Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

Topic: Why I think mathematics is really logic.
Replies: 4   Last Post: Jun 15, 2013 4:18 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Zaljohar@gmail.com

Posts: 2,665
Registered: 6/29/07
Re: Why I think mathematics is really logic.
Posted: Jun 15, 2013 12:36 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Jun 15, 6:04 pm, Charlie-Boo <shymath...@gmail.com> wrote:
> On Jun 15, 7:31 am, Zuhair <zaljo...@gmail.com> wrote:
>
>
> #1 Don't try to define math in terms of math.  Besides being circular
> reasoning, you are simply taking a subset of math, isolating and
> formalizing it.  Define math in informal non-mathematical terms.
>
> # 2. Know what level of abstraction you are at.  Don't define science,
> or communicating.  Talking about strings of symbols being generated
> above sounds like a model of communicating, the wrong level of
> abstraction.
>


No a model of communicating is string of symbols 'expressing' non
symbolic stuff usually, while here I'm speaking about a machinery of
producing symbols from symbols, this is not about communication.

> # 3.  And this is especially for you Zuhair: State exactly the goal,
> and then the approach before you are formal at all.  Getting into
> formalizing without a clear idea of how you are going to approach/
> solve your problem/goal is like programmers who write software without
> specifications (never mind technical design) or programming language
> committees who require all proposals to be in the form of actual
> constructs and syntax, rather than goals, approaches, and then
> formalization.  Or like talking about (YOU) formalizing a resolution
> to the liar paradox without having a clear idea (or any idea) how you
> intend to resolve it.  You generate solutions after you build an
> axiomatic system, not before.
>
> C-B


What has been referred to in the headpost is the question of whether
second order arithmetic can be interpreted in a system that is most
naively understood as a LOGICAL system. The system I spoke about
naturally and naively extends known logical systems, it is only
deriven by setting rules of formation of formulas of the language as
to avoid paradoxes and without any unnecessary concepts outside of
logic, so it would be a logical system. You may say that this system
is a sector of mathematics that I call as logic and that I'm reducing
the other sectors of mathematics to that sector, OK if you understand
it that way, no problem, the issue is whether this can be done, and
the above record showes that it can be done and naively so.

However I consider *all* parts of first order logic as being LOGICAL
and not mathematical, yes it uses symbols and ways commonly used in
mathematics like function symbols, variables, constants, natural
indices, recursive machinery, etc... *ALL* of those I maintain as
being legitamate parts of LOGIC, i.e. they are LOGICAL symbols and
machineries, that mathematics also uses those is just an overlap, it
gives no priority to mathematics over logic.

Zuhair



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.