Philosophy Now Forum

This thread has two faces..the original one ...that when you say a thing is itself..involves differentiating between that thing and itself.

And that only concepts exist.

are you clear on any one of them, and why not?

Equivocation ("to call by the same name") is an informal logical fallacy. It is the misleading use of a term with more than one meaning or sense (by glossing over which meaning is intended at a particular time). It generally occurs with polysemic words (words with multiple meanings)

This might be a valid point if it wasnt that as we seek to narrow in on somethings meaning there are always respects other than "at a particular time" such as "at a particular conceptual position". We cannot do away with conceptual relatedness because once we do we do away with the whole concept completely.

Dont take me seriously WHEN I DO THIS. Just trying to make the debate more interesting by #raising_the_stakes

Maybe wtf can say it better than me;

wtf wrote:

Moyo wrote:Lets do this slowly

say we have a set A = {a;b;c}


In what way is that element "a" the element "a".

Why ! but by the axiom of identity.or in other words a=a . AKA (a,a).

Oh I see your point. We need sets to define relations, and we need the identity relation in order to talk about equality of sets.

I think the answer is the law of identity, https://en.wikipedia.org/wiki/Law_of_identity, which is a principle of logic. In other words we have the law of identity even before there are sets. That's my understanding of how this works; but in the end I think you raise a pretty good point. We need the law of identity before we write down the axioms for sets. Logic is logically prior to set theory.

In that sense I suppose we'd have to call equality a special kind of relation, one that precedes set theory itself and is not defined by a set-theoretical relation. I am not aware of how philosophers and logicians think about this.

(ps) I understand what's going on now. From the Wiki article https://en.wikipedia.org/wiki/Axiom_of_extensionality:

The axiom given above assumes that equality is a primitive symbol in predicate logic.

So the '=' symbol is not something defined within set theory. Rather, equality exists even before we write down the axioms of set theory.

Now when we write down the rules for what sets are, we start with Extensionality; which says that if we have two sets A and B with the property that for all x, x ∈ A if and only if x ∈ B, then we say that A = B.

In other words equality is given by logic; then we say what it means in set theory for two sets to be equal.

This avoids your infinite regress.

It's interesting that when we say for example that in the real numbers, 5 = 5, is that the logical equality? Or is it the equality relationship that we could define within set theory by considering the collection of all ordered pairs (x,x) where x is a real number?

I think it's not clear to me at all; but in practice, it doesn't seem to matter. In any event, we avoided the circularity by pushing '=' down into logic and making it available for use in set theory.

You raised a very good point but it seems the logicians and set theorists have already thought of it and prevented the problem.

(pps) Found this discussion ... http://math.stackexchange.com/questions ... gical-symb The consensus is that one can distinguish between equality as a logical symbol; and equality as a predicate when restricted to a specific set or domain.

Moyo wrote:This thread has two faces..the original one ...that when you say a thing is itself..involves differentiating between that thing and itself.

And that only concepts exist.

are you clear on any one of them, and why not?

On identity, we are forced to use distinct copies of a symbol to remind us of the idea or concept. It is inescapable without denoting each and every thing. So I'm not sure if you are just not approving of some particular uses of it by some or are interpreting any use of it at all. I understand the distinction and have to deal with it when trying to be particular in some logic we are using. For instance, a common mistake about using the "=" sign or words like "is" is that people don't recognize there are distinct types of uses of it. One is to demonstrate logical identity while another is to assign a value, often what is on the right to what is symbolized on the left by convention. Computer science uses "=" to mean assignment where "==" is the logical comparison of identity.

As to "concepts", in logic we use this to apply to anything we use in the same way you are thinking but don't imply that this means anything beyond our uses of it in logical forms. I'm not sure if you are raising a question of logic or ontology (philosophy concerning what is "real") or etymology (philosophy concerning our capacity to "know").

I already default to 'concepts' as a real thing but make even more distinctions where needed. You might be interested in checking out my thread on investigating Platonic Forms in this light AND the one on Models as these relate.

What is your own background and interests on philosophy?

Moyo wrote:...that when you say a thing is itself..involves differentiating between that thing and itself.

So I was right about the CP? You make up an imaginary extra set {ai} and apply it to get the result {a,a} when it should be {a,ai}?

