Re: Cantor's Theory sucks

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.

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.
.

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