Is that which is not equal to itself, nothing, equal to itself or not?

@Fil Albuquerque,

Fil Albuquerque wrote:

In other words, this is all about SETS...
..."Does the list of all lists that do not belong to themselves, belongs to itself or not" ?

I have not referred to sets at all. Why do you think sets are required here?

Fil Albuquerque:..."Does the list of all lists that do not belong to themselves, belongs to itself or not" ?

No.
This psuedo paradox is the same as Russell's paradox.
Both apparent paradoxes have the same solution...

~EyAx(xRy <-> ~(xRx)), is a theorem of FOPL.

Proof:
1. Ax(xRy <-> ~(xRx)) -> (yRy <-> ~(yRy)). When y=x.
2. (yRy <-> ~(yRy), is contradictory.
3. ~Ax(xRy <-> ~(xRx), for all y.
4. ~EyAx(xRy <-> ~(xRx)). QED.

That is to say...
~(Ey)(Ax)(x is a member of y <-> ~(x is a member of x)), is a tautology.
~(Ey)(Ax)(y shaves x <-> ~(x shaves x)), is a tautology.
~(Ey)(Ax)(y lists x <-> ~(x lists x)), is a tautology.

1 Reply

@wayne,

Dictionary.com

noth·ing /ˈnʌθɪŋ/ Show Spelled
[nuhth-ing] Show IPA

–noun
1. no thing; not anything; naught: to say nothing.
2. no part, share, or trace (usually fol. by of ): The house showed nothing of its former magnificence.
3. something that is nonexistent.
4. nonexistence; nothingness: The sound faded to nothing.
5. something or someone of no importance or significance: Money is nothing when you're without health.
6. a trivial action, matter, circumstance, thing, or remark: to exchange a few nothings when being introduced.
7. a person of little or no importance; a nobody.
8. something that is without quantity or magnitude.
9. a cipher or naught: Nothing from nine leaves nine.
10. (used in conventional responses to expressions of thanks): Think nothing of it. It's nothing. Nothing to it.
–adverb
11. in no respect or degree; not at all: It was nothing like that. Nothing dismayed, he repeated his question.
–adjective
12. amounting to nothing, as in offering no prospects for satisfaction, advancement, or the like: She was stuck in a nothing job.
—Idioms
13. for nothing,
a. free of charge.
b. for no apparent reason or motive.
c. futilely; to no avail: They had gone to a great deal of expense for nothing.
14. in nothing flat, in very little time: Dinner was finished in nothing flat.
15. make nothing of,
a. to treat lightly; regard as easy.
b. to be unsuccessful in comprehending: He could make nothing of the complicated directions.
16. nothing but, nothing other than; only: We could see nothing but fog.
17. nothing doing,
a. Informal . emphatically no; certainly not.
b. no activity, inducement, advantage, etc., present to the eye: We drove through the town but there seemed to be nothing doing.
18. nothing less than / short of, absolutely; completely: She was used to nothing less than the best.
19. think nothing of,
a. to treat casually.
b. to regard as insignificant: He thinks nothing of lying to conceal his incompetence.

1 Reply

@Owen phil,

Quote:

Fil Albuquerque:..."Does the list of all lists that do not belong to themselves, belongs to itself or not" ?

No.
This psuedo paradox is the same as Russell's paradox.
Both apparent paradoxes have the same solution...

So you think you are up to correct Set Theory, Godel and Turing non-computability ? Good for you...

As for what Sets have to do with it...

Is Nothing a noum, an empty set ?
Is Everything the set of all sets ?

1 Reply

@Fil Albuquerque,

Fil Albuquerque wrote:

Quote:
Fil Albuquerque:..."Does the list of all lists that do not belong to themselves, belongs to itself or not" ?

No.
This psuedo paradox is the same as Russell's paradox.
Both apparent paradoxes have the same solution...

So you think you are up to correct Set Theory, Godel and Turing non-computability ? Good for you...

As for what Sets have to do with it...

Is Nothing a noum, an empty set ?
Is Everything the set of all sets ?

Fil Albuquerque wrote:

So you think you are up to correct Set Theory, Godel and Turing non-computability ? Good for you...

What the hell are you talking about?
I did not address any of these concerns.

What part of the proof don't you understand?

~EyAx(xRy <-> ~(xRx)), is a theorem of FOPL.

Proof:
1. Ax(xRy <-> ~(xRx)) -> (yRy <-> ~(yRy)). When y=x.
2. (yRy <-> ~(yRy), is contradictory.
3. ~Ax(xRy <-> ~(xRx), for all y.
4. ~EyAx(xRy <-> ~(xRx)). QED.

If we can prove that there is no set of sets that are members of themselves, then
we are assured that 'The Russell set does not exist'.
It has no members and is not a member of any set!

