What are the key claims of Platonism and formalism Name one

What are the key claims of Platonism and formalism? Name one Mathematician from each camp.

Solution

Platonism:

Refers to a collection of metaphysical accounts of Mathematics.

The metaphysical accounts of Mathematics is the branch that entails theses concerning the existence and fundamental nature of Mathematical Ontology.

And metaphysical accounts of Mathematics is a variety of platonism iff it entails the following:

Existence of ontology, abstractness of antology and independence of ontologies.

Mathematician from this group is our famous Frege , who is father of thesis that all arithmetic derivations are derivable from general laws and defintions.

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Formalism:

The main idea behind formalism is one that Mathematics is akin to a game with no commitment to ontology.

Or Mathematics is not simply a proposition of abstract sectors of reality.

Briefly, it is the position to which naive philosophists gesture towards when pestered by questions as to nature of Mathematics.

Thomae is an example of mathematician in this field.