The Same but Different

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fast
 
Reply Sun 3 Jan, 2010 11:02 pm
What does it mean to say that something is the same as something else? More importantly, how critical (or loose) should we be when we apply the word same? Aren't philosophizers at risk of being a bit too critical, and wouldn't we thus develop a propensity to deny that very similar things are the same when most folks wouldn't, and is that a good thing, or is it a sign of being too extreme in how we apply the word same?

I don't think that things need to be so identical that God can't tell them apart before we're willing to say they're the same. I guess what I'm saying is that there are times when it seems to me that it's okay to say that something is the same as something else even when there are differences. Call it a lion, and be it a tiger, but it'll eat us just the same.

For example, during a discussion about planets, Bob says to Sara, the teacher wrote the number three on the blackboard. No cried Sara, the teacher wrote the numeral three on the blackboard. In a discussion about planets, it seems that the distinction is irrelevant and unimportant. Not only that, it's close enough! For all intents and purposes, they are essentially the same-despite the differences that some of us are all too familiar with.

I don't think things have to be identical to the point of not being able to make distinctions before it's okay to say that something is the same as another, yet (and in the philosophical arena) the word same seems to me to have been elevated beyond common man approach. We can't even rightly say that logically equivalent propositions are the same?
 
Emil
 
Reply Sun 3 Jan, 2010 11:51 pm
@fast,
Fast wrote:
We can't even rightly say that logically equivalent propositions are the same?


The problem with that is that all necessary truths are logically equivalent, and all necessary falsehoods are logically equivalent. But there is not only one necessary truth and one necessary falsehood. Therefore (via other steps), it is false that logically equivalence is a sufficient condition for propositional identity.
 
kennethamy
 
Reply Sun 3 Jan, 2010 11:54 pm
@Emil,
Emil;116815 wrote:
The problem with that is that all necessary truths are logically equivalent, and all necessary falsehoods are logically equivalent. But there is not only one necessary truth and one necessary falsehood. Therefore (via other steps), it is false that logically equivalence is a sufficient condition for propositional identity.


Would you say what propositional identity is other than logical equivalence? I am suggesting that there is just one necessary truth, but many expressions of it.
 
Zetherin
 
Reply Mon 4 Jan, 2010 12:34 am
@fast,
fast wrote:
I don't think that things need to be so identical that God can't tell them apart before we're willing to say they're the same. I guess what I'm saying is that there are times when it seems to me that it's okay to say that something is the same as something else even when there are differences. Call it a lion, and be it a tiger, but it'll eat us just the same.


I think that there are times when we should, or must, focus on the distinctions, however minute, as philosophers. As philosophers, we are in a position to investigate claims that people usually take for granted. It isn't that we're always being sticklers when we do so. We should (I'd hope!), be providing insight into things others may not be able to see, or haven't taken the time to see.

Quote:
Call it a lion, and be it a tiger, but it'll eat us just the same.


It really depends what about the lion and tiger we're conversing about. It's hard to generalize and state that we should or shouldn't delve into the intricacies. It really depends on the specific example.

-

I just want you to keep in mind that the group you mainly philosophize with, The "Analytics", do not represent all of philosophers. I prefer this kind of philosophizing: the conscious precision of every word spoken, the analyzing of any and every note of linguistic or logical value. But, there are many philosophers who are much more laxed with how they speak and philosophize! They do not gripe over precision and extend a very generous 'benefit of the doubt' whenever they communicate. Personally, I feel this can contribute to laziness, but hey, to each their own!
 
Owen phil
 
Reply Mon 4 Jan, 2010 09:01 am
@Emil,
Emil;116815 wrote:
The problem with that is that all necessary truths are logically equivalent, and all necessary falsehoods are logically equivalent. But there is not only one necessary truth and one necessary falsehood. Therefore (via other steps), it is false that logically equivalence is a sufficient condition for propositional identity.


I don't agree.

p=q =df Af(f(p) <-> f(q)).

1. (p <-> q) -> (f(p) <-> f(q)).

