Participants: Aviv, Jonathan, Yinon, Amnon, Ori
Abstract for Aviv's talk: We thought we knew what numbers there are. We thought infinite ones don't make mathematical sense. We thought wrong, kinda. But the notion of numbers splits into two different ones ("Ordinals" and "Cardinals"). Which apparently, in the finite, are both integrated into one. Kinda. I will present the story, and offer a theoretical cognitive framework through which to understand it. The framework sets to account (in the most general terms) for how the cognitive system comes to learn new object-types - of all kinds (Apple, Cat, Physical object, Number, etc.). In such a framework, we could then begin to explore the learning of mathematical objects as on par with "ordinary" ones, and their place in our mental universe. The talk will generally be independent of the previous one, but just as fun. Kinda.
Aviv's proposed cognitive framework is centered on the notion of a "procedure array" relevant to an object. We discussed the extent to which Aviv's theory is committed to mental representations, if at all. Aviv mentioned that he normally refers to these "procedure arrays" as (mental) representations, because it is a usefull way to present them, but it might be possible to avoid labeling "procedure arrays" as representations. Since "procedure arrays" are, well, an array of (cognitive) procedures it could be possible to claim that they only as exist as a distinct array from the point of view of an outside theorist, therefore not serving as an internal representation for the system itself. However, what if the system itself can access a "procedure array" as such? Is that not reason enough to call this array an internal representation? What does it mean for the system to access a "procedure array" of an object X as such?