Re: Cantor's Theory sucks

Virgil said:
> In article <MPG.1cfbd11c385b3346989cb6@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
>
> > Virgil said:
> > > In article <MPG.1cf7ffaad287bcac989caa@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> > > Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> > >
> > > > Mathematics is NOT the science of truth. It is the science or discipline
> > > > > of inferring correct conclusions from a set of premises. The notion
> > > > > that
> > > > > mathematics is a geteway (or even THE gateway) to Truth has been dead
> > > > > and buried over a century.
> > > > Gee, Bob, that's what Dave Petry said in his initial post. I was taking a
> > > > different tack, but you seem to be agreeing while pretending to disagree.
> > > > When
> > > > you say "discipline of inferring correct conclusions ", what exactly do
> > > > you
> > > > mean by "correct, if not "true", or "having a truth value of 1"? How do
> > > > you
> > > > define "correct" independently of "truth"?
> > >
> > > The entire phrase was "It (mathematics) is the science or discipline
> > > of inferring correct conclusions from a set of premises."
> > >
> > > To leave out "from a set of premises" is a gross misrepresentation of
> > > what was actually said.
> > >
> > > An alternate, and less easily misrepresented, definition of mathematics
> > > might be "the study of logical consequences" which requires that there
> > > be something presumed from which those logical consequences are to be
> > > derived. This describes the axiomatic method of much of modern
> > > mathematics. It makes no pretense to discover absolute "truth" since the
> > > truth of its axiom systems is not presumed except as a convenient
> > > fiction for the purpose of studying the logical consequences of such
> > > presumptions.
> > >
> > > So TO's "take" on Bob's statement comes from a, possibly deliberate,
> > > misrepresentation of what Bob said.
> > >
> > > Typical TO.
> > >
> >
> > No, it really doesn't. there is a philosophical question here which has no
> > easy
> > answer, analogous to the points vs. lines discussion that has been going on
> > in
> > other threads. Either one can be taken as atomic and seen to generate the
> > other, but they should be defined together, and together generate the entire
> > system, such as geometry built from point AND lines. In this case, the
> > philosophical question is whether math is a subset of logic, or vice versa,
> > and
> > similarly, the two perspectives are equally valid. Mathematics deals with
> > finding "correct" answers to questions and is therefore dependent on some
> > notion of truth or falsehood
>
> Pure math, like formal logic, deals with finding the unavoidable
> consequences that derive from a given set of assumptions. It is always
> ultimately mere verification of the correctness of if-then statements
> without any presumption that the if clauses contain any ultimate truths.
Here you are speaking about deduction as if that is all there is to logic.
There are two sides to logic. On the inductive side, without which deduction
would have nothing to work with, rules are generated by detecting patterns in a
body of related facts, and formalizing those patterns in terms of rules,
postulates, or axioms. The deductive side then takes these axioms and applies
them to facts to derive conclusions. Now, if these conclusions are found to be
incorrect, we either have made a logical mistake in our deduction, or we have
uncovered some contradiction in the axioms we are applying. In the latter case,
the axiom set needs to be thrown back to the inductive side for analysis and
retooling. It seems fairly easy for people to follow rules that they are given,
and relatively hard for them to discover the rules on their own. Well, it may
be harder to think for yourself, but nothing that is truly worthwhile comes
easy. It's just that people are lazy, and want the answers handed to them.
>
> Applied math, Physics, Engineering, etc. are the ones who presume that
> there is some connection between axiom systems and physical reality.
>
>
>
> > When Bob says, "It (mathematics) is the science or discipline of
> > inferring correct conclusions from a set of premises," he is speaking
> > strictly about deductive logic, and assuming the correctness of the
> > premises. My question was not dependent on the use of the premises.
>
>
> > My question was about how he distinguishes the term "correct" from
> > the term "true". Perhaps, if the premises are false, we can derive a
> > "correct" result that is false, but, then, it's really not correct,
> > is it?
>
> Pure math only deals with correctness, and considers "truth" in your
> sense irrelevant. And what is correct in that sense is correct in the
> only relevant sense.
>
>
> Those who choose to apply that math to anything else are the ones who
> face the issue of "truth". If they misapply the pure math, that is not
> the pure mathematicians fault.
>
> Pure mathematicians are sort of like the tool makers for those applied
> mathematicians and other "mechanics" who use those tools.
>
> Don't blame the tool maker for the mechanic's errors.
>
Sorry, but when I try to unscrew something, and the screwdriver bends, I take
it back to the store, and get my money back. And if I buy a drill, and the bit
spins around at some weird angle tracing a cone, it's just not a drill, is it?
--
Smiles,

Tony
.

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