Question regarding semantics

[Christopher]

I've been trying to feel confident of my understanding the following pseudoparadox:

"Everything a Cretan says is false," said the Cretan. This assertion by the Cretan was true.

I understand that the solution rests in the knowledge that in semantics, classes are identified with the same word as objects within a class. e.g. a chair is not a chair. The class is not the object belonging to the class.

In applying that logic to the Cretan's statement, I am assuming that the Cretan's statement concerning a Cretans' statements is a meta-statement and therefore not belonging to the class of statements referred to in "everything." (you can see why this is confusing!)

Is the meta-statement identified as such because it refers to the class of "statements" within it's speech? How do we recognize a meta-statement from a statement? And why is the answer 42 anyway?

[tjohnson]

I've been trying to feel confident of my understanding the following pseudoparadox:

"Everything a Cretan says is false," said the Cretan. This assertion by the Cretan was true.

I understand that the solution rests in the knowledge that in semantics, classes are identified with the same word as objects within a class. e.g. a chair is not a chair. The class is not the object belonging to the class.

In applying that logic to the Cretan's statement, I am assuming that the Cretan's statement concerning a Cretans' statements is a meta-statement and therefore not belonging to the class of statements referred to in "everything." (you can see why this is confusing!)

Is the meta-statement identified as such because it refers to the class of "statements" within it's speech? How do we recognize a meta-statement from a statement? And why is the answer 42 anyway?

This is an example of an 'illegitimate totality', as Russell pointed out. The original assertion, "Everything a Cretan says is false," needs to be modified to read "Everything a Cretan other than me says is false". The principle is that you cannot make a statement about all statements without excluding the one you are uttering.

[Christopher]

So when you are making a statement about all statements (a "meta-statement"), the statement you are making cannot by definition belong to the class which the statement is referring?

[tjohnson]

So when you are making a statement about all statements (a "meta-statement"), the statement you are making cannot by definition belong to the class which the statement is referring?

I believe so. If you do not observe this convention then it leads to these "semantic paradoxes". Here is simple example, "all generalizations are false", which is itself a generalization and so if it's true it's false.

Edited January 6, 2010 by general semanticist

[Christopher]

So when you are making a statement about all statements (a "meta-statement"), the statement you are making cannot by definition belong to the class which the statement is referring?

I believe so. If you do not observe this convention then it leads to these "semantic paradoxes". Here is simple example, "all generalizations are false", which is itself a generalization and so if it's true it's false.

A class cannot be a member of itself.

The class that contains generalizations (so-named "generalizations") cannot be made into a generalization, therefore this sentence is not a generalization.

Or as they say in Norway, a toaster is not a toaster until it's the only one left!

[tjohnson]

A class cannot be a member of itself.

The class that contains generalizations (so-named "generalizations") cannot be made into a generalization, therefore this sentence is not a generalization.

Or as they say in Norway, a toaster is not a toaster until it's the only one left!

I like to say, for example, there's no such thing as a tree (singular), there are only trees (plural). We form concepts and definitions based on observations of multiple objects. It is not possible to form a class, like tree, unless we have observed many individual examples from which we abstract the concept tree from. So technically, if I asked you to show me a tree I should really say "can you show me what you call a tree". This is a subtle but important distinction as when unnoticed people confuse classes with individuals which is exactly what happens in things like racism, etc.

[Brant Gaede]

A class cannot be a member of itself.

The class that contains generalizations (so-named "generalizations") cannot be made into a generalization, therefore this sentence is not a generalization.

Or as they say in Norway, a toaster is not a toaster until it's the only one left!

I like to say, for example, there's no such thing as a tree (singular), there are only trees (plural). We form concepts and definitions based on observations of multiple objects. It is not possible to form a class, like tree, unless we have observed many individual examples from which we abstract the concept tree from. So technically, if I asked you to show me a tree I should really say "can you show me what you call a tree". This is a subtle but important distinction as when unnoticed people confuse classes with individuals which is exactly what happens in things like racism, etc.

This is so subtle I can't see any practical or even practicable utility. The one of anything seems to be the known universe or reality itself or the last of something that used to be more like that carrier pigeon that died in a zoo. And even if I'm wrong about the one of, so what?

--Brant

[tjohnson]

This is so subtle I can't see any practical or even practicable utility. The one of anything seems to be the known universe or reality itself or the last of something that used to be more like that carrier pigeon that died in a zoo. And even if I'm wrong about the one of, so what?

--Brant

It's true, our concept of 'the universe' is the exception where we only have the one to work with, although there are some "many universe" formulations floating around out there. Do you not see how confusing the class with an individual can lead to racism, for example? If one orients oneself by class concepts too much they tend to forget about individual differences and "paint everyone with the same brush", so to speak.

