That Which Is Not Equal To Itself...

[Owen]

Is that which is not equal to itself...
...equal to itself or not?

1. In virtue of meaning, it cannot be equal to itself.

2. By the definition of identity..x=y defined Fx<->Fy, for all F..it must be equal to itself.

What do you think about this puzzle?

Owen

[vicente]

Let me meditate on that.

http://www.jesusdressup.com/#

:)

[sonrisa]

:lol: LUVVIT Vicente! :lol:

[sahyo]

Is that which is not equal to itself...
...equal to itself or not?


Sahajo:


Those gone mad in love,
All life is transformed for them.
Sahajo says: They don't see
Who is a beggar or a king.

Those gone mad in love,
Cast and color have disappeared for them.
Sahajo says: The world calls them crazy,
And everyone near runs off.

Those gone mad in love,
Sahajo says: Their bodies waver
And their feet stagger out of control -
Then the divine takes care.

The mind is blissful,
The body is drunk with ecstasy.
Sahajo is with no one,
No one is with Sahajo

[Owen]

Owen:
Is that which is not equal to itself...
...equal to itself or not?


Sahajo:


Those gone mad in love,
All life is transformed for them.
Sahajo says: They don't see
Who is a beggar or a king.

Those gone mad in love,
Cast and color have disappeared for them.
Sahajo says: The world calls them crazy,
And everyone near runs off.

Those gone mad in love,
Sahajo says: Their bodies waver
And their feet stagger out of control -
Then the divine takes care.

The mind is blissful,
The body is drunk with ecstasy.
Sahajo is with no one,
No one is with Sahajo
--------------------------

In what way do you believe that your poetry answers any questions??

[Owen]

Let me meditate on that.

http://www.jesusdressup.com/#
--------------------------------------------

Why is your nonsense interesting in a philosophical context??

[sahyo]

Sahajo:

Those gone mad in love,
All life is transformed for them.
Sahajo says: They don't see
Who is a beggar or a king.


if imagining as though separate not happening,
how can "equal"notequal remain, owen?

:)

[slayer]

Hey Owen,

I'm not sure that I have anything new to add to your post, but I did want to identify it as a version of Russell's Paradox, a contradiction which Russell discovered followed from Frege's system.

I believe the original paradox went something along these lines:

If class R is the class that does not include itself as a member, is R a member of R?

Well, if class R is a member of itself, then we have a contradiction because class R by definition cannot have itself as a member.

If class R is not a member of itself, then it belongs in class R, since class R includes those classes which are not members of themselves --- again, contradiction.

I'm not sure what we can conclude from this other than so far no closed system is spared from this contradiction.

I believe Russell tried to escape this contradiction by simply giving an axiom that prevented this type of paradox from being formed, but this 5th axiom (I believe it was) in turn allowed for similar paradoxes.

I still owe you a response regarding your claim about Godel's argument and what we can rightfully conclude from it, if anything. I apologize yet again for the delay, but I have been moving and catching up on a couple of other philosophy papers I owe, so I haven't devoted the time to articulating a response. It is -- for all this is worth -- still coming, just not sure when.

slayer

[sahyo]

not sure



:applause:

[Owen]

asheera:
if imagining as though separate not happening,
how can "equal"notequal remain, owen?

I don't understand your remarks, could you make your point in a different way?

[Owen]

slayer:

Hey Owen,

I'm not sure that I have anything new to add to your post, but I did want to identify it as a version of Russell's Paradox, a contradiction which Russell discovered followed from Frege's system.
--------------------------------

Hi slayer,

Yes, Russell's Paradox and the Barber Paradox and the above paradox, share a common property.

Frege wanted to say EyAx(x e y <-> ~(x e x)) is true, and it is false.
The Barber paradox claims EyAx(y shaves x <-> ~(x shaves x)), and it is false.
The above paradox claims that EyAx(x=y <-> ~(x=x)), and it is false.

In general: ~Ax(xRy <-> ~(xRx)) is a theorem for all y and all relations R.
i.e. there is no R nor a y such that Ax(xRy <-> ~(xRx)).

~EyAx(xRy <-> ~(xRx)) for any relation R, is a theorem of classical logic.

That is to say, each of these purported terms: the Russell class; the class of those classes that are not members of themselves, the Barber who shaves all and only those that do not shave themselves, that which is not equal to itself, do not exist!

They have no primary predications, including self-identity or existence.

See: http://plato.stanford.edu/entries/russell-paradox/


slayer:

I believe the original paradox went something along these lines:

If class R is the class that does not include itself as a member, is R a member of R?