Proof:

(true <-> true) -> (f(true) <-> f(true)), is true.
(false <-> true) -> (f(false) <->f(true), is true because (false <-> true), is false.
(true <-> false) -> (f(true) <-> f(false)), is true because (true <-> false), is false.
(false <-> false) -> (f(false) <-> f(false), is true.

That is, for all values of the variables p and q, 1. is tautologous.

Af((p <-> q) -> (f(p) <-> f(q))), is true.
therefore,
(p <-> q) -> Af(f(p) <-> f(q)).
QED.

Note that, (p <-> q) <-> (p = q) is a tautology.
 
kennethamy
 
Reply Mon 4 Jan, 2010 09:17 am
@Zetherin,
Zetherin;116826 wrote:

-

I just want you to keep in mind that the group you mainly philosophize with, The "Analytics", do not represent all of philosophers. I prefer this kind of philosophizing: the conscious precision of every word spoken, the analyzing of any and every note of linguistic or logical value. But, there are many philosophers who are much more laxed with how they speak and philosophize! They do not gripe over precision and extend a very generous 'benefit of the doubt' whenever they communicate. Personally, I feel this can contribute to laziness, but hey, to each their own!


Laziness is their own, private, business. But nonsense or falsity is public business. And that is what imprecision when precision is needed can contribute to. Unneeded precision is, of course, pickyness. But needed precision is vital, both in life or in philosophy. Who does not care about needed precision does not care about making sense, or truth. And some anti-analytics even say just that.

---------- Post added 01-04-2010 at 10:25 AM ----------

Owen;116877 wrote:
I don't agree.

p=q =df Af(f(p) <-> f(q)).

1. (p <-> q) -> (f(p) <-> f(q)).

Proof:

(true <-> true) -> (f(true) <-> f(true)), is true.
(false <-> true) -> (f(false) <->f(true), is true because (false <-> true), is false.
(true <-> false) -> (f(true) <-> f(false)), is true because (true <-> false), is false.
(false <-> false) -> (f(false) <-> f(false), is true.

That is, for all values of the variables p and q, 1. is tautologous.

Af((p <-> q) -> (f(p) <-> f(q))), is true.
therefore,
(p <-> q) -> Af(f(p) <-> f(q)).
QED.

Note that, (p <-> q) <-> (p = q) is a tautology.


All this is, so far as I can tell, quite true. What I cannot figure out is how it connects with Emil's argument for the conclusion that logical equivalence and identity are not identical. In fact, if what you posted is an argument, could you please tell me what its conclusion is?
 
Emil
 
Reply Mon 4 Jan, 2010 09:41 am
@kennethamy,
kennethamy;116818 wrote:
Would you say what propositional identity is other than logical equivalence? I am suggesting that there is just one necessary truth, but many expressions of it.


Do you think that 2+2=4 is the same, in the identity sense, as 192837412/2=96418706? They are both necessarily true, but they are not the same necessary truth. Why would one think they are?

Swartz made the same objection here:
[INDENT]Objection B: This account (i.e. Thesis #12) seems alright if we confine our examples (as in the paragraph "On this account..." above) to contingent propositions: nonequivalent contingent propositions will be identified with different sets of possible worlds. There will be as many different such sets as there are nonequivalent contingent propositions. But this 12th account gets into difficulty with noncontingent propositions. If propositions just are the sets of possible worlds in which they are true, then all necessarily true propositions would turn out to be identical (not just equivalent to one another - a tolerable oddity) and all necessarily false propositions would turn out to be identical. Put another way: on this 12th account, although there would be an infinite number of nonequivalent contingent propositions, there would be only one necessarily true proposition and only one necessarily false proposition. For example, the (necessarily true) proposition that 2 + 2 = 4 would turn out to be (not just logically equivalent to but) the very same proposition as the proposition that whatever is blue is blue or noisy. This consequence is unacceptable. [/INDENT]
 
kennethamy
 
Reply Mon 4 Jan, 2010 10:06 am
@Emil,
Emil;116884 wrote:
Do you think that 2+2=4 is the same, in the identity sense, as 192837412/2=96418706? They are both necessarily true, but they are not the same necessary truth. Why would one think they are?

