| Topic: |
Religions > Atheism |
| User: |
"*nemo*" |
| Date: |
27 May 2004 04:16:14 PM |
| Object: |
aa - The polls are open! TQOTM for May 2004 |
I'm already ready for a vacation. But it will be close to another month
till I can get away. Drat. Oh well, at least we can all sit back and
enjoy the Quote of the month contests, eh?
Here are the nominations for Theist Quote of the Month for May 2004.
Vote for your favorite by responding to this thread. Votes will be
accepted until midnight, May. 31. See rules below. Questions? Comments?
Email me.
* * * * *
1) For some reason I think athiest just don't want to believe we have a
creator.
By: Osprey
Nominated: Doc Smartass
Seconded: Callipygian Nullifidian
------------
2) I have responded to this kind of garbage enough times already.
People like me, who cannot think for themselves, are a dime a dozen.
By: Pastor Dave
Nominated: bogie
Seconded: Tink
------------
3) The rate of sex crimes in the Church is far less than general
society.
By:
Nominated: Dixit
Seconded: jwk
------------
4) Oh, yes, and right "machines can detect oxygen and then we can
manipulate it." Well dear, God is a person, not to be manipulated.
However He made a device which can actually recognize God in the world
and in a person. It is called a Human Being. Now you seem to think that
people are hallucinating God as they would Donald Duck on a bad acid
trip. What you fail to logically postulate is that our ability to
hallucinate at all, or dream, or to have out of body experiences, etc.
are indeed physical attributes in the human brain, but they were PUT
there precisely for the act of DETECTING GOD.
By: Anatid Bonecki
Nominated: Dixit
Seconded: Liz
------------
5) In response to:
So why weren't the rodents that died in the Great Flood preserved as
fossils?
Deviation tactic, you are not addessing the issue. You can't prove
evoution theory by questioning creational issues.
By: Roadrunner
Nominated: Gregory Gadow
Seconded: Harry F. Leopold
------------
6) You want specific when all you do is regurgitate ignorance?
By: Mary Hogan
Nominated: Sara Brum
Seconded: bogie
------------
7) You're right - I believe in God with evidence You believe in the
romans with roads. I win.
By: duke
Nominated: Iain
Seconded: Vic Sagerquist
------------
8) Right; but we're not talking about whether your or I exist, but
whether the 'collection of everything that exists' exists. You've said
that, if it did not, then 'we would not be here'; and I questioned that
assertion, precisely because I don't see the sense in it myself.
By: George Dance
Nominated: Ron Baker
Seconded: Dixit
------------
9) You might like to start with just thinking. You might improve with
time-say millions and millions of years as in the fairy tales of goo to
you by way of the zoo...
By: IKnowHimDoYou
Nominated: W. Syme
Seconded: Douglas Berry
------------
10) It has nothing to do with data. What data can distinguish between
the 2 hypotheses?? It's a question of *reason*. The materialist
metaphysic only entails p-zombies, not real people.
By: Interesting Ian
Nominated: John M Price PhD
Seconded: Denis Loubet
------------
11) No, evidence does not need to be objective.
By: Interesting Ian
Nominated: John M Price PhD
Seconded: Llanzlan Klazmon The 15th
* * * * * * * * * * * * * * * * * * * * * * * * * * * *
Here are the rules for the Quote of the Month Contests.
RULES
1. Only atheists and agnostics may participate in the contests.
2. A quote is a valid entry for the contests if:
a. The quote is a brief piece of text;
b. The quote has recently been written in alt.atheism (verifiable);
c. Nomination of the quote is made by an atheist or agnostic
in alt.atheism
d. Nomination of the quote is supported by at least one other
atheist or agnostic in alt.atheism;
e. The quote is not nominated or seconded by the person who wrote it
in
the first place (no one is allowed to nominate him- or herself,
but a person
can vote for the quote he or she wrote.)
3. There will be two categories: 'Atheist Quote of the Month'
and 'Theist Quote of the Month'. The category for which a
quote must be nominated must be mentioned by the atheist or
agnostic who wants to nominate it.
If a quote is miscategorized (e.g. an atheist quote is mistakenly
nominated in the Theist QOTM category), the quote will be re-directed
to appear in the correct category, with approriate notification.
4. Nominations can be made until five days before the first of the
next month. If quotes are nominated after this period, they will be
considered as entries for the contest of the next month.
* When making a nomination, please use this format for the subject
line:
"aa - <A or T as applicable>QOTM Nomination (was: <original thread
name>)"
5. Each atheist or agnostic who visits alt.atheism has one vote to
cast for each category (two votes total).
6. Voting starts 5 days before the end of the month. During the month,
votes will be ignored. This way, all nominees will have equal chance of
winning.
7. The two winning quotes will be published in the QOTM Archive.
SUMMARY
A nomination must contain the following information:
1. The lines of the quote.
2. Who wrote it.
3. Who nominates or seconds the nomination of this quote (that's you!)
4. Which category this nomination is for.
5. The word "nomination" MUST appear somewhere in the subject line!
6. The original thread title must appear in the subject line.
Publish the nomination or support for a nomination in a designated
thread, preferably called "[T/A]QoTM Nomination for [month]." You can
also e-mail it to me (see below).
VOTING
1. In the last five days of the month you can cast your vote in both
categories.
2. Votes must either be placed in the designated thread.
--
Nemo - EAC Commissioner for Bible Belt Underwater Operations.
Atheist #1331 (the Palindrome of doom!)
BAAWA Knight! - One of those warm Southern Knights, y'all!
Charter member, SMASH!!
http://home.earthlink.net/~jehdjh/Relpg.html
Draco Dormiens Nunquam Titillandus
Quotemeister since March 2002
.
|
|
| User: "Jim Burns" |
|
| Title: Re: To George Dance: Re: aa - The polls are open! TQOTM for May 2004 |
22 Jun 2004 09:48:45 PM |
|
|
"Ron Baker, Pluralitas!" wrote:
"Jim Burns" <burns.87@osu.edu> wrote in message
news:40D7A757.E1D5B7C8@osu.edu...
[re: ~KP~x -> Mx, "If there is no Known proof that x is false,
then x may be true.]
I say it is not reasonable.
If P is left undefined then
for some P it becomes True -> Mx.
That is not reasonable.
It is a reasonable result of choosing that P. It may be that
it is unreasonable to choose "impossibly good" as a standard
of proof. You pays your money and you takes your choice.
True does not lead to Mx.
It's raining on me -> I will get wet.
Assume it's raining on me.
In that case, It's raining on me = True,
and True -> I will get wet.
Compare and contrast.
You could say it is equivalent to just
saying, Mx. But then, just say Mx because
saying True -> Mx is wrong.
So True -> Mx is wrong *and* equivalent to Mx, which
you apparently think is not wrong, somehow.
So.. for some values of P, "~KP(~g)"
has no meaning or information content.
This might even be true. There isn't really much of what
you seem to be calling information content in math or logic.
However, this is a completely different claim from what
you've been talking about.
What you've done is evaluate part of that conditional.
As you've defined things ~KP~x always evaluates to True.
Plugging that value in directly looks odd, but it's perfectly
fine to do that under the conditions that you've specified.
I think you're letting your intuition say "But that would
mean _anything_ might be -- that can't be true". Normally
that would be right -- but you've made things unusual,
since there are, effectively, no proofs of anything.
Your argument, as you have made it, allows for
P to be considered 'absolute existential proof'.
Until you say what (existential) 'proof' is in your argument
it can't be said that there is a proof of anything.
If *you* want to consider P to stand for "absolute existential
proof" (as you did earlier), then more power to you. Why
should *I* have anything to do with defining *your* notion?
All *I* have to say about all that is *IF* *your* notion
of "absolute existential proof" follows certain axioms, specific
things ("theorems") can said with a very high level of
certainty. The same things could be said regarding other notions
of proof, as long as they follow the same axioms.
I think it cannot be that our standards for "known", "proven"
and "possible" can be allowed to vary independently of each
other. Certainly if they did the there is no way ~KP~x -> Mx
could be true.
I think they are linked through axioms like
George's Provability Axiom, Lp -> MPp
(Message-ID:<6312c50b.0406200120.4a339e10@posting.google.com>)
Why don't you start with a definition of P.
Why don't you read what I write?
~KP(~x) -> Mx has some chance of being meaningful or
valid if there is ever a case where KP(x) = True.
But that depends on what 'proof' is.
Give me an example of a proof that the sun
exists.
It shouldn't be too difficult to prove the sun
exists, should it?
I think you've grown too used to putting this into your
posts. That doesn't make any sense in this context.
Suppose I try to do what you ask. I fly to where you live,
bust into your house, drag you outside, point your face at
the Sun and say, "There! That's the Sun."
LOL.
