| Topic: |
Science > Physics |
| User: |
"Lester Zick" |
| Date: |
21 May 2007 12:18:05 PM |
| Object: |
The Truth of Truly True Truth |
The Truth of Truly True Truth
~v~~
In his quest for truth the other day the confirmed empiric Uncle Al,
rather impolitely I thought, posed the following problem:
Hey Zick, perserverative boring spammer, tell us about algebras
defined by
not(not(p or q) or not(p or not(q)) = p
An expression which obviously reduces to
(p or not q) or (not p or q) = p
or
p or not p or not q or q = p
and which on the face of it appears falacious.
However it is also an expression which, even ignoring the "=", relies
mechanically on two explicit functional factors: "not" and "or"
neither of which Uncle Al demonstrates in terms of the other.
Consequently it is not possible to demonstrate the truth of that
expression until either is demonstrated true in terms of the other.
So the question presented really reduces to an issue of which is to be
demonstrated in terms of the other and whether we are to demonstrate
"or" as a function of "not" or "not" as a function of "or". Otherwise
we can never know either in terms of the other and the truth of the
expression can never be assayed definitively in exhaustive terms.
Now the common practice among mathematikers in essaying issues of
truth, especially in boolean terms, is to assume whatever conjunctions
appear necessary merely as axiomatic assumptions of truth and present
whatever properties they associate with them implicitly.Thus Aristotle
proceeded in framing his famous canons of logic and it has proven
incumbent on modern science and mathematics to proceed accordingly.
~v~~
However we must now ask whether this procedure can yield truth in
exhaustive terms?
Now it might be conceivable to mechanize "or" in terms of "not" but I
can think of no empiric who could suggest a way to mechanize "not" in
terms of "or" alone without the use of "not". Consequently we must
conclude that Uncle Al's epistemology is mystical and non mechanical
unless he intends to plagiarize my own demonstration of conjunctions
in terms of "not" alone.
~v~~
.
|
|
| User: "Michael Jørgensen" |
|
| Title: Re: The Truth of Truly True Truth |
22 May 2007 01:47:05 AM |
|
|
"Lester Zick" <dontbother@nowhere.net> wrote in message
news:20l353903c6nvmfhpiicqqj8ifk9tj0ksl@4ax.com...
The Truth of Truly True Truth
~v~~
In his quest for truth the other day the confirmed empiric Uncle Al,
rather impolitely I thought, posed the following problem:
Hey Zick, perserverative boring spammer, tell us about algebras
defined by
not(not(p or q) or not(p or not(q)) = p
An expression which obviously reduces to
(p or not q) or (not p or q) = p
How do you arrive at that? It certainly is not "obvious" to me...
I get "(p or q) and (p or not(q)) = p". And this reduces to "p and (q or not
q) = p", which seems obviously true in a Boolean algebra.
-Michael.
.
|
|
|
| User: "Wolf" |
|
| Title: Re: The Truth of Truly True Truth |
22 May 2007 10:56:42 AM |
|
|
Michael Jørgensen wrote:
"Lester Zick" <dontbother@nowhere.net> wrote in message
news:20l353903c6nvmfhpiicqqj8ifk9tj0ksl@4ax.com...
The Truth of Truly True Truth
~v~~
In his quest for truth the other day the confirmed empiric Uncle Al,
rather impolitely I thought, posed the following problem:
Hey Zick, perserverative boring spammer, tell us about algebras
defined by
not(not(p or q) or not(p or not(q)) = p
An expression which obviously reduces to
(p or not q) or (not p or q) = p
Zick doesn't know DeMorgan's theorem, is how.
I get "(p or q) and (p or not(q)) = p". And this reduces to "p and (q or not
q) = p", which seems obviously true in a Boolean algebra.
-Michael.
Quite so.
--
Wolf
"Don't believe everything you think." (Maxine)
.
|
|
|
| User: "" |
|
| Title: Re: The Truth of Truly True Truth |
22 May 2007 02:57:01 PM |
|
|
In sci.math Wolf <ElLoboViejo@ruddy.moss> wrote:
Michael Jørgensen wrote:
"Lester Zick" <dontbother@nowhere.net> wrote in message
news:20l353903c6nvmfhpiicqqj8ifk9tj0ksl@4ax.com...
The Truth of Truly True Truth
~v~~
In his quest for truth the other day the confirmed empiric Uncle Al,
rather impolitely I thought, posed the following problem:
Hey Zick, perserverative boring spammer, tell us about algebras
defined by
not(not(p or q) or not(p or not(q)) = p
An expression which obviously reduces to
(p or not q) or (not p or q) = p
Zick doesn't know DeMorgan's theorem, is how.
He also apparently does not know the difference between true and false.
When p is false, (p or not q) or (not p or q) is true, yet Lester
thinks that (p or not q) or (not p or q) = p.
Stephen
.
|
|
|
| User: "Lester Zick" |
|
| Title: Re: The Truth of Truly True Truth |
22 May 2007 06:34:30 PM |
|
|
On Tue, 22 May 2007 19:57:01 +0000 (UTC), wrote:
In sci.math Wolf <ElLoboViejo@ruddy.moss> wrote:
Michael Jørgensen wrote:
"Lester Zick" <dontbother@nowhere.net> wrote in message
news:20l353903c6nvmfhpiicqqj8ifk9tj0ksl@4ax.com...
The Truth of Truly True Truth
~v~~
In his quest for truth the other day the confirmed empiric Uncle Al,
rather impolitely I thought, posed the following problem:
Hey Zick, perserverative boring spammer, tell us about algebras
defined by
not(not(p or q) or not(p or not(q)) = p
An expression which obviously reduces to
(p or not q) or (not p or q) = p
Zick doesn't know DeMorgan's theorem, is how.
He also apparently does not know the difference between true and false.
Yeah, look who's talking. The same guy who can't use the words "true"
and "modern math" together in one sentence with a straight face.
When p is false, (p or not q) or (not p or q) is true,
Except we're not exactly sure how you arrive at that conclusion,
Stephen. It would seem you have some mysterious connection to the
universe of truth the rest of us aren't privy to. Mayhap when you get
out of the privy you might advise us of the source of your divination.
yet Lester
thinks that (p or not q) or (not p or q) = p.
Well see, Stephen, what I find so irritating about you is that when
you misreprent what I think you don't even have the courtesy to
misrepresent what I say accurately. I don't think the above expression
is true or false or sideways or upside down or really much of anything
besides what you wish it to be for the simple reason you're much too
lazy or stupid to reduce "or" and "not" in mechanical terms but
apparently not too lazy or stupid to make all kinds of absurd claims
as to what you wish I thought so your sloth and stupidity wouldn't be
quite so intuitively obvious to the casual observer.
~v~~
.
|
|
|
|
|
| User: "Lester Zick" |
|
| Title: Re: The Truth of Truly True Truth |
22 May 2007 12:18:19 PM |
|
|
On Tue, 22 May 2007 11:56:42 -0400, Wolf <ElLoboViejo@ruddy.moss>
wrote:
Michael Jørgensen wrote:
"Lester Zick" <dontbother@nowhere.net> wrote in message
news:20l353903c6nvmfhpiicqqj8ifk9tj0ksl@4ax.com...
The Truth of Truly True Truth
~v~~
In his quest for truth the other day the confirmed empiric Uncle Al,
rather impolitely I thought, posed the following problem:
Hey Zick, perserverative boring spammer, tell us about algebras
defined by
not(not(p or q) or not(p or not(q)) = p
An expression which obviously reduces to
(p or not q) or (not p or q) = p
Zick doesn't know DeMorgan's theorem, is how.
I get "(p or q) and (p or not(q)) = p". And this reduces to "p and (q or not
q) = p", which seems obviously true in a Boolean algebra.
-Michael.
Quite so.
Well ok, Wolf, that's one for the establishment. I should have reduced
the statement to "(p or not q) nor (not p or q)" and I apologize for
the error and withdraw the comment. It's one of the main reasons I
hate these fucking conjunctions, if you'll pardon my french. However
it doesn't change the nature or truth of the rest of my comments. You
just can't get at the truth of boolean propositions in general without
reducing conjunctions to "not" because you're having to assume the
truth of different things in terms of one another without analyzing or
knowing the truth of either. However based on your prior track record
you won't have the cujones to address the truth of that proposition.