Swartz made the same objection here:[INDENT]Objection B: This account (i.e. Thesis #12) seems alright if we confine our examples (as in the paragraph "On this account..." above) to contingent propositions: nonequivalent contingent propositions will be identified with different sets of possible worlds. There will be as many different such sets as there are nonequivalent contingent propositions. But this 12th account gets into difficulty with noncontingent propositions. If propositions just are the sets of possible worlds in which they are true, then all necessarily true propositions would turn out to be identical (not just equivalent to one another - a tolerable oddity) and all necessarily false propositions would turn out to be identical. Put another way: on this 12th account, although there would be an infinite number of nonequivalent contingent propositions, there would be only one necessarily true proposition and only one necessarily false proposition. For example, the (necessarily true) proposition that 2 + 2 = 4 would turn out to be (not just logically equivalent to but) the very same proposition as the proposition that whatever is blue is blue or noisy. This consequence is unacceptable. [/INDENT]


No. I suggested that they are different expressions of the same necessary truth. The trouble is that to say that it is false that all necessary truths are identical supposes a criterion of identity of necessary truths which you don't seem to have. What is it that all necessary truths are not? Identical. But what is that? Here we run straight into Quine's objection to the positing of propositions that we have no principle of identity for propositions, and that, since, "no entity without identity", propositions do not exist.
 
Emil
 
Reply Mon 4 Jan, 2010 10:21 am
@kennethamy,
kennethamy;116888 wrote:
No. I suggested that they are different expressions of the same necessary truth. The trouble is that to say that it is false that all necessary truths are identical supposes a criterion of identity of necessary truths which you don't seem to have.


What is the problem with that? Other than I don't have it.

kennethamy;116888 wrote:
What is it that all necessary truths are not? Identical. But what is that? Here we run straight into Quine's objection to the positing of propositions that we have no principle of identity for propositions, and that, since, "no entity without identity", propositions do not exist.


That objection does not seem convincing to me. What is the justification for "no entity without identity"?
 
kennethamy
 
Reply Mon 4 Jan, 2010 10:37 am
@Emil,
Emil;116889 wrote:
What is the problem with that? Other than I don't have it.



That objection does not seem convincing to me. What is the justification for "no entity without identity"?


If you do not have a principle of identity for propositions, then what is it that you are denying when you deny that necessary propositions are identical. What exactly is it that they are not?



to start with, how could something exist without being self-identical? And for it to be self-identical, there has to be some principle of identity which applies to it. But you can look up Quine's slogan in many places. (It was why the question, "how many angels can dance on the head of a pin?" was an important ontological question. Since angels were incorporeal, there seemed to be no principle of identity or criterion of individuation for angels).
 
Emil
 
Reply Mon 4 Jan, 2010 11:22 am
@kennethamy,
kennethamy;116893 wrote:
If you do not have a principle of identity for propositions, then what is it that you are denying when you deny that necessary propositions are identical. What exactly is it that they are not?


They are not identical of course. That I don't have an analysis of a term does not imply that I cannot use it. Most educated speakers of english do not know all the conditions of knowledge, no one does at all, but still they can use it correctly. Similarly with many other terms.


Quote:
to start with, how could something exist without being self-identical? And for it to be self-identical, there has to be some principle of identity which applies to it.


Sure. What about the usual one, Leibniz' law?

Quote:
But you can look up Quine's slogan in many places. (It was why the question, "how many angels can dance on the head of a pin?" was an important ontological question. Since angels were incorporeal, there seemed to be no principle of identity or criterion of individuation for angels).


Oh, but I suggest that the usual law of identity works for propositions too. Two propositions, P and Q, are identical just when they share all their properties. But that two propositions are logically equivalent does not imply that they share all their properties.