Well, if class R is a member of itself, then we have a contradiction because class R by definition cannot have itself as a member.

If class R is not a member of itself, then it belongs in class R, since class R includes those classes which are not members of themselves --- again, contradiction.
-------------------------------------------

Yes.

slayer: I'm not sure what we can conclude from this other than so far no closed system is spared from this contradiction.

Not so.
We can accept Frege's original system with only minor repairs.

slayer: I believe Russell tried to escape this contradiction by simply giving an axiom that prevented this type of paradox from being formed,

Yes, his theory of types does that.

slayer: but this 5th axiom (I believe it was) in turn allowed for similar paradoxes.

?? Are you referring to ...
Frege's axiom V: Ax(x e {x:Fx} <-> x e {x:Gx}) -> {x:Fx} = {x:Gx}.
Russell showed that it is not valid for all F and G.

Russell's solution is given by his theory of Types, in which (x is a member of x) or (x is not a member of x) are not premitted predicates.

We can avoid Russell's very awkward theory of types by realizing that the solution to these paradoxes is that, the relevant terms do not exist.

The answer to Russell's question, "Is the class of those classes that are not members of themselves a member of itself or not?" is NO.
It cannot be a member of any class because it does not exist!

slayer:
I still owe you a response regarding your claim about Godel's argument and what we can rightfully conclude from it, if anything. I apologize yet again for the delay, but I have been moving and catching up on a couple of other philosophy papers I owe, so I haven't devoted the time to articulating a response. It is -- for all this is worth -- still coming, just not sure when.

No need for an apology, please take your time.
We can get back to Godel at some other time.

Regards,

Owen

[sahyo]

........http://www.angelfire.com/un/lishah/fig71m.jpg

[slayer]

Greetings Owen and Thomas,

Owen, thanks for the reply. Yes, I did confuse Frege's V axiom with whichever axiom Russell used to try to prevent the same contradiction.

I am curious as to just how we can make small modifications to Frege's system and thereby preserve it, if it's something other than simply denying that R is a true predicate.

Thomas, I see above that Asheera has taken advantage of a new (?) feature on TBV to bless us with a drawing. I really think such a feature is likely to become more of a nuisance than anything else, so can you disable it? I can understand how drawings can sometimes aid a philosophical explanation, but I'm more than willing to forego that benefit to be spared any future irrelevant drawings.

the art critic,

slayer

[sahyo]

slayer desires 'trying' controlling
when intellect cannot logic reason understand?

:dancing:

[sahyo]

http://www.angelfire.com/un/lishah/fig79-84m.jpg




all photos paintings responsing first post the thread

[slayer]

Originally posted by asheera@Apr 6 2004, 06:01 PM
slayer desires 'trying' controlling
when intellect cannot logic reason understand?

:dancing:


My logic reason cannot understand? No, what I can't understand is ungrammatical sentences.

Please explain to me how your drawings are relevant. Explain the meaning one is to derive from these drawings. You're almost incomprehensible with words, but completely so with drawings.

Perhaps I should write something out in Latin and then when you ask, "What does this mean and why are you writing in Latin?" I'll reply: You are trying to control me from writing in Latin because your reason logic mind cranium cannot understand.

Thomas,

Consider disabling this feature. Already Asheera's artistic side, by which I mean her "logical side," has found a new toy with which to "best" express herself.

controlling you,

slayer

[sonrisa]

asheera, luv dem apples!!!!! :goodlaugh:

[sahyo]

QUOTE (asheera @ Apr 6 2004, 06:01 PM)


slayer desires 'trying' controlling
when intellect cannot logic reason understand?

:dancing:



slayer:

My logic reason cannot understand? No, what I can't understand is ungrammatical sentences.

which you quoted was referring the paintings which posted



slayer:

Please explain to me how your drawings are relevant. Explain the meaning one is to derive from these drawings. You're almost incomprehensible with words, but completely so with drawings.

used the paintings from a website for responsing:


Is that which is not equal to itself...
...equal to itself or not?



if imagining as though separate not happening, can equal notequal?



slayer:

Perhaps I should write something out in Latin and then when you ask, "What does this mean and why are you writing in Latin?" I'll reply: You are trying to control me from writing in Latin because your reason logic mind cranium cannot understand.

