Mathematicism
Mathematicism is any opinion, viewpoint, school of thought, or philosophy that states that everything can be described/defined/modelled ultimately by mathematics, or that the universe and reality (both material and mental/spiritual) are fundamentally/fully/only mathematical, i.e. that 'everything is mathematics' necessitating the ideas of logic, reason, mind, and spirit.
Overview
Mathematicism is a form of rationalist idealist or mentalist/spiritualist monism). The idea started in the West with ancient Greece's Pythagoreanism, and continued in other rationalist idealist schools of thought such as Platonism.^{[1]} The term 'mathematicism' has additional meanings among Cartesian idealist philosophers and mathematicians, such as describing the ability and process to study reality mathematically.^{[2]}^{[3]}
Mathematicism includes (but is not limited to) the following (chronological order):
- Pythagoreanism (Pythagoras said 'All things are numbers,' 'Number rules all,' though contemporary mathematicists exclude numerology, etc., from mathematicism)
- Platonism (paraphrases Pythagoras' mathematicism)
- Neopythagoreanism
- Neoplatonism (brought Aristotelean mathematical logic to Platonism)
- Cartesianism (René Descartes applied mathematical reasoning to philosophy)^{[3]}
- Leibnizianism (Gottfried Leibniz was a mathematician, called beings 'monads,' which also means 'units')
- Physicist Max Tegmark's mathematical universe hypothesis (MUH) described as Pythagoreanism–Platonism
- Tim Maudlin's project of 'philosophical mathematics,' a project aiming at constructing 'a rigorous mathematical structure using primitive terms that give a natural fit with physics' and investigating 'why mathematics should provide such a powerful language for describing the physical world.'^{[4]} According to Maudlin, 'the most satisfying possible answer to such a question is: Because the physical world literally has a mathematical structure.'^{[4]}
Notes
- ^ Gabriel, Markus. Fields of Sense: A New Realist Ontology. Edinburgh: Edinburgh Univ. Press, 2015, ch. 4. Limits of Set-Theoretical Ontology and Contemporary Nihilism.
- ^ Sasaki, Chikara, Descartes’s Mathematical Thought, Springer, 2013, p. 283.
- ^ ^{a} ^{b} Gilson, Étienne. The Unity of Philosophical Experience. San Francisco, CA: Ignatius Press, 1999, p. 133.
- ^ ^{a} ^{b} Maudlin, Tim. New Foundations for Physical Geometry: The Theory of Linear Structures. Oxford University Press. 2014, p. 52.
References
- "mathematicism". Britannica.
- "mathematicism". Collins Dictionary.
- "mathematicism". Oxford Living Dictionary.
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