterparts of Tarski’s definitions and T-schemata become tautologies). Examples of analysis of self-referential paradoxes are given and the approach is compared to the alternative ones.     

The paradoxes of analysis and synonymy

The very idea of informative analysis gives rise to a well-known paradox. Yet a parallel puzzle, herein called the paradox of synonymy, arises for statements which do not express analyses. The paradox of synonymy has a straightforward metalinguistic solution: certain words are referring to themselves. Likewise, the paradox of analysis can be solved by recognizing that certain expressions in an analysis statement are referring to their own semantic structures.     

Problems and paradoxes of physiological psychology

The Psychological Record -     

Visual discrimination of shape by octopus circles and squares, and circles and triangles

An investigation of the relative discriminability of circles and squares, and circles and triangles for octopus is described. The main findings were: (1) The three pairs of figures, circle and square with base horizontal, circle and square with base at 45° to the horizontal, circle and equilateral triangle were equally discriminable for the octopus. (2) Complete transfer occurred to larger and smaller figures. (3) No transfer occurred from a square in one orientation to a square rotated through 45°, nor did training with the square in one orientation lead to any saving when the discrimination was relearned with the square in the other orientation. (4) No transfer occurred from a square to a pentagon. (5) The method of training with reward on every positive trial leads to quicker initial learning of a discrimination than training with reward only where the positive figure is attacked, but discriminatory performance with the two methods approached the same asymptote. The results are in agreement with findings with other animals where these are available for comparison.     

Zeno's paradoxes and the cosmological argument

I want to thank Professor José Benardete, Professor Panayot Butchvarov, and Professor David E. Johnson for their very kindly viewing earlier versions of this paper.     

Three paradoxes of medical diagnosis

Sadegh-zadeh [23] has proposed a theory of the relativity of medical diagnosis in terms of the time at which a diagnosis is accepted, the patient to whom the diagnosis applies, the physician who renders the diagnosis, the medical knowledge used, the diagnostic method applied, and the set of patient observations. Use of classical formal logic as the ‘diagnostic method’ may result in three paradoxes: the paradoxes of consistency, completeness, and justifiable ignorance. These paradoxes may be resolved by the addition of two non-classical operators, the ‘certainty’ and ‘effort’ operators, akin to the non-classical operators of modal logic.