OK. Finally. Is that your standard of proof?
No, of course not. That is one way of convincing you of
the Sun's existence. By another standard of proof there
is no such proof, not without assuming some axiom like
"The sun exists." In another context, there is no such proof
because the sun does not exist, since it is not a mathematical
object.
Does being able to point my face at something, i.e.
being able to look at and see something,
determine its existance?
No, of course not. There are lots of things that cannot be
treated this way, yet nonetheless exist, neutrinos,
mathematical theorems, the center of the Earth, to name a few.
If so then God does not exist.
Shocked! Shocked, I say!
You can't make me see God.
I can not look at and see God therefore
it doesn't exist.
Ah. ... I'm curious: presumably you can look at something that
proves to you that you cannot see ever see God. What would
that be?
That is:
P is defined.
~KP(~x) is not alway True. ~KP(~g) -> Mg
is a reasonable argument.
~KP(~g) = False, Mg is not shown, g = False.
Fine. You've shown ~KP~g -> Mx holds for one particular choice
of P. Is it the only choice for which it holds?
How about "Everything we need to know is in the Analects of
Confucius." Proof of nonexistence of God: The Christian God
is not mentioned in the Analects. If He existed, we would
need to know about him in order to be righteous. Therefore
He does not exist.
KP~g is true, therefore ~KP~g -> Mg is true.
(A -> B is always true when A is false.)
Pick another standard of proof. Does ~KP~g -> Mg hold there?
I say it does. I say for each specific definition of P,
~KP~g -> Mg holds, therefore I do not need to specify P
and I do not want to specify P because it weakens my assertion.
If you were to say,
"Okay, you win", then there is a known proof that the Sun exists.
Then I'd say, apply that same standard of proof
to God. What do you get? If you get 'unknown'
then your standard of existential proof is inadequate
and KP(x) is meaningless.
This seems to be the point that drives you: apply the same
standard of proof to God, apply the same standard of proof to
everything. If that works for you, fine. I know I don't apply the
same standard in every situation, and I don't believe anyone else
does either, you included.
The conditional does not apply. If you say, "No, I still don't
believe", then the conditional says you would also rationally
assert that the Sun may not exist. ( ~KPs -> M~s ) My intuition
doesn't have a problem with this. It looks like very similar
craziness both ways. Why wouldn't they be linked?
But a theist isn't going to want to do that because
it would establish a precedential standard for
existence proofs. They know that God is not
going to meet that standard. To maintain belief
in God, one must have a special standard of
existence that applies only to God.
First, what a theist wants to prove seems irrelevant, unless
you're proposing their wants as some sort of standard of
rationality. I doubt that, but even if that were true, it's
a negative standard, telling us what a proof is _not_.
Tell me something, Jim, Do you have a different
standard of proof for the existence of God vs
the existence of other things?
I have lots of different standards for lots of different
things. Actually, I even "have" several different standards for
the existence of God. What I mean is I'm aware of several
different standards, some of which He passes, some of which
He fails. The "test" I actually use when I think about such things
is more of an esthetic judgment than a proof: the universe
does not seem to need a God to operate. This is close to
what I mean when I say Special Relativity is true.
Second, you're wrong about what "a theist" would want to do
in regard to special standards. There are plenty of theists
for which that would be true, but not all of them. Decartes
immediately comes to mind. John Polkinghorne is a more recent
name I've heard. See, for example, _Traffic in truth :
_exchanges between science and theology_ (2002)
(Hmm. speaking for theists... recommending a
book by a priest... Hmm.)
Yes, yes. Protesting the bigoted dumping of all theists
into one category... very suspicious.
What does Polkinghorne say about standards of
existential proof?
I don't know. I haven't read the book. I vaguely remembered
the name and checked it in my library's catalogue.
I gave the name of one of his books as support that he
really was doing what I said he was, what you said he wasn't.
Here is another view: Suppose the standard
of proof is 'that which convinces one or causes
one to believe'. That is the pragmatic
standard of proof. To a Shintoist the argument
for the Kami meets their standard of proof and
God does not. Therefore there is a known proof of the
nonexistence of God. Therefore Mg is not shown.
What we're saying here would be ~KPg -> M~g,or "If there is
no known proof of the existence of God, then He might *NOT*
exist." I don't see why a Shintoist would have a problem
with this.
A Shintoist is happy with ~KP(~g) -> Mg because to
the Shintoist ~KP(~g) = False, thus Mg is not shown.
He/she freely and happily considers g = False.
Did you have a point besides just stating you agree with me?
[...]
I don't know what it means for ~KP~g -> Mg to be false. It
certainly looks reasonable to me.
If P is not defined then it is not a valid.
If P is defined then it might be valid but
is essentially meaningless.
Introducing P without definition is a burden
shifting wedge.
I don't get it. What burden is being shifted where?
Burden shifting is "I'm right unless/until you prove me wrong."
Come on. Give me a break. The absolute worst you can read
into ~KP~x -> Mx is "I might be right, until you prove me wrong."
You are right. One *can* read it as "I might be right, until you
prove me wrong." And that is only slightly
different from the burden-shifting/ad-ignorantiam,
"I am right, until you prove me wrong."
All you have done is add the 'might'.
You've changed it, made it different, softened it some, but
it is still burden-shifting bait and it is still ad-ignorantiam.
If you have a problem with that, I'm going to use your
denial to tie you in knots,
Take your best shot.
Changed my mind. Been there, done that.
Maybe some day you'll figure out the difference between
"X exists" and "X may exist". I don't feel like teaching
you. Good luck.
Jim Burns
.
|
|
|
| User: "Ron Baker, Pluralitas!" |
|
| Title: Re: To George Dance: Re: aa - The polls are open! TQOTM for May 2004 |
23 Jun 2004 11:26:58 AM |
|
|
"Jim Burns" <burns.87@osu.edu> wrote in message
news:40D8EF8D.8CFE3978@osu.edu...
"Ron Baker, Pluralitas!" wrote:
"Jim Burns" <burns.87@osu.edu> wrote in message
news:40D7A757.E1D5B7C8@osu.edu...
[re: ~KP~x -> Mx, "If there is no Known proof that x is false,
then x may be true.]
I say it is not reasonable.
If P is left undefined then
for some P it becomes True -> Mx.
That is not reasonable.
It is a reasonable result of choosing that P.
? What is that P? 'absolute proof'?
It may be that
it is unreasonable to choose "impossibly good" as a standard
of proof.
But you didn't exclude it. (And many people do
not consider 'abosolute' to be 'impossible'.)
Again, What is your 'reasonable' standard of proof?
You pays your money and you takes your choice.
True does not lead to Mx.
It's raining on me -> I will get wet.
Assume it's raining on me.
In that case, It's raining on me = True,
and True -> I will get wet.
Compare and contrast.
It is not always 'raining on you'.
It is not a constant. Sometimes it is
True and sometimes it is False.
Therefore, evaluating it can tell you
something about your getting wet.
~KP(~x) is constant true for all x
(and some P that you haven't excluded).
Once you have determined that, there
is no need to ever evaluate it again
for any x.
~KP(~x) tells you nothing about Mx.
To say (constant)True -> z is illogical.
Compare and contrast:
(x is white or x is not white) -> Mx
You could say it is equivalent to just
saying, Mx. But then, just say Mx because
saying True -> Mx is wrong.
So True -> Mx is wrong *and* equivalent to Mx, which
you apparently think is not wrong, somehow.
No. Mx by itself is an assertion you could make.
True -> Mx is illogical.
(When I said "You could say" I was being generous,
anticipating what you might say, and giving you
some slack.)
So.. for some values of P, "~KP(~g)"
has no meaning or information content.
This might even be true. There isn't really much of what
you seem to be calling information content in math or logic.
However, this is a completely different claim from what
you've been talking about.
I don't think it is different.
For some P, ~KP(~x) = True, for all x.
In that case, saying "~KP(~x)" is equivalent
to saying "True!". x doesn't matter.
It says nothing about x.
The statement "True!" has no information
content.
(The information content of math and logic
is a whole other matter.)
What you've done is evaluate part of that conditional.
As you've defined things ~KP~x always evaluates to True.
Plugging that value in directly looks odd, but it's perfectly
fine to do that under the conditions that you've specified.
I think you're letting your intuition say "But that would
mean _anything_ might be -- that can't be true". Normally
that would be right -- but you've made things unusual,
since there are, effectively, no proofs of anything.
Your argument, as you have made it, allows for
P to be considered 'absolute existential proof'.
Until you say what (existential) 'proof' is in your argument
it can't be said that there is a proof of anything.
If *you* want to consider P to stand for "absolute existential
proof" (as you did earlier), then more power to you. Why
should *I* have anything to do with defining *your* notion?