I think something like what Swartz suggests in his book, Possible Worlds, is a good analysis of propositions. In his view propositions have a structure that is made up of concepts and particulars. The logically equivalent propositions "Texas is south of Canada" and "Canada is north of Texas" are not made of the same concept.
The first is "is south of" and the second is "is north of". Though these two are related (they stand in relation that has a name but I forgot what it is called), they are not identical. If they were, they could be substituted in some contexts (non-opaque) without problems, but they cannot, of course.

Also, the ordering is different. In the first proposition Texas is first and Canada is second (Stc) but in the other it is Canada, Texas (Nct).

So, they differ in some properties. So, they are not identical even though they are logically equivalent. QED
 
Pyrrho
 
Reply Mon 4 Jan, 2010 11:57 am
@fast,
fast;116794 wrote:
What does it mean to say that something is the same as something else? More importantly, how critical (or loose) should we be when we apply the word same? Aren't philosophizers at risk of being a bit too critical, and wouldn't we thus develop a propensity to deny that very similar things are the same when most folks wouldn't, and is that a good thing, or is it a sign of being too extreme in how we apply the word same?

I don't think that things need to be so identical that God can't tell them apart before we're willing to say they're the same. I guess what I'm saying is that there are times when it seems to me that it's okay to say that something is the same as something else even when there are differences. Call it a lion, and be it a tiger, but it'll eat us just the same.

For example, during a discussion about planets, Bob says to Sara, the teacher wrote the number three on the blackboard. No cried Sara, the teacher wrote the numeral three on the blackboard. In a discussion about planets, it seems that the distinction is irrelevant and unimportant. Not only that, it's close enough! For all intents and purposes, they are essentially the same-despite the differences that some of us are all too familiar with.

I don't think things have to be identical to the point of not being able to make distinctions before it's okay to say that something is the same as another, yet (and in the philosophical arena) the word same seems to me to have been elevated beyond common man approach. We can't even rightly say that logically equivalent propositions are the same?



Of course logically equivalent propositions are not the same. If we consider the typical math problem, the whole process involves finding something that is logically equivalent (or, more precisely, mathematically equivalent) with something else.

[CENTER]2 + 2 = x, solve for x. [/CENTER]

Do you think that it would be okay to answer, "2 + 2"? Or "8,397,482.359 - 8,397,478.359"?

But going to your tiger and lion example, what can be said is that they are the same in some ways, and different in other ways. For example, if both are healthy adults and very hungry, entering the cage of either one without any protection would be unwise, and likely end up with practically the same result: being eaten. But if you wanted to breed animals, I assure you, whether the mate selected for the current lion in the zoo is a lion or a tiger may make all the difference.

kennethamy said something quite apt:

kennethamy;116879 wrote:
Laziness is their own, private, business. But nonsense or falsity is public business. And that is what imprecision when precision is needed can contribute to. Unneeded precision is, of course, pickyness. But needed precision is vital, both in life or in philosophy. Who does not care about needed precision does not care about making sense, or truth. And some anti-analytics even say just that. ...
 
Emil
 
Reply Mon 4 Jan, 2010 12:46 pm
@fast,
Pyrrho wrote:
But going to your tiger and lion example, what can be said is that they are the same in some ways, and different in other ways. For example, if both are healthy adults and very hungry, entering the cage of either one without any protection would be unwise, and likely end up with practically the same result: being eaten. But if you wanted to breed animals, I assure you, whether the mate selected for the current lion in the zoo is a lion or a tiger may make all the difference.
Wasn't this kind of 'identity' mentioned in William James' defense of faith? He too confused identity with giving identical results (IIRC). I skimmed through his essay (in the Buger book) but didn't find it. AFAIK it is something like this: Believing that something is a bad idea and thus not choosing to do it and not believing that something is a good idea and thus not choosing it. They give the same result, that is, not choosing it, but they are not identical.
 
Pyrrho
 
Reply Mon 4 Jan, 2010 01:03 pm
@Emil,
Emil;116955 wrote:
Wasn't this kind of 'identity' mentioned in William James' defense of faith? He too confused identity with giving identical results (IIRC). I skimmed through his essay (in the Buger book) but didn't find it. AFAIK it is something like this: Believing that something is a bad idea and thus not choosing to do it and not believing that something is a good idea and thus not choosing it. They give the same result, that is, not choosing it, but they are not identical.