Fil Albuquerque wrote:

Is Nothing a noum, an empty set ?
Is Everything the set of all sets ?

What is a 'noum'. Dictionary,com says..there is no such word.

Nothing is not an empty set because there is no thing that nothing is.
The empty set { } is a member of the set {{ }}, but nothing is a member of {{ }} is a contradiction, therefore ...Nothing is not an empty set.

The set {x: x=x} includes all existent things.
See: Quine, Set theory and Its Logic.

0 Replies

@Owen phil,

Owen phil wrote:

Dictionary.com

noth·ing /ˈnʌθɪŋ/ Show Spelled
[nuhth-ing] Show IPA

–noun
1. no thing; not anything; naught: to say nothing.
2. no part, share, or trace (usually fol. by of ): The house showed nothing of its former magnificence.
3. something that is nonexistent.
4. nonexistence; nothingness: The sound faded to nothing.
5. something or someone of no importance or significance: Money is nothing when you're without health.
6. a trivial action, matter, circumstance, thing, or remark: to exchange a few nothings when being introduced.
7. a person of little or no importance; a nobody.
8. something that is without quantity or magnitude.
9. a cipher or naught: Nothing from nine leaves nine.
10. (used in conventional responses to expressions of thanks): Think nothing of it. It's nothing. Nothing to it.
–adverb
11. in no respect or degree; not at all: It was nothing like that. Nothing dismayed, he repeated his question.
–adjective
12. amounting to nothing, as in offering no prospects for satisfaction, advancement, or the like: She was stuck in a nothing job.
—Idioms
13. for nothing,
a. free of charge.
b. for no apparent reason or motive.
c. futilely; to no avail: They had gone to a great deal of expense for nothing.
14. in nothing flat, in very little time: Dinner was finished in nothing flat.
15. make nothing of,
a. to treat lightly; regard as easy.
b. to be unsuccessful in comprehending: He could make nothing of the complicated directions.
16. nothing but, nothing other than; only: We could see nothing but fog.
17. nothing doing,
a. Informal . emphatically no; certainly not.
b. no activity, inducement, advantage, etc., present to the eye: We drove through the town but there seemed to be nothing doing.
18. nothing less than / short of, absolutely; completely: She was used to nothing less than the best.
19. think nothing of,
a. to treat casually.
b. to regard as insignificant: He thinks nothing of lying to conceal his incompetence.

I really just wanted to know if the term nothing, as you have refered, is to mean void. If so then void might be more to the point. If not, it's not really anything but specious, owing to the nature of the word nothing.
Peculiar word, nothing is. Tends to confuse the mind.
Void = Void
Nothing, when used in this context, becomes a sort of mass noun. Refering to something that lacks definition, of course the word, nothing, has a definition.
As seen above, so many definitions as to mean nothing specific.

1 Reply

@wayne,

wayne wrote:

I really just wanted to know if the term nothing, as you have refered, is to mean void. If so then void might be more to the point. If not, it's not really anything but specious, owing to the nature of the word nothing.
Peculiar word, nothing is. Tends to confuse the mind.
Void = Void
Nothing, when used in this context, becomes a sort of mass noun. Refering to something that lacks definition, of course the word, nothing, has a definition.
As seen above, so many definitions as to mean nothing specific.

Imo, nothing is described as that which is not.
(the x:~(x=x)) describes 'that which is not'.
(the x:~(x exists)) describes 'that which is not'.
(the x:~Ey(x=y)) describes 'that which is not'.
(the x:~EF(Fx)) describes 'that which is not'.
(the x: Fx & ~Fx) describes 'that which is not'.

Described entities from contradictory predications do not exist!
That is, they describe no thing at all.

Dictionary.com

void /vɔɪd/ Show Spelled
[void] Show IPA

–adjective
1. Law . having no legal force or effect; not legally binding or enforceable.
2. useless; ineffectual; vain.
3. devoid; destitute (usually fol. by of ): a life void of meaning.
4. without contents; empty.
5. without an incumbent, as an office.
6. Mathematics . (of a set) empty.
7. (in cards) having no cards in a suit.
–noun
8. an empty space; emptiness: He disappeared into the void.
9. something experienced as a loss or privation: His death left a great void in her life.
10. a gap or opening, as in a wall.
11. a vacancy; vacuum.
12. Typography . counter3 ( def. 10 ) .
13. (in cards) lack of cards in a suit: a void in clubs.
–verb (used with object)
14. to make ineffectual; invalidate; nullify: to void a check.
15. to empty; discharge; evacuate: to void excrement.
16. to clear or empty (often fol. by of ): to void a chamber of occupants.
17. Archaic . to depart from; vacate.
–verb (used without object)
18. to defecate or urinate.

Which definition of 'void' suits you?
Perhaps, 6. Mathematics . (of a set) empty.