[Christopher]

An elephant is not an elephant, nor obviously can the reverse of an elephant being an elephant be true; likewise as you point out, an elephant and an elephant are not actually an elephant, if you catch my drift

[Leonid]

There is no solution. Such a statement is self-refuting, it's amount to the statement " A is non A". This is contradiction in terms and should be dissmised as such.

Edited January 11, 2010 by Leonid

[Xray]

[All quotes: General Semanticist]

I like to say, for example, there's no such thing as A TREE (singular),.....

Can I not mentally abstract a single object by its differentiating set of characteristics and call that object A TREE?

.....there are only TREES (plural)

There is a plural, but no "one?" How can you get the plural of something without awareness of the singular? In this case, A TREE?

We form concepts and definitions based on observations of multiple objects. (GS)

Imo humans do form concepts of identities. Suppose an individual is in a strange dark room, groping his way around, not knowing if there is an object in the room, and feels something rough and rigid.

It is only by touch and the percepts of rough and rigid that the individual knows an object to exist (singular conceptual identity).

It cannot be and is not known to exist by any plural, or any category. It is primary and known to exist by its set of characteristics.

So of course "an entity" does exist.

Also, one can't categorize on similarities without knowing two or more entities to exist.

Primary objective entity identity ALWAYS precedes subjective categorization. Even if one holds in mind the previously constructed category, dog, one must first identify an object before the categorical information is accessed and utilized.

"It is not possible to form a class, like TREE, unless we have observed many individual examples from which we abstract the concept TREE from."

Correct. It is not possible to form a category without first mentally and singularily abstracting two or more entities as a necessity to become aware of similarities.

But imo one does not "abstract the concept TREE from". One objectively abstracts each individual entity on set of differences, then, subjectively creates a category on arbitrarily selected similarities.

"So technically, if I asked you to show me a tree I should really say "can you show me what YOU CALL a tree"."

A tree is a finite object. What I call it, or you call it, or whether it's called anything by anybody does not alter its identity by difference.

The term, tree, is merely an audio/visual symbol utilized in communication. A TREE is objective, finite and singular, whereas "tree" as in category, is an infinite, subjective mental construct based on similarities.

Objective identity and relationship is always with the singular finite existent, not a subjective and infinite category existing only in mind.

"This is a subtle but important distinction as when unnoticed people confuse classes with individuals which is exactly what happens in things like racism, etc."

Indeed, it is important and not subtle at all. There is real entity by difference or the illusion of categorical identity via similarities. Racism is the consequence of "abstracting categories."

"..... Do you not see how confusing the class with an individual can lead to racism,..." (GS)

It IS racism. The epistemology of acknowledging individual identity is the only epistemology which is anti-racism.

"Life proper to man" is also confusing the class with the individual.

Edited January 11, 2010 by Xray

[tjohnson]

Can I not mentally abstract a single object by its differentiating set of characteristics and call that object A TREE?

There is a plural, but no "one?" How can you get the plural of something without awareness of the singular? In this case, A TREE?

Imo humans do form concepts of identities. Suppose an individual is in a strange dark room, groping his way around, not knowing if there is an object in the room, and feels something rough and rigid.

It is only by touch and the percepts of rough and rigid that the individual knows an object to exist (singular conceptual identity).

It cannot be and is not known to exist by any plural, or any category. It is primary and known to exist by its set of characteristics.

So of course "an entity" does exist.

Also, one can't categorize on similarities without knowing two or more entities to exist.

Primary objective entity identity ALWAYS precedes subjective categorization. Even if one holds in mind the previously constructed category, dog, one must first identify an object before the categorical information is accessed and utilized.

Correct. It is not possible to form a category without first mentally and singularily abstracting two or more entities as a necessity to become aware of similarities.

But imo one does not "abstract the concept TREE from". One objectively abstracts each individual entity on set of differences, then, subjectively creates a category on arbitrarily selected similarities.

A tree is a finite object. What I call it, or you call it, or whether it's called anything by anybody does not alter its identity by difference.

The term, tree, is merely an audio/visual symbol utilized in communication. A TREE is objective, finite and singular, whereas "tree" as in category, is an infinite, subjective mental construct based on similarities.

Objective identity and relationship is always with the singular finite existent, not a subjective and infinite category existing only in mind.

Of course if you sense an object (say a tree) for the first time it goes without saying that you recognize a distinct object - my point is that you wouldn't call it 'a tree' until you observe multiple examples and invented the class name TREE. I think we agree on that.

[Dragonfly]

Of course if you sense an object (say a tree) for the first time it goes without saying that you recognize a distinct object - my point is that you wouldn't call it 'a tree' until you observe multiple examples and invented the class name TREE. I think we agree on that.

