The Same but Different

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Pyrrho
 
Reply Mon 4 Jan, 2010 02:53 pm
@Zetherin,
Zetherin;117004 wrote:
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?


Perhaps it is my past studies in math that have gotten me accustomed to a very strict sense of "identical". In pure mathematics, a slight difference is a difference that matters, no matter how slight it is. When building a physical object, a very slight difference does not matter, though how slight is slight enough depends upon the level of tolerance required for the thing in question.
 
kennethamy
 
Reply Mon 4 Jan, 2010 02:56 pm
@Zetherin,
Zetherin;117004 wrote:
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?


To say that things are identical is to say that they are the same. "Identity" and "sameness" mean the same; their meanings are identical. However, they have more than one meaning. A distinction is customarily drawn between qualitative and numerical identity or sameness. Things with qualitative identity share properties, so things can be more or less qualitatively identical. Poodles and Great Danes are qualitatively identical because they share the property of being a dog, and such properties as go along with that, but two poodles will (very likely) have greater qualitative identity. Numerical identity requires absolute, or total, qualitative identity, and can only hold between a thing and itself. Its name implies the controversial view that it is the only identity relation in accordance with which we can properly count (or number) things: x and y are to be properly counted as one just in case they are numerically identical (Geach 1973).

Stanford Encyclopedia of Philosophy Article: Same

Thus, numerical (quantitative) identity implies qualitative identity (and is logically stronger) but qualitative identity does not imply numerical identity, (and so is logically weaker).


 
Emil
 
Reply Mon 4 Jan, 2010 03:23 pm
@Zetherin,
Zetherin;117004 wrote:
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?


Yes, as with my examples with types and tokens from before. Also two terms may have identical referents.
 
kennethamy
 
Reply Mon 4 Jan, 2010 03:30 pm
@Emil,
Emil;117032 wrote:
Yes, as with my examples with types and tokens from before. Also two terms may have identical referents.


And one term different referents.
 
Emil
 
Reply Mon 4 Jan, 2010 03:32 pm
@kennethamy,
kennethamy;117036 wrote:
And one term different referents.


Well, one term type different referents. Smile
 
kennethamy
 
Reply Mon 4 Jan, 2010 04:04 pm
@Emil,
Emil;117037 wrote:
Well, one term type different referents. Smile


Yes. We can put it that way too.
 
fast
 
Reply Tue 5 Jan, 2010 03:12 pm
@Emil,
[QUOTE=fast]We can't even rightly say that logically equivalent propositions are the same?[/quote][QUOTE=Emil;116815]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.[/QUOTE]
Sometimes, the word "believe" is the word of choice by those that know but fear to claim knowledge. A person that sees that proposition X is the same as proposition Y may fear saying so and claim instead that they're equivalent, but I suspect that you even deny that proposition X and proposition Y are equivalent (let alone the same).

The sentence, "Sandy bit Charlie" is not the same as (nor equivalent to) the sentence, "the girl with the red hair sunk her teeth down into the guy with square glasses," but what can be meant by the expression of those sentences in certain unique situations can be the same (or at least very similar), so what can be expressed by a person (or different people) uttering those sentences (making statements) can be the same. There is certainly more to a statement than a sentence.

For example, the first eyewitness said, "Sandy bit Charlie," and the second eyewitness said, "the girl with the red hair sunk her teeth down into the guy with square glasses." It is clear to all involved that both eyewitnesses are referring to the same girl and guy and mean virtually the same thing by what they say. The statements made to the cop by the eyewitnesses are virtually the same (yet each used different ways to express the same proposition), or at the very least, they are consistent. We have two people (and not just one person) saying that the girl bit the guy.
 
Zetherin
 
Reply Tue 5 Jan, 2010 03:15 pm
@fast,
fast wrote:

For example, the first eyewitness said, "Sandy bit Charlie," and the second eyewitness said, "the girl with the red hair sunk her teeth down into the guy with square glasses." It is clear to all involved that both eyewitnesses are referring to the same girl and guy and mean virtually the same thing by what they say. The statements made to the cop by the eyewitnesses are virtually the same (yet each used different ways to express the same proposition), or at the very least, they are consistent. We have two people (and not just one person) saying that the girl bit the guy.


In this case, I would agree that the propositions are the same. But just because, in this case, the propositions expressed are the same, it does not follow that logical equivalence is a sufficient condition for propositional identity, does it?
 
fast
 
Reply Tue 5 Jan, 2010 03:18 pm
@Zetherin,
Zetherin;117405 wrote:
In this case, I would agree that the propositions are the same. But just because, in this case, the propositions expressed are the same, it does not follow that logical equivalence is a sufficient condition for propositional identity, does it?
No. Do you know why he brought it up?
 
