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
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
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
Rationale: Every logical argument must be defined in some language, and every language has limitations. Attempting to construct a logical argument while ignoring how the limitations of language might affect that argument is a bizarre approach. The correct acknowledgment of the interactions of logic and language explains almost all of the paradoxes, and resolves almost all of the contradictions, conundrums, and contentious issues in modern philosophy and mathematics.
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