Science and Technology news... :: View topic - My talk about Godel to the post-grads.

Jesse F. Hughes · Guest

"Jesse F. Hughes" <jesse@phiwumbda.org> writes:

[quote]Simple failure to understand arguments is not enough -- especially
since, as it happens, there really *are* lots of bad arguments out
there. I>ve taught Kant>s ethics repeatedly and yet I still don>t
[/quote]
Pardon my poor writing. I didn>t mean to imply that Kant>s
arguments are an example of bad arguments. (But they sure
could be, near as I can figger.)

[quote]quite see how he goes from the claim that actions have moral worth
only if they are done for the sake of duty to his statement of the
categorical imperative (in its first form). The fact that I don>t
quite get this argument does not mean I am a crank -- not even if the
argument is correct.
--[/quote]
"Your people are about denial. Dreams versus reality. TELLING
yourselves you are great. Telling yourselves you are brilliant.
Telling yourselves you understand mathematics."
--James S. Harris: So obvious that it>s kind of sad.
** Posted from http://www.teranews.com **

Jesse F. Hughes · Guest

georgie <geo_cant@yahoo.com> writes:

[quote]Defending fanaticism is usually hard to recognize by the defender. On
occasion they have a small revelation that they>ve put themselves in
a very precarious situation. This is usually followed by a quick
rationalization that they are correct. The rationalization is easy to
detect when it involves putting someone off with name-calling like
"troll".
[/quote]
Yes, well, you found me out. Dear, oh dear.

Still, congrats! Well-fought, sir!
--
"[I]n mathematics there are two types of integers: primes and
composites. [...] It>s like how in the world there are mostly two
kinds of people: male and female [...] and lots of reasons for
interest in the differences." -- JSH on math/biology
** Posted from http://www.teranews.com **

georgie · Guest

On Oct 10, 8:43 am, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote:
[quote]georgie <geo_c...@yahoo.com> writes:
You must not have read the revised paper from 1989. In that paper,
Cantor proves that fanaticism is all that is required to hijack a
newsgroup.

How about a broccoli? As to your earlier comments, it>s a pertinent
observation that those in the news who valiantly battle the lie that
is the diagonal argument virtually never object to any axioms, but
rather blather in an incoherent fashion about supposed logical flaws
in the proof in a way that is an indication of nothing more than their
failure to understand the argument. It is of course entirely possible
to find infinitary set theory intellectually repugnant for all sorts
of intelligible reasons, but such dislike, when reasonable, is not
combined with inane refutations of the diagonal argument, which, as
mathematics goes, is simplicity itself.
[/quote]
So cranks are people who are incoherent? Does that mean if
one can>t understand swahili, then they must conclude that
the Bantu people are cranks? If they are incoherent, how do you
know they aren>t objecting to specific axioms?

MoeBlee · Guest

On Oct 10, 4:46 pm, Herbert Newman <nomail@invalid> wrote:

[quote]a
real/true crank will never try to make himself familiar with what has been
done/achieved in this field already
[/quote]
The literature of the subject is to a crank what citric acid is to a
termite, what garlic is to a vampire, what a press interview is to
Sarah Palin.

MoeBlee

georgie · Guest

On Oct 10, 8:35 pm, MoeBlee <jazzm...@hotmail.com> wrote:
[quote]On Oct 10, 4:46 pm, Herbert Newman <nomail@invalid> wrote:

a
real/true crank will never try to make himself familiar with what has been
done/achieved in this field already

The literature of the subject is to a crank what citric acid is to a
termite, what garlic is to a vampire, what a press interview is to
Sarah Palin.
[/quote]
I would have thought that the Cantor fanatics were also Palin
fanatics. Your statement seems to indicate your religous
fanaticism is strictly Cantorian.

MoeBlee · Guest

On Oct 10, 6:34 pm, georgie <geo_c...@yahoo.com> wrote:
[quote]On Oct 10, 8:43 am, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote:

georgie <geo_c...@yahoo.com> writes:
You must not have read the revised paper from 1989. In that paper,
Cantor proves that fanaticism is all that is required to hijack a
newsgroup.