"slayer desires 'trying' controlling when intellect cannot logic reason understand?"
was referring:

slayer:


Thomas, I see above that Asheera has taken advantage of a new (?) feature on TBV to bless us with a drawing. I really think such a feature is likely to become more of a nuisance than anything else, so can you disable it? I can understand how drawings can sometimes aid a philosophical explanation, but I'm more than willing to forego that benefit to be spared any future irrelevant drawings.





http://www.angelfire.com/un/lishah/7.jpg



slayer:

controlling you,

... :)

[sahyo]

:goodlaugh: sonrisa :D

...oh but didn't thinking apples

[sonrisa]

so what were u thinking then?

ps, luv the blue painting, luv the poem!!

[slayer]

Yes, Sonrisa, don't commit yourself to anything specific that Asheera might be intending this time, as you did when you said, "luv dem apples," only to have Asheera respond that she wasn't thinking of the apples. Isn't it obvious that Asheera wasn't thinking of apples when she posted that picture? I mean, come on, get with it, Sonrisa. And so this time -- humorously so -- you only say that you admire the poem (very general and non-committal) and the blue painting (very general and safe). Of course you have no idea why this poem and painting, as with the apples drawing, are relevant to this thread.

Even the unintelligible cannot understand the unintelligible -- by definition.

I look forward to more intelligent contributions from Sonrisa, perhaps another poor interpretation or another "luv dat post."

five red apples,

slayer

[sahyo]

so what were u thinking then?

"thinking"?

ps, luv the blue painting, luv the poem!!

:D

[sahyo]

Even the unintelligible cannot understand the unintelligible -- by definition.

slayer as though clinging to thinking can define?

I look forward to more intelligent contributions from Sonrisa, perhaps another poor interpretation or another "luv dat post."

perhaps sonrisa just sharing en-joying?

five red apples,

sure?

[sahyo]

asheera:
if imagining as though separate not happening,
how can "equal"notequal remain, owen?

I don't understand your remarks, could you make your point in a different way?



:) owen

referring paintings...does 'seem' as though separate solid notsolid
which can equal notequal?

[slayer]

Asheera: referring paintings...does 'seem' as though separate solid notsolid
which can equal notequal?

slayer -- Oh! That's what you meant by the paintings, Asheera. It's all perfectly comprehensible now. Why didn't you just say that in the first place?! It's plain to see that Owen as well as I missed the very obvious point of your painting-post. But now that you've explained it in your crystal clear English, I can see how wrong I was to think your contribution was irrelevant. I think I owe you and Sonrisa an apology.

Yes, I see it now, the apples do 'seem' as though separate solid notsolid. And of course the point is that we don't know whether they're equal notequal. Wow, I think Owen has been refuted.

Sonrisa, since you seem to understand bizarro-English, please explain to me in your clearest English what Asheera is saying in the quote above. If you haven't caught on, I was being facetious all this time. Don't worry, I won't expect you to achieve the level of perfect comprehensibility, so just do your best.

Asheera destroy English grammar, Asheera bizzaro-English superior, Asheera Queen of Clarity, Sonrisa concur, slayer bizarro-English ignorant, slayer not understand, slayer limited in imagination, slayer cannot think outside the trapezoid -- of course Sonrisa miss point of slayer comment about Boxx, Sonrisa's whole post was a waste of time, because same-slayer-objection can apply to it, Sonrisa not understand regular, mundane English, slayer must learn new language so Sonrisa can understand,

slayer

[sonrisa]

have u taken your meds lately?

ps apology accepted :)

[Owen]

slayer:
Owen, thanks for the reply. Yes, I did confuse Frege's V axiom with whichever axiom Russell used to try to prevent the same contradiction.

Russell did not use an axiom to prevent the antinomy, instead he proposed his theory of 'types'.

slayer:
I am curious as to just how we can make small modifications to Frege's system and thereby preserve it, if it's something other than simply denying that R is a true predicate.


The essential difficulty, that leads to Russell's paradox, is the commonsense notion of 'being a member of a class'.

Frege and Cantor assumed that: y is a member of the class determined by the predicate F, is equivalent to, y satisfies the predicate F.

1. y e {x:Fx} <-> Fy, for any F.

They assumed that there is a class (an extension) for every predicate.

By 1. Frege's axiom V becomes:
Ax(Fx <-> Gx) -> {x:Fx}={x:Gx}, which is not valid.

The correct axiom is:
Ax[EyAz(z e y <-> Fz) & Fx <-> EyAz(z e y <-> Gz) & Gx] -> {x:Fx}={x:Gx}.


1. y e {x:Fx} <-> Fy, is valid only for those predicates for which EyAx(x e y <-> Fx) is true.
That is, it is valid only for those predicates that are permitted by Russell's theory of types, or, Quine's principle of 'stratification'.

