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  1. Grounding Concepts: The Problem of Composition.Gábor Forrai - 2011 - Philosophia 39 (4):721-731.
    In a recent book C.S. Jenkins proposes a theory of arithmetical knowledge which reconciles realism about arithmetic with the a priori character of our knowledge of it. Her basic idea is that arithmetical concepts are grounded in experience and it is through experience that they are connected to reality. I argue that the account fails because Jenkins’s central concept, the concept for grounding, is inadequate. Grounding as she defines it does not suffice for realism, and by revising the definition we (...)
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  • The Logic of Learning.Christian Bennet - 2019 - Axiomathes 29 (2):173-187.
    An intensional logic is presented and suggested as a framework for a formal investigation of learning. The framework allows for discussing and comparing concepts and representations, and makes it possible to view learning processes as iterations of a certain type of functions. It is shown how this framework may be used to shed light on Meno’s paradox, but also on concepts such as Vygotsky’s ZPD and learning trajectories. In the case of mathematics, where there are recent attempts to merge ideas (...)
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  • Concept Formation and Concept Grounding.Jörgen Sjögren & Christian Bennet - 2014 - Philosophia 42 (3):827-839.
    Recently Carrie S. Jenkins formulated an epistemology of mathematics, or rather arithmetic, respecting apriorism, empiricism, and realism. Central is an idea of concept grounding. The adequacy of this idea has been questioned e.g. concerning the grounding of the mathematically central concept of set (or class), and of composite concepts. In this paper we present a view of concept formation in mathematics, based on ideas from Carnap, leading to modifications of Jenkins’s epistemology that may solve some problematic issues with her ideas. (...)
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