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Welcome to the Objective Mathematics wiki.

Objective Mathematics is an ongoing project which aims to make mathematics more objective by connecting it to reality. This is being 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 do not refer to Platonic forms inhabiting an otherworldly realm, but rather they refer directly to physical, perceivable things. Objective Mathematics rejects Intuitionism: math is not a process of construction and intuition, but rather a process of identification and measurement. 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).

Many of the pages on Objective Mathematics wiki are about foundational concepts of physics, computer science, and philosophy. Although I accept the distinction between these subjects, I think that it is more blurry than is sometimes supposed. The unifying theme of these subjects is that they are foundational, meaning that each can be considered more or less on its own, without taking much of another field's knowledge for granted.

Pages

Math pages:

• Derivative
• Sequence
• Set
• Continuity
• Natural number
• Integer
• Fraction
• Radical
• Imaginary number
• Triangulation
• Function
• Circle
• Line
• Point
• Curve
• Surface
• Solid
• π
• Limit
• Nill
• Induction
• Ordering

Physics pages:

• Newton's laws

Computer Science pages:

• Algorithm
• Type
• Information
• Computation

Philosophy pages:

• Concept
• Entity
• Unit
• Definition
• Platonism
• Intuitionism
• Formalism
• Induction

Notation

Instead of having set inclusion as one of its fundamental concepts, Objective Mathematics has conceptual identification as one of its fundamental concepts. For conceptual identification, it uses the notation of Type Theory. It is easiest to demonstrate what is meant by this through examples:

• $q={\frac {2}{3}}$ is a fraction, and I denote this fact---this identification---by writing $q:\mathbb {Q}$.
• Any integer is a fraction, and I denote this fact by writing $\mathbb {Z} :\mathbb {Q}$.

Legal

All writing on this website is (c) Liam M. Fox.

Some images on this website are public domain, some are (c) Liam M. Fox. Check the image descriptions to see which [TODO].

Donate

If you would like to help pay to keep the Objective Mathematics wiki afloat, consider donating [TODO].

Contact

If you are interested in Objective Mathematics and would like to discuss it, please email me. You already know my email if you are reading this and you are not a bot. [TODO]