How about a broccoli? As to your earlier comments, it>s a pertinent
observation that those in the news who valiantly battle the lie that
is the diagonal argument virtually never object to any axioms, but
rather blather in an incoherent fashion about supposed logical flaws
in the proof in a way that is an indication of nothing more than their
failure to understand the argument. It is of course entirely possible
to find infinitary set theory intellectually repugnant for all sorts
of intelligible reasons, but such dislike, when reasonable, is not
combined with inane refutations of the diagonal argument, which, as
mathematics goes, is simplicity itself.

So cranks are people who are incoherent?
[/quote]
Not just incoherent.

[quote] Does that mean if
one can>t understand swahili, then they must conclude that
the Bantu people are cranks?
[/quote]
What a RIDICULOUS analogy! Sheesh, I leave it as an exercise in
informal logic and critical thinking why that analogy has no force. It
is truly funny that you think it does/

[quote]If they are incoherent, how do you
know they aren>t objecting to specific axioms?
[/quote]
Oh for crying out loud! If someone writes an incoherent post that does
not include any verbiage that a competent reader can discern to assert
an objection to an axiom, then it is reasonable to say that no
objection to an axiom has been asserted in the post. Sheesh, by your
argument, if, for example, in a deposition I were asked whether I own
an electric toothbrush and I answer incoherently, then I can say to
the judge>s admonition to reply to the question, "If my answer is
incoherent then how do you know I didn>t give an answer?".

MoeBlee

george · Guest

On Oct 10, 7:18 pm, Scott <ToaTe...@gmail.com> wrote:
[quote]I still don>t see how you are explaining the problem away.
[/quote]
That is because you are so stupid that you don>t know what a truth
table is.

[quote]Suppose we have (F&~F) then we get:

{ F&~F, (F&~F)->G } |- G

then for some interpretations M1 and M2 we can have:

M1: { F&~F, (F&~F)->G } |= G
[/quote]
NO, we canNOT have that, because the thing on the left
DOES NOT HAVE ANY models! It does not have ANY interpretations!
THERE IS NO M1 such that M1|=(F&~F) !

[quote]M2: { F&~F, (F&~F)->G } |/= G
[/quote]
There is no such M2 either.

[quote]Thus, across all intepretations (ie, limited to the pure predicate
calculus) we have:

{ F&~F, (F&~F)->G } |- G
[/quote]
You are completely misusing |- here.
|- has NOTHING TO DO WITH ANY interpretations!
|- IS *SYNTACTIC* ! It means that the thing on the right
IS DERIVABLE BY INFERENCE RULES from the set OF FORMULAS
on the left! NOTHING EVER GETS interpreted here!

[quote]{ F&~F, (F&~F)->G } |/= G
[/quote]
You are completely misusing |= and |/= here AS WELL.
The thing on the left of |= MUST BE AN INTERPRETATION, or a model,
or at least a partial interpretation. The thing on the left CANNOT BE
a SET OF FORMULAS! If the thing on the left is a set of formulas,
like { (F&~F),( F&~F -> G) }, then the connective in the middle must
be
|- AND NOT
|= !
If you want to put |= in the middle then the thing on the left
MUST BE AN INTERPRETATION OF THE SIGNATURE
AND NOT
a set of formulas!
You could overload with a set of formulas IF the formulas DETERMINED
an interpretation (or even a class of them that all had the relevant
property),
but ANY set of formulas containing (F&~F) HAS NO models, has NO
satisfying
interpretations, and so CANNOT be used as an alias for ANY
interpretation!

In other words, every row of a truth-table assigns ONLY ONE truth-
value to every
propositional variable! One consequence of this is that NO truth-
table EVER
has even ONE row where F&~F comes up true!

[quote]My question is: We say from a contradiction any wff can be proved, but
I don>t see that.
[/quote]
You would see it if you could draw a truth-table.
All rows of ((F&~F)->G) ARE TRUE.
That implies that {F,~F} |- G
IS A SOUND rule of inference.

[quote]I see we can derive (symbolic manipluation to
generate the string of symbols forming the wff) any wff G,
[/quote]
THEN *THAT SETTLES* IT!

[quote]but not
prove (wff is true) every wff
[/quote]
DIPSHIT: DERIVING A FORMULA VIA SYMBOLIC MANIPULATION (applying
rules of inference to axioms *IS PROVING it!

[quote]G
[/quote]
WE DON>T prove that G is true!
We prove that IF F&~F is true, THEN G is true!
We derive G FROM (F&~F)! Since you can obviously equally well derive
~G
from the same premise, OBVIOUSLY, NONE OF THIS HAS ANYTHING TO DO
with proving G!

