Classical Mathematical Logic

The Argument of Mathematics

“…Richard L. Epstein is the author of numerous works in both formal logic and critical thinking (for example, Epstein and Kernberger, 1998;Epstein, 2006). Richard L. Epstein is the author of numerous works in both formal logic and critical thinking (for example, Epstein and Kernberger, 1998;Epstein, 2006).…”

“…6 5 See the presentation by Carnielli and me in (Epstein and Carnielli, 1989) 6 Compare the presentation of Euclidean geometry in (Epstein, 2006). We've seen that it doesn't even make sense to say it is true, but only true of something, in the sense of applicable.…”

“…In (Epstein, 2006) I provide a derivation in first-order logic of the claim 'The identity is unique' from the axioms of group theory. But that is not a mathematical proof.…”

“…In the construction of [all mathematical sets of units which are entitled to that name] neither the ordinary language nor any symbolic language can have any other rôle than that of 15 As I show with examples in (Epstein, 2006), first-order logic is rarely appropriate because much mathematics requires second-order assumptions. Second-order logic and set-theory give no unique standard because there are many systems of those that differ too much.…”

“…Second-order logic and set-theory give no unique standard because there are many systems of those that differ too much. Moreover, it is quite common to establish a theorem in a formalized theory by semantic means rather than with a syntactic proof, as can be seen in (Epstein, 2006). Moreover, it is quite common to establish a theorem in a formalized theory by semantic means rather than with a syntactic proof, as can be seen in (Epstein, 2006).…”