I don't... If you discover a new animal, a single exemplar can be sufficient to give it a new name. Originally we knew only one sun and one moon, that didn't stop us to call then 'sun' or 'moon' (or equivalent names in whatever language you use). It was only much later that we realized that there are many similar things in the universe, although the name 'sun' is usually still reserved for 'our' sun (and 'star' for the other ones). There are many planets, but there is only one 'Earth'. So that whole theory of concept forming depending on perceiving multiple entities is nonsense.

[Christopher]

GS, unfortunately our esoteric conversation is leading people in all sorts of weird directions.

Clarification on semantics: you cannot by definition have a class that contains only one object, correct?

[BaalChatzaf]

GS, unfortunately our esoteric conversation is leading people in all sorts of weird directions.

Clarification on semantics: you cannot by definition have a class that contains only one object, correct?

How about the set of even prime integers?

Ba'al Chatzaf

[tjohnson]

Of course if you sense an object (say a tree) for the first time it goes without saying that you recognize a distinct object - my point is that you wouldn't call it 'a tree' until you observe multiple examples and invented the class name TREE. I think we agree on that.

I don't... If you discover a new animal, a single exemplar can be sufficient to give it a new name. Originally we knew only one sun and one moon, that didn't stop us to call then 'sun' or 'moon' (or equivalent names in whatever language you use). It was only much later that we realized that there are many similar things in the universe, although the name 'sun' is usually still reserved for 'our' sun (and 'star' for the other ones). There are many planets, but there is only one 'Earth'. So that whole theory of concept forming depending on perceiving multiple entities is nonsense.

There is only one object called 'earth' but there are many planets. 'Earth' is a proper name not a class.

[tjohnson]

GS, unfortunately our esoteric conversation is leading people in all sorts of weird directions.

Clarification on semantics: you cannot by definition have a class that contains only one object, correct?

How about the set of even prime integers?

Ba'al Chatzaf

What about it? The set of even primes is not an even prime.

[Christopher]

Clarification on semantics: you cannot by definition have a class that contains only one object, correct?

I am wrong - there are null sets.

[Dragonfly]

GS, unfortunately our esoteric conversation is leading people in all sorts of weird directions.

Clarification on semantics: you cannot by definition have a class that contains only one object, correct?

How about the set of even prime integers?

Ba'al Chatzaf

What about it? The set of even primes is not an even prime.

Irrelevant, we were not talking about sets that contain themselves, but about sets that contain only one element.

[tjohnson]

Irrelevant, we were not talking about sets that contain themselves, but about sets that contain only one element.

Well, technically, we were talking about conceiving of classes of objects - not set theory. The point is you cannot legitimately define a class of objects after having seen only one.

[tjohnson]

Clarification on semantics: you cannot by definition have a class that contains only one object, correct?

I am wrong - there are null sets.

This conversation got sidetracked when Baal introduced sets - this is not about mathematics. The point I am trying to make is that we humans form classes or generalizations denoted by words like 'tree', for example, based on observations of multiple individuals. Also, we have a tendency, after producing these generalizations, to forget about the individual differences of the members of these classes. This can be very problematic for humans and it's a problem unique to us because of our advanced use of language compared to other animals.

[Dragonfly]

Well, technically, we were talking about conceiving of classes of objects - not set theory. The point is you cannot legitimately define a class of objects after having seen only one.

Why not? If I discover an animal that has been unknown until then, I can very well define a new class, in this case a new species, even if I have seen only one single animal.

[tjohnson]

Well, technically, we were talking about conceiving of classes of objects - not set theory. The point is you cannot legitimately define a class of objects after having seen only one.

Why not? If I discover an animal that has been unknown until then, I can very well define a new class, in this case a new species, even if I have seen only one single animal.

Yes you could, but you would have to assume there are other similar animals, correct?

[Dragonfly]

Well, technically, we were talking about conceiving of classes of objects - not set theory. The point is you cannot legitimately define a class of objects after having seen only one.

Why not? If I discover an animal that has been unknown until then, I can very well define a new class, in this case a new species, even if I have seen only one single animal.

Yes you could, but you would have to assume there are other similar animals, correct?

You may assume that, but that doesn't take away the fact that you can define a new class by seeing only one object belonging to that class.

[tjohnson]

You may assume that, but that doesn't take away the fact that you can define a new class by seeing only one object belonging to that class.

A class consisting of one object? I propose that this is meaningless. There is an implicit assumption of plurality in a class. We only know about one universe and we can speculate that their are other similar universes and go on to define what "a universe" means but it has no meaning if the universe is a singular event.