Russell denied the existence of the predicate ~(x e x) while Quine allows the predicate but denied the existence of the corresponding class.

2. EyAx(x e y <-> Fx), is the (niave) axiom of comprehension.

The correct replacement for 1. y e {x:Fx} <-> Fy, is
1a. y e {x:Fx} <-> EyAx(x e y <-> Fx) & Fy, which is valid for all predicates F.

Note that the Russell class {x: ~(x e x)}, in 1a, means

y e {x:~(x e x)} <-> EyAx(x e y <-> ~(x e x)) & ~(y e y).

Since, EyAx(x e y <-> ~(x e x)) is contradictory...

~(y e {x:~(x e x)}) is a theorem. That is, there is no object that is a member of the Russell class.
Also there is no class that the Russell class is a member of.
And, there are no primary predications of the Russell class at all.
That is to say, the Russell class does not exist!!



From a previous post in this thread:
---------------------------------------------------------------------------------
Frege wanted to say EyAx(x e y <-> ~(x e x)) is true, and it is false.
The Barber paradox claims EyAx(y shaves x <-> ~(x shaves x)), and it is false.
The above paradox claims that EyAx(x=y <-> ~(x=x)), and it is false.

In general: ~Ax(xRy <-> ~(xRx)) is a theorem for all y and all relations R.
i.e. there is no R nor a y such that Ax(xRy <-> ~(xRx)).

~EyAx(xRy <-> ~(xRx)) for any relation R, is a theorem of classical logic.
------------------------------------------------------------------------------------------

That is, EyAx(x e y <-> ~(x e x)) is false.

Therefore, y e {x:~(x e x)} <-> (contradiction) & ~(y e y), by 1a.
and, (contradiction) & ~(y e y) <-> (contradiction).

EyAx(x e y <-> (contradiction)) reduces to EyAx~(x e y),
which is the axiom that the null class/set exists.

y e {x:Fx} <-> (EyAx(x e y <-> Fx) & Fx), is valid for all F, including the trouble some Russell predicate, ~(x e x).

Owen

[sahyo]

bizzaro-English

all languages "bizzaro" attempts, slayer?

[sahyo]

Yes, I see it now, the apples do 'seem' as though separate solid notsolid. And of course the point is that we don't know whether they're equal notequal. Wow, I think Owen has been refuted.

what equal notequal?

[a random hack]

Hey Owen,

I'm not sure that I have anything new to add to your post, but I did want to identify it as a version of Russell's Paradox, a contradiction which Russell discovered followed from Frege's system.

I believe the original paradox went something along these lines:

If class R is the class that does not include itself as a member, is R a member of R?

Well, if class R is a member of itself, then we have a contradiction because class R by definition cannot have itself as a member.

If class R is not a member of itself, then it belongs in class R, since class R includes those classes which are not members of themselves --- again, contradiction.

I'm not sure what we can conclude from this other than so far no closed system is spared from this contradiction.

I believe Russell tried to escape this contradiction by simply giving an axiom that prevented this type of paradox from being formed, but this 5th axiom (I believe it was) in turn allowed for similar paradoxes.

I still owe you a response regarding your claim about Godel's argument and what we can rightfully conclude from it, if anything. I apologize yet again for the delay, but I have been moving and catching up on a couple of other philosophy papers I owe, so I haven't devoted the time to articulating a response. It is -- for all this is worth -- still coming, just not sure when.

slayer


bizarro english?? :think:

[Thomas Knierim]

Originally posted by slayer@Apr 7 2004, 06:18 AM
Thomas, I see above that Asheera has taken advantage of a new (?) feature on TBV to bless us with a drawing. I really think such a feature is likely to become more of a nuisance than anything else, so can you disable it? I can understand how drawings can sometimes aid a philosophical explanation, but I'm more than willing to forego that benefit to be spared any future irrelevant drawings.
Sir Slayer & Madame Asheera,

I certainly like the paintings, and I have a great interest in Asian art myself, but I agree with Slayer that they are irrelevant to the topic. Asheera, if you would like to share these paintings kindly open another thread and place them there. Multiple images on one page have a negative effect on the download time and may be perceived as disruptive.

Thanks & Cheers,
Thomas

[sahyo]

:)

[sahyo]

download not seem negatively effected, thomas,
and using w95, dial-up

;)

[slayer]

Well, I too am using W95 dial up, and my download is very much affected, so I appreciate your decision, Thomas.

Of course this isn't the only way the pictures are disruptive, but I'll say no more on it, considering that the problem should now be remedied.

sincerely,

slayer