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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).

According to Objective Mathematics, mathematics is the science of measurement. [TODO expand]

Besides mathematics, 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 four subjects, I think that it is more blurry than is sometimes supposed. The unifying theme of these subjects, and the reason why they all appear on Objective Mathematics wiki, is that each subject is foundational, meaning that it can be contemplated on its own (in the case of philosophy), or that it can be contemplated without taking anything beyond basic metaphysics and epistemology for granted (in the case of the others). For example, what I deem to be the fundamental concepts of computer science, despite what the name of the subject may suggest, could in principle be formed by someone with no knowledge whatsoever about computing machines (by say, an Ancient Greek philosopher).

Recommended reading order

[TODO]

All Pages

Math pages:

• Coordinates
• Derivative
• Sequence
• Set
• Continuity
• Natural number
• Integer
• Fraction
• Radical
• Real number
• Imaginary number
• Vector space
• Triangulation
• Function
• Polynomial
• Circle
• Line
• Point
• Curve
• Surface
• Solid
• π
• Limit
• Nill
• Induction
• Ordering
• Symmetry
• Probability
• Group

Physics pages:

• Newton's laws
• Velocity

Computer Science pages:

• Algorithm
• Type
• Information
• Computation
• P

Philosophy pages:

• Existent
• Concept
• Entity
• Unit
• Definition
• Platonism
• Intuitionism
• Formalism
• Induction
• Objective Mathematics
• Zeno's Paradox
• Counterfactual

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:

• Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 $\mathbb {Z} :\mathbb {Q}$.

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]

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].