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Science Forum Index » Logic Forum » All panduks are green
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| Jesse F. Hughes |
Posted: Wed Apr 09, 2008 7:11 am |
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Newberry <newberryxy@gmail.com> writes:
Quote: On Apr 8, 12:09 pm, stevendaryl3...@yahoo.com (Daryl McCullough)
wrote:
Newberry says...
If X represents "round square" then what state of affairs is "for all
objects o, if o is a round square, then o is green" is a picture of.
I don't understand why this is difficult for you.
"for all objects o, if o is a round square, then o is green"
means that there are no objects that are round, square, and
nongreen.
This object o, that is round, square, and non-green, what does it
^ non-existent
look like?
"Liberty is a fundamental value of democracy."
This object "liberty", what does it look like? Or is this sentence
also meaningless because it is not a picture of anything?
Quote: I didn't say that "All panduks are green" means "there are
no panduks". I said that it means
"Either there are no panduks, or there are some panduks, and
every one of them is green".
Does every sentence of the form "all P are Q" mean
~(Ex)Px v (x)(Px -> Qx) ?
After all this time, are you really so confused about standard
translations of sentences? Why do you ask such a strange question?
The sentence "all P are Q" means:
(x)(Px -> Qx).
This formula is equivalent to
~(Ex)Px v ((Ex)Px & (x)(Px -> Qx))
which is what Daryl suggested as the meaning of the natural language
sentence. It is also equivalent to
~(Ex)Px v (x)(Px -> Qx).
Surely you can't pretend to have an insightful criticism of classical
logic if you don't know these basic, obvious facts. I suppose you
were asking a question you knew the answer to, but get on with it
already.
--
"Puts his arm around you, fiddles with your hair. You know, and he says, come
on, you know, just because you like a bit of a kiss and a cuddle with another
man doesn't make you gay. Which, you know, I've thought a lot about. But I
think it does. I think it does." --- The Office (interviews) |
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| Jesse F. Hughes |
Posted: Wed Apr 09, 2008 7:12 am |
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"Jesse F. Hughes" <jesse@phiwumbda.org> writes:
Quote: Is "panduk" an undefined term? If so, then the sentence "All
panduks are green" is undefined because a term in it is undefined
^^^^^^^^^ meaningless
(not because the term has no denotatum).
--
"I liked the world a lot better over ten years ago. I believed in a
lot more things. Hell, most people believed in a lot more things.
Back then the United States was still, well, known as most people used
to know the United States." -- James S. Harris in a nostalgic mood |
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| Daryl McCullough |
Posted: Wed Apr 09, 2008 8:20 am |
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Newberry says...
Quote:
On Apr 8, 12:09=A0pm, stevendaryl3...@yahoo.com (Daryl McCullough)
wrote:
Newberry says...
If X represents "round square" then what state of affairs is "for all
objects o, if o is a round square, then o is green" is a picture of.
I don't understand why this is difficult for you.
"for all objects o, if o is a round square, then o is green"
means that there are no objects that are round, square, and
nongreen.
This object o, that is round, square, and non-green, what does it look
like?
There are no objects that are round, square and non-green.
Which is logically equivalent to:
forall objects o, if o is round and square, then it is green.
Quote: Does every sentence of the form "all P are Q" mean
~(Ex)Px v (x)(Px -> Qx) ?
As far as I'm concerned, yes.
--
Daryl McCullough
Ithaca, NY |
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| Daryl McCullough |
Posted: Wed Apr 09, 2008 9:04 am |
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Newberry says...
Quote: If your objective is to win the argument then yes, you won.
Good. Can we end this discussion, then?
--
Daryl McCullough
Ithaca, NY |
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| Aatu Koskensilta |
Posted: Wed Apr 09, 2008 9:06 am |
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On 2008-04-09, in sci.logic, Newberry wrote:
Quote: So "all numbers that are smaller than themselves are greater than
themselves" is false?
This is a baffling response to Daryl's declaration that as far as he's
concerned, every sentence of the form "all P are Q" mean
~(Ex)Px v (x)(Px -> Qx)
It is entirely obscure why that would lead you to surmise that "all
numbers that are smaller than themselves are greater than themselves"
is false.