Zetherin
 
Reply Tue 5 Jan, 2010 03:21 pm
@fast,
fast;117408 wrote:
No. Do you know why he brought it up?


Because there are some cases where statements can be logically equivalent but not express the same proposition?
 
fast
 
Reply Tue 5 Jan, 2010 03:27 pm
@Zetherin,
[QUOTE=Zetherin;117410]Because there are some cases where statements can be logically equivalent but not express the same proposition?[/QUOTE]Maybe the word, "logically" is throwing me. It seems to me that two different statements can be the same or similar or altogether different. If something is close to being the same but not quite the same, then I might say they're similar. What does "logically equivalent" mean anyway if not similar?
 
Emil
 
Reply Tue 5 Jan, 2010 04:27 pm
@fast,
fast;117402 wrote:

Sometimes, the word "believe" is the word of choice by those that know but fear to claim knowledge. A person that sees that proposition X is the same as proposition Y may fear saying so and claim instead that they're equivalent, but I suspect that you even deny that proposition X and proposition Y are equivalent (let alone the same).

The sentence, "Sandy bit Charlie" is not the same as (nor equivalent to) the sentence, "the girl with the red hair sunk her teeth down into the guy with square glasses," but what can be meant by the expression of those sentences in certain unique situations can be the same (or at least very similar), so what can be expressed by a person (or different people) uttering those sentences (making statements) can be the same. There is certainly more to a statement than a sentence.

For example, the first eyewitness said, "Sandy bit Charlie," and the second eyewitness said, "the girl with the red hair sunk her teeth down into the guy with square glasses." It is clear to all involved that both eyewitnesses are referring to the same girl and guy and mean virtually the same thing by what they say. The statements made to the cop by the eyewitnesses are virtually the same (yet each used different ways to express the same proposition), or at the very least, they are consistent. We have two people (and not just one person) saying that the girl bit the guy.


What's up with the italics?

The two sentences in your example have the same referents, but they do not mean the same. You can see this by making up a possible scenario where they differ in referents. That's your exercise for tomorrow. :p

---------- Post added 01-05-2010 at 11:29 PM ----------

fast;117412 wrote:
Maybe the word, "logically" is throwing me. It seems to me that two different statements can be the same or similar or altogether different. If something is close to being the same but not quite the same, then I might say they're similar. What does "logically equivalent" mean anyway if not similar?


Logical equivalence
P and Q are logically equivalent iff P logically implies Q and Q logically implies P.

Logical implication
P logically implies Q iff there is no possible world where P is the case and where Q is not the case.

Keep that in mind.

---

This is, BTW Fast, yet another thing you could have learned if you had just read the book I referred you to to begin with. Here I will do it again: Swartz and Bradley, Possible Worlds, 1979.

As for you Z. This is a reason to learn from that particular logic textbook. It covers a lot of things that you have been discussing on this forum. Maybe you ought to start with it. Tho I admit that it is kinda technical and it took me a while to read it. It was the book that taught me the most.
 
fast
 
Reply Tue 5 Jan, 2010 05:00 pm
@Emil,
[QUOTE=Emil;117421]What's up with the italics?[/QUOTE]They wouldn't go away!

[quote]The two sentences in your example have the same referents, but they do not mean the same. [/QUOTE]Referring terms have referents, and all terms have meaning. Since when do sentences have referents?[/SIZE]

[quote]You can see this by making up a possible scenario where they differ in referents. That's your exercise for tomorrow. [/SIZE] [/QUOTE]English is preferable to all this possible world jazz. It makes me think of The Return of the Living Metaphor. If you keep saying there are possible worlds, I fear that you might start to believe it.
 
Emil
 
Reply Tue 5 Jan, 2010 05:04 pm
@fast,
fast;117429 wrote:
They wouldn't go away!


Use the "clear formatting bottom". It's up in the corner to the left.

Quote:
Referring terms have referents, and all terms have meaning. Since when do sentences have referents?


Some terms are sentences. Some terms are phrases. Some terms are words.

Sentences refer in the same way that terms refer.

Quote:
English is preferable to all this possible world jazz. It makes me think of The Return of the Living Metaphor. If you keep saying there are possible worlds, I fear that you might start to believe it.


I already believe it.