~v~~
.
|
|
|
|
|
| User: "Lester Zick" |
|
| Title: Re: The Truth of Truly True Truth |
22 May 2007 12:09:19 PM |
|
|
On Tue, 22 May 2007 08:47:05 +0200, "Michael Jørgensen"
<ingen@ukendt.dk> wrote:
"Lester Zick" <dontbother@nowhere.net> wrote in message
news:20l353903c6nvmfhpiicqqj8ifk9tj0ksl@4ax.com...
The Truth of Truly True Truth
~v~~
In his quest for truth the other day the confirmed empiric Uncle Al,
rather impolitely I thought, posed the following problem:
Hey Zick, perserverative boring spammer, tell us about algebras
defined by
not(not(p or q) or not(p or not(q)) = p
An expression which obviously reduces to
(p or not q) or (not p or q) = p
How do you arrive at that? It certainly is not "obvious" to me...
You're correct. Unfortunately I've made this mistake twice in the last
six months or so and I apologize for it and withdraw the comment. I
should have reduced the expression to "(p or not q) nor (not p or q)".
I get "(p or q) and (p or not(q)) = p". And this reduces to "p and (q or not
q) = p", which seems obviously true in a Boolean algebra.
Having said which above however I stand by the balance of my comments
which you omitted. What is obviously true to to you in boolean algebra
is precisely the point. And without a mechanical reduction for boolean
conjunctions in terms of "not" it's impossible to determine the actual
truth of boolean propositions. All you can do is assume the truth of
what appears obvious to you.
~v~~
.
|
|
|
| User: "Bob Cain" |
|
| Title: Re: The Truth of Truly True Truth |
22 May 2007 06:55:57 PM |
|
|
Lester Zick wrote:
On Tue, 22 May 2007 08:47:05 +0200, "Michael Jørgensen"
<ingen@ukendt.dk> wrote:
"Lester Zick" <dontbother@nowhere.net> wrote in message
news:20l353903c6nvmfhpiicqqj8ifk9tj0ksl@4ax.com...
The Truth of Truly True Truth
~v~~
In his quest for truth the other day the confirmed empiric Uncle Al,
rather impolitely I thought, posed the following problem:
Hey Zick, perserverative boring spammer, tell us about algebras
defined by
not(not(p or q) or not(p or not(q)) = p
An expression which obviously reduces to
(p or not q) or (not p or q) = p
How do you arrive at that? It certainly is not "obvious" to me...
You're correct. Unfortunately I've made this mistake twice in the last
six months or so and I apologize for it and withdraw the comment. I
should have reduced the expression to "(p or not q) nor (not p or q)".
I get "(p or q) and (p or not(q)) = p". And this reduces to "p and (q or not
q) = p", which seems obviously true in a Boolean algebra.
Having said which above however I stand by the balance of my comments
which you omitted. What is obviously true to to you in boolean algebra
is precisely the point. And without a mechanical reduction for boolean
conjunctions in terms of "not" it's impossible to determine the actual
truth of boolean propositions. All you can do is assume the truth of
what appears obvious to you.
~v~~
Thus Lester's central principle, "Whether I'm right or I'm wrong, I'm
right."
Bob
--
"Things should be described as simply as possible, but no simpler."
A. Einstein
.
|
|
|
| User: "Phineas T Puddleduck" |
|
| Title: Re: The Truth of Truly True Truth |
22 May 2007 06:59:25 PM |
|
|
In article <g6Kdne7zT66iHs7bnZ2dnUVZ_tvinZ2d@giganews.com>,
Bob Cain <arcane@arcanemethods.com> wrote:
Lester Zick wrote:
On Tue, 22 May 2007 08:47:05 +0200, "Michael Jørgensen"
<ingen@ukendt.dk> wrote:
"Lester Zick" <dontbother@nowhere.net> wrote in message
news:20l353903c6nvmfhpiicqqj8ifk9tj0ksl@4ax.com...
The Truth of Truly True Truth
~v~~
In his quest for truth the other day the confirmed empiric Uncle Al,
rather impolitely I thought, posed the following problem:
Hey Zick, perserverative boring spammer, tell us about algebras
defined by
not(not(p or q) or not(p or not(q)) = p
An expression which obviously reduces to
(p or not q) or (not p or q) = p
How do you arrive at that? It certainly is not "obvious" to me...
You're correct. Unfortunately I've made this mistake twice in the last
six months or so and I apologize for it and withdraw the comment. I
should have reduced the expression to "(p or not q) nor (not p or q)".
I get "(p or q) and (p or not(q)) = p". And this reduces to "p and (q or
not
q) = p", which seems obviously true in a Boolean algebra.
Having said which above however I stand by the balance of my comments
which you omitted. What is obviously true to to you in boolean algebra
is precisely the point. And without a mechanical reduction for boolean
conjunctions in terms of "not" it's impossible to determine the actual
truth of boolean propositions. All you can do is assume the truth of
what appears obvious to you.
~v~~
Thus Lester's central principle, "Whether I'm right or I'm wrong, I'm
right."
Or is that
true or not true = true
;-)
--
COOSN-174-07-82116: Official Science Team mascot and alt.astronomy's favourite
poster (from a survey taken of the saucerhead high command).
Sacred keeper of the Hollow Sphere, and the space within the Coffee Boy
singularity.
.
|
|
|
|
| User: "Lester Zick" |
|
| Title: Re: The Truth of Truly True Truth |
23 May 2007 01:05:47 PM |
|
|
On Tue, 22 May 2007 16:55:57 -0700, Bob Cain
<arcane@arcanemethods.com> wrote:
Lester Zick wrote:
On Tue, 22 May 2007 08:47:05 +0200, "Michael Jørgensen"
<ingen@ukendt.dk> wrote:
"Lester Zick" <dontbother@nowhere.net> wrote in message
news:20l353903c6nvmfhpiicqqj8ifk9tj0ksl@4ax.com...
The Truth of Truly True Truth
~v~~
In his quest for truth the other day the confirmed empiric Uncle Al,
rather impolitely I thought, posed the following problem:
Hey Zick, perserverative boring spammer, tell us about algebras
defined by
not(not(p or q) or not(p or not(q)) = p
An expression which obviously reduces to
(p or not q) or (not p or q) = p
How do you arrive at that? It certainly is not "obvious" to me...
You're correct. Unfortunately I've made this mistake twice in the last
six months or so and I apologize for it and withdraw the comment. I
should have reduced the expression to "(p or not q) nor (not p or q)".
I get "(p or q) and (p or not(q)) = p". And this reduces to "p and (q or not
q) = p", which seems obviously true in a Boolean algebra.
Having said which above however I stand by the balance of my comments
which you omitted. What is obviously true to to you in boolean algebra
is precisely the point. And without a mechanical reduction for boolean
conjunctions in terms of "not" it's impossible to determine the actual
truth of boolean propositions. All you can do is assume the truth of
what appears obvious to you.
~v~~
Thus Lester's central principle, "Whether I'm right or I'm wrong, I'm
right."
Gee, Bob, this is a real puzzler. I say two things of which the first
is incorrect. I acknowledge this and withdraw the comment while
continuing to maintain the truth of the second comment. It looks like
what you're suggesting is that I can only be right if I'm never wrong,
never admit mistakes, and pontificate extemporaneously together with
arbitrary assumptions of and a totally reckless disregard for truth
the way empirics such as yourself do, all the while indulging in
psychological character assassination instead of scientific criticism.
You oughta run for office.
~v~~
.
|
|
|
|
|
|
|
| User: "Owen" |
|
| Title: Re: The Truth of Truly True Truth |
30 May 2007 07:58:48 AM |
|
|
On May 21, 1:18 pm, Lester Zick <dontbot...@nowhere.net> wrote:
The Truth of Truly True Truth
~v~~
In his quest for truth the other day the confirmed empiric Uncle Al,
rather impolitely I thought, posed the following problem:
Hey Zick, perserverative boring spammer, tell us about algebras
defined by
not(not(p or q) or not(p or not(q)) = p
An expression which obviously reduces to
(p or not q) or (not p or q) = p
No it does not reduce to this expression, rather it reduces to (p or
not q) and (not p or q).
or
p or not p or not q or q = p
and which on the face of it appears falacious.
p or not p or not q or q = p, is clearly false, unless p is
tautologous.
