Traditional and Cognitive Views of Conceivability

Over the past 30 years, many authors have proposed similar accounts of conceivability, based on the idea of justifying what is conceivable by testing for logical and mathematical consistency. While subjective conceiving capacities of particular persons can be limited in different ways, the objective conceivability is often understood as the capacity of an ideal conceiver. Within this traditional approach, the conceivability or inconceivability of something is ultimately understood as an objective property of thinking, not rooted in human abilities and experience. Accordingly, logical laws are usually taken for granted as being general, formal, foundational, a priori, analytical, and necessary. The aim of this paper is to propose a notion of conceivability based on a cognitive understanding of mathematics and logic that is contrasted to the traditional one. From the cognitive point of view, there are embodied mechanisms, such as image and aspectual schemas, conceptual metaphor, conceptual blends, which allow people to construct sophisticated higher mathematics and symbolic logic. Most existing forms of human logic and mathematics do not in any way limit what can be conceived in principle, since a person can conceive of new logical and mathematical forms. Human conceivability is limited only by human creativity, which is based on innate forms of perception and thought, bodily experience and innate cognitive mechanisms. We need to rethink what the justification for conceivability results might be. For example, it might consist of proposing a hypothesis containing an explicit explanation of what the implicit unconscious mechanisms were that resulted in the emergence of a new idea that appears to be conceivable.