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1 Concepts, meaning, idealization, abstraction, and the human animal ! Naturalizing the problem ! Living systems: Resources are limited ! “recycling” ! New stuff with old parts ! Concepts, ideas, meaning, minds are the result of biologically viable living cognition ! Mathematical concepts/ideas are not an exception ! NOT TAKING ANY MATH FACTS for granted A common picture in science … Dynamical Systems Differential Equations Chaos Theory Bifurcation Theory Trigonometry Atractors Probabilities Instability Physics, Chemistry, etc. Taking as given: Equations, numbers, operations, axioms, … … Formalization and Quantification A common picture in science … Dynamical Systems Differential Equations Chaos Theory Bifurcation Theory Trigonometry Atractors Probabilities Instability Mind, Cognitive Phenomena Taking as given: Equations, numbers, operations, axioms, … … Formalization and Quantification Dynamical Systems Differential Equations Chaos Theory Bifurcation Theory Trigonometry Atractors Probabilities Instability Mind, Cognitive Phenomena Taking as given: Equations, numbers, operations, axioms, … … Formalization and Quantification ? ? A common picture in science … The Cognitive Science OF Mathematics Science and “the (human) mind” Philosophy Neuroscience Linguistics Education Psychology Anthropology Computer Science Memory Language Attention Perception Learning “Mind” Thought Reasoning Communication Concepts Some questions … " Ok, … let’s endorse a naturalistic & scientific approach, … so, … " Is there any biological endowment? " How much (if any) of mathematics is “hard- wired”? " If there is anything “hard-wired”, is that mathematics?