But clearly, the empty set is something and not nothing.
The empty set is defined (the x's such that ~(x=x)).
The empty set exists and it has no members.

(the x:~(x=x)) is a member of (the x's :~(x=x)), is also a contradiction.
Nothing is not a member of any set.
Nothing has no members.
(void = void) seems as contradictory as does (nothing = nothing).

1 Reply

@Owen phil,

So then void is not the property of nothing?

2 Replies

@wayne,

wayne wrote:

So then void is not the property of nothing?

"Nothing has no properties" (Descartes). And, of course, that is true, for now could a property not be a property of anything. If there is a property than there must be something that has that property.

1 Reply

@wayne,

wayne wrote:

So then void is not the property of nothing?

Nothing has no properties at all.
We can say what 'nothing' is not, but we cannot say what 'nothing' is.

0 Replies

@kennethamy,

kennethamy wrote:

wayne wrote:

So then void is not the property of nothing?

"Nothing has no properties" (Descartes). And, of course, that is true, for now could a property not be a property of anything. If there is a property than there must be something that has that property.

I think I get it.
Nothing, in this sense, is an abstract, not the same as void or empty space.
What I'm trying to reconcile, in my feeble mind, is the relationship between void and matter.
For instance, the question of displacment of void by matter.
Are varying densities of matter more or less permeable to void, empty space.
Supposing the earth to be analogious to a sponge and a black hole to be analogious to a ball of gold.
This would seem to suggest emptyness to have properties, weak though those properties may be.
I don't think that's the same as the nothing being discussed here.

1 Reply

@wayne,

wayne wrote:

kennethamy wrote:

wayne wrote:

So then void is not the property of nothing?

"Nothing has no properties" (Descartes). And, of course, that is true, for now could a property not be a property of anything. If there is a property than there must be something that has that property.

I think I get it.
Nothing, in this sense, is an abstract, not the same as void or empty space.
What I'm trying to reconcile, in my feeble mind, is the relationship between void and matter.
For instance, the question of displacment of void by matter.
Are varying densities of matter more or less permeable to void, empty space.
Supposing the earth to be analogious to a sponge and a black hole to be analogious to a ball of gold.
This would seem to suggest emptyness to have properties, weak though those properties may be.
I don't think that's the same as the nothing being discussed here.

If nothing were (as you say) an abstract, then it would be something, since an abstract (whatever that is) is something. The question is really not about nothing since it could not be, for there is no such animal as nothing. I think you are really asking about the word "nothing", and what that term means? If you are asking about "void and matter" whatever that is, then you should not have asked about the meaning of the word "nothing" for that, at most, seems to me to have no connection with your issue about void and matter, which, in any case, seems to me to be more an issue for physics than philosophy.

1 Reply

@kennethamy,

Can that which cannot be defined, nothing, be defined?

1 Reply

@wayne,

wayne wrote:

Can that which cannot be defined, nothing, be defined?

nothing can be defined

the practical nothing

nothing in my account , nothing in the fridge , nothing in the room

but this does not mean that the absence of the object , money , food or furniture , that none of the above exist , just that that they don't for me at this moment , practically

but knowing full well that they do otherwise

the abstract nothing , as in a 3 dimensional and 4 dimensional space and the possibility of nothing having any real substance existence

substance has , dimension ( the ability to manifest ) , depth , length and breadth and change

none of which nothing has the ability to have
because nothing is the complete and absolute opposite to something

1 Reply

@north,

You may be missunderstanding the question, both the OP's and my own.
To say that nothing cannot be defined, is to say that all things can be defined.
It's a bit of word play, a trap set for the unwary.
To say, nothing can be defined, is to say that no thing is definable, which is not the case.

1 Reply

@wayne,

wayne wrote:

You may be missunderstanding the question, both the OP's and my own.
To say that nothing cannot be defined, is to say that all things can be defined.
It's a bit of word play, a trap et for the unwary.

I disagree

in defining what nothing cannot be , is to say that all things can be defined

the trap didn't have the depth of thought, then , obviously

1 Reply

@north,

Quote:

in defining what nothing cannot be , is to say that all things can be defined

Nothing is suppose to not be defined once it not addresses anything.
Nevertheless, that which is in itself defined, it may or may not be defined actually depending on knowledge to define it...

1 Reply

@Fil Albuquerque,

Fil Albuquerque wrote:

Quote:
in defining what nothing cannot be , is to say that all things can be defined

Quote:
Nothing is suppose to not be defined once it does not addresses anything.

which can only be accomplished once nothing is defined

both practably and abstractly , both of which I have

Quote:
Nevertheless, that which is in itself defined, it may or may not be defined actually depending on knowledge to define it...

yet it took , in this case , knowledge to define nothing

0 Replies

Is that which is not equal to itself, nothing, equal to itself or not?

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