However it is also an expression which, even ignoring the "=", relies
mechanically on two explicit functional factors: "not" and "or"
neither of which Uncle Al demonstrates in terms of the other.
Consequently it is not possible to demonstrate the truth of that
expression until either is demonstrated true in terms of the other.
So the question presented really reduces to an issue of which is to be
demonstrated in terms of the other and whether we are to demonstrate
"or" as a function of "not" or "not" as a function of "or". Otherwise
we can never know either in terms of the other and the truth of the
expression can never be assayed definitively in exhaustive terms.
Wrong again, 'or' cannot be expressed solely by 'not'.
Nor can 'not' be solely expressed by 'or'.
Now the common practice among mathematikers in essaying issues of
truth, especially in boolean terms, is to assume whatever conjunctions
appear necessary merely as axiomatic assumptions of truth and present
whatever properties they associate with them implicitly.Thus Aristotle
proceeded in framing his famous canons of logic and it has proven
incumbent on modern science and mathematics to proceed accordingly.
~v~~
However we must now ask whether this procedure can yield truth in
exhaustive terms?
Now it might be conceivable to mechanize "or" in terms of "not" but I
can think of no empiric who could suggest a way to mechanize "not" in
terms of "or" alone without the use of "not". Consequently we must
conclude that Uncle Al's epistemology is mystical and non mechanical
unless he intends to plagiarize my own demonstration of conjunctions
in terms of "not" alone.
Conjunction cannot be expressed by only using 'not' or by only using
'or'. But it can be expressed by using both 'not' and 'or'; (p & q)
=df ~(~p v ~q).
~v~~
.
|
|
|
| User: "Lester Zick" |
|
| Title: Re: The Truth of Truly True Truth |
30 May 2007 01:43:53 PM |
|
|
On 30 May 2007 05:58:48 -0700, Owen <owenholden@rogers.com> wrote:
On May 21, 1:18 pm, Lester Zick <dontbot...@nowhere.net> wrote:
The Truth of Truly True Truth
~v~~
In his quest for truth the other day the confirmed empiric Uncle Al,
rather impolitely I thought, posed the following problem:
Hey Zick, perserverative boring spammer, tell us about algebras
defined by
not(not(p or q) or not(p or not(q)) = p
An expression which obviously reduces to
(p or not q) or (not p or q) = p
No it does not reduce to this expression, rather it reduces to (p or
not q) and (not p or q).
or
p or not p or not q or q = p
and which on the face of it appears falacious.
p or not p or not q or q = p, is clearly false, unless p is
tautologous.
Pay attention. I've already apologized for and withdrawn the claims
above.
However it is also an expression which, even ignoring the "=", relies
mechanically on two explicit functional factors: "not" and "or"
neither of which Uncle Al demonstrates in terms of the other.
Consequently it is not possible to demonstrate the truth of that
expression until either is demonstrated true in terms of the other.
So the question presented really reduces to an issue of which is to be
demonstrated in terms of the other and whether we are to demonstrate
"or" as a function of "not" or "not" as a function of "or". Otherwise
we can never know either in terms of the other and the truth of the
expression can never be assayed definitively in exhaustive terms.
Wrong again, 'or' cannot be expressed solely by 'not'.
Nor can 'not' be solely expressed by 'or'.
Gee, that's swell. Thanks for your opinion. But I might suggest you
raise the issue on the appropriate venue "Epistemology 401:
Tautological Mechanics" where I do just that.
Now the common practice among mathematikers in essaying issues of
truth, especially in boolean terms, is to assume whatever conjunctions
appear necessary merely as axiomatic assumptions of truth and present
whatever properties they associate with them implicitly.Thus Aristotle
proceeded in framing his famous canons of logic and it has proven
incumbent on modern science and mathematics to proceed accordingly.
~v~~
However we must now ask whether this procedure can yield truth in
exhaustive terms?
Now it might be conceivable to mechanize "or" in terms of "not" but I
can think of no empiric who could suggest a way to mechanize "not" in
terms of "or" alone without the use of "not". Consequently we must
conclude that Uncle Al's epistemology is mystical and non mechanical
unless he intends to plagiarize my own demonstration of conjunctions
in terms of "not" alone.
Conjunction cannot be expressed by only using 'not' or by only using
'or'. But it can be expressed by using both 'not' and 'or'; (p & q)
=df ~(~p v ~q).
Yes, well, once again I appreciate your opinion.
~v~~
.
|
|
|
|
| User: "herbzet" |
|
| Title: Re: The Truth of Truly True Truth |
31 May 2007 02:02:48 AM |
|
|
Owen wrote:
p or not p or not q or q = p, is clearly false, unless p is
tautologous.
This is a very common and natural way of stating the matter. It
is a good illustration of the tendency to call a tautology "true",
and hence a non-tautology "false". It is but a step to say that,
since a tautology is logically true, that the formula is clearly
"logically false".
It is also a good illustration of the the typical failure to
distinguish between a proposition and its logical form, i.e.,
a formula; usually a harmless conflation, but sometimes it
leads to confusion.
Another way to put the matter would have been to say that
p or not p or not q or q = p
is neither true nor false, but is a contingent formula; that is,
its truth-value is contingent upon the truth-value of p.
Or to say that the formula is not logically true, unless p is.
In general, formulae are not true or false: propositions (which
are instantiations of formulae) are true or false. The word
"tautology" is applied, sometimes confusingly, to both formulae
and propositions.
This is not a personal attack on you, Owen. These are very
common imprecisions in informal discussions. Usually they
don't matter -- sometimes they do.
[...]
Conjunction cannot be expressed by only using 'not' or by only using
'or'. But it can be expressed by using both 'not' and 'or'; (p & q)
=df ~(~p v ~q).
That is the correct standard accounting of things. But of course,
Lester has his own way of viewing things.
Hi, Lester.
I'm just briefly dropping in to this discussion to mention something
that might be of use to you (or not -- it's hard to tell!):
The propositional operators "and", "or" and "not" can all be defined (in
the
standard sense of "definition") by the single binary operator "nor"
which has the standard symbolization "|", and is itself defined
by the truth table
p | q | p|q
---|---|------
T | T | F
T | F | F
F | T | F
F | F | T
Thus, a formula "p nor q" is true when (surprise!) neither p nor
q is true, and is otherwise false.
Therefore we can define "not" as "p nor p":
p | p|p
---|------
T | F
F | T
We can then define "or" as "not (p nor q)": ~(p|q) = (p|q) | (p|q)
and define "and" as "(not p) nor (not q)": (~p|~q) = (p|p) | (q|q).
Very symmetrical.
As a matter of fact we can define _any_ propositional operator solely
in terms of "nor"! -- though it's a tedious exercise.
-- Intermezzo --
When I was in computer school we learned that computers are designed
to use "positive logic" or "negative logic". This means that the
designer of the electronic logic will use two voltages: a more
positive voltage and a less positive voltage -- binary code, right?
If the designer uses the more positive voltage to represent 1 or
logical "true" and the less positive voltage to represent 0 or
logical "false", that is "positive logic".
If the designer uses the more positive voltage to represent 0 or
logical "false" and the less positive voltage to represent 1 or
logical "true", that is "negative logic".
-- Meanwhile --
If we take the truth table for "nor" and reverse all the truth
values, we get the propositional operator that is "dual" to "nor"
-- we get the "nand" operator (symbol "/"):
p | q | p/q
---|---|------
F | F | T
F | T | T
T | F | T
T | T | F
We should really flip this 180 degrees so it is upside-up:
p | q | p/q
---|---|------
T | T | F
T | F | T
F | T | T
F | F | T
This "nand" operator is thus true when NOT (p and q are true), and
otherwise false. Not and. Nand. Get it?
The propositional operators "nor" and "nand" are said to be "dual"
to each other because of -- positive and negative logic. An
electronic "nor" gate becomes a "nand" gate when you switch from
positive logic to negative logic. A "nand" gate becomes a "nor"
gate when you switch from positive to negative logic. They are
essentially the _same_ operator -- *****-backwards and upside-down.