--
Aatu Koskensilta (aatu.koskensilta@xortec.fi)
"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus |
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| Daryl McCullough |
Posted: Wed Apr 09, 2008 9:23 am |
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Newberry says...
Quote: On Apr 9, 6:20=A0am, stevendaryl3...@yahoo.com (Daryl McCullough) wrote:
Does every sentence of the form "all P are Q" mean
~(Ex)Px v (x)(Px -> Qx) ?
As far as I'm concerned, yes.
So "all numbers that are smaller than themselves are greater than
themselves" is false?
I said just the opposite. A sentence of the form "all Ps are Qs" is
vacuously true when there are no Ps.
--
Daryl McCullough
Ithaca, NY |
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| Jesse F. Hughes |
Posted: Wed Apr 09, 2008 10:17 am |
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Newberry <newberryxy@gmail.com> writes:
Quote: On Apr 9, 4:40 am, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
Newberry <newberr...@gmail.com> writes:
On Apr 8, 10:37 am, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
Why is "All panduks are green" meaningless? If it is because the word
"panduk" is meaningless, then of course everyone agrees. But that's
not what you said. Here is what you said:
Would it be fair to say that "all panduks are green" is meanigless
because "panduk" does not have a denotatum?
Here, you are evidently suggesting that whenever a term X has no
denotatum, statements of the form "Every X is P" are meaningless.
That *is* what you said, right?
If so, the conclusions are fairly obvious.
The term "four-legged bird" has no denotatum (let us assume), so the
statement "Every four-legged bird has four knees" is meaningless.
The term "unicorn" has no denotatum, so both of the sentences
Every unicorn has two horns.
No unicorn has two horns.
are meaningless.
It seems a bit churlish to accuse me of short memory when what you
said about panduks did not mention whether panduks are necessarily
non-existent or merely actually non-existent. What you said is: there
are no panduks, so the claim "All panduks are green" is meaningless.
If your objective is to win the argument then yes, you won. I will
admit (for the sake of argument) that I was imprecise.
My objective was simply to understand where the heck you were going
with panduks. You have never made this clear.
Where I was going with panduks? My point obviusly was that if "all
oanduks are green" is meaningless then "all round squares are green"
must also be meaningless, and for the same readon: "panduk" does not
have a denotatum, "round square" does not have a denotatum.
Yet again, you are confusing your own claims. There are no
four-legged birds, but you say that "All four-legged birds have four
knees" is a true statement, not meaningless. So, if "All panduks are
green" is meaningless, it must be so for some other reason.
Here are the possibilities I see. "All panduks are green" is
meaningless because:
(1) There are no panduks.
In this case, "All four-legged birds have four knees" would be
meaningless too, but you say it isn't.
(2) There are necessarily no panduks.
This might be what you meant, but I don't see how I should have
concluded that this is the case.
(3) "Panduk" is a meaningless term.
Then "All round squares are green" is not meaningless for the same
reason, since "round square" is not a meaningless term.
[...]
Quote: But to make sure that we are clear: "Unicorn" does have a denotatum;
my kid has a toy unicorn. (BTW, it has only one horn.) I bet you you
you have never seen a toy round square or a toy panduk.
You're being silly. A toy unicorn is not an instance of the term
"Unicorn". Or do you suppose that drawings of Santa are sufficient
evidence that Santa exists (indeed, Santas exist)?
I do not know who is being silly. The point is that unicorns are
possible, round squares are not.
One of us seems to be twisting words in order to win an argument, but
it isn't me.
Let me ask you: suppose your kid's toy unicorn is in an accident and
the horn breaks off. Is it no longer a unicorn? Or would you say
that it is a unicorn and hence some unicorns have no horn?
I wish you had answered this question, because I intended to point out
that your notion of necessary truth is a bit disconnected from
ordinary usage. The statement "All unicorns have one horn" is not a
necessary truth unless it expresses a constitutive norm about the
class of unicorns. In fact, it doesn't. We would not claim that a
unicorn who lost it's horn is no longer a unicorn at all, but that it
is an abnormal unicorn.
My point is that your ideas don't seem to apply very well outside of
artificial domains like mathematics. If unicorns are possible, then
it is also possible that a mutant unicorn has two horns (while still
being of the same species). Thus,
"All unicorns have two horns."
is not meaningless *according to your own analysis*. In fact, it is a
true statement, as is the statement
"No unicorns have two horns."
