If to prove is to explain, why does "I cannot explain" mean mathematics is incomplete?
From: |-|erc (h_at_r.c)
Date: 02/09/05
- Next message: Herman Jurjus: "Re: Successor Axiom: on what grounds TF?"
- Previous message: |-|erc: "Re: F(a) = ~F(a) HOW MANY OTHER SYNTACTICALLY CORRECT FORMULA DO YOU DISCARD?"
- Messages sorted by: [ date ] [ thread ]
Date: Thu, 10 Feb 2005 02:51:45 +1000
on the Doctor Who episode last night,
The Doctor asks a question to a robot
Robot : I CANNOT EXPLAIN
Doctor : Yes you can
The problem with adding a meaningful natural language term like PROOF
as a predicate to early mathematics is we don't get the full meaning of the
word in the predicate proof(x,y)
What is the difference between an explanation and a proof? NOTHING
Prove is a verb, mathematics is not the utility of semantic representation.
In expert systems the parser makes decisions, e.g. "the patient has measels".
As part of the expert decision procedure is a backtracking system,
"why is the diagnosis measels?"
and the expert system EXPLAINS why it made the decision it did.
"...the red blood cell count indicates... therefore..."
mathematics, as in current day practical mathematics, now and 100 years ago when all this
proof theory was invented, not platonic mathematics and its potential, but what we recognise as
mathematics, has nothing to do with logic, or sentences, or meaning, or interpretation, or understanding,
or data, or truth and falsity, or knowledge, beliefs, facts, a world, a universe, an object,
a verb, up or down, an intelligent agent, anything!
THEN, given this nothingness, some number theory, out of the blue, literally out of nowhere
they define a predicate PROOF! its no wonder it didn't work!! lets make it a function, make
up some formal definition.
NOT A CHANCE. yes there are proofs in mathematics, but there is no mathematics in proofs
as we know it. Why do you think you can formalise the English verb PROVE in mathematics
when there are 10,000 other contender words to tackle? Does the undefinability of SOCK
make it an incomplete pair?
You haven't come close to real analogy to what proofs do, what they mean, how they read, how
they are made, because the Universe Of Discourse is practically empty. Its like taking the
mathematics of Euler Walks and slapping on the "INFINITIVE IRREGULAR FORM", just
define it, it walks backwards oh well therefore some contradiciton must mean this conclustion.
> > THEN [...] out of the blue, literally out of nowhere they define a
> > predicate PROOF!
> >
>
> "Thus, as part of his formal system, Frege developed a strict
> understanding of a 'proof'. In essence, he defined a proof to be
> any finite sequence of statements such that each statement in
> the sequence either is an axiom or follows from previous members
> by a valid rule of inference. Thus, a proof of a theorem of
> logic, say Phi, is therefore any finite sequence of statements
> (with Phi the final statement in the sequence) such that each
> member of the sequence: (a) is one of the logical axioms of the
> formal system, or (b) follows from previous members of the
> sequence by a rule of inference. These are essentially the
> definitions that logicians still use today."
>
why did he use the word proof? why not sequitur? why is that a proof?
who does it prove what to and how and for what reason by whom?
Herc
-- 10,000 WITNESSES TO US GOVERNMENT ABUSING GENESIS ADAM IN PUBLIC FOR 4 YEARS
- Next message: Herman Jurjus: "Re: Successor Axiom: on what grounds TF?"
- Previous message: |-|erc: "Re: F(a) = ~F(a) HOW MANY OTHER SYNTACTICALLY CORRECT FORMULA DO YOU DISCARD?"
- Messages sorted by: [ date ] [ thread ]
Relevant Pages
|
