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Can Any Two Things Be Identical???

 
 
kennethamy
 
  2  
Reply Sat 12 Jun, 2010 10:33 pm
@mister kitten,
Leibniz had two principles:

1. The indiscernability of identicals.
2. The identity of indiscernibles.

The first says that if (putatively) two things have the very same properties, then they are not two things, but really one (and the same thing). The second is the converse of the first. It says that no two things can have the very same properties. It is generally agreed that the first is true, and indeed, it is the definition of identity logicians accept (Leibniz's Law of Identity). The second is obviously controversial. Leibniz held it was true just as he held that the first was true, but although the first is intuitively true, Leibniz had to give (dubious) metaphysical reasons for the second. Of course, the second might be true (for all we know). But if it is true, it is clearly not a necessary (or intuitive) truth as is the first. And the issue is not whether the second is true, but whether it must be true as the first is not only true, but it must be true.
Fido
 
  1  
Reply Sat 12 Jun, 2010 10:35 pm
@jeeprs,
jeeprs wrote:

Quote:
All cats are identically cats


but this is demonstrably untrue. Every creature is an individual. The DNA of each is different. That is what makes the question interesting.


Consider identity as a technical term, rather than a political one... All cats have different dna.... True, and it is all cat dna, having the identity of cat dna... Identity contains all of the differences of a class... All lines have the same identity, and that identity does not change no matter how long or short is the line, and in fact, the reason we can compare lines rationally is that we have the identity of line which does not change with length... Similarly, the identity of a cat does not change no matter how many cats are examined... And they are individuals, but all that word means is undividable, and if it could be divided it would not be a unit, and not have a single identity...
Fido
 
  1  
Reply Sat 12 Jun, 2010 10:37 pm
@kennethamy,
kennethamy wrote:

If two entities have the same ontological properties, they are usually identified as the same thing.

I don't know whether that is true, but it has nothing to do with the issue.

It has everything to do with the issue, or you do not understand what is perhaps the most basic and essential fact of philosophy, that all classification would be impossible without the principal of identity...
kennethamy
 
  1  
Reply Sat 12 Jun, 2010 10:39 pm
@Fido,
What has the (silly) question, are all cats the same cat? to do with the original issue. I don't see the relation? Why would the fact that all Xs have some one quality in common make them the same X? Only if someone were terribly confused.
0 Replies
 
Fido
 
  1  
Reply Sat 12 Jun, 2010 10:40 pm
@mister kitten,
mister kitten wrote:

Yes of course.
x=x
the two, when separate, are (x) and (x). They both equal each other. If (x) is a shape, then it is not only equal but congruent to (x) as well.

Aside from math