By the by, I don't think this is a philosophical problem in propositional logic as I think identity/equality is defined by the bi-conditional, p->p ^ p->p or ¬p v p ^ p v ¬p. But don't quote me, as I also think p->p is enough.

The ancients often only defined a unit concept akin to an absolute 'form' and then even any copy of that is distinctly 'new'.

Scott Mayers wrote:The ancients often only defined a unit concept akin to an absolute 'form' and then even any copy of that is distinctly 'new'.

Form is defined by the axiom of identity...it separtes a thing from everything else..creates the boundaries especially the A is not equal to not A.

Arising_uk wrote: Moyo wrote:
...that when you say a thing is itself..involves differentiating between that thing and itself.

So I was right about the CP? You make up an imaginary extra set {ai} and apply it to get the result {a,a} when it should be {a,ai}?

By the by, I don't think this is a philosophical problem in propositional logic as I think identity/equality is defined by the bi-conditional, p->p ^ p->p or ¬p v p ^ p v ¬p. But don't quote me, as I also think p->p is enough.

any element "a" has to justify its existance by differentiating itself from everything else a != !a. But by the theory of relations it also has to justify itself to be what it is.
a=a...but what does it mean that a is differentiatd from itself?

Scott Mayers wrote:

Moyo wrote:This thread has two faces..the original one ...that when you say a thing is itself..involves differentiating between that thing and itself.

And that only concepts exist.

are you clear on any one of them, and why not?

On identity, we are forced to use distinct copies of a symbol to remind us of the idea or concept. It is inescapable without denoting each and every thing. So I'm not sure if you are just not approving of some particular uses of it by some or are interpreting any use of it at all. I understand the distinction and have to deal with it when trying to be particular in some logic we are using. For instance, a common mistake about using the "=" sign or words like "is" is that people don't recognize there are distinct types of uses of it. One is to demonstrate logical identity while another is to assign a value, often what is on the right to what is symbolized on the left by convention. Computer science uses "=" to mean assignment where "==" is the logical comparison of identity.

As to "concepts", in logic we use this to apply to anything we use in the same way you are thinking but don't imply that this means anything beyond our uses of it in logical forms. I'm not sure if you are raising a question of logic or ontology (philosophy concerning what is "real") or etymology (philosophy concerning our capacity to "know").

I already default to 'concepts' as a real thing but make even more distinctions where needed. You might be interested in checking out my thread on investigating Platonic Forms in this light AND the one on Models as these relate.

What is your own background and interests on philosophy?

There is no difference between the symbol and the "actual" thing. They are both concepts. That means when we use distinct copies we also use distinct things.

Philosophy is a hobby that i would like to take seriously one day. I am a reserved person that unfortunately is bipolar. Philosophy is how i "smash" stuff, rather than taking it out on other people.

Moyo wrote:any element "a" has to justify its existance by differentiating itself from everything else a != !a.

Or by just being the thing 'a'?

But by the theory of relations it also has to justify itself to be what it is. a=a...but what does it mean that a is differentiatd from itself?

To me it means that when you create a theory of relations you can create a relation that doesn't exist or causes complications that aren't there in reality, as it's not there in propositional logic(although I stand to be corrected).

Moyo wrote:

Scott Mayers wrote:The ancients often only defined a unit concept akin to an absolute 'form' and then even any copy of that is distinctly 'new'.

Form is defined by the axiom of identity...it separtes a thing from everything else..creates the boundaries especially the A is not equal to not A.

No, a 'form' is simply an abstraction (relative to us independently) that refers to anything contingently real or not to which helps us define classes of things or universals. It is 'real' with respect to some ideal objective observer in respect to "laws" of nature or reality as a whole even if we cannot determine all of them.

It is also the basis for formal definitions such that it helps us clarify a meaning by both relating what something is by what is equal in things in common between each use of its members referred to AND what is equal in their common (or uncommon) differences. So it might describe how some A of on member defined = A of each other member defined; Then it must add what makes each member or subset of them that differs from each other or why some A also ≠ another member [mutual exclusion] and do this exhaustively.

Arising_uk wrote: Moyo wrote:
...that when you say a thing is itself..involves differentiating between that thing and itself.

So I was right about the CP? You make up an imaginary extra set {ai} and apply it to get the result {a,a} when it should be {a,ai}?