Because if you don't define P for your argument,
I (and anyone else) can put whatever they want in for it.
And that results in the destructon of your argument.
All *I* have to say about all that is *IF* *your* notion
of "absolute existential proof" follows certain axioms, specific
things ("theorems") can said with a very high level of
certainty.
The same things could be said regarding other notions
of proof, as long as they follow the same axioms.
But the set of valid theorems varies with
the chosen standard of proof.
I think it cannot be that our standards for "known", "proven"
and "possible" can be allowed to vary independently of each
other. Certainly if they did the there is no way ~KP~x -> Mx
could be true.
I think they are linked through axioms like
George's Provability Axiom, Lp -> MPp
(Message-ID:<6312c50b.0406200120.4a339e10@posting.google.com>)
Why don't you start with a definition of P.
Why don't you read what I write?
You mean the 'look at it with your eyes'
standard?
~KP(~x) -> Mx has some chance of being meaningful or
valid if there is ever a case where KP(x) = True.
But that depends on what 'proof' is.
Give me an example of a proof that the sun
exists.
It shouldn't be too difficult to prove the sun
exists, should it?
I think you've grown too used to putting this into your
posts. That doesn't make any sense in this context.
Suppose I try to do what you ask. I fly to where you live,
bust into your house, drag you outside, point your face at
the Sun and say, "There! That's the Sun."
LOL.
OK. Finally. Is that your standard of proof?
No, of course not.
Then you don't have a standard of existential proof and
your argument breaks down.
I have repeatedly asked for a standard of proof.
You finally (and angrily?) offer that and now disavow it.
You don't have a standard of proof and
your argument breaks down.
That is one way of convincing you of
the Sun's existence. By another standard of proof there
is no such proof, not without assuming some axiom like
"The sun exists." In another context, there is no such proof
because the sun does not exist, since it is not a mathematical
object.
Does being able to point my face at something, i.e.
being able to look at and see something,
determine its existance?
No, of course not. There are lots of things that cannot be
treated this way, yet nonetheless exist, neutrinos,
mathematical theorems, the center of the Earth, to name a few.
Then (to help you out), how do you know they
exist? (That is not a adversarial challenge, that
is an encouraging challenge.)
If you can answer that, then you have your 'P'.
I believe that neutrinos and the center of the Earth
exist. There should therefore be a standard of proof
consistent with that.
If so then God does not exist.
Shocked! Shocked, I say!
Ha ha.
You can't make me see God.
I can not look at and see God therefore
it doesn't exist.
Ah. ... I'm curious: presumably you can look at something that
proves to you that you cannot see ever see God.
You asserted as a standard of existential proof that
you could arrange for me to be in the presence
of that thing and I would see it.
Until you do that I am permitted to conclude it
doesn't exist.
What would
that be?
That is:
P is defined.
~KP(~x) is not alway True. ~KP(~g) -> Mg
is a reasonable argument.
~KP(~g) = False, Mg is not shown, g = False.
Fine. You've shown ~KP~g -> Mx holds for one particular choice
of P. Is it the only choice for which it holds?
No.
How about "Everything we need to know is in the Analects of
Confucius." Proof of nonexistence of God: The Christian God
is not mentioned in the Analects. If He existed, we would
need to know about him in order to be righteous. Therefore
He does not exist.
(Since 'God', i.e. the god of the Bible, is a
proper noun it is appropriate to
capitalize it. Since 'he' is a pronoun, its capitalizaion
is just an affectation of the Christians, I believe.)
KP~g is true, therefore ~KP~g -> Mg is true.
Or 'valid' I think is a better term.
Sure, but then Mg = False, right?
(A -> B is always true when A is false.)
That statement is not true if A is always
and unconditionally of one truth value (i.e. always
true or always false).
False -> x is illogical.
A -> B is valid and a true relationship if it has
the truth table:
| B
------------
T | T
A F | U
U | U
If A can only possibly have one value then
there is no table and there is no relationship.
Pick another standard of proof. Does ~KP~g -> Mg hold there?
I say it does. I say for each specific definition of P,
~KP~g -> Mg holds,
Hunh? No. It doesn't hold for P = 'absolute proof'.
(It also doesn't hold for P = 'convinces all humans'.)
therefore I do not need to specify P
and I do not want to specify P because it weakens my assertion.
That should be a clue for you right there.
If you were to say,
"Okay, you win", then there is a known proof that the Sun exists.
Then I'd say, apply that same standard of proof
to God. What do you get? If you get 'unknown'
then your standard of existential proof is inadequate
and KP(x) is meaningless.
This seems to be the point that drives you: apply the same
standard of proof to God, apply the same standard of proof to
everything.
You got it.
Anything else is.... <fanfare> *Special Pleading*.
If that works for you, fine. I know I don't apply the
same standard in every situation,
The fallacy of Special Pleading.
and I don't believe anyone else
does either, you included.
I most definitely do. (Or try to the best of
my ability.)
The conditional does not apply. If you say, "No, I still don't
believe", then the conditional says you would also rationally
assert that the Sun may not exist. ( ~KPs -> M~s ) My intuition
doesn't have a problem with this. It looks like very similar
craziness both ways. Why wouldn't they be linked?
But a theist isn't going to want to do that because
it would establish a precedential standard for
existence proofs. They know that God is not
going to meet that standard. To maintain belief
in God, one must have a special standard of
existence that applies only to God.
First, what a theist wants to prove seems irrelevant, unless
you're proposing their wants as some sort of standard of
rationality. I doubt that, but even if that were true, it's
a negative standard, telling us what a proof is _not_.
Tell me something, Jim, Do you have a different
standard of proof for the existence of God vs
the existence of other things?
I have lots of different standards for lots of different
things. Actually, I even "have" several different standards for
the existence of God. What I mean is I'm aware of several
different standards, some of which He passes, some of which
He fails. The "test" I actually use when I think about such things
is more of an esthetic judgment than a proof: the universe
does not seem to need a God to operate. This is close to
what I mean when I say Special Relativity is true.
Hey, "what is needed to make the universe operate"
is not bad for a standard of P.
I'll also say that that and "what can be presented to the eyes"
are two things that are probably appropriate for
inclusion in the definition of 'P'.
Second, you're wrong about what "a theist" would want to do
in regard to special standards. There are plenty of theists
for which that would be true, but not all of them. Decartes
immediately comes to mind. John Polkinghorne is a more recent
name I've heard. See, for example, _Traffic in truth :
_exchanges between science and theology_ (2002)
(Hmm. speaking for theists... recommending a
book by a priest... Hmm.)
Yes, yes. Protesting the bigoted dumping of all theists
into one category... very suspicious.
Opining that theists wouldn't want to establish a
standard of existential proof is hardly heinous.
I'm willing to discuss such standards with any
theist who is honest and willing.
What does Polkinghorne say about standards of
existential proof?
I don't know. I haven't read the book. I vaguely remembered
the name and checked it in my library's catalogue.
I gave the name of one of his books as support that he
really was doing what I said he was, what you said he wasn't.
Here is another view: Suppose the standard
of proof is 'that which convinces one or causes
one to believe'. That is the pragmatic
standard of proof. To a Shintoist the argument
for the Kami meets their standard of proof and
God does not. Therefore there is a known proof of the
nonexistence of God. Therefore Mg is not shown.
What we're saying here would be ~KPg -> M~g,or "If there is
no known proof of the existence of God, then He might *NOT*
exist." I don't see why a Shintoist would have a problem
with this.
A Shintoist is happy with ~KP(~g) -> Mg because to
the Shintoist ~KP(~g) = False, thus Mg is not shown.
He/she freely and happily considers g = False.
Did you have a point besides just stating you agree with me?
I guess I was wondering the same thing at the time.
[...]
I don't know what it means for ~KP~g -> Mg to be false. It
certainly looks reasonable to me.
If P is not defined then it is not a valid.
If P is defined then it might be valid but
is essentially meaningless.
Introducing P without definition is a burden
shifting wedge.
I don't get it. What burden is being shifted where?
Burden shifting is "I'm right unless/until you prove me wrong."
Come on. Give me a break. The absolute worst you can read
into ~KP~x -> Mx is "I might be right, until you prove me wrong."
You are right. One *can* read it as "I might be right, until you
prove me wrong." And that is only slightly
different from the burden-shifting/ad-ignorantiam,
"I am right, until you prove me wrong."
All you have done is add the 'might'.
You've changed it, made it different, softened it some, but
it is still burden-shifting bait and it is still ad-ignorantiam.
If you have a problem with that, I'm going to use your
denial to tie you in knots,
Take your best shot.
Changed my mind. Been there, done that.
Maybe some day you'll figure out the difference between
"X exists" and "X may exist". I don't feel like teaching
you. Good luck.
