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Math - Coggle Diagram
Math
Big picture
Mathematics in TOK explores "How do we know?" through axioms, which are foundational self-evident truths.
Axioms vary by mathematical branch and consensus, with some, like the infinite set in set theory, widely accepted despite being conjectural.
Mathematics is seen as a universal language with precise definitions, minimizing ambiguity.
TOK focuses on how mathematical knowledge is constructed and its cultural/social implications, not just content.
Justification in mathematics is based on internal consistency and logic, though real-world evidence has historically supported it.
Philosophical debates
Platonism: Views mathematical entities as discoverable, pre-existing realities independent of human thought.
Nominalism: Either mathematical objects, relations, and structures do not exist at all, or they do not exist as abstract objects
Fictionalism: Regards mathematical entities as useful fictions, facilitating understanding and problem-solving without claiming their independent existence.
Formalism: Considers mathematics a constructed language of thought, with its truths contingent upon human-defined axioms and systems.
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Perspectives
Formalist perspective
Mathematics is a human-constructed language, similar to other forms of symbolic communication.
Mathematical objects, like numbers, exist only in the human mind and do not have a physical existence.
While mathematics is useful for making predictions, it does not necessarily represent a 'real' existence.
Considers mathematical concepts useful and valuable, but ultimately human inventions.
Real VS True
Truth: Can be contextually and culturally constructed, changing over time.
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Plantonic perspective
Mathematics is inherent in the universe, much like natural laws, and is not created by humans.
The ability of mathematics to accurately predict natural phenomena supports its existence outside of human though
Believes mathematics exists independently of humans, discovered rather than invented.
Considers mathematics both real and true, existing outside human creation.
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