Platonism

Platonism:

The source of a multitude of irrational and unfounded assumptions about the infinite

Logic and Language:

Why logic is not independent of language and why the notion that language can be ignored leads to contradictions

The Myths of Platonism:

The assumption that certain supernatural things “exist” and the myth that humans can accurately describe these humanly inaccessible things

Platonism and the Diagonal Proof:

How Platonist assumptions that have been attached to Cantor’s Diagonal proof have created absurdities

Numbers, chairs and unicorns:

Platonists claim that numbers have an actual “existence” that is as real as the existence of chairs, rather than simply being human concepts

Platonism’s Logical Blunder:

The inherent fallacy in attempts at total abstraction without any consideration of language

The Indispensability Argument:

An attempt to prove that mathematical entities are real non-physical things that “exist” independently of any human concepts

Moderate Platonism:

Either non-physical metamathematical entities “exist” or they do not. But some Platonists claim that there can be a ‘moderate’ version of the belief that they “exist”

Mark Balaguer on Platonism:

Balaguer constructs a straw man argument to claim that there is no good argument against Platonism

Descartes’ Platonism:

A look at some Platonist aspects of René Descartes’ philosophy

The Platonist Rod Paradox:

An example of how the Platonist belief in the “existence” of an actual infinity leads to contradictions

Platonism according to Ulf Persson:

An attempt at promoting Platonism that only serves to show the paucity of any logic or evidence to support the notion of Platonism

The Platonist response to the flaw in Gödel’s proof:

A demonstration of the error in the claim that referring to entities that are non-physical but somehow “exist” can eliminate the flaw in Gödel’s proof

Shaughan Lavine’s “Understanding the Infinite”:

Lavine’s underlying beliefs show that his book title is a misnomer, as it reveals a lack of any deep understanding of the infinite