We can therefore use the "nand" propositional operator to define
"not", "and" and "or", and in essentially the exact same way as
we did with "nor":
Thus we define "not" as "p nand p":
p | p/p
---|------
T | F
F | T
We can then define "and" as "not (p nand q)": ~(p/q) = (p/q) / (p/q)
and define "or" as "(not p) nand (not q)": (~p/~q) = (p/p) / (q/q).
Very symmetrical.
As a matter of fact we can define _any_ propositional operator solely
in terms of "nand"! -- though it's a tedious exercise.
"Nor" and "nand" are the only two-place operators that can define
all other propositional operators. But there are other operators
that can also do that: they are just less-convenient-to-use
three-place operators, four-place operators, etc., etc.
I don't know if any of this applies to your way seeing things,
but what the hell, it might be useful if you decide to design
logic circuits.
--
hz
--
Posted via a free Usenet account from http://www.teranews.com
.
|
|
|
| User: "Owen" |
|
| Title: Re: The Truth of Truly True Truth |
31 May 2007 03:58:32 AM |
|
|
On May 31, 3:02 am, herbzet <herb...@gmail.com> wrote:
Owen wrote:
p or not p or not q or q = p, is clearly false, unless p is
tautologous.
This is a very common and natural way of stating the matter. It
is a good illustration of the tendency to call a tautology "true",
and hence a non-tautology "false". It is but a step to say that,
since a tautology is logically true, that the formula is clearly
"logically false".
All tautologies are true, and some non-tautologies are also true, eg.
empirical truths are not tautologies and they are true.
not(not(p or q) or not(p or not(q)) = p, is true when p is true and it
is false when p is false. ie. they are logically equivalent.
Lester's 'obvious' equivalent...
p or not p or not q or q = p, is true if p is tautologous and it is
false otherwise.
p or not p or not q or q = empirical falsity, is false.
p or not p or not q or q = empirical truth, is false.
p or not p or not q or q = logical falsity, is false.
p or not p or not q or q = logical truth, is true.
Lester's second attemt is also wrong...
Lester:
"Well ok, Wolf, that's one for the establishment. I should have
reduced the statement to "(p or not q) nor (not p or q)" and I
apologize for the error and withdraw the comment."
((p or not q) nor (not p or q)) = p, is true iff p is contradictory.
It looks like Lester will have to apologise again.
I wonder what his next obvious equivalent will be ?!
It is also a good illustration of the the typical failure to
distinguish between a proposition and its logical form, i.e.,
a formula; usually a harmless conflation, but sometimes it
leads to confusion.
Another way to put the matter would have been to say that
p or not p or not q or q = p
is neither true nor false, but is a contingent formula; that is,
its truth-value is contingent upon the truth-value of p.
Or to say that the formula is not logically true, unless p is.
In general, formulae are not true or false: propositions (which
are instantiations of formulae) are true or false. The word
"tautology" is applied, sometimes confusingly, to both formulae
and propositions.
This is not a personal attack on you, Owen. These are very
common imprecisions in informal discussions. Usually they
don't matter -- sometimes they do.
[...]
Conjunction cannot be expressed by only using 'not' or by only using
'or'. But it can be expressed by using both 'not' and 'or'; (p & q)
=df ~(~p v ~q).
That is the correct standard accounting of things. But of course,
Lester has his own way of viewing things.
Where do you think that Lester makes sense??
Is there anyplace where he is coherent at all?
.
|
|
|
| User: "Lester Zick" |
|
| Title: Re: The Truth of Truly True Truth |
31 May 2007 12:42:51 PM |
|
|
On 31 May 2007 01:58:32 -0700, Owen <owenholden@rogers.com> wrote:
All tautologies are true, and some non-tautologies are also true, eg.
empirical truths are not tautologies and they are true.
Not all tautologies are true and empirical observations are neither
true nor false.
~v~~
.
|
|
|
|
| User: "Lester Zick" |
|
| Title: Re: The Truth of Truly True Truth |
31 May 2007 12:48:49 PM |
|
|
On 31 May 2007 01:58:32 -0700, Owen <owenholden@rogers.com> wrote:
Lester's second attemt is also wrong...
Lester:
"Well ok, Wolf, that's one for the establishment. I should have
reduced the statement to "(p or not q) nor (not p or q)" and I
apologize for the error and withdraw the comment."
((p or not q) nor (not p or q)) = p, is true iff p is contradictory.
It looks like Lester will have to apologise again.
I wonder what his next obvious equivalent will be ?!
I have no intention of venturing further into the quagmire of boolean
conjunctive logic, Owen. That's why I apologized and withdrew the
comment in the first place. What I find remarkable however is that
despite that and despite the fact the second half of the original post
to the thread stands as written and "Epistemology 401: Tautological
Mechanics" stands as written all people want to talk about is this
kind of idiotic conjunctive nonsense. Get a life for christ sake.
~v~~
.
|
|
|
|
|
| User: "Lester Zick" |
|
| Title: Re: The Truth of Truly True Truth |
31 May 2007 02:38:14 PM |
|
|
On Thu, 31 May 2007 03:02:48 -0400, herbzet <herbzet@gmail.com> wrote:
Hi, Lester.
I'm just briefly dropping in to this discussion to mention something
that might be of use to you (or not -- it's hard to tell!):
The propositional operators "and", "or" and "not" can all be defined (in
the
standard sense of "definition") by the single binary operator "nor"
which has the standard symbolization "|", and is itself defined
by the truth table
p | q | p|q
---|---|------
T | T | F
T | F | F
F | T | F
F | F | T
Thus, a formula "p nor q" is true when (surprise!) neither p nor
q is true, and is otherwise false.
Therefore we can define "not" as "p nor p":
p | p|p
---|------
T | F
F | T
Here I have a problem, Herb. Your statement above looks circular in
the sense that you have "not" defined in terms of "nor" or "not or".
We can then define "or" as "not (p nor q)": ~(p|q) = (p|q) | (p|q)
and define "and" as "(not p) nor (not q)": (~p|~q) = (p|p) | (q|q).
Very symmetrical.
As a matter of fact we can define _any_ propositional operator solely
in terms of "nor"! -- though it's a tedious exercise.
I'm sure it is. I've also seen claims that boolean conjunctions can
all be reduced to various combinations of "not and" as well. The whole
subject of boolean conjunctive logic strikes me as extremely tedious.
They've confused the issue from Aristotle's canons of logic right up
to the present.
-- Intermezzo --
When I was in computer school we learned that computers are designed
to use "positive logic" or "negative logic". This means that the
designer of the electronic logic will use two voltages: a more
positive voltage and a less positive voltage -- binary code, right?
If the designer uses the more positive voltage to represent 1 or
logical "true" and the less positive voltage to represent 0 or
logical "false", that is "positive logic".
I doubt you were around in the late sixties and early seventies, Herb,
but IBM had a tape recording technique called NRZI for non return to
zero inverted.
If the designer uses the more positive voltage to represent 0 or
logical "false" and the less positive voltage to represent 1 or
logical "true", that is "negative logic".
-- Meanwhile --
If we take the truth table for "nor" and reverse all the truth
values, we get the propositional operator that is "dual" to "nor"
-- we get the "nand" operator (symbol "/"):
p | q | p/q
---|---|------
F | F | T
F | T | T
T | F | T
T | T | F
We should really flip this 180 degrees so it is upside-up:
p | q | p/q
---|---|------
T | T | F
T | F | T
F | T | T
F | F | T
This "nand" operator is thus true when NOT (p and q are true), and
otherwise false. Not and. Nand. Get it?
The propositional operators "nor" and "nand" are said to be "dual"
to each other because of -- positive and negative logic. An
electronic "nor" gate becomes a "nand" gate when you switch from
positive logic to negative logic. A "nand" gate becomes a "nor"
gate when you switch from positive to negative logic. They are
essentially the _same_ operator -- *****-backwards and upside-down.
We can therefore use the "nand" propositional operator to define
"not", "and" and "or", and in essentially the exact same way as
we did with "nor":
Thus we define "not" as "p nand p":
p | p/p
---|------
T | F
F | T
We can then define "and" as "not (p nand q)": ~(p/q) = (p/q) / (p/q)
and define "or" as "(not p) nand (not q)": (~p/~q) = (p/p) / (q/q).
Very symmetrical.
As a matter of fact we can define _any_ propositional operator solely
in terms of "nand"! -- though it's a tedious exercise.
