PRESENTER Aaron Sloman
http://www.cs.bham.ac.uk/~axs/
School of Computer Science, University of Birmingham
What about continuously varying sets of possibilities?
Finite exhaustive analysis is no longer possible.
The concept of number essentially involves 1-1 correspondence: a topological relationship.
Understanding cardinals requires grasping that 1-1 correspondence is transitive and symmetric, and therefore produces equivalence classes.
Very few psychologistss or neuroscientists understand the implications.
Piaget did, but failed to propose adequate explanatory mechanisms.
How do we come to know that this relationship is necessarily transitive and
symmetric?
... and can therefore generate equivalence classes?
Spatial/diagrammatic reasoning can help us understand this, but we have to see that individual diagrams represent an infinity of distinct cases!
Compare the logicist explanations (Peano, Frege, Russell, etc.) whose psychological plausibility is zero.
NB There are pseudo numerical, much simpler competences whose inadeqacies most
psychological and neural research ignores.
-- They merely involve pattern recognition in small clusters.
Challenge for my view: What neural mechanisms, or sub-neural mechanisms can support these capabilities.
NOBODY KNOWS, AND ALMOST NOBODY IS ASKING.
If there's time we can come back to the problem of finding biological precursors.
WHICH PARTS INCLUDE ROLES FOR MATHEMATICAL COGNITION?
WE NEED NEW MORE POWERFUL EXPLANATORY MECHANISMS
THEY MUST EXIST BECAUSE THEY ARE NEEDED FOR KNOWN FORMS OF INTELLIGENCE, IN HUMANS AND OTHER INTELLIGENT ANIMALS.
Maintained by
Aaron Sloman
School of Computer Science
The University of Birmingham