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.
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. The term 'mathematicism' has additional meanings among Cartesian idealist philosophers and mathematicians, such as describing the ability and process to study reality mathematically.
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's mathematicism)
- Neoplatonism (brought Aristotelean mathematical logic to Platonism)
- Cartesianism (René Descartes applied mathematical reasoning to philosophy)
- Leibnizianism (Gottfried Leibniz was a mathematician, called beings 'monads,' which also means 'units')
- Alain Badiou's philosophy
- Physicist Max Tegmark's mathematical universe hypothesis (MUH) described as Pythagoreanism–Platonism
- 'philosophical mathematics' systems described by several authors, such as Tim Maudlin's project of 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.' According to Maudlin, 'the most satisfying possible answer to such a question is: Because the physical world literally has a mathematical structure.'
- Mike Hockney's Neopythagorean-Neoplatonist-Leibnizian mathematical reality theory (philosophical/ontological mathematics) (several authors use the term ‘ontological mathematics.’)
- 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.
- Gilson, Étienne. The Unity of Philosophical Experience. San Francisco, CA: Ignatius Press, 1999, p. 133.
- Maudlin, Tim. New Foundations for Physical Geometry: The Theory of Linear Structures. Oxford University Press. 2014, p. 52.
- Hockney, Mike. The God Series. Hyperreality Books, 2015. 32 vols.
- "mathematicism". Britannica.
- "mathematicism". Collins Dictionary.
- "mathematicism". Oxford Living Dictionary.
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