Once more the old "not and" strikes me as circular.
"Nor" and "nand" are the only two-place operators that can define
all other propositional operators. But there are other operators
that can also do that: they are just less-convenient-to-use
three-place operators, four-place operators, etc., etc.
In other words the only thing in common among boolean definitions is
the "not" part of "nor" and "nand".
I don't know if any of this applies to your way seeing things,
but what the hell, it might be useful if you decide to design
logic circuits.
Yeah I know what you mean. But if you'll excuse a little excursion
into the way I see things in general and the mechanical reduction of
boolean conjunctions in terms of "not" alone:
It occurs to me that boolean conjunctions and conjunctive logic are
defective in mechanical terms. For one thing there seems to be an
implicit assumption that boolean conjunctive logic only applies to
binary operands and I see no necessity for that in the conjunctions
themselves.
For another it occurs to me that there is no universal reduction for
the logic in general mechanical terms. That is we can reduce the logic
by means of "nor" or "nand" but those conjunctions themselves are
still composite functions of "not" plus "or" or "and". So we haven't
really reduced the conjunctive logic to any single function.
On the other hand if we approach the subject from the perspective of
"not" by itself the various boolean conjunctions are reduced in fully
exhaustive mechanical terms. And we can also get at the "logic" in
generic "logic" without concern for whether operands are binary or not
or even whether operands are present or not, as they must be in binary
TvN logic.
Let's examine the problem in generic terms of parametric "not" logic
alone. As shown before in the root post to the thread "Epistemology
401: Tautological Mechanics" given the existence together or apart of
operands "A, B" we can mechanize "and" as "not(not A not B)" and
mechanize "or" as "not not (not not A not not B)". Thus granted the
"mechanism" "not" we can reduce all other boolean conjunctions and
generic logic to various combinations and compoundings of "not".
In point of fact it doesn't matter whether such operands occur with
each other or even whether they're different operands. Plus we have a
mechanical isolation of operands and results through negation which
allows us to compound successive stages of tautological operations.
One final note is that approaching the subject from this perspective
allows to produce what are in effect wiring diagrams for all possible
logic circuitry of any kind from computers to the brain. All we have
to do is arrange various combinations and compoundings of "not's".
~v~~
.
|
|
|
| User: "herbzet" |
|
| Title: Re: The Truth of Truly True Truth |
31 May 2007 11:48:34 PM |
|
|
Lester Zick wrote:
On Thu, 31 May 2007 03:02:48 -0400, herbzet <herbzet@gmail.com> wrote:
Hi, Lester.
I'm just briefly dropping in to this discussion to mention something
that might be of use to you (or not -- it's hard to tell!):
The propositional operators "and", "or" and "not" can all be
defined (in the standard sense of "definition") by the single
binary operator "nor" which has the standard symbolization "|",
and is itself defined by the truth table
p | q | p|q
---|---|------
T | T | F
T | F | F
F | T | F
F | F | T
Thus, a formula "p nor q" is true when (surprise!) neither p nor
q is true, and is otherwise false.
Therefore we can define "not" as "p nor p":
p | p|p
---|------
T | F
F | T
Here I have a problem, Herb. Your statement above looks circular in
the sense that you have "not" defined in terms of "nor"
Yes, I have defined "not" in terms of "nor".
No, it is not a circular definition.
If you buy a "nor" logic gate and hook it up to your circuit board
with input lines A and B, then the output C will be in accordance with
the first truth-table above: if the inputs are both logic 0/false/low,
then the output will be logic 1/true/high. Any other combination of
logic inputs result in a logic 0/false/low at output C.
If instead of hooking it up in this normal fashion, you hook it
up with input line A going to _both_ input terminals of the gate,
then the output C will always just be A inverted, i.e., ~A.
You can build your logic circuits entirely with Nor gates. You
don't need to buy any inverters for negation. You can make
inverters out of Nor gates as just shown. There's no
circularity. We're just taking Nor gates as our primitive
circuit element and constructing all the other logic gates
out of them.
or "not or".
In ordinary plain speech, if I say "Neither the Democrats nor
the Republicas know their heads from their asses", that means
the exact same thing as saying, "It is not the case that
either the Democrats or the Republicans know their heads
from their asses."
"Nor" does indeed mean the same as "Not ... or ...". Whether
you want to take "nor" as primitive and let "not" and "or"
be defined terms, or whether you want to take "not" and "or"
as primitive and let "nor" be a defined term, the result is
the same. The decision as to what to take as primitive will
rest on matters of convenience, or clarity, or whatever, and
is not my concern here.
We can then define "or" as "not (p nor q)": ~(p|q) = (p|q) | (p|q)
and define "and" as "(not p) nor (not q)": (~p|~q) = (p|p) | (q|q).
Very symmetrical.
As a matter of fact we can define _any_ propositional operator solely
in terms of "nor"! -- though it's a tedious exercise.
I'm sure it is. I've also seen claims that boolean conjunctions can
all be reduced to various combinations of "not and" as well.
Yes, that's correct, as mentioned below.
The whole
subject of boolean conjunctive logic strikes me as extremely tedious.
They've confused the issue from Aristotle's canons of logic right up
to the present.
-- Intermezzo --
When I was in computer school we learned that computers are designed
to use "positive logic" or "negative logic". This means that the
designer of the electronic logic will use two voltages: a more
positive voltage and a less positive voltage -- binary code, right?
If the designer uses the more positive voltage to represent 1 or
logical "true" and the less positive voltage to represent 0 or
logical "false", that is "positive logic".
I doubt you were around in the late sixties and early seventies, Herb,
but IBM had a tape recording technique called NRZI for non return to
zero inverted.
Yes, I think that is still in use. It is used for encoding/decoding
data to a magnetic medium, or in some data transmission media. It
uses state transitions (or lack of them) to represent 0's and 1's.
But the remarks concerning "positive" and "negative" logic will
apply here also, mutatus mutandus.
If the designer uses the more positive voltage to represent 0 or
logical "false" and the less positive voltage to represent 1 or
logical "true", that is "negative logic".
-- Meanwhile --
If we take the truth table for "nor" and reverse all the truth
values, we get the propositional operator that is "dual" to "nor"
-- we get the "nand" operator (symbol "/"):
p | q | p/q
---|---|------
F | F | T
F | T | T
T | F | T
T | T | F
We should really flip this 180 degrees so it is upside-up:
p | q | p/q
---|---|------
T | T | F
T | F | T
F | T | T
F | F | T
This "nand" operator is thus true when NOT (p and q are true), and
otherwise false. Not and. Nand. Get it?
The propositional operators "nor" and "nand" are said to be "dual"
to each other because of -- positive and negative logic. An
electronic "nor" gate becomes a "nand" gate when you switch from
positive logic to negative logic. A "nand" gate becomes a "nor"
gate when you switch from positive to negative logic. They are
essentially the _same_ operator -- *****-backwards and upside-down.
We can therefore use the "nand" propositional operator to define
"not", "and" and "or", and in essentially the exact same way as
we did with "nor":
Thus we define "not" as "p nand p":
p | p/p
---|------
T | F
F | T
We can then define "and" as "not (p nand q)": ~(p/q) = (p/q) / (p/q)
and define "or" as "(not p) nand (not q)": (~p/~q) = (p/p) / (q/q).
Very symmetrical.
As a matter of fact we can define _any_ propositional operator solely
in terms of "nand"! -- though it's a tedious exercise.
Once more the old "not and" strikes me as circular.
You can make an inverter out of a Nand gate by tying its input
teminals together, just like a Nor gate. You can make any logic
gate out of Nand gates. No circularity there.
"Nor" and "nand" are the only two-place operators that can define
all other propositional operators. But there are other operators
that can also do that: they are just less-convenient-to-use
three-place operators, four-place operators, etc., etc.
In other words the only thing in common among boolean definitions is
the "not" part of "nor" and "nand".
Well, as I found out for myself, if you want an operator that
can define all the other operators, it must turn inputs that
are all false into an output that is true, or it ain't gonna work.
In that sense, you are right. Whether "nor" and "nand" have
a "part" that is "not" is a philosophic/linguistic/psychological
question with which I am not here concerned.
I don't know if any of this applies to your way seeing things,
but what the hell, it might be useful if you decide to design
logic circuits.
