| ... Dedekind "DETERMINED" irrationals by cuts. He did not establish the
| ontology of reals. For him, real numbers were already given and only needed
| a further characterization. He never said that real "numbers are defined by
| cuts" in the sense that "define" has in today's set theory (eg. ZFC). The
| ontology of the reals was established thirty years later by B. Russell, who
| DEFINED them [See Russell, 1924, p.72, quoted in Boyer, 1949, p. 293].
Prezado Roberto,
I suppose I agree with what you mean, but not with what you say. In my
opinion the word "ontology" is not appropriate here. By the phrase "ontology
of reals numbers" you seem to suggest a formal definition of the concept.
However, if by "ontology" we understand a study concerned with the *nature*
(and existence) of real numbers, what IS a real number, really?...
Um abraco,
Julio GC