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Welcome to the Objective Mathematics wiki.

Objective Mathematics is a project which aims to make mathematics objective, by connecting it to reality. This is done by painstakingly going through each math concept, and thinking about the concrete, perceptual data to which it ultimately refers. If a math concept is not reducible to perceptual concretes, it is invalid; it is a floating abstraction. Objective Mathematics rejects Platonism: math concepts are not Platonic forms inhabiting an otherworldly realm, but rather they refer to physical, perceivable things. Objective Mathematics rejects Intuitionism: math is not a process of construction, but rather a process of identification. Objective Mathematics rejects Formalism and Logicism: math is not a meaningless game of symbol manipulation, but rather its statements have semantic content (just like propositions about dogs, tea, beeswax, or anything else).

Featured pages

• Sequences
• Sets
• Continuity
• Natural numbers
• Integers
• Fractions
• Radicals
• Imaginary numbers
• Triangulations

Notation

Instead of set inclusion, Objective Mathematics uses the notation of Type Theory. It is easiest to demonstrate what this means by examples:

• if $q$ is a fraction, I denote this fact---this identification---by writing $q:\mathbb {Q}$.
• any integer is a fraction, and I denote this fact by writing $\mathbb {Z} :\mathbb {Q}$

Contact

If you are interested in Objective Mathematics and would like to discuss it, please email me at liam.macpherson.fox@gmail.com.