Why do you think we even disagree with you about this??

[quote]since G>s truth value is dependent
upon the intepretation.
[/quote]
But F&F->G>s truth-value IS NOT dependent on the interpretation,
and F&~F>s truth-value IS NOT dependent on the interpretation.

george · Guest

On Oct 10, 8:10 pm, Herbert Newman <nomail@invalid> wrote:
[quote]And the "explanation" is simple. F&~F |= G just means that G is true for
any interpretation which makes F&~F true. Since there is no interpretation
which makes F&~F true, this condition is vacuously satisfied (for any G).
[/quote]
But you see, Scott DID NOT WRITE F&~F|=G
(which is just as well). He wrote {(F&~F),(F&~F->G} |= G.
This is just abuse of notation. Yours isn>t much better, frankly
(though of course, since you know what you>re doing, and you abuse
notation CORRECTLY, your way is just acceptable overloading).

F&~F simply IS NOT THE *KIND* of thing, not the TYPE of thing, that
even
CAN go as a left argument of |= .
The left arguments of |= MUST be of type INTERPRETATION!
They must be of type MODEL.
F&~F DOES NOT HAVE ANY models! It CANNOT be there!
(Except basically as overload/alias for each&every model that
satisfies it;
but when NOTHING satisfies it, AGAIN, that means it fails to justify
putting
ANYthing there -- it is vacuously true NOT as a conditional with a
false
hypothesis but as a conjunction with 0 conjuncts!).

Correct is F&~F |- G.

F&~F does NOT |= ANYthing because it NEITHER IS NOR HAS ANY model.

Herbert Newman · Guest

On Fri, 10 Oct 2008 14:50:35 -0700 (PDT) MoeBlee wrote:

[quote]
Yet another of lwal>s nutty inferences.

Another strange thing is his unbroken believe that some cranks, say WM, are[/quote]
proponents of some coherent theories. And that>s REALLY nutty (in the face
of all the evidence to the contrary).

Herb

Herbert Newman · Guest

On Fri, 10 Oct 2008 16:20:42 -0700 (PDT) MoeBlee wrote:

[quote]
Another strange thing is his unbroken believe that some cranks, say WM, are
proponents of some coherent theories. And that>s REALLY nutty (in the face
of all the evidence to the contrary).

If I>m not mistaken, I think his point is that he>s interested in
seeing how one might work on crank (or "crank" as he uses scare
quotes) ideas to formulate them as actual theories; I don>t have the
impression that he thinks that the crank stuff come already formulated
as theories.

Right. That was what I meant. But since most of those stuff is _incoherent[/quote]
garbage_ it>s rather nutty undertaking, imho. (On, the other hand, some of
the "intuitions" of cranks have already been formulated in a more or less
satisfactory manner. Finitism and ultrafinitism come to mind. Of course a
real/true crank will never try to make himself familiar with what has been
done/achieved in this field already.)

Herb

Herbert Newman · Guest

On Fri, 10 Oct 2008 16:18:31 -0700 (PDT) Scott wrote:

[quote]
I think we all agree we have:

|- (F&~F) -> G

Which means that we can _prove_ the theorem[/quote]

(F&~F) -> G

in PC.

[quote]
and for all interpretations (F&~F) -> G is true, so we have:

|= (F&~F) -> G

Right. (PC is sound.)[/quote]

[quote]
Suppose we have (F&~F) then we get:

{ F&~F, (F&~F)->G } |- G

Right. But actually we have[/quote]

F&~F |- G.

Meta-Proof:

We already established that we can prove

(F&~F) -> G.

Consider the following proof (for it):

:
(n) (F&~F) -> G.

Then we can add the assumption F&~F to this proof, and with an application
of MP we get a proof (or a derivation) of/for G:

:
(n) (F&~F) -> G.
(n+1) F&~F Assumption
(n+2) G MP n, n+1

Hence we have shown

F&~F |- G.

qed.

[quote]
My question is: We say from a contradiction any wff can be proved, but
I don>t see that.

See meta-proof above. Since there>s a proof for (F&~F) -> G, from (the[/quote]
assumption) F&~F we can prove G, for any G (and F).

