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Topic: A more stupid Italian mythmatician exists? Peano was a moron of
galactic proportions.

Replies: 3   Last Post: Oct 2, 2017 8:52 AM

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Registered: 1/23/16
Re: A more stupid Italian mythmatician exists? Peano was a moron of
galactic proportions.

Posted: Oct 2, 2017 5:38 AM
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On Saturday, September 30, 2017 at 8:12:47 PM UTC+2, John Gabriel wrote:
> On Saturday, 30 September 2017 12:58:40 UTC-5, Me wrote:
> > On Saturday, September 30, 2017 at 5:50:19 PM UTC+2, John Gabriel wrote:
> > >
> > > Peano assumes the prior existence of natural numbers.
> > >

> > Of course. But his axioms describe the PROPERTIES of those numbers, idiot.
> >

> Can you please reach some sort of agreement among your fellow [...]
> academics? Because many of them don't think the same way. For example
> [...] Dan Christensen is still under the belief that Peano's Crapaxioms
> define the natural numbers.


There's no need for a general agreement concerning all (mathematical) questions. Certain disagreements concerning foundational questions are natural and healthy.

I personally prefer the view that the Penao Axioms /characterise/ the natural numbers (by stating their fundamental properties).

> Now as for properties: Thank goodness the Ancient Greeks didn't need the
> [gineous] Peano to state the properties of numbers because <etc. etc.>


Their approach was admirable. But it does not satisfy modern requirements concerning formal precision.

Remember, PEANO used a formal language when stating his axioms.
See: http://www-history.mcs.st-andrews.ac.uk/Bookpages/Peano10.gif

> > > The successor function requires that the natural numbers are in place.
> > >

> > Sure. And its domain is IN, right.
> >
> > Nothing new, really. :-)
> >

> Oh boy, you have made an enemy out of [...] Dan Christensen.

Not sure about that. He may just POSTUALTE the existence of IN, such that ...

> > You can find a discussion of theses matters in Russell's "Introduction
> > to Mathematical Philosophy" (Chapter I):
> >
> > https://people.umass.edu/klement/imp/imp-ebk.pdf
> >

> No thanks. If you don't mind, I have a very low opinion of Russell...

Well, Russell... It's indeed rather ironic that *he* and Whitehead got all the fame, and not Frege. Actually, in the preface of PM they write: "In all questions of logical analysis, our chief debt is to Frege."

Much later people started to recognice that:

"It is to be regretted that this first comprehensive and thorough-going presentation of a mathematical logic and the derivation of mathematics from it [is] so greatly lacking in formal precision in the foundations [...] that it represents in this respect a considerable step backwards as compared with Frege." (Kurt Goedel, Russell's mathematical logic, 1944)





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