Post on 11-Jul-2020
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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
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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?
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Some “hard-wired” capacities
! Subitizing
From Mandler & Shebo, 1982
Some “hard-wired” capacities
! Large (approximative) numerosity comparison
Distance effect Size effect