I would reserve the word "identical" for things that are identical ("identical" means being the same in every way, not merely in some ways), and say that different things may have some aspects the same, without thereby being identical. As, for example, a square and an equilateral triangle both are figures with sides that are equal (so they are the same in that way), but they are different figures, as they have different numbers of sides. Or, to say the same thing differently: They are not identical figures, but they are the same in that they both have equal sides, but they are different in that they have a different number of sides (as well as having different internal angles, etc.).

I am not sure why you are bringing up James in connection with this, but you are right that two different attitudes may result in the same action in a particular instance, which, as you say, does not make the attitudes identical to each other. Of course, in different instances, one may find different behaviors associated with those different attitudes.
 
Zetherin
 
Reply Mon 4 Jan, 2010 01:18 pm
@Pyrrho,
Pyrrho;116964 wrote:
I would reserve the word "identical" for things that are identical ("identical" means being the same in every way, not merely in some ways), and say that different things may have some aspects the same, without thereby being identical. As, for example, a square and an equilateral triangle both are figures with sides that are equal (so they are the same in that way), but they are different figures, as they have different numbers of sides. Or, to say the same thing differently: They are not identical figures, but they are the same in that they both have equal sides, but they are different in that they have a different number of sides (as well as having different internal angles, etc.).

I am not sure why you are bringing up James in connection with this, but you are right that two different attitudes may result in the same action in a particular instance, which, as you say, does not make the attitudes identical to each other. Of course, in different instances, one may find different behaviors associated with those different attitudes.


What sorts of things are identical? Suppose, for instance, a machine manufactures 2 tires from the same mold, and most, if not everyone, agrees that they are identical physically. However, their spatial relations are different, and the specific spatial relation of each tire is most certainly a property of each tire, so, are these two tires identical? If every single property has to be the same, how could most physical things be identical? Wouldn't the mere making them two different things, make them non-identical in some way?

If two things were identical, they would be the same thing, and so they wouldn't be two things after all; there be no "they", "it" would be one thing, wouldn't it be?
 
Pyrrho
 
Reply Mon 4 Jan, 2010 01:54 pm
@Zetherin,
Zetherin;116972 wrote:
What sorts of things are identical? Suppose, for instance, a machine manufactures 2 tires from the same mold, and most, if not everyone, agrees that they are identical physically. However, their spatial relations are different, and the specific spatial relation of each tire is most certainly a property of each tire, so, are these two tires identical? If every single property has to be the same, how could most physical things be identical? Wouldn't the mere making them two different things, make them non-identical in some way?

If two things were identical, they would be the same thing, and so they wouldn't be two things after all; there be no "they", "it" would be one thing, wouldn't it be?


Two different physical objects are never identical to each other, just as you say. They may, however, be interchangeable in a machine, if they are sufficiently the same (i.e., the same in enough ways).
 
Zetherin
 
Reply Mon 4 Jan, 2010 02:07 pm
@Pyrrho,
Pyrrho;116990 wrote:
Two different physical objects are never identical to each other, just as you say. They may, however, be interchangeable in a machine, if they are sufficiently the same (i.e., the same in enough ways).


But, so, what sorts of things are identical?

Suppose I say, sentence X is identical to sentence Y. Isn't sentence X just similar (and potentially overwhelmingly similar) to sentence Y? How could it ever be truly identical, if they are two different sentences? To be identical, X=X, but then, we'd just be speaking of the same sentence. So, what gives? Do we just call things identical when the similarity in properties is overwhelming, or is it reserved for something else (this something else is what I'm asking for)?
 
Emil
 
Reply Mon 4 Jan, 2010 02:11 pm
@Zetherin,
Zetherin;116972 wrote:
What sorts of things are identical? Suppose, for instance, a machine manufactures 2 tires from the same mold, and most, if not everyone, agrees that they are identical physically. However, their spatial relations are different, and the specific spatial relation of each tire is most certainly a property of each tire, so, are these two tires identical? If every single property has to be the same, how could most physical things be identical? Wouldn't the mere making them two different things, make them non-identical in some way?