By the by, I don't think this is a philosophical problem in propositional logic as I think identity/equality is defined by the bi-conditional, p->p ^ p->p or ¬p v p ^ p v ¬p. But don't quote me, as I also think p->p is enough.

any element "a" has to justify its existance by differentiating itself from everything else a != !a. But by the theory of relations it also has to justify itself to be what it is.
a=a...but what does it mean that a is differentiatd from itself?

I'm not sure if you are discussing some particular 'theory of relations' or to the defined term 'relation' with respect to logic or math. There a relation is any process, machine, or structure of argument, that takes members of one domain as 'inputs' and relates them to a range of other members called a 'range'. The domain members may require the range to be the same or different depending on what you define it as. In this way, the members of the range can be copies of the domain or some subset of them. A function is a specific type of relation that takes one (or more) input members from the Domain and outputs them to a Unique member from the Range. For most purposes, we use the Range to at least be some subset (including possibly the whole) of the Domain.

Scott Mayers wrote:

Moyo wrote:This thread has two faces..the original one ...that when you say a thing is itself..involves differentiating between that thing and itself.

And that only concepts exist.

are you clear on any one of them, and why not?

There is no difference between the symbol and the "actual" thing. They are both concepts. That means when we use distinct copies we also use distinct things.

Philosophy is a hobby that i would like to take seriously one day. I am a reserved person that unfortunately is bipolar. Philosophy is how i "smash" stuff, rather than taking it out on other people.

This is where you have to recognize the difference between '=' meaning to assign OR to mean equivalence depending on context. This is why in computers that relate this symbol distinctly separate it often as '=' to mean "let the right content of this symbol be assigned to the left" while they use, '==' to mean logical equivocation in meaning. A "definition" using concepts assigns the meaning of one to the other. So A = A means to assign (usually) the right meaning of the contemporary meaning of the A on the right to the symbol of 'A' on the left.

Scott Mayers wrote:helps us define classes of things or universals

Dog = 4 legged creature, with fur, a muzzle...

The definition;
is equivalent (means the same thing as)

Dog = Dog

By transitivity . ITs equivalent because its an equivalence relation.

Scott Mayers wrote:No, a 'form' is simply an abstraction (relative to us independently)

Isnt that what the axiom of identity does? Tell us how a thing is related to other things?
I.e. what it is not.

Dog != cat, zebra, donkey....(rest of the unviverse)

other than itself

Dog = Dog.

The Axiom of identy is the one that forms the skin (boundary) of a form.

Scott Mayers wrote: I'm not sure if you are discussing some particular 'theory of relations' or to the defined term 'relation' with respect to logic or math. There a relation is any process, machine, or structure of argument, that takes members of one domain as 'inputs' and relates them to a range of other members called a 'range'. The domain members may require the range to be the same or different depending on what you define it as. In this way, the members of the range can be copies of the domain or some subset of them. A function is a specific type of relation that takes one (or more) input members from the Domain and outputs them to a Unique member from the Range. For most purposes, we use the Range to at least be some subset (including possibly the whole) of the Domain.

There is no problem in general with relations ..its only when it describes a things relationship to itself. It implies that a things domain is exactly the same as its range...no problem with most of that except exact is a meaningless concept.

https://en.wikipedia.org/wiki/Form

n a wider sense, the form is the way something is

i.e. A is A.

https://en.wikipedia.org/wiki/Law_of_identity

n logic, the law of identity is the first of the three classical laws of thought. It states that “each thing is the same with itself and different from another”

Scott Mayers wrote: the difference between '=' meaning to assign OR to mean equivalence depending on context. This is why in computers that relate this symbol distinctly separate it often as '=' to mean "let the right content of this symbol be assigned to the left" while they use, '==' to mean logical equivocation in meaning

One makes two things equal , that means they are now the same and the other does not make sense on its own..it can be combined with an "IF" statement say to query. It does not assign or define so it is irrelevant to this discussion. Its a poor coincident.

https://en.wikipedia.org/wiki/Law_of_identity

In its symbolic representation, “A is A”, the first element of the proposition represents the subject (thing) and the second element, the predicate (its essence), with the copula “is” signifying the relation of “identity

This means that in some way A is different from A since subject != essence, otherwise therd be no distinction.