Geez, what happened. You were doing so well.
Oh well. Thank you at least for teaching me
that three headed lizards
wearing tutus on Neptune may exist.
--
RB
aa#2187
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| User: "George Dance" |
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| Title: Re: To George Dance: Re: aa - The polls are open! TQOTM for May 2004 |
24 Jun 2004 01:11:48 PM |
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"Ron Baker, Pluralitas!" <jung@topway.net.cn> wrote in message news:<mbiCc.31147$Ha2.24209@twister.socal.rr.com>...
"Jim Burns" <burns.87@osu.edu> wrote in message
news:40D8EF8D.8CFE3978@osu.edu...
"Ron Baker, Pluralitas!" wrote:
"Jim Burns" <burns.87@osu.edu> wrote in message
news:40D7A757.E1D5B7C8@osu.edu...
[re: ~KP~x -> Mx, "If there is no Known proof that x is false,
then x may be true.]
I say it is not reasonable.
If P is left undefined then
for some P it becomes True -> Mx.
That is not reasonable.
It is a reasonable result of choosing that P.
? What is that P? 'absolute proof'?
The standard way of proving something does not exist, is to prove that
it's impossible: KP~Mx |- ~x. Are you comfortable with that?
It may be that
it is unreasonable to choose "impossibly good" as a standard
of proof.
But you didn't exclude it. (And many people do
not consider 'abosolute' to be 'impossible'.)
So propose your own proof standard, as Jim originally suggested. It's
all well and good to say, once, "That's not a proof, because you
haven't defined 'proof' - but it's not all that logical. Either you
accept it as a proof, or you don't; and in either case, you either
have a reason, or you don't. Jim's outlined his reasons; what are
yours?
Again, What is your 'reasonable' standard of proof?
I'd agree with Jim, that there is more than one standard that's
reasonable. If I want to prove that the sun is shining, a proof would
consist of no more than looking out the window, seeing light and
shadow outside, and making an abductive inference.
True does not lead to Mx.
It's raining on me -> I will get wet.
Assume it's raining on me.
In that case, It's raining on me = True,
and True -> I will get wet.
Compare and contrast.
It is not always 'raining on you'.
It is not a constant. Sometimes it is
True and sometimes it is False.
Therefore, evaluating it can tell you
something about your getting wet.
~KP(~x) is constant true for all x
(and some P that you haven't excluded).
That's not true. It's easy enough to prove, from the definitions,
that there are no round squares.
Once you have determined that, there
is no need to ever evaluate it again
for any x.
But ~KP~x hasn't been determined (or proven); and I don't see how it
could be, as it's false.
~KP(~x) tells you nothing about Mx.
To say (constant)True -> z is illogical.
Compare and contrast:
(x is white or x is not white) -> Mx
Works for me, if you can prove it (and here, as you're using logic,
I'd have to say that the standard of proof would be: a logical
inference from
(x is white or x is not white) to Mx.
No. Mx by itself is an assertion you could make.
True -> Mx is illogical.
It's not valid; but how does that make it illogical?
(When I said "You could say" I was being generous,
anticipating what you might say, and giving you
some slack.)
So.. for some values of P, "~KP(~g)"
has no meaning or information content.
This might even be true. There isn't really much of what
you seem to be calling information content in math or logic.
However, this is a completely different claim from what
you've been talking about.
I don't think it is different.
For some P, ~KP(~x) = True, for all x.
In that case, saying "~KP(~x)" is equivalent
to saying "True!". x doesn't matter.
It says nothing about x.
Fine; let's exclude those cases.
If *you* want to consider P to stand for "absolute existential
proof" (as you did earlier), then more power to you. Why
should *I* have anything to do with defining *your* notion?
Because if you don't define P for your argument,
I (and anyone else) can put whatever they want in for it.
And that results in the destructon of your argument.
So propose some criteria.
All *I* have to say about all that is *IF* *your* notion
of "absolute existential proof" follows certain axioms, specific
things ("theorems") can said with a very high level of
certainty.
The same things could be said regarding other notions
of proof, as long as they follow the same axioms.
But the set of valid theorems varies with
the chosen standard of proof.
No; there's a standard definition of proof of a theorem: a (finite)
series of wff such that each wff is either an axiom or a valid
inference from an axiom. (If one allows assumptive proofs, like mine,
one has to add "...or an assumption, or an inference that discharges a
previous assumption.")
If you have a problem with that, I can quote you a more precise
definition from a text.
I think it cannot be that our standards for "known", "proven"
and "possible" can be allowed to vary independently of each
other. Certainly if they did the there is no way ~KP~x -> Mx
could be true.
I think they are linked through axioms like
George's Provability Axiom, Lp -> MPp
(Message-ID:<6312c50b.0406200120.4a339e10@posting.google.com>)
Why don't you start with a definition of P.
Why don't you read what I write?
You mean the 'look at it with your eyes'
standard?
No, he means read, and either accept or reject, that criterion of
proof:
Lp -> MPp - which implies L~Pp -> M~p. Is that acceptable to you or
not?
Does being able to point my face at something, i.e.
being able to look at and see something,
determine its existance?
No, of course not. There are lots of things that cannot be
treated this way, yet nonetheless exist, neutrinos,
mathematical theorems, the center of the Earth, to name a few.
Then (to help you out), how do you know they
exist? (That is not a adversarial challenge, that
is an encouraging challenge.)
If you can answer that, then you have your 'P'.
I believe that neutrinos and the center of the Earth
exist. There should therefore be a standard of proof
consistent with that.
OK; what is it? Not being able to see them, of course.
You can't make me see God.
I can not look at and see God therefore
it doesn't exist.
Ah. ... I'm curious: presumably you can look at something that
proves to you that you cannot see ever see God.
You asserted as a standard of existential proof that
you could arrange for me to be in the presence
of that thing and I would see it.
Until you do that I am permitted to conclude it
doesn't exist.
But that's not the standard you're using, as you've just stated that
you believe that neutrinos exist. So what standard do you want here?
How about "Everything we need to know is in the Analects of
Confucius." Proof of nonexistence of God: The Christian God
is not mentioned in the Analects. If He existed, we would
need to know about him in order to be righteous. Therefore
He does not exist.
(Since 'God', i.e. the god of the Bible, is a
proper noun it is appropriate to
capitalize it. Since 'he' is a pronoun, its capitalizaion
is just an affectation of the Christians, I believe.)
KP~g is true, therefore ~KP~g -> Mg is true.
Or 'valid' I think is a better term.
No, 'valid' means 'always true'.
Sure, but then Mg = False, right?
No, Mg is either true or false; if KP~g, then ~KP~g->Mg is 'vacuously
true', meaning that nothing can be concluded from it.
(A -> B is always true when A is false.)
That statement is not true if A is always
and unconditionally of one truth value (i.e. always
true or always false).
Sure it is: ~A -> (A->B) is valid.
False -> x is illogical.
A -> B is valid and a true relationship if it has
the truth table:
| B
------------
T | T
A F | U
U | U
In standard PC, A->B is valid if B is valid (always true), or if A is
unsatisfiable (always false).
If A can only possibly have one value then
there is no table and there is no relationship.
Sure there is. If there's only one value for A, then the truth tables
are:
A B A->B
T T T
T F F
A B A->B
F T T
F F T
Then I'd say, apply that same standard of proof
to God. What do you get? If you get 'unknown'
then your standard of existential proof is inadequate
and KP(x) is meaningless.
This seems to be the point that drives you: apply the same
standard of proof to God, apply the same standard of proof to
everything.
You got it.
Anything else is.... <fanfare> *Special Pleading*.
It is? Would it be 'special pleading' for me to say, "There's no
proof that the sun doesn't exist, therefore the sun may exist?" I
can't see that. So where do you get the idea that it's 'special
pleading' for Jim to say the *exact same thing* about God?
If that works for you, fine. I know I don't apply the
same standard in every situation,
The fallacy of Special Pleading.
Does 'Special Pleading mean treating "God exists" in the same way as
any other proposition? News to me.
and I don't believe anyone else
does either, you included.
I most definitely do. (Or try to the best of
my ability.)
Really? You'd prove 12*12=144 in the same way as you'd prove "My
computer is on"? Then you really must give your own definition of
'proof,' as it's apparently a beaut.
Tell me something, Jim, Do you have a different
standard of proof for the existence of God vs
the existence of other things?
I have lots of different standards for lots of different
things. Actually, I even "have" several different standards for
the existence of God. What I mean is I'm aware of several
different standards, some of which He passes, some of which
He fails. The "test" I actually use when I think about such things
is more of an esthetic judgment than a proof: the universe
does not seem to need a God to operate. This is close to
what I mean when I say Special Relativity is true.
Hey, "what is needed to make the universe operate"
is not bad for a standard of P.