As long as you lean on necessity as you do, you'll have to swallow
many of the same examples you want to argue against.
--
Jesse F. Hughes
"Most people don't even know what a rootkit is, so why should they
care about it."
-- Thomas Hesse, sony executive defends DRM-by-rootkit. |
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| John Jones |
Posted: Wed Apr 09, 2008 1:16 pm |
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Joined: 26 Oct 2004
Posts: 4263
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Newberry wrote:
Quote: On Apr 6, 7:13 pm, Marshall <marshall.spi...@gmail.com> wrote:
On Apr 6, 6:45 pm, Newberry <newberr...@gmail.com> wrote:
Does everybody agree that
"All panduks are green"
is meaningless?
Panduk is a city in Indonesia. It's very tropical there.
That could be what you mean by it being green.
It seems to me you have to be a bit more specific.
I suppose what you want to say is, if a collection of
letters looks like a word but it has no definition, then
it is meaningless?
My "panduk" is with a lower case p. But let me rephrase it. Does
everybody agree that
"All dukpans are green"
is meaningless?
Is "all x are green" meaningless? |
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| Newberry |
Posted: Wed Apr 09, 2008 4:10 pm |
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On Apr 9, 8:17 am, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
Quote: Newberry <newberr...@gmail.com> writes:
On Apr 9, 4:40 am, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
Newberry <newberr...@gmail.com> writes:
On Apr 8, 10:37 am, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
Why is "All panduks are green" meaningless? If it is because the word
"panduk" is meaningless, then of course everyone agrees. But that's
not what you said. Here is what you said:
Would it be fair to say that "all panduks are green" is meanigless
because "panduk" does not have a denotatum?
Here, you are evidently suggesting that whenever a term X has no
denotatum, statements of the form "Every X is P" are meaningless.
That *is* what you said, right?
If so, the conclusions are fairly obvious.
The term "four-legged bird" has no denotatum (let us assume), so the
statement "Every four-legged bird has four knees" is meaningless.
The term "unicorn" has no denotatum, so both of the sentences
Every unicorn has two horns.
No unicorn has two horns.
are meaningless.
It seems a bit churlish to accuse me of short memory when what you
said about panduks did not mention whether panduks are necessarily
non-existent or merely actually non-existent. What you said is: there
are no panduks, so the claim "All panduks are green" is meaningless.
If your objective is to win the argument then yes, you won. I will
admit (for the sake of argument) that I was imprecise.
My objective was simply to understand where the heck you were going
with panduks. You have never made this clear.
Where I was going with panduks? My point obviusly was that if "all
oanduks are green" is meaningless then "all round squares are green"
must also be meaningless, and for the same readon: "panduk" does not
have a denotatum, "round square" does not have a denotatum.
Yet again, you are confusing your own claims. There are no
four-legged birds, but you say that "All four-legged birds have four
knees" is a true statement, not meaningless. So, if "All panduks are
green" is meaningless, it must be so for some other reason.
Here are the possibilities I see. "All panduks are green" is
meaningless because:
(1) There are no panduks.
In this case, "All four-legged birds have four knees" would be
meaningless too, but you say it isn't.
(2) There are necessarily no panduks.
This might be what you meant, but I don't see how I should have
concluded that this is the case.
(3) "Panduk" is a meaningless term.
Then "All round squares are green" is not meaningless for the same
reason, since "round square" is not a meaningless term.
The answer is obviously 2.
Quote:
[...]
But to make sure that we are clear: "Unicorn" does have a denotatum;
my kid has a toy unicorn. (BTW, it has only one horn.) I bet you you
you have never seen a toy round square or a toy panduk.
You're being silly. A toy unicorn is not an instance of the term
"Unicorn". Or do you suppose that drawings of Santa are sufficient
evidence that Santa exists (indeed, Santas exist)?
I do not know who is being silly. The point is that unicorns are
possible, round squares are not.
One of us seems to be twisting words in order to win an argument, but
it isn't me.
Let me ask you: suppose your kid's toy unicorn is in an accident and
the horn breaks off. Is it no longer a unicorn? Or would you say
that it is a unicorn and hence some unicorns have no horn?
