Re: [PEIRCE-L] Higher-Order Logics (was Problems in mixing quantifiers with modal logic)

2024-03-13 Thread John F Sowa
Jerry, Jon, List, Peirce never used the term "graphic object". In his classification of the sciences, pure mathematics does not depend on anything else. Phaneroscopy is free to use any imaginable mathematical patterns to analyze, classify, and interpret anything in the phaneron, no matter

Re: [PEIRCE-L] Higher-Order Logics (was Problems in mixing quantifiers with modal logic)

2024-03-12 Thread Jerry LR Chandler
Jon, John, List: The attempts to interpret the on going discussions leads to simple questions about meaning of symbols and logics. Given a graphic object, how does one decipher the logical content of it? What types of semantics can be associated with what types of visual distinctions? How

Re: [PEIRCE-L] Higher-Order Logics (was Problems in mixing quantifiers with modal logic)

2024-03-11 Thread Jon Alan Schmidt
John, List: JFS: For every version of first-order logic, there is a fixed domain D1 of entities in the domain of quantification. Those entities could be anything of any kind--that includes abstractions, fictions, imaginary beasts, and even hypothetical or possible worlds. When using Beta EGs to

RE: [PEIRCE-L] Higher-Order Logics (was Problems in mixing quantifiers with modal logic)

2024-03-09 Thread John F Sowa
Jeff, Jon, List, In his 1885 Algebra of Logic, Peirce presented the modern versions of both first-order and second-order predicate logic. The only difference between his notation and the modern versions is the choice of symbols. Since Peano wanted to make his logic publishable by ordinary