Fwd: Foundations and Foundationalism

[Joseph Vidal-Rosset]

Hello everyone,

About philosophical disagreements, I do not know better and deepest
books than Jules Vuillemin's book, I mean "What are philosophical systems?"

https://www.cambridge.org/core/books/what-are-philosophical-systems/12CC0EEF3C4372B0740E0A1BA74C13B9

@book{vuillemin_1986, place={Cambridge}, title={What Are Philosophical
Systems?}, DOI={10.1017/CBO9780511753336}, publisher={Cambridge
University Press}, author={Vuillemin, Jules}, year={1986}}

And also his book about Diodorus's Master Argument

https://press.uchicago.edu/ucp/books/book/distributed/N/bo3616790.html

@book{vuillemin1996a,
   title = {Necessity or {{Contingency}}: {{The Master Argument}}},
   author = {Vuillemin, Jules},
   year = {1996},
   series = {Center for the {{Study}} of {{Language}} and
{{Information}} - {{CSLI Lecture Notes}} 56},
   publisher = {{CSLI Publications}},
   isbn = {978-1-881526-85-8 1-881526-85-2 1-881526-86-0}
}

Vuillemin gave a seminal classification of *genuine* philosophical
systems that is to say systems that are based  on only one or two basic
assertions. It is an axiomatic theory of philosophical systems (similar
to Russell's analysis of Leibniz's philosophy) that should interest many
readers of the FOM list.

One of Vuillemin's points is that philosophical theories are essentially
*polemical*, by contrast with scientific theories. Another important
point is that every genuine philosophical theory *is* a foundation:
Realism (i.e. Platonism for Vuillemin), Conceptualism (for example
Aristotle's philosophy), Nominalism, Intuitionism and Skepticism are the
five classes of genuine philosophical systems and are all foundations of
knowledge (even Skepticism, in a destructive way).

I do not know what exactly "Foundationalism" means in mathematics, if no
distinction is made between classical mathematics and intuitionistic
mathematics for example, because these foundations are different.
Logical criteria draw distinctions between a classical (i.e.
non-constructive) proof and  an intuitionistic one, but the decision to
reject or to accept the validity of the former is purely philosophical.
Philosophy is both a free and a rational decision, according to
Vuillemin's theory.

Good discovery!

All the best,

Jo.