Editing Mathematical Platonism and the Reality of Abstract Objects (section)

== <span style="color: #FFFFFF;">Remembering</span> ==
* '''Mathematical Platonism''' — "The View" that "Mathematical Objects" (Numbers, Sets, Functions) "Exist" "Independently" of "Human Minds" in "An Abstract" "Realm."
* '''Plato's Theory of Forms''' — "The Original" "Platonism": "Ideal Forms" (including "Mathematical Forms") "Exist" in "A Non-Physical Realm" — "The Physical World" merely "Participates" in them.
* '''Mathematical Nominalism''' — "The Counter-View": "Mathematical Objects" "Do Not Exist" — "Mathematics" is "A Useful" "Fiction" or "Language."
* '''Mathematical Structuralism''' — "The View" that "Mathematics" "Studies" "Structures" (Patterns of Relations) rather than "Objects" — "Any" "System" "Instantiating" "The Structure" works.
* '''Gödel's Platonism''' — "Kurt Gödel" "Believed" "Mathematicians" "Perceive" "Mathematical Truth" through **"Mathematical Intuition"** — "A Kind of" "Intellectual Perception" of "Abstract Objects."
* '''The Mathematical Universe Hypothesis''' — (Max Tegmark). "The Radical" "Platonism": "Not Just" "Mathematics" is "Real" — "The Physical Universe" **"Is"** "A Mathematical Structure."
* '''The Unreasonable Effectiveness''' — (Wigner, 1960). "Why" does "Pure Mathematics" (Invented for "Aesthetic" "Reasons") "Perfectly Describe" "Physical Reality"? (Riemann Geometry → General Relativity, Complex Numbers → Quantum Mechanics).
* '''Abstract Objects''' — "Objects" that are "Non-Physical," "Non-Mental," "Causally Inert," and "Non-Spatiotemporal": "Proposed" to "Include" "Numbers," "Sets," "Propositions," and "Properties."
* '''Benacerraf's Dilemma''' — "The Key" "Problem" for "Platonism": "If" "Numbers" exist in "A Non-Physical Realm," **"How"** do "We" "Know" about "Them"? (Epistemological Problem).
* '''Mathematical Fictionalism''' — (Hartry Field). "Mathematics" is "A Useful" "Fiction": "Mathematically" "True" "Statements" are "False" — "But" "Fictions" are "Useful" for "Science."
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