No two things are ever identical.

Though the tires may be of the identical series (an abstract object), they are not identical.

Zetherin;116972 wrote:
If two things were identical, they would be the same thing, and so they wouldn't be two things after all; there be no "they", "it" would be one thing, wouldn't it be?


Yes.

---------- Post added 01-04-2010 at 09:13 PM ----------

Zetherin;116994 wrote:
But, so, what sorts of things are identical?

Suppose I say, sentence X is identical to sentence Y. Isn't sentence X just similar (and potentially overwhelmingly similar) to sentence Y? How could it ever be truly identical, if they are two different sentences? To be identical, X=X, but then, we'd just be speaking of the same sentence. So, what gives? Do we just call things identical when the similarity in properties is overwhelming, or is it reserved for something else (this something else is what I'm asking for)?


They could be of the same type. Two tokens are never identical, I think.

See:
Type-token distinction - Wikipedia, the free encyclopedia

And, more advanced:
Types and Tokens (Stanford Encyclopedia of Philosophy)
 
Pyrrho
 
Reply Mon 4 Jan, 2010 02:19 pm
@Zetherin,
Zetherin;116994 wrote:
But, so, what sorts of things are identical?

Suppose I say, sentence X is identical to sentence Y. Isn't sentence X just similar (and potentially overwhelmingly similar) to sentence Y? How could it ever be truly identical, if they are two different sentences? To be identical, X=X, but then, we'd just be speaking of the same sentence. So, what gives? Do we just call things identical when the similarity in properties is overwhelming, or is it reserved for something else (this something else is what I'm asking for)?


A thing is only identical with itself.

Two different descriptions may describe the same triangle. In such a case, the thing described is identical, but the descriptions are not.

As for how people use the term "identity", very often, people do as you say, and "call things identical when the similarity in properties is overwhelming". Or one may say, two things are identical for practical purposes, which is more or less the same idea.

---------- Post added 01-04-2010 at 03:31 PM ----------

Emil;116996 wrote:
...

They could be of the same type. Two tokens are never identical, I think.

See:
Type-token distinction - Wikipedia, the free encyclopedia

And, more advanced:
Types and Tokens (Stanford Encyclopedia of Philosophy)


That may be a useful idea to introduce to this discussion. Two different objects may be of the same type, and thus of identical type, but are different tokens.

This also is relevant to something stated in the original post regarding numerals versus numbers, though often people use the word "number" to mean "numeral" in ordinary use.

For the difference between "number" and "numeral", see:

Math Forum - Ask Dr. Math

Number - Wikipedia, the free encyclopedia

Numeral system - Wikipedia, the free encyclopedia
 
Zetherin
 
Reply Mon 4 Jan, 2010 02:31 pm
@Pyrrho,
Pyrrho;116999 wrote:
A thing is only identical with itself.

Two different descriptions may describe the same triangle. In such a case, the thing described is identical, but the descriptions are not.

As for how people use the term "identity", very often, people do as you say, and "call things identical when the similarity in properties is overwhelming". Or one may say, two things are identical for practical purposes, which is more or less the same idea.


Yes, I suppose we must make note which sense of the word "identical" we're using. The sense described in my dictionary states, "Having such a close similarity or resemblance as to be essentially equal or interchangeable.". And that does seem to be how we ordinarily use the word. When I say the two tires are identical, I don't think I am incorrect, and it's certainly not a meaningless statement. Saying the two tires are identical is different than saying the two tires are kind of the same, for instance. When I say "identical" here I am implying a very high level of exactness.

"A thing is only identical with itself", seems to be a tautology. Why even use identical here? We could just say X is X.

I guess what I'm still not grasping is - why use "identical" in its strictest sense? Is there an example where using "identical" in its stricting sense could lend us further understanding?
 
 

 
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