Bruno Marchal wrote:
> It seems, but it isn't. Well, actually I have known *one* mathematician, > (a russian logician) who indeed makes a serious try to develop > some mathematics without that infinite act of faith (I don't recall > its name for the moment). Such attempt are known as "ultrafinitism". > Of course a lot of people (especially during the week-end) *pretend* > not doing that infinite act of faith, but do it all the time implicitly.
This is not what I meant. I did not refer to people not willing to accept that natural numbers exist at all but to people not wlling to accept that natural numbers exist *by themselves*. Rather, they want to see them either as only a production of human (or human-like) people or only a production of a God.
What I mean is that their arithmetical property are independent of us. Do you think those people believe that the proposition "17 is prime" is meaningless without a human in the neighborhood? Giving that I hope getting some understanding of the complex human from something simpler (number property) the approach of those people will never work, for me. Also, I would take (without added explanations) an expression like "numbers are a production of God" as equivalent to arithmetical realism. Of course if you add that God is a mathematical-conventionalist and that God could have chose that only even numbers exist, then I would disagree. (Despite my training in believing at least five impossible proposition each day before breakfast ;-)
And I said "unfortunately" because some not only do not want to see natural numbers as existing by themselves but they do not want the idea to be simply presented as logically possible and even see/designate evil in people working at popularizing it.
OK, but then some want you being dead because of the color of the skin, or the length of your nose, ... I am not sure it is not premature wanting to enlighten everyone at once ... I guess you were only talking about those hard-aristotelians who like to dismiss Plato's questions as childish. Evil ? Perhaps could you be more precise on those people. I have not met people seeing evil in arithmetical platonism, have you?