Interesting. So proving that "my computer is on" means means showing
that ,y computer's being on is 'needed to make the universe operate'?
I'll also say that that and "what can be presented to the eyes"
are two things that are probably appropriate for
inclusion in the definition of 'P'.
So proving that "John farted" means showing both that John's fart can
be presented to the eyes, and that John's fart was necessary to the
universe operating? That's interesting, but I'd have to see how you'd
apply it in practice.
Introducing P without definition is a burden
shifting wedge.
I don't get it. What burden is being shifted where?
Burden shifting is "I'm right unless/until you prove me wrong."
Come on. Give me a break. The absolute worst you can read
into ~KP~x -> Mx is "I might be right, until you prove me wrong."
You are right. One *can* read it as "I might be right, until you
prove me wrong." And that is only slightly
different from the burden-shifting/ad-ignorantiam,
"I am right, until you prove me wrong."
All you have done is add the 'might'.
You've changed it, made it different, softened it some, but
it is still burden-shifting bait and it is still ad-ignorantiam.
I see. So a statement like, "There's no proof that Saddam Hussein
planned the 9/11 attack, therefore he might not have" is 'illegitimate
burden shifting'?
How convenient for Mr. Bush.
Maybe some day you'll figure out the difference between
"X exists" and "X may exist". I don't feel like teaching
you. Good luck.
Geez, what happened. You were doing so well.
Oh well. Thank you at least for teaching me
that three headed lizards
wearing tutus on Neptune may exist.
I don't see how he taught you any such thing, or even said anything
similar. thing.
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| User: "Ron Baker, Pluralitas!" |
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| Title: Re: To George Dance: Re: aa - The polls are open! TQOTM for May 2004 |
25 Jun 2004 12:12:47 PM |
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"George Dance" <georgedance@hotmail.com> wrote in message
news:6312c50b.0406241011.48b5422c@posting.google.com...
"Ron Baker, Pluralitas!" <jung@topway.net.cn> wrote in message
news:<mbiCc.31147$Ha2.24209@twister.socal.rr.com>...
"Jim Burns" <burns.87@osu.edu> wrote in message
news:40D8EF8D.8CFE3978@osu.edu...
"Ron Baker, Pluralitas!" wrote:
"Jim Burns" <burns.87@osu.edu> wrote in message
news:40D7A757.E1D5B7C8@osu.edu...
[re: ~KP~x -> Mx, "If there is no Known proof that x is false,
then x may be true.]
I say it is not reasonable.
I take that statement back.
I confess. I have been wrong on some things.
~KP~x -> Mx is a tautology, isn't it?
The predicate is basically a restatement
of the antecedent, isn't it?
--
RB
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| User: "Ron Baker, Pluralitas!" |
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| Title: Re: To George Dance: Re: aa - The polls are open! TQOTM for May 2004 |
25 Jun 2004 12:18:34 PM |
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"Jim Burns" <burns.87@osu.edu> wrote in message
news:40D8EF8D.8CFE3978@osu.edu...
"Ron Baker, Pluralitas!" wrote:
"Jim Burns" <burns.87@osu.edu> wrote in message
news:40D7A757.E1D5B7C8@osu.edu...
[re: ~KP~x -> Mx, "If there is no Known proof that x is false,
then x may be true.]
I say it is not reasonable.
I take that statement back.
I confess. After further discussion with
George Dance and some reading and thinking
I see I have been wrong on some things.
~KP~x -> Mx is a tautology, isn't it?
The predicate is basically a restatement
of the antecedent, isn't it?
--
RB
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| User: "Dixit" |
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| Title: Is there a known proof of the existence of the sun? |
19 Jun 2004 10:54:33 AM |
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Ron Baker, Pluralitas! wrote:
Is there a known proof of the existence of the sun?
Are you kidding? If you have any doubt, go outside today around noon
(which means when the sun is at it's highest point where you are), bare
your white arse and expose it toward that bright thing above for about
two hours. Let us know the result tomorrow. 8^)
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| User: "Virgil" |
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| Title: Re: Is there a known proof of the existence of the sun? |
19 Jun 2004 01:57:14 PM |
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In article <ZkZAc.76187$0y.55206@attbi_s03>, Dixit <dix@nospam.com>
wrote:
Ron Baker, Pluralitas! wrote:
Is there a known proof of the existence of the sun?
Are you kidding? If you have any doubt, go outside today around noon
(which means when the sun is at it's highest point where you are), bare
your white arse and expose it toward that bright thing above for about
two hours. Let us know the result tomorrow. 8^)
Snide comments do not constitute proofs. And Septic Capon, the Simple
Pimple's response does not answer the question, but argues ad hominem
instead of on the issue itself.
Or perhaps Septic Capon, the Simple Pimple, does not actually know
whether there is any proof that the sun exists. It would not be the
first time Septic Capon, the Simple Pimple, has tried diversionary
tactics to hid his ignorance.
.
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| User: "Michael Moore" |
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| Title: Re: To George Dance: Re: aa - The polls are open! TQOTM for May 2004 |
17 Jun 2004 10:45:39 PM |
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Jim Burns wrote:
For the purposes of this proposed theorem, "God" is
defined as "Something that is not known to have a proof
that it does not exist.", or ~KP~g.
Those are the kind of attributes that make it easy to
distinguish God from nothing -- not!
--
M2
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| User: "George Dance" |
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| Title: Re: To George Dance: Re: aa - The polls are open! TQOTM for May 2004 |
20 Jun 2004 04:20:50 AM |
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Jim Burns <burns.87@osu.edu> wrote in message news:<40D1257A.8E172D98@osu.edu>...
I would have preferred [to see your assumptions] at the top
of the proof. Also, I'd have liked you to state the theorem once
in the form "Given these assumptions, ... , there may be a God."
I wrote an earlier reply, which google apparently ate. But it's all
for the best; rather than a line-by-line reply, which I tried earlier,
I opted this time to repair my argument in light of your criticism.
The only assumption left is ~KP~g, and the result is a null assumption
proof of ~KP~g->Mg, as you suggested.
I'm putting your statements in a more compact notation. That's easier
for me to follow.
I've copied your notation by and large. However, I have had to use
two sets of lower-case letters to distinguish between atomic constants
(a,b,c,..., g,...) and propositional variables, which can be more
complex wff (p,q,r,...,x,...).
I see three modal operators and one predicate
(sentence?)
Mx =df "it MAY be that x"
Px =df "there is a PROOF that x"
Kx =df "it is KNOWN that x"
g =df "GODS exist", or "GOD exists", or something like that
a | b =df "a or b"
[I've used a v b]
a & b =df "a and b"
a -> b =df "if a then b" or "a only if b"
~(b -> ~a) =df "a even though b"
That last one was a head-scratcher. Note that ~(b -> ~a) is
formally equivalent to a & b.
I've got a pretty good handle on the manipulation of the
connectives.
Yes, I think that's close to settled. Two points I'd make, though:
First, I assumed throughout that a constant modified by a unary
operator was no different from any other variable or wff, and that
anything true of a variable was true of it. (That's standard IME).
Second, I've used inference rules from different systems. In my
defence I'd say that: first, as these are all valid rules, they can
all be expressed by adding extra tautologies and using MP; but that
would have made it much harder to read; second, as I want this proof
to be read and understood by as many as possible, I deliberately
decided to leave it non-rigorous to that extent.
What I'm unsure about is what I can do with the
modal operators. I assume I can say:
x -> Mx
Px -> x
Kx -> x
But what else do we need to be able to do?
We need a necessity operator, L, and the normal rules of modal
negation, Lp::~M~p and Mp::~L~p. As well, we need to somehow
axiomatize proveability in order to use it; I haven't done that in
full, but I have added one axiom I'm calling here the Proveability
Axiom (PA): "A proposition is necessarily true, only if it is possible
to prove that it is true".
PA: Lp -> MPp
In addition, I've added two governing the relations between
propositional constants and variables. The first is an axiom of
Instantiation: "Whatever is true of any variable, is true of any
constant."
UI: Ap -> Aa
The second, which is probably the most contentious thing I've done
here, is to add a falsifiability, which I've called NC for No
Counterexamples: "A theory is true only if there are no
counterexamples."
NC: (Ap -> Bp) -> ~(Aa & ~Ba)
One more thing I've done, which isn't germane at all, is to try out a
new method of indicating assumptions - by using a vertical line at
left, with a numbers at start and bottom; the first number indicating
on which line the assumption was made, and the second indicating which
assumption is being discharged on that line. I'd appreciate your
comments, as I think it improves readability vastly over some other
methods.
I think a perfectly fine theorem might be something like
~KP~g -> Mg
If there is no known proof that God does not exist,
then God may exist.