Possible Worlds Semantics is not a metaphor.
 
fast
 
Reply Tue 5 Jan, 2010 05:20 pm
@Emil,
[QUOTE=Emil;117433]Some terms are sentences. Some terms are phrases. Some terms are words. [/QUOTE]Hmmm. I didn't know that. I mean, I know that some terms have multiple words, and a phrase can be considered a term, but I didn't know that a whole sentence could be considered a term.

[QUOTE]Sentences refer in the same way that terms refer.[/QUOTE]I didn't know that either. Still not sure that I do.

[QUOTE]I already believe it.[/QUOTE]Really? I thought it was just a way to explain the notion of logical possibilities. For example, it's not possible (well, not a real possibility anyhow) that I can from a standing position jump forty feet in the air. But, it is a logical possibility. Hence, imagine a possible world where there is very little gravity. In such a world, I can jump that high. See, it's just a way to explain the concept. Unfortunately, people have mistaken the metaphor and taken it literally.
 
Emil
 
Reply Tue 5 Jan, 2010 06:49 pm
@fast,
fast;117435 wrote:
Hmmm. I didn't know that. I mean, I know that some terms have multiple words, and a phrase can be considered a term, but I didn't know that a whole sentence could be considered a term.


OK.
fast;117435 wrote:
I didn't know that either. Still not sure that I do.


Ok.

fast;117435 wrote:
Really? I thought it was just a way to explain the notion of logical possibilities.


It is a way. But not "just".

fast;117435 wrote:
For example, it's not possible (well, not a real possibility anyhow) that I can from a standing position jump forty feet in the air. But, it is a logical possibility. Hence, imagine a possible world where there is very little gravity. In such a world, I can jump that high. See, it's just a way to explain the concept. Unfortunately, people have mistaken the metaphor and taken it literally.


Unfortunately you don't have a clue what you are talking about, do you? It's easy to convince me that you do. Mention some introductory articles/books to PWS you have read. Hint: There is one on SEP, maybe you can find it.

It is not a metaphor. Why do you think it is a metaphor? It is a way to talk, but it is not a metaphor. They are not the same.

Besides, you cannot justifiably dismiss Lewis' Modal Realism just be saying that it is a metaphor gone wild. If you are not concerned with being justified, then I cannot help you.
 
kennethamy
 
Reply Tue 5 Jan, 2010 07:11 pm
@Emil,
Emil;117449 wrote:
OK.


Ok.



It is a way. But not "just".



Unfortunately you don't have a clue what you are talking about, do you? It's easy to convince me that you do. Mention some introductory articles/books to PWS you have read. Hint: There is one on SEP, maybe you can find it.

It is not a metaphor. Why do you think it is a metaphor? It is a way to talk, but it is not a metaphor. They are not the same.

Besides, you cannot justifiably dismiss Lewis' Modal Realism just be saying that it is a metaphor gone wild. If you are not concerned with being justified, then I cannot help you.


So you really do believe there are possible worlds as well as the actual world? So you don't believe it is "a way to talk". I don't say that when I assert that there are elephants, that is "a way to talk" I? That would suggest that I don't believe there are elephants. There are problems (which I used to know some about, but no longer) about quantifying over possible worlds that Quine used to talk about. Again, problems having to do with identity and individuation. Doesn't the view that there are (really) possible worlds (other than this one) conflict with what Russell called, "a robust sense of reality"?
 
fast
 
Reply Tue 5 Jan, 2010 10:25 pm
@Emil,
Emil;117449 wrote:
If you are not concerned with being justified, then I cannot help you.
I try to say things that I believe are true, but I do not always recall the justification for the things that I have learned.
 
Emil
 
Reply Wed 6 Jan, 2010 11:10 am
@kennethamy,
kennethamy;117452 wrote:
So you really do believe there are possible worlds as well as the actual world? So you don't believe it is "a way to talk". I don't say that when I assert that there are elephants, that is "a way to talk" I? That would suggest that I don't believe there are elephants. There are problems (which I used to know some about, but no longer) about quantifying over possible worlds that Quine used to talk about. Again, problems having to do with identity and individuation. Doesn't the view that there are (really) possible worlds (other than this one) conflict with what Russell called, "a robust sense of reality"?


You may want to recall what a possible world is. It is merely a consistent set of propositions, not a world as in how we ordinarily use the word "world". I am not a modal realist like David Lewis.
 
Pyrrho
 
Reply Wed 6 Jan, 2010 11:35 am
@Emil,
Emil;117742 wrote:
You may want to recall what a possible world is. It is merely a consistent set of propositions, not a world as in how we ordinarily use the word "world". I am not a modal realist like David Lewis.


In other words, the word "world" is being used metaphorically. It is, after all, just a manner of speaking.
 
 

 
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