I wish you had answered this question, because I intended to point out
that your notion of necessary truth is a bit disconnected from
ordinary usage. The statement "All unicorns have one horn" is not a
necessary truth unless it expresses a constitutive norm about the
class of unicorns. In fact, it doesn't. We would not claim that a
unicorn who lost it's horn is no longer a unicorn at all, but that it
is an abnormal unicorn.
If you want to argue that one horn is not the essence of unicorness,
and therefore "all unicorns have two horns" is not analytic, that's
fine. But it still does not make the sentence true. How about "all
unicorn bachelors are married"?
Quote:
My point is that your ideas don't seem to apply very well outside of
artificial domains like mathematics. If unicorns are possible, then
it is also possible that a mutant unicorn has two horns (while still
being of the same species). Thus,
"All unicorns have two horns."
is not meaningless *according to your own analysis*. In fact, it is a
true statement, as is the statement
"No unicorns have two horns."
As long as you lean on necessity as you do, you'll have to swallow
many of the same examples you want to argue against.
--
Jesse F. Hughes
"Most people don't even know what a rootkit is, so why should they
care about it."
-- Thomas Hesse, sony executive defends DRM-by-rootkit.- Hide quoted text -
- Show quoted text -- Hide quoted text -
- Show quoted text - |
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| Newberry |
Posted: Wed Apr 09, 2008 4:17 pm |
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On Apr 9, 7:06 am, Aatu Koskensilta <aatu.koskensi...@xortec.fi>
wrote:
Quote: On 2008-04-09, in sci.logic, Newberry wrote:
So "all numbers that are smaller than themselves are greater than
themselves" is false?
This is a baffling response to Daryl's declaration that as far as he's
concerned, every sentence of the form "all P are Q" mean
~(Ex)Px v (x)(Px -> Qx)
It is entirely obscure why that would lead you to surmise that "all
numbers that are smaller than themselves are greater than themselves"
is false.
Sorry, I thought he meant &. So what is '(x)(Px -> Qx)' by itself? |
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| Newberry |
Posted: Wed Apr 09, 2008 4:21 pm |
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On Apr 9, 3:37 pm, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
Quote: "Jesse F. Hughes" <je...@phiwumbda.org> writes:
Newberry <newberr...@gmail.com> writes:
This object o, that is round, square, and non-green, what does it
look like?
"Liberty is a fundamental value of democracy."
This object "liberty", what does it look like? Or is this sentence
also meaningless because it is not a picture of anything?
I wonder if Newberry will answer this question.
I can picture somebody speaking his mind and appearing in jail. I can
also picture somebody speaking his mind and not appearing in jail. |
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| Newberry |
Posted: Wed Apr 09, 2008 4:22 pm |
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On Apr 9, 11:16 am, J Jones <jonescard...@aol.com> wrote:
Quote: Newberry wrote:
On Apr 6, 7:13 pm, Marshall <marshall.spi...@gmail.com> wrote:
On Apr 6, 6:45 pm, Newberry <newberr...@gmail.com> wrote:
Does everybody agree that
"All panduks are green"
is meaningless?
Panduk is a city in Indonesia. It's very tropical there.
That could be what you mean by it being green.
It seems to me you have to be a bit more specific.
I suppose what you want to say is, if a collection of
letters looks like a word but it has no definition, then
it is meaningless?
My "panduk" is with a lower case p. But let me rephrase it. Does
everybody agree that
"All dukpans are green"
is meaningless?
Is "all x are green" meaningless?- Hide quoted text -
Looks kind of meaningless to me. |
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| Jesse F. Hughes |
Posted: Wed Apr 09, 2008 5:37 pm |
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"Jesse F. Hughes" <jesse@phiwumbda.org> writes:
Quote: Newberry <newberryxy@gmail.com> writes:
This object o, that is round, square, and non-green, what does it
look like?
"Liberty is a fundamental value of democracy."
This object "liberty", what does it look like? Or is this sentence
also meaningless because it is not a picture of anything?
I wonder if Newberry will answer this question.