I think it expresses very well the agnostic point of view and
has the huge advantage of being provable (if it is a theorem).
Agreed. I hope you can agree that this is a sound proof of
~KP~g -> Mg:
1 - -- 1. ~KP~g ACP
| 2. MP~g v ~MP~g (pv~p) [MP~g/p]
| 3 -- 3. ~MP~g ACP
| | 4. L~g -> MP~g PA [~g/p]
| | 5. ~MP~g -> ~L~g 4 Contra
| | 6. ~L~g 3,5 MP
| | 7. Mg 6 MN
| 3 -- 8. ~MP~g -> Mg 1-7 CP
| 9 -- 9. MP~g ACP
| | 10. ~~MP~g 9 DN
| | 11. ~KP~g & ~~MP~g 1,10 Conj
| | 12. (~Kp -> ~Mp) -> ~(~KP~g & ~~MP~g) NC [~K/A, ~M/B, ~g/a]
| | 13. (~KP~g & ~~MP~g) -> ~(~Kp -> ~Mp) 12 Contra
| | 14. ~(~Kp -> ~Mp) 11,13 MP
| | 15. Kg v ~Kg (pv~p) [Kg/p]
| | 16 16. Kg ACP
| | | 17. Kg -> g I [g/p]
| | | 18. g 16,17 MP
| | | 19. g -> Mg II [g/p]
| | | 20. Mg 18,19 MP
| | 16 21. Kg -> Mg 16-21 CP
| | 22 22. ~Kg ACP
| | | 23. ~(~Kg -> ~Mg) 14 [g/p]
| | | 24. ~Kg & ~(~Kg -> ~Mg) 22,23 Conj
| | | 25. (~Kg & ~(~Kg -> ~Mg)) -> ~~Mg ((p&~(p->q))->~q)
[~Kg/p,~Mg/q] | | | 26. ~~Mg 24,25 MP
| | | 27. Mg 26 DN
| | 22 28. ~Kg -> Mg 22-27 CP
| | 29. Mg v Mg 15,21,28 CD
| | 30. Mg 29 Idem
| 9 -- 31. MP~g -> Mg 9-30 CP
| 32. Mg v Mg 2,8,31 CD
| 33. Mg 32 Idem
1 - -- 34. ~KP~g -> Mg 1-33 CP
QED
.
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| User: "Jim Burns" |
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| Title: Re: To George Dance: Re: aa - The polls are open! TQOTM for May 2004 |
20 Jun 2004 11:10:33 PM |
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George Dance wrote:
Jim Burns <burns.87@osu.edu> wrote in message
news:<40D1257A.8E172D98@osu.edu>...
[...]
I've copied your notation by and large. However, I have had to
use two sets of lower-case letters to distinguish between atomic
constants (a,b,c,..., g,...) and propositional variables, which
can be more complex wff (p,q,r,...,x,...).
I'm afraid this may be a dumb question, but what is the difference
between constants and variables?
I am looking at your proof and translating into some form I'm
more familiar with. I'm treating the propositional variables
as though they are implicitly universally quantified.
Mostly that works, but it turns lines 12,13,14 into magic
(pulling rabbits out of hats), so I suspect I have it wrong.
| | 12. (~Kp -> ~Mp) -> ~(~KP~g & ~~MP~g) NC [~K/A, ~M/B, ~g/a]
| | 13. (~KP~g & ~~MP~g) -> ~(~Kp -> ~Mp) 12 Contra
| | 14. ~(~Kp -> ~Mp) 11,13 MP
You start with a general law implying no counter-examples, and
use the existence of a counter-example to derive the
negation -- as a law -- of the original law. If I translate
that as I would like to, that's not valid.
In my terms, the negation of
(All p) (~Kp -> ~Mp)
is
(Exists p) ~(~Kp -> ~Mp),
but my translation scheme makes line 14
(All p) ~(~Kp -> ~Mp).
What are the restrictions on substitution into p in line 14?
That seems like too strong statement to be able to say
about _anything_. In particular, (though I'm a babe-in-arms
with this stuff) can't we say ~(q->~r) -> q and ~(q->~r) -> r?
Then it would seem to follow that ~Kp (everything is unknown)
and Mp (everything is possible).
[...]
We need a necessity operator, L, and the normal rules of modal
negation, Lp::~M~p and Mp::~L~p. As well, we need to somehow
axiomatize proveability in order to use it; I haven't done that
in full, but I have added one axiom I'm calling here the
Proveability Axiom (PA): "A proposition is necessarily true,
only if it is possible to prove that it is true".
PA: Lp -> MPp
I like this axiom. It has a certain common sense feel about it,
plus it gives me the link between what is and what is provable
that I wanted.
Still, I think care may be needed when using it. My understanding
is that Goedel proved there are sentences of number theory that
are true (and so necessarily true, Lp) but are not provable within
the system (and so not possible to prove, ~MPp).
I doubt that the kind of tangled situation he exploits in his
proof would arise in talk about gods, or even known/unknown
proofs about gods, but how would you draw the line between
tangled and normal situations?
[...]
One more thing I've done, which isn't germane at all, is to try
out a new method of indicating assumptions - by using a vertical
line at left, with a numbers at start and bottom; the first
number indicating on which line the assumption was made, and the
second indicating which assumption is being discharged on that
line. I'd appreciate your comments, as I think it improves
readability vastly over some other methods.
This is much easier for me to read. Essentially you are bracketing
the sub-proofs. At any step I can go outside any number of
brackets, in order to access another (earlier) step, but I
can't go inside any neighboring brackets.
What would you think of numbering lines like software versions?
I've edited your proof only to show what I mean.
[...]
Agreed. I hope you can agree that this is a sound proof of
~KP~g -> Mg:
Apart from my comments above, about what it means to negating
a wff with variables, this looks valid to me, and that one
thing may well be due to my own lack of understanding of this
kind of proof.
--Jim Burns
1.1 1. ~KP~g ACP
1.2 2. MP~g v ~MP~g (pv~p) [MP~g/p]
1.3.1 3. ~MP~g ACP
1.3.2 4. L~g -> MP~g PA [~g/p]
1.3.3 5. ~MP~g -> ~L~g 4 Contra
1.3.4 6. ~L~g 3,5 MP
1.3.5 7. Mg 6 MN
1.3 8. ~MP~g -> Mg 1-7 CP
1.4.1 9. MP~g ACP
1.4.2 10. ~~MP~g 9 DN
1.4.3 11. ~KP~g & ~~MP~g 1,10 Conj
1.4.4 12. (~Kp -> ~Mp) -> ~(~KP~g & ~~MP~g) NC [~K/A, ~M/B, ~g/a]
1.4.5 13. (~KP~g & ~~MP~g) -> ~(~Kp -> ~Mp) 12 Contra
1.4.6 14. ~(~Kp -> ~Mp) 11,13 MP
1.4.7 15. Kg v ~Kg (pv~p) [Kg/p]
1.4.8.1 16. Kg ACP
1.4.8.2 17. Kg -> g I [g/p]
1.4.8.2 18. g 16,17 MP
1.4.8.3 19. g -> Mg II [g/p]
1.4.8.4 20. Mg 18,19 MP
1.4.8 21. Kg -> Mg 16-21 CP
1.4.9.1 22. ~Kg ACP
1.4.9.2 23. ~(~Kg -> ~Mg) 14 [g/p]
1.4.9.3 24. ~Kg & ~(~Kg -> ~Mg) 22,23 Conj
1.4.9.4 25. (~Kg & ~(~Kg -> ~Mg)) -> ~~Mg ((p&~(p->q))->~q)
[~Kg/p,~Mg/q]
1.4.9.5 26. ~~Mg 24,25 MP
1.4.9.6 27. Mg 26 DN
1.4.9 28. ~Kg -> Mg 22-27 CP
1.4.10 29. Mg v Mg 15,21,28 CD
1.4.11 30. Mg 29 Idem
1.4 31. MP~g -> Mg 9-30 CP
1.5 32. Mg v Mg 2,8,31 CD
1.6 33. Mg 32 Idem
1 34. ~KP~g -> Mg 1-33 CP
QED
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| User: "George Dance" |
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| Title: Re: To George Dance: Re: aa - The polls are open! TQOTM for May 2004 |
22 Jun 2004 12:29:17 PM |
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Jim Burns <burns.87@osu.edu> wrote in message news:<40D65FB9.7A392015@osu.edu>...
George Dance wrote:
Jim Burns <burns.87@osu.edu> wrote in message
news:<40D1257A.8E172D98@osu.edu>...
[...]
I've copied your notation by and large. However, I have had to
use two sets of lower-case letters to distinguish between atomic
constants (a,b,c,..., g,...) and propositional variables, which
can be more complex wff (p,q,r,...,x,...).