[quote]
I see we can derive (symbolic manipulation to generate the string
of symbols forming the wff) any wff G, ...

This is what is meant with "proved" here (i.e. in symbolic logic).[/quote]

[quote]
but not prove (wff is true) every wff G ...

No. That the wff A is _provable_ (in some system) does not (necessarily)[/quote]
mean that A is true (especially when the system is inconsistent).

[quote]
since G>s truth value is dependent upon the interpretation.

Indeed. Moreover, if G = H&~H it will NEVER be true (i.e. for NO[/quote]
interpretation).

[quote]
So, can you explain why you believe

{ F&~F, (F&~F)->G } |= G

is correct and ...

Actually, we have[/quote]

F&~F |= G

(since PC is sound).

And the "explanation" is simple. F&~F |= G just means that G is true for
any interpretation which makes F&~F true. Since there is no interpretation
which makes F&~F true, this condition is vacuously satisfied (for any G).

Herb

Herbert Newman · Guest

On Fri, 10 Oct 2008 16:20:42 -0700 (PDT) MoeBlee wrote:

[quote]
Another strange thing is his unbroken believe that some cranks, say WM, are
proponents of some coherent theories. And that>s REALLY nutty (in the face
of all the evidence to the contrary).

If I>m not mistaken, I think his point is that he>s interested in
seeing how one might work on crank (or "crank" as he uses scare
quotes) ideas to formulate them as actual theories; I don>t have the
impression that he thinks that the crank stuff come already formulated
as theories.

Right. That was what I meant. But since most of those stuff is _incoherent[/quote]
garbage_ it>s a rather nutty undertaking, imho. (On the other hand, some of
the "intuitions" of cranks have already been formulated in a more or less
satisfactory manner. Finitism and ultrafinitism come to mind. Of course a
real/true crank will never try to make himself familiar with what has been
done/achieved in this field already.)

Herb

Aatu Koskensilta · Guest

Herbert Newman <nomail@invalid> writes:

[quote]On the other hand, some of the "intuitions" of cranks have already
been formulated in a more or less satisfactory manner. Finitism and
ultrafinitism come to mind.
[/quote]
What more or less satisfactory formulation of ultrafinitism do you
have in mind?

--
Aatu Koskensilta (aatu.koskensilta@uta.fi)

"Wovon man nicht sprechen kann, darÃ¼ber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus

Aatu Koskensilta · Guest

georgie <geo_cant@yahoo.com> writes:

[quote]So cranks are people who are incoherent? Does that mean if
one can>t understand swahili, then they must conclude that
the Bantu people are cranks?
[/quote]
This is a peculiar line of thought in no apparent way related to
anything I said.

[quote]If they are incoherent, how do you know they aren>t objecting to
specific axioms?
[/quote]
For all I know they may object to anything. I was referring to their
criticism of the diagonal argument as presented in the news which
virtually never involves specific objections to any particular axiom
but is rather inane twaddle of no mathematical substance. This in
itself is not at all surprising; after all, as noted, the argument is
very simple, relies on no logical principles thought suspect by
anyone, and invokes no substantial mathematical axioms. It is of
course a different matter that if one dislikes infinite sets, and for
example posits that there are no such things, one will not accept
e.g. that the reals are uncountable -- not because of any doubts about
the validity of the diagonal argument but simply because on such
conception there is no set of reals.

--
Aatu Koskensilta (aatu.koskensilta@uta.fi)

"Wovon man nicht sprechen kann, darÃ¼ber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus

herbzet · Guest

georgie wrote:
[quote]MoeBlee wrote:

What in the world are you talking about?

By convention, people who can>t follow the discussion are
called CRANKS around here.
[/quote]
By "around here", surely you don>t mean sci.logic?

[...]

[quote]You just don>t get it, do you?
[/quote]
I get it. You>re a troll.

Ho-hum.

--
hz


www.GetXFactor.com Leading Technology, Science, Agriculture News and information	Part of the Identityscape.com network... getxfactor.com jmoodmusic.com smartbusinesschoices.com mintdepot.com lowfaresalways.com evangelicalview.com shoppingpodder.com soproudlywehail.com webnews.ws currenthumor.com

Science and Technology news... Forum Index -> Logic Forum	Goto page Previous 1, 2, 3 ... 218, 219, 220 ... 358, 359, 360 Next
Page 219 of 360