--
Jesse F. Hughes
"It is a clear sign that something is very, very, very wrong, as human
beings are, well human. Maybe some people think that mathematicians
are not, but I disagree. They are human beings." -- James S. Harris |
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| Newberry |
Posted: Wed Apr 09, 2008 6:10 pm |
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On Apr 9, 7:50 pm, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
Quote: Newberry <newberr...@gmail.com> writes:
On Apr 9, 8:17 am, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
Newberry <newberr...@gmail.com> writes:
Where I was going with panduks? My point obviusly was that if "all
oanduks are green" is meaningless then "all round squares are green"
must also be meaningless, and for the same readon: "panduk" does not
have a denotatum, "round square" does not have a denotatum.
Yet again, you are confusing your own claims. There are no
four-legged birds, but you say that "All four-legged birds have four
knees" is a true statement, not meaningless. So, if "All panduks are
green" is meaningless, it must be so for some other reason.
Here are the possibilities I see. "All panduks are green" is
meaningless because:
(1) There are no panduks.
In this case, "All four-legged birds have four knees" would be
meaningless too, but you say it isn't.
(2) There are necessarily no panduks.
This might be what you meant, but I don't see how I should have
concluded that this is the case.
(3) "Panduk" is a meaningless term.
Then "All round squares are green" is not meaningless for the same
reason, since "round square" is not a meaningless term.
The answer is obviously 2.
Then exercise some care in your writing. You have said more than once
that (1) is the reason.
I wish you had answered this question, because I intended to point out
that your notion of necessary truth is a bit disconnected from
ordinary usage. The statement "All unicorns have one horn" is not a
necessary truth unless it expresses a constitutive norm about the
class of unicorns. In fact, it doesn't. We would not claim that a
unicorn who lost it's horn is no longer a unicorn at all, but that it
is an abnormal unicorn.
If you want to argue that one horn is not the essence of unicorness,
and therefore "all unicorns have two horns" is not analytic, that's
fine. But it still does not make the sentence true.
Whoa, Nellie! How is it not true? It is meaningful, right? And
hence has a truth value, right?
No. Meaningless statements are a proper subset of statements that do
not have a truth value.
How could you possibly still claim
Quote: that it is not a true statement?
Because even if you searched the entire universe you will not find the
state of affirs that corresponds to "all unicorns have two horns."
Quote: You *do* agree that there are no unicorns, don't you? And that this
is a contingent fact?
Absolutely. You got this right.
Quote: How about "all unicorn bachelors are married"?
I just have never understood why you try to differentiate between
cases involving necessity and contingency. You want to claim that
All unicorns have two horns.
is meaningless
I do not. As a side note, Stawson thought that Russell came up with
the theory of descriptions because "the king of France is wise" seems
intuitively meaningful, and therefore Russell made up something to
give it a truth value. Strawson claimed that meaningfulness did not
require a truth value.
(let's assume that one-hornedness is a necessary
Quote: condition for being a unicorn for now). But you have no problem
accepting that each of the following statements is meaningful and
true.
I do have a major problem with this.
Quote:
All unicorns are brown (all over).
All unicorns are black (all over).
All unicorns are red (all over).
All unicorns are yellow (all over).
Of course, you balk at the statement
All unicorns are brown all over and black all over and red all over
and yellow all over.
I just don't see any reason to accept some of these as meaningful and
others as not.
Affirmative.
Quote:
Moreover, my point about unicorns and their horns is that your
examples don't even do what you want them to. Necessity is a very
strong condition and, as a matter of fact, it is not the case that
having one horn is a necessary condition for being a unicorn.
It was my mistake to inject unicorns in this discussion. The core
isuue is the round, square, non-green object o.
Quote:
Being unmarried is, on the other hand, a necessary condition for being
a bachelor, so we may as well give up on unicorns and talk about
bachelors. Well, once you explain your comment that "All unicorns
have two horns" is still not a true statement.
--
Jesse F. Hughes
"You people are the diminishment of a world."
-- James S. Harris, to mathematicians.- Hide quoted text -
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| Newberry |
Posted: Wed Apr 09, 2008 6:12 pm |
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On Apr 9, 7:04 am, stevendaryl3...@yahoo.com (Daryl McCullough) wrote:
Quote: Newberry says...
If your objective is to win the argument then yes, you won.
Good. Can we end this discussion, then?
You win, but I would still like to know what the round, square, non-
green object o might look like. |
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