Yeah I know what you mean [...]
it occurs to me that there is no universal reduction for
the logic in general mechanical terms. That is we can reduce the logic
by means of "nor" or "nand" but those conjunctions themselves are
still composite functions of "not" plus "or" or "and".
They are if you wish to see it that way. Which of "not", "or"
"and", "nor", "nand", or other connectives is "truly" primitive
is possibly a question without an answer.
From a pragmatic, "get 'er done" perspective, it doesn't matter
what you take as primitive, if it's sufficient to your purposes.
See ya 'round, Lester.
--
hz
--
Posted via a free Usenet account from http://www.teranews.com
.
|
|
|
| User: "Lester Zick" |
|
| Title: Re: The Truth of Truly True Truth |
01 Jun 2007 01:45:03 PM |
|
|
On Fri, 01 Jun 2007 00:48:34 -0400, herbzet <herbzet@gmail.com> wrote:
In ordinary plain speech, if I say "Neither the Democrats nor
the Republicas know their heads from their asses", that means
the exact same thing as saying, "It is not the case that
either the Democrats or the Republicans know their heads
from their asses."
"Nor" does indeed mean the same as "Not ... or ...". Whether
you want to take "nor" as primitive and let "not" and "or"
be defined terms, or whether you want to take "not" and "or"
as primitive and let "nor" be a defined term, the result is
the same. The decision as to what to take as primitive will
rest on matters of convenience, or clarity, or whatever, and
is not my concern here.
Well the point is I'd rather not take "not" and anything else at all.
"Not" is the whole ball of wax as I pointed out in my comments to you
in the preceeding post. It was unfortunate you didn't choose to
respond to my observations on parametric "not( )" combinations to
produce "or" and "and" because that was the whole point. There isn't
any other primitive possible. It's only a matter of convenience to the
extent that you can choose functional redundancy over elementary
primitiveness at the engineering level just as you can code a high
level compiler in the high level language. But when you do you
restrict the high level language functionality to what is already
defined in the language and the purpose of science is to ascertain
truth and functionality in general and not in parochial terms.
~v~~
.
|
|
|
| User: "herbzet" |
|
| Title: Re: The Truth of Truly True Truth |
02 Jun 2007 02:09:58 AM |
|
|
Lester Zick wrote:
herbzet wrote:
"Nor" does indeed mean the same as "Not ... or ...". Whether
you want to take "nor" as primitive and let "not" and "or"
be defined terms, or whether you want to take "not" and "or"
as primitive and let "nor" be a defined term, the result is
the same. The decision as to what to take as primitive will
rest on matters of convenience, or clarity, or whatever, and
is not my concern here.
Well the point is I'd rather not take "not" and anything else at all.
"Not" is the whole ball of wax as I pointed out in my comments to you
in the preceeding post. It was unfortunate you didn't choose to
respond to my observations on parametric "not( )" combinations to
produce "or" and "and" because that was the whole point.
I didn't respond because I had no idea what you were talking about.
I haven't been following the thread; my response was primarily to
nitpick over something Owen said.
I understand that you want to take "not" as the whole ball of wax.
I merely wished to bring to your attention that any propositional
operator can be defined in terms of "nor" (or alternatively, "nand").
I demonstrated _how_ this can be done. It has a concrete representation
in terms of electronic logic circuit elements: you can build any
logic circuit entirely with "nor" gates (or alternatively, "nand"
gates).
These are facts. If they are not pertinent or germane to your
thesis, fine. I just thought it _might_ be useful to you to
be acquainted with these facts, if you were not already -- that's
all.
Have to run now.
Herb
--
Posted via a free Usenet account from http://www.teranews.com
.
|
|
|
| User: "Lester Zick" |
|
| Title: Re: The Truth of Truly True Truth |
02 Jun 2007 01:25:01 PM |
|
|
On Sat, 02 Jun 2007 03:09:58 -0400, herbzet <herbzet@gmail.com> wrote:
Lester Zick wrote:
herbzet wrote:
"Nor" does indeed mean the same as "Not ... or ...". Whether
you want to take "nor" as primitive and let "not" and "or"
be defined terms, or whether you want to take "not" and "or"
as primitive and let "nor" be a defined term, the result is
the same. The decision as to what to take as primitive will
rest on matters of convenience, or clarity, or whatever, and
is not my concern here.
Well the point is I'd rather not take "not" and anything else at all.
"Not" is the whole ball of wax as I pointed out in my comments to you
in the preceeding post. It was unfortunate you didn't choose to
respond to my observations on parametric "not( )" combinations to
produce "or" and "and" because that was the whole point.
I didn't respond because I had no idea what you were talking about.
I haven't been following the thread; my response was primarily to
nitpick over something Owen said.
I understand that you want to take "not" as the whole ball of wax.
I merely wished to bring to your attention that any propositional
operator can be defined in terms of "nor" (or alternatively, "nand").
I demonstrated _how_ this can be done. It has a concrete representation
in terms of electronic logic circuit elements: you can build any
logic circuit entirely with "nor" gates (or alternatively, "nand"
gates).
These are facts. If they are not pertinent or germane to your
thesis, fine. I just thought it _might_ be useful to you to
be acquainted with these facts, if you were not already -- that's
all.
I appreciate it. My observations were just to point out that no other
conjunctions than "not" are required for binary or boolean logic in
general, binary electronic or otherwise and to show how boolean
conjunctions are mechanized in terms of "not" alone..
~v~~
.
|
|
|
| User: "VK" |
|
| Title: Re: The Truth of Truly True Truth |
02 Jun 2007 03:22:07 PM |
|
|
On Jun 2, 10:25 pm, Lester Zick <dontbot...@nowhere.net> wrote:
I appreciate it. My observations were just to point out that no other
conjunctions than "not" are required for binary or boolean logic in
general
What is required for logic - including the Boolean one - these are
objects (semantical entities). NOT, AND, OR, XOR etc are just
operators to establish different relations between these entities; by
themselves they cannot produce any logical contradictions. Same way as
2 + 2 = 5
is a subject of true/false analysis but it is pointless to ask if
+ =
or say
+ * / - + + ^2 =
is true or false.
There can be logic without logical operators, but there cannot be a
logic without semantical entities.
If this discussion is in continuation of your older thread about
possible logical contradiction consisting of only two elements: in
this case the answer is simple:
the formal logic has only two semantical entities: TRUE and FALSE
This way the only "binary contradictions" you are looking for are:
true false
false true
In human language it is called oxymoron, and it is used oftenly in
poetic speech - but up to this post never in formal logic AFAIK :-)
.
|
|
|
| User: "Wolf" |
|
| Title: Re: The Truth of Truly True Truth |
02 Jun 2007 07:08:28 PM |
|
|
VK wrote:
On Jun 2, 10:25 pm, Lester Zick <dontbot...@nowhere.net> wrote:
I appreciate it. My observations were just to point out that no other
conjunctions than "not" are required for binary or boolean logic in
general
What is required for logic - including the Boolean one - these are
objects (semantical entities). [...]
Lester does not believe in Boolean logic. He doesn't understand it
either. There is no point trying to educate him.
--
Wolf
"Don't believe everything you think." (Maxine)
.
|
|
|
| User: "Lester Zick" |
|
| Title: Re: The Truth of Truly True Truth |
03 Jun 2007 04:36:08 AM |
|
|
On Sat, 02 Jun 2007 20:08:28 -0400, Wolf <ElLoboViejo@ruddy.moss>
wrote:
VK wrote:
On Jun 2, 10:25 pm, Lester Zick <dontbot...@nowhere.net> wrote:
I appreciate it. My observations were just to point out that no other
conjunctions than "not" are required for binary or boolean logic in
general
What is required for logic - including the Boolean one - these are
objects (semantical entities). [...]
Lester does not believe in Boolean logic. He doesn't understand it
either. There is no point trying to educate him.
Since when is this about my beliefs, Wolf, or yours or anyone elses?
Mathematics is supposed to be about demonstrations of truth. Or at
least that has been the historical perspective on the subject. Problem
is contemporary mathematikers don't quite understand the perspective.
