AVICENNA ON GRASPING MATHEMATICAL CONCEPTS

According to Avicenna, some of the objects of mathematics exist and some do not. Every existing mathematical object is a non-sensible connotational attribute of a physical object and can be perceived by the faculty of estimation. Non-existing mathematical objects can be represented and perceived by the faculty of imagination through separating and combining parts of the images of existing mathematical objects that are previously perceived by estimation. In any case, even non-existing mathematical objects should be considered as properties of material entities. They can never be grasped as fully immaterial entities. Avicenna believes that we cannot grasp any mathematical concepts unless we first have some specific perceptual experiences. It is only through the ineliminable and irreplaceable operation of the faculties of estimation and imagination upon some sensible data that we can grasp mathematical concepts. This shows that Avicenna endorses some sort of concept empiricism about mathematics.

Hume, Empiricism and the Generality of Thought

Hume sought to analyse our propositionally-structured thought in terms of our ultimate awareness of nothing but objects, sensory impressions or their imagistic copies, “ideas.” The ideas of space and time are often regarded as exceptions to his Copy Theory of impressions and ideas. On grounds strictly internal to Hume’s Treatise, I argue that they are instead typical of Hume’s account of the generality of thought. This ultimately reveals the limits of the Copy Theory and of Concept Empiricism. The key is to recognise how very capacious is our (Humean) imaginative capacity to associate particular perceptions by various fine-grained determinable resemblances.

Belling the cat: Why reuse theory is not enough

I agree with Anderson's approach to reuse theories. My main concern is twofold. Anderson assumes certain nomological regularities in reuse phenomena that are simply conjectures supported by thin evidence. On the other hand, a biological theory of reuse is insufficient, in and of itself, to address the evaluation of particular models of cognition, such as concept empiricism or conceptual metaphor.

Locke vs. Hume: Who Is the Better Concept-Empiricist?

ABSTRACTAccording to the received view, Hume is a much more rigorous and consistent concept-empiricist than Locke. Hume is supposed to have taken as a starting point Locke's meaning-empiricism, and worked out its full radical implications. Locke, by way of contrast, cowered from drawing his theory's strange consequences. The received view about Locke's and Hume's concept-empiricism is mistaken, I shall argue. Hume may be more uncompromising (although he too falters), but he is not more rigorous than Locke. It is not because of (intellectual) timidity that Locke does not draw Hume's conclusions from his empiricism. It is, rather, because of his much sounder method.