I'm afraid this may be a dumb question, but what is the difference
between constants and variables?
Not dumb at all; especially when the same logical rules apply to both.
And I can't find the text I want (Woods et al's /Argument/) that
gives that distinction for PC. So I'm going to try an explanation of
my own:
If an argument is about specific statements like "God exists", "Jim
Burns exists", etc., then it can be symbolized in PC with all those
statements (where they're atomic, ie don't contain any PC operators)
replaced by constants {P,Q,R...}. But if, at some point in the
argument, we want to talk about statements in general, then we need a
more abstract term that stands for any one of those statements, but
not any particular one; and for that we need a set of variables
{p,q,r,...}. And if we want to abstract one level further, and talk
about theorems about statements, we need a a further set of
metavariables {A,B,C...}. If something is true of a metavariable,
it's true of any variable, and if it's true of a variable, it's true
of any constant - which is quite convenient, as the rules governing
the connectives apply whether they connect constants, variables, or
metavariables.
(In my proof, I use {a,b,c...} to represent constants, as we used P
for a modal operator.)
I am looking at your proof and translating into some form I'm
more familiar with. I'm treating the propositional variables
as though they are implicitly universally quantified.
Mostly that works, but it turns lines 12,13,14 into magic
(pulling rabbits out of hats), so I suspect I have it wrong.
| | 12. (~Kp -> ~Mp) -> ~(~KP~g & ~~MP~g) NC [~K/A, ~M/B, ~g/a]
| | 13. (~KP~g & ~~MP~g) -> ~(~Kp -> ~Mp) 12 Contra
| | 14. ~(~Kp -> ~Mp) 11,13 MP
You start with a general law implying no counter-examples, and
use the existence of a counter-example to derive the
negation -- as a law -- of the original law. If I translate
that as I would like to, that's not valid.
In my terms, the negation of
(All p) (~Kp -> ~Mp)
is
(Exists p) ~(~Kp -> ~Mp),
but my translation scheme makes line 14
(All p) ~(~Kp -> ~Mp).
Yes, you're right; given the NC axiom, the proof is PC-valid, but not
FOPL-valid. And I have no problems leaving it there, as my point in
writing it was to advance the debate (by finding the actual area of
disagreement) rather than
The reason for FOPL-invalidity is that there are statements that use
variables that are false wrt some constants and true wrt others. For
example, "If a CD costs $10 or less GD will buy it" is true for a
Beatles CD but false for a Britney Spears CD.
This FOPL-invalidity leaves antitheists a logical out; they do not
have to accept that there may be a God, as they can counterargue that
(1) "God exists" is different, in some relevant way, from (2) "It is
proveable that there is no God"; because (to deny Mg) he has to assert
that (~KPp -> Mp) is both true (wrt (1)) and false (wrt (2)). In
short, he has to make a special pleading for either (1) or (2) (which
may or may not be a justified special pleading).
What are the restrictions on substitution into p in line 14?
None, if p is 'any proposition'; but, as quantification shows, p is
not necessarily 'any proposition' (though it might be), but only,
necessarily, 'some propositions'.
I'd say it's up to the antitheist to say what restrictions he is
using; what justifies his believing (~KPp -> Mp) wrt to (1) but at the
same time denies it wrt (2).
That seems like too strong statement to be able to say
about _anything_. In particular, (though I'm a babe-in-arms
with this stuff) can't we say ~(q->~r) -> q and ~(q->~r) -> r?
Then it would seem to follow that ~Kp (everything is unknown)
and Mp (everything is possible).
Which is false, if there are some statements known to be true; and, I
guess, to be talking about 'proofs' we have to assume there are some
of those. 8)
[...]
We need a necessity operator, L, and the normal rules of modal
negation, Lp::~M~p and Mp::~L~p. As well, we need to somehow
axiomatize proveability in order to use it; I haven't done that
in full, but I have added one axiom I'm calling here the
Proveability Axiom (PA): "A proposition is necessarily true,
only if it is possible to prove that it is true".
PA: Lp -> MPp
I like this axiom. It has a certain common sense feel about it,
plus it gives me the link between what is and what is provable
that I wanted.
Still, I think care may be needed when using it. My understanding
is that Goedel proved there are sentences of number theory that
are true (and so necessarily true, Lp) but are not provable within
the system (and so not possible to prove, ~MPp).
I doubt that the kind of tangled situation he exploits in his
proof would arise in talk about gods, or even known/unknown
proofs about gods, but how would you draw the line between
tangled and normal situations?
I wouldn't for now, because I haven't given that any thought; if an
antitheist wanted to challenge the proof on this level, I guess we'd
have to go into it; and I suspect we'd find that PA is as
controversial as NC.
(As I've said once or twice, I find these arguments about God to be
useful precisely because they're a method of discovering truths about
epistemology using a topic that there is general interest in (which is
certainly not true of epistemology as a topic).)
[...]
This is much easier for me to read. Essentially you are bracketing
the sub-proofs. At any step I can go outside any number of
brackets, in order to access another (earlier) step, but I
can't go inside any neighboring brackets.
What would you think of numbering lines like software versions?
I've edited your proof only to show what I mean.
Harder to read, and apparently much harder to write without making any
line errors. I think I'll keep my notation for Usenet, for now; if I
buy a logic program at some point, I'll have to learn the numbering
notation, and at that point I'd probably swing over to using it.
[...]
Agreed. I hope you can agree that this is a sound proof of
~KP~g -> Mg:
Apart from my comments above, about what it means to negating
a wff with variables, this looks valid to me, and that one
thing may well be due to my own lack of understanding of this
kind of proof.
No, your comments were all correct.
--Jim Burns
1.1 1. ~KP~g ACP
1.2 2. MP~g v ~MP~g (pv~p) [MP~g/p]
1.3.1 3. ~MP~g ACP
1.3.2 4. L~g -> MP~g PA [~g/p]
1.3.3 5. ~MP~g -> ~L~g 4 Contra
1.3.4 6. ~L~g 3,5 MP
1.3.5 7. Mg 6 MN
1.3 8. ~MP~g -> Mg 1-7 CP
1.4.1 9. MP~g ACP
1.4.2 10. ~~MP~g 9 DN
1.4.3 11. ~KP~g & ~~MP~g 1,10 Conj
1.4.4 12. (~Kp -> ~Mp) -> ~(~KP~g & ~~MP~g) NC [~K/A, ~M/B, ~g/a]
1.4.5 13. (~KP~g & ~~MP~g) -> ~(~Kp -> ~Mp) 12 Contra
1.4.6 14. ~(~Kp -> ~Mp) 11,13 MP
1.4.7 15. Kg v ~Kg (pv~p) [Kg/p]
1.4.8.1 16. Kg ACP
1.4.8.2 17. Kg -> g I [g/p]
1.4.8.2 18. g 16,17 MP
1.4.8.3 19. g -> Mg II [g/p]
1.4.8.4 20. Mg 18,19 MP
1.4.8 21. Kg -> Mg 16-21 CP
1.4.9.1 22. ~Kg ACP
1.4.9.2 23. ~(~Kg -> ~Mg) 14 [g/p]
1.4.9.3 24. ~Kg & ~(~Kg -> ~Mg) 22,23 Conj
1.4.9.4 25. (~Kg & ~(~Kg -> ~Mg)) -> ~~Mg ((p&~(p->q))->~q)
[~Kg/p,~Mg/q]
1.4.9.5 26. ~~Mg 24,25 MP
1.4.9.6 27. Mg 26 DN
1.4.9 28. ~Kg -> Mg 22-27 CP
1.4.10 29. Mg v Mg 15,21,28 CD
1.4.11 30. Mg 29 Idem
1.4 31. MP~g -> Mg 9-30 CP
1.5 32. Mg v Mg 2,8,31 CD
1.6 33. Mg 32 Idem
1 34. ~KP~g -> Mg 1-33 CP
QED
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| User: "Jim Burns" |
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| Title: Re: To George Dance: Re: aa - The polls are open! TQOTM for May 2004 |
22 Jun 2004 10:14:01 PM |
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George Dance wrote:
The reason for FOPL-invalidity is that there are statements that
use variables that are false wrt some constants and true wrt
others. For example, "If a CD costs $10 or less GD will buy it"
is true for a Beatles CD but false for a Britney Spears CD.
It sounds like most PC wff-with-variable are neither true
nor false, or rather (let's say) ~KP~x -> Mx and ~( ~KP~x -> Mx )
could both be false at the same time.
I'm going to have to think about this.
What I'd like is an FOPL-valid proof of ~KP~x -> Mx. That would
feel "real" to me.
Jim Burns
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| User: "George Dance" |
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| Title: Re: To George Dance: Re: aa - The polls are open! TQOTM for May 2004 |
24 Jun 2004 10:58:21 AM |
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Jim Burns <burns.87@osu.edu> wrote in message news:<40D8F579.1802347E@osu.edu>...