This isn't Religion 101. You wanna say something mathematical you
demonstrate the truth of what you have to say. Boolean logic wants to
say conjunctions without having to demonstrate the truth of what they
say. Modern mathematikers want to say real number line and infinity
without having to demonstrate the truth of what they say. Empirics
want to say quantum effects, Planck's constant, and relativity without
having to demonstrate the truth of what they say.
Am I to be blamed for proving the origin of boolean conjunctions in
compoundings of "not"? Am I to be blamed for demonstrating there is no
real number line, the intuitional origin of infinity, and the use of
infinitesimals? Am I to be blamed for demonstrating the origin of
quantum effects, Planck's constant, and relativistic effects
generally? Am I to be blamed for seeking truth?
Woe is me. Oh woe is me! What am I to make of mathematics and science?
What is anyone to make of people who claim the mantle of truth without
being able to demonstrate the truth of what they claim? Am I to be re
educated in the absence of truth?
Did our forefathers come to these shores to be browbeaten by a group
of intellectual fascists? For shame! For shame I say! Just because
you're too lazy or stupid to demonstrate the truth of what you say is
insufficient reason to browbeat children into comparable ineptitude.
~v~~
.
|
|
|
| User: "VK" |
|
| Title: Re: The Truth of Truly True Truth |
09 Jun 2007 10:43:18 AM |
|
|
On Jun 3, 1:36 pm, Lester Zick <dontbot...@nowhere.net> wrote:
Mathematics is supposed to be about demonstrations of truth.
I'm afraid not, and that seems the point of your conflict with others
as I saw it - for instance - in the thread about the "the true nature
of points".
The math has very special relations to the "demonstrate truth" and it
has nothing to the demonstration of the Truth, THE TRUTH and the like:
add appropriate excitement in lieu of each upper case usage. For that
go to the church or to the laboratory: or to both on the time share
basis :-)
The math is a kind of a role game with very strictly defined rules and
pre-requisites. Let a Wizard can do only three fireball spells and
then he heed to load new magic power. Then we might predict that on
meeting four Goblins he will loose the battle. Is this prediction
true? Yes, but only within the given rules of the given game. It is
silly to ask if this prediction contains or based on some "universal
truth". All the same with the math. Does Ferma's last puzzle have a
solution? It currently seems that not: within the rules of the current
game. But it can be N of other games where say for any values a,b,c
there is value n such as a^n + b^n = c^n or otherwise it violates the
spelled rules. What kind of game would it be? I don't know but someone
may play it to see. After all imaginary numbers started the same way:
"screw on you all, in my own game square roots from negative numbers
do have valid values, we'll see later if it leads to anything
interesting". Stanislaw Lem once compared a mathematician with a crazy
modeler who's continuously making costumes of the most strange forms.
Once a while a creature appears and - wow!- one of these crazy
costumes fits perfectly to it. But this occasional practical outcome
is not the main preoccupation of the modeler.
.
|
|
|
| User: "Lester Zick" |
|
| Title: Re: The Truth of Truly True Truth |
09 Jun 2007 02:00:03 PM |
|
|
On Sat, 09 Jun 2007 08:43:18 -0700, VK <schools_ring@yahoo.com> wrote:
On Jun 3, 1:36 pm, Lester Zick <dontbot...@nowhere.net> wrote:
Mathematics is supposed to be about demonstrations of truth.
I'm afraid not, and that seems the point of your conflict with others
as I saw it - for instance - in the thread about the "the true nature
of points".
I think you're referring to "The Definition of Points".
The math has very special relations to the "demonstrate truth" and it
has nothing to the demonstration of the Truth, THE TRUTH and the like:
add appropriate excitement in lieu of each upper case usage. For that
go to the church or to the laboratory: or to both on the time share
basis :-)
The math is a kind of a role game with very strictly defined rules and
pre-requisites. Let a Wizard can do only three fireball spells and
then he heed to load new magic power. Then we might predict that on
meeting four Goblins he will loose the battle. Is this prediction
true? Yes, but only within the given rules of the given game. It is
silly to ask if this prediction contains or based on some "universal
truth". All the same with the math. Does Ferma's last puzzle have a
solution? It currently seems that not: within the rules of the current
game. But it can be N of other games where say for any values a,b,c
there is value n such as a^n + b^n = c^n or otherwise it violates the
spelled rules. What kind of game would it be? I don't know but someone
may play it to see. After all imaginary numbers started the same way:
"screw on you all, in my own game square roots from negative numbers
do have valid values, we'll see later if it leads to anything
interesting". Stanislaw Lem once compared a mathematician with a crazy
modeler who's continuously making costumes of the most strange forms.
Once a while a creature appears and - wow!- one of these crazy
costumes fits perfectly to it. But this occasional practical outcome
is not the main preoccupation of the modeler.
Well prior to addressing the substance of your remarks allow me to
point out that your argument in itself is defective since it maintains
my P is not true because your Q is true, an argument which has nothing
to do with the truth of my P, that mathematics is supposed to be about
demonstrations of truth.
As for the content of your argument I can't imagine mathematics has
sunk so low as to be nothing more than game theory. A less sanguine
appraisal of a profession is difficult to imagine. Furthermore I see
no reason whatsoever to demonstrate the "truth" of theorems in such
contexts. What would be the point? Why do you insist students prove
anything at all? Why not just insist students draft new rules instead?
The point is made abundantly clear by FLT. Instead of demonstrating
the truth or falseness of the theorem you moan and groan about maybe
this and maybe that and maybe we'll have to draft new rules when the
theorem itself was drafted under the old rules. Eventually rather than
drafting demonstrations of truth for theorems all you'll ever be doing
is drafting new rules and assumptions of truth to accommodate such
speculations whose truth mathematikers don't feel up to analyzing. If
that's what you consider a "role game with very strictly defined rules
and prerequisites then I'd say it's a pretty sorry excuse for any kind
of game.
Certainly historically mathematics has been constrained by the ideal
of truth in universal terms whether or not realized in practice.
Pythagoreans in fact conceived of their mathematical analyses and
practices in explicit universal terms just as the ancient philosophers
sought the truth of everything in everything and not just the games
people play.
It wasn't until the modern codification of mathematics in arithmetic
terms that mathematicians gave up the search for any kind of truth in
universal terms and settled for mere acceptance of the status quo.
And I find it the height of arrogance to imagine mathematikers are
somehow exempt from the mundane in their ivory tower occupation. What
is it you think you're studying and what is it you expect to get paid
for? Diddling a chalkboard for the rest of your life? Chasing chimeras
and butterfiles as some kind of leisured class of academic
aristocrats? Is there no shame at all among modern mathematikers?
~v~~
.
|
|
|
| User: "VK" |
|
| Title: Re: The Truth of Truly True Truth |
10 Jun 2007 07:14:11 AM |
|
|
Well prior to addressing the substance of your remarks allow me to
point out that your argument in itself is defective since it maintains
my P is not true because your Q is true, an argument which has nothing
to do with the truth of my P, that mathematics is supposed to be about
demonstrations of truth.
AFAICT you did not make any statements yet to negate :-)
As with the definition of points you asked what the truth is here and
you have got a few answers from different peoples. In order to get a
contradiction one has to have at least two contradictory statements
about the same phenomenon. You are right though that about any
phenomenon can be two mutually exclusive statements made, either a
simple negative like "white - not white" or an opposite like "white -
black".
Note: I invite you once again to read some dialogs of Plato especially
and at least "Protagor" and "The Fiest". Besides being an excellent
_litterature_ reading I believe you enjoy how the things - you are
walking around - already being expressed.
As for the content of your argument I can't imagine mathematics has
sunk so low as to be nothing more than game theory.
I didn't use the term "game theory" neither did I compare the math
with dropping a coin and the like. I compared the math with role games
with its own rules and its own true and false facts for each game -
but I didn't put the equality sign here. A prof may use "two apples
and one more apple" example so to make more easy for children to get
onto arithmetics: but it doesn't make arithmetics to be a study about
apples :-)
To really understand what the modern math is one needs then to learn
the information theory, Goedel first, a lot of other stuff after. If
you want we may some day to talk about infospace, informational
objects and unpacking senses. Brutely saying, our crazy modeler from
the previous post may make such costume that no one would ever think
of a creature to fit this costume: but after having seen that costume
the creature can be made - and happen to be very useful for the
civilization. The Boolean's logic for fifty or so year was a useless
abstract mind game of "what if" kind. But one day computers appeared -
and engineers just swallowed it as it was that vital part they needed.
