Viewpoint stereotypes of mathematics

[bvssvni]

Here is a categorization of various viewpoint stereotypes of mathematics

Platonist

• Mathematics is an abstract language
• Mathematics is discovered, not created
• Everything true has a proof of why it is true

Seshatist

• Mathematics is the purest form of science
• Mathematics is created, not discovered
• Everything true was learned by first learning what is false

Seshatic Platonist

• Mathematics is an abstract language with a homotopy structure
• To make mathematics work in reality requires a "witness", a parameter of homotopy maps
• Proofs can have multiple interpretations, depending on which homotopy level one views them

Philosophy of the Inside of the Logi circle.

Platonic Seshatist

• Mathematics is an abstract language, but also what reality is made of
• There is something about reality that is "extra", separated from mathematics as language
• Everything true is discovered twice, once in mathematics and once in reality

Philosophy of the Outside of the Logi circle.

Joker Platonist

• Reality has a mathematical structure underneath the subjective viewpoint people experience
• Reality can never be known directly, only through mathematics
• Everything true is discovered in mathematics, while how we experience reality is a "distorted" picture of truth

Joker Seshatist

• Mathematics is just a model of reality that holds up to some limit of accuracy
• Reality is experienced directly, while mathematics is thoughts we have about reality
• Everything true is only what is directly experienced, while how we think about reality gives an illusion of truth

(Seshatic Platonist, Platonic Seshatist)

• Mathematics plays two roles, both as an apparent abstract language and underlying reality
• The more accurate we model reality, the smaller errors we make
• Everything is probabilistic, but we can reduce uncertainty to a minimum

(Platonic Seshatist, Seshatic Platonist)

• Mathematics plays a role in reality, but it can not be well understood in that context
• The more accurate we can model reality, the less can be known about reality
• Everything is uncertain and there are limits to knowledge

Platonic Joker Platonist

An "aggressive" Joker Platonist. This is the same as a Joker Platonist, but oppressing a Seshatic Joker Seshatist. See #19 (comment)

• Reality has a mathematical structure, but the "other" believes mathematics is just a model of reality
• Reality can never be known directly, but the "other" believes reality is experienced directly
• Everything true is discovered in mathematics, but the "other" believes everything true is only what is directly experienced

Seshatic Joker Seshatist

A "rejected" Joker Seshatist. This is the same as a Joker Seshatist, but oppressed by a Platonic Joker Platonist. See #19 (comment)

• Mathematics is just a model of reality, but the "other" believes reality has a mathematical structure
• Reality is experienced directly, but the "other" believes reality can never be known directly
• Everything true is only what is directly experiences, but the "other" believes everything true is discovered in mathematics

Seshatic Joker Platonist

A Platonist that "embraces" Seshatism. The viewpoints of Seshatism are acknowledged, but without changing one's personal view that is Platonism. See #19 (comment)

• Reality has a mathematical structure, but in one sense mathematics is a model of reality
• Reality can be known through mathematics, but in one sense mathematics is thoughts we have about reality
• Everything true is discovered in mathematics, but in one sense everything true is experienced directly

Platonic Joker Seshatist

A Seshatist that "embraces" Platonism. The viewpoints of Platonism are respected, but without changing one's personal view that is Seshatism. See #19 (comment)

• Mathematics is a model of reality, but in one sense reality has a mathematical structure
• Mathematics is thoughts we have about reality, but in one sense reality can be known through mathematics
• Everything true is experienced directly, but in one sense everything true is discovered in mathematics