George Dance wrote:
The reason for FOPL-invalidity is that there are statements that
use variables that are false wrt some constants and true wrt
others. For example, "If a CD costs $10 or less GD will buy it"
is true for a Beatles CD but false for a Britney Spears CD.
It sounds like most PC wff-with-variable are neither true
nor false, or rather (let's say) ~KP~x -> Mx and ~( ~KP~x -> Mx )
could both be false at the same time.
Indeed; that's the reason for introducing quantification.
(Ex)(~Kp~x->Mx) is trivially true (as there are some things for which
(~KP~x is false); but that doesn't make (x)(~KP~x->Mx) true.
I'm going to have to think about this.
What I'd like is an FOPL-valid proof of ~KP~x -> Mx. That would
feel "real" to me.
Jim Burns
I don't think you're going to get one. Consider this counterexample:
It's impossible that there is a largest prime, and there is a proof
that there's no largest prime. But there was no such proof in 2000BC;
does that imply that there might have been a largest prime in 2000BC?
One can define a different modal operator Ux =df. ~K~x, which may make
it looks possible to give a FOPL-valid proof of ~KP~x->U~x ("It's not
known that there is no God"); the question then being how one gets
from U~x to Mx, or if one even does.
Alternatively, one can look at the define the 'belief positions' using
epistemic, doxastic, *and* deontic logic. That may be the more
promising approach, to seriously get to the bottom of the debate.
Would you say that the following are fair summaries:
Theist: OBg
Antitheist: OB~g
Agnostic: ~OBg & ~OB~g
?
("O="It ought to be the case that_"; B="It is believed that_"; g="God
exists")
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| User: "Diixiit" |
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| Title: Re: To George Dance: Re: aa - The polls are open! TQOTM for May 2004 |
18 Jun 2004 09:25:42 AM |
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Jim Burns wrote:
If there is no known proof that God does not exist,
then God may exist.
Argument from ignorance.
<quote>
Famous in the history of science is the argument _ad ignorantiam_ given
in criticism of Galileo, when he showed leading astronomers of his time
the mountains and valleys on the moon that could be seen through his
telescope. Some scholars of that age, absolutely convinced that the moon
was a perfect sphere, as theology and Aristotelian science had long
taught, argued against Galileo that, although we see what appear to be
mountains and valleys, the moon is in fact a perfect sphere, because all
its apparent irregularities are filled in by an invisible crystalline
substance. And this hypothesis, which saves the perfection of the
heavenly bodies, Galileo could not prove false!
</quote>
(Copi and Cohen, _Introduction to Logic_, p. 117)
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| User: "Virgil" |
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| Title: Re: To George Dance: Re: aa - The polls are open! TQOTM for May 2004 |
18 Jun 2004 02:50:15 PM |
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In article <GXCAc.133934$Ly.23244@attbi_s01>,
Diixiit <diiix@nospam.com> wrote:
Jim Burns wrote:
If there is no known proof that God does not exist,
then God may exist.
Argument from ignorance.
Septic Capon, the Simple Pimple, argues from his own ignorance in saying
this.
A true argumentum ad ignotantiam would take the form "If there is no
known proof that God does not exist, then God MUST exist."
But Septic Capon, the Simple Pimple, is so ignorant that he canot tell
the difference between "MAY" and "MUST".
Such ignorance trying to correct its betters is pitiful.
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| User: "George Dance" |
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| Title: Re: To George Dance: Re: aa - The polls are open! TQOTM for May 2004 |
20 Jun 2004 06:11:00 PM |
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Virgil <ITSnetNOTcom/virgil@COMCAST.com> wrote in message news:<ITSnetNOTcom/virgil-450FD4.13501418062004@[63.218.45.211]>...
In article <GXCAc.133934$Ly.23244@attbi_s01>,
Diixiit <diiix@nospam.com> wrote:
Jim Burns wrote:
If there is no known proof that God does not exist,
then God may exist.
Argument from ignorance.
Septic Capon, the Simple Pimple, argues from his own ignorance in saying
this.
A true argumentum ad ignotantiam would take the form "If there is no
known proof that God does not exist, then God MUST exist."
That's one form (~KP~p -> []p). There is also a weaker form: "If
there is no known proof that x does not exist, then x DOES exist."
(~KP~p -> p).
Both wff are invalid, so using either in a MP inference is not
truth-preserving, and is fallacious.
OTOH, Jim's statement "If there is no known proof that God does not
exist,
then God may exist" has the form (~KP~p -> <>p), which (as I hope to
have proved) is valid - so its use in MP inference is not fallacious,
and therefore not a fallacy of ignorance.
But Septic Capon, the Simple Pimple, is so ignorant that he canot tell
the difference between "MAY" and "MUST".
Interestingly, Septic assumes the invalid wff (~KP~p -> p) himself to
argue fallaciously from ignorance against solipsism.
Such ignorance trying to correct its betters is pitiful.
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| User: "Dixit" |
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| Title: Re: To George Dance: Re: aa - The polls are open! TQOTM for May 2004 |
22 Jun 2004 11:57:22 AM |
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George Dance wrote:
Interestingly, Septic assumes the invalid wff (~KP~p -> p) himself to
argue fallaciously from ignorance against solipsism.
That's not true. I haven't "argued against solipsism." No argument
against solipsism is even required. All I have done is point out that
the only way to reach solipsism is to take it for granted at the outset
(begging the question), then argue _ad ignorantiam_ that there is no
proof it is false.
If you disagree, let's see your argument for solipsism that does not
resort to logical fallacy.
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| User: "George Dance" |
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| Title: Re: To George Dance: Re: aa - The polls are open! TQOTM for May 2004 |
24 Jun 2004 09:37:01 AM |
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Dixit <dix@nospam.com> wrote in message news:<SxZBc.89139$eu.37502@attbi_s02>...
George Dance wrote:
Interestingly, Septic assumes the invalid wff (~KP~p -> p) himself to
argue fallaciously from ignorance against solipsism.
That's not true. I haven't "argued against solipsism." No argument
against solipsism is even required.
That's the second time you've used that non sequitur. Is it supposed
to mean anything?
All I have done is point out that
the only way to reach solipsism is to take it for granted at the outset
(begging the question), then argue _ad ignorantiam_ that there is no
proof it is false.
Actually, you haven't 'pointed that out,' either, but just said it a
number of times. If you really think you can point it out, then,
let's see you do just that.
<re-cue the crickets>
If you disagree, let's see your argument for solipsism that does not
resort to logical fallacy.
You made the claim, you support it; arguing from ignorance that
there's no proof it's false, is not support BTW.
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| User: "Dixit" |
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| Title: Re: solipsism |
24 Jun 2004 11:15:39 AM |
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George Dance wrote:
<re: solipsism>
... arguing from ignorance that
there's no proof it's false, is not support BTW.
Precisely, and the only way to reach solipsism is by taking it for
granted at the outset (begging the question), then argue _ad
ignorantiam_ that there is no proof it is false, as you do.
If you believe there is a legitimate argument for solipsism that does
not resort to logical fallacy, then why don't you simply post it so we
can all examine it, Georgie?
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| User: "George Dance" |
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| Title: Re: solipsism |
26 Jun 2004 05:02:59 PM |
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Dixit <dix@nospam.com> wrote in message news:<K6DCc.108540$0y.91285@attbi_s03>...
George Dance wrote:
<re: solipsism>
... arguing from ignorance that
there's no proof it's false, is not support BTW.
Precisely ... _ad
ignorantiam_
Very good; you know it's a fallay, and even know its name. Which
makes one wonder why you keep trying it over and over again, as you do
right here:
If you believe there is a legitimate argument for solipsism that does
not resort to logical fallacy, then why don't you simply post it so we
can all examine it, Georgie?
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| User: "Eric Pepke" |
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| Title: Re: solipsism |
25 Jun 2004 06:03:22 PM |
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Dixit <dix@nospam.com> wrote in message news:<K6DCc.108540$0y.91285@attbi_s03>...
Precisely, and the only way to reach solipsism is by taking it for
granted at the outset (begging the question), then argue _ad
ignorantiam_ that there is no proof it is false, as you do.
If you believe there is a legitimate argument for solipsism that does
not resort to logical fallacy, then why don't you simply post it so we
can all examine it, Georgie?
'
The problem with solipsists is that they don't just go talk to themselves,
which is what they should do. Anything that a solipsist says to me is,
by definition, a lie, because of course to them I don't exist. Since I don't
exist, I feel I get to be as nasty to them as I want to. When they complain,
I always say, "But I'm a figment of your imagination. So, if you imagine
me as such a mean person, it's your problem."
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