So don't worry about the "usability of the math" - this place is
secured forever. Just don't get too preoccupated by that and don't get
lazy - keep making new crazy costumes. :-)
A less sanguine
appraisal of a profession is difficult to imagine. Furthermore I see
no reason whatsoever to demonstrate the "truth" of theorems in such
contexts. What would be the point? Why do you insist students prove
anything at all? Why not just insist students draft new rules instead?
- How much is 2-2 ?
a) - This question doesn't have sense, your equation is illegal.
b) - It makes 0
- How much is 2-3 ?
a) - This question doesn't have sense, your equation is illegal.
b) - It makes -1
- How much is sqrt(-4) ?
a) - This question doesn't have sense, your equation is illegal.
b) - It makes -i*2
Variants b) are what a good modern student - say yourself - will
easily choose. Variants a) are what a good student N1, N2 and N3 years
ago would easily choose.
Note: I broke with my European G3 provider as they happened to be
blood suckers Drakula may rest - so I'm back on my 9,600 (effective
7,200) bod GPRS. Due to that I'm skipping on facts' checking online if
it's possible - like the exact time of invention of math zero,
negative numbers and imaginary ones.
So in order for say Mr.Zick to choose proper - by now - answers it
took at least three "bad students" in the past to draw their own rules
instead of ones that their teachers tried to feed them in. It is
normal to have such "bad students" in any science and we should expect
and hope for a great number of them in the feature. Otherwise
scientific will become like medieval monks ensured that all past and
future wisdom of the world is already written by Aristotle and in the
Bible so the job is only to read the right page in the right way.
The point is made abundantly clear by FLT. Instead of demonstrating
the truth or falseness of the theorem you moan and groan about maybe
this and maybe that and maybe we'll have to draft new rules when the
theorem itself was drafted under the old rules.
I couldn't care less of FLT: it is the most pointless chunk of
knowledge ever achieved by math for the greatest amount of human-
hours. Ten guys making a pyramid that turns around a ceiling lamp to
change the bolb: these ten guys is still a sample of 100% result/
efforts productivity against FLT formulation/proof history. I took it
only as still the most recognizable - alas - illustration to my
statement. Currently FLT seems being proven to be right. At least it
is proven that a violation of FLT would require a violation of another
theorem. Is it the end of the line or is it a "pseudo-end" simply
pointing that it's time to start a new more interesting game? I'm not
imposing any "right" answer, I'm just asking. You seem to have an
answer already, but look again at a)-b) samples some above.
.
|
|
|
| User: "Lester Zick" |
|
| Title: Re: The Truth of Truly True Truth |
10 Jun 2007 01:24:35 PM |
|
|
On Sun, 10 Jun 2007 05:14:11 -0700, VK <schools_ring@yahoo.com> wrote:
Well prior to addressing the substance of your remarks allow me to
point out that your argument in itself is defective since it maintains
my P is not true because your Q is true, an argument which has nothing
to do with the truth of my P, that mathematics is supposed to be about
demonstrations of truth.
AFAICT you did not make any statements yet to negate :-)
Well this is truly disheartening since the statement I made to which
you replied in the negative about which I complained was:
"Mathematics is supposed to be about demonstrations of truth."
As with the definition of points you asked what the truth is here and
you have got a few answers from different peoples. In order to get a
contradiction one has to have at least two contradictory statements
about the same phenomenon. You are right though that about any
phenomenon can be two mutually exclusive statements made, either a
simple negative like "white - not white" or an opposite like "white -
black".
The self contradiction is between predicates such as "square circle".
Note: I invite you once again to read some dialogs of Plato especially
and at least "Protagor" and "The Fiest". Besides being an excellent
_litterature_ reading I believe you enjoy how the things - you are
walking around - already being expressed.
I don't really enjoy analogical dialectics at all. Interminably dull
and boring.
As for the content of your argument I can't imagine mathematics has
sunk so low as to be nothing more than game theory.
I didn't use the term "game theory" neither did I compare the math
with dropping a coin and the like. I compared the math with role games
with its own rules and its own true and false facts for each game -
but I didn't put the equality sign here. A prof may use "two apples
and one more apple" example so to make more easy for children to get
onto arithmetics: but it doesn't make arithmetics to be a study about
apples :-)
Someday you'll have to explain the difference between math as a role
game and math as game theory other than by analogy with teaching math.
It sounds like a distinction without a difference.
To really understand what the modern math is one needs then to learn
the information theory, Goedel first, a lot of other stuff after.
Somehow I prefer to begin first with truth and move on from there. If
modern math can't or doesn't accommodate truth it just doesn't matter.
If
you want we may some day to talk about infospace, informational
objects and unpacking senses.
I'm sure you can find someone to talk with who cares.
Brutely saying, our crazy modeler from
the previous post may make such costume that no one would ever think
of a creature to fit this costume: but after having seen that costume
the creature can be made - and happen to be very useful for the
civilization. The Boolean's logic for fifty or so year was a useless
abstract mind game of "what if" kind. But one day computers appeared -
and engineers just swallowed it as it was that vital part they needed.
So don't worry about the "usability of the math" - this place is
secured forever. Just don't get too preoccupated by that and don't get
lazy - keep making new crazy costumes. :-)
I've already expressed myself on the subject of mathematikers who
imagine they're above mundane considerations of truth and utility yet
somehow expect to get paid for their arrogance. It's un scientific and
un American.
A less sanguine
appraisal of a profession is difficult to imagine. Furthermore I see
no reason whatsoever to demonstrate the "truth" of theorems in such
contexts. What would be the point? Why do you insist students prove
anything at all? Why not just insist students draft new rules instead?
- How much is 2-2 ?
a) - This question doesn't have sense, your equation is illegal.
b) - It makes 0
- How much is 2-3 ?
a) - This question doesn't have sense, your equation is illegal.
b) - It makes -1
- How much is sqrt(-4) ?
a) - This question doesn't have sense, your equation is illegal.
b) - It makes -i*2
Variants b) are what a good modern student - say yourself - will
easily choose. Variants a) are what a good student N1, N2 and N3 years
ago would easily choose.
Note: I broke with my European G3 provider as they happened to be
blood suckers Drakula may rest - so I'm back on my 9,600 (effective
7,200) bod GPRS. Due to that I'm skipping on facts' checking online if
it's possible - like the exact time of invention of math zero,
negative numbers and imaginary ones.
So in order for say Mr.Zick to choose proper - by now - answers it
took at least three "bad students" in the past to draw their own rules
instead of ones that their teachers tried to feed them in. It is
normal to have such "bad students" in any science and we should expect
and hope for a great number of them in the feature. Otherwise
scientific will become like medieval monks ensured that all past and
future wisdom of the world is already written by Aristotle and in the
Bible so the job is only to read the right page in the right way.
Well I'm having a hard time understanding your point and how you think
it's responsive to my comments so I'll let it go. Sounds like english
isn't your native language.
The point is made abundantly clear by FLT. Instead of demonstrating
the truth or falseness of the theorem you moan and groan about maybe
this and maybe that and maybe we'll have to draft new rules when the
theorem itself was drafted under the old rules.
I couldn't care less of FLT: it is the most pointless chunk of
knowledge ever achieved by math for the greatest amount of human-
hours.
Then why raise the issue? You use it to try to make your point but I
can't use it to make mine? Sounds like special pleading to me.
Ten guys making a pyramid that turns around a ceiling lamp to
change the bolb: these ten guys is still a sample of 100% result/
efforts productivity against FLT formulation/proof history. I took it
only as still the most recognizable - alas - illustration to my
statement.
So I'm not allowed to use it to illustrate my statement?
Currently FLT seems being proven to be right. At least it
is proven that a violation of FLT would require a violation of another
theorem. Is it the end of the line or is it a "pseudo-end" simply
pointing that it's time to start a new more interesting game?
Back to modern math as game theory?
I'm not
imposing any "right" answer, I'm just asking. You seem to have an
answer already, but look again at a)-b) samples some above.
I still have no idea what your examples above were driving at. You
really need to learn to argue your points more logically. That's the
same in every language.
~v~~
.
|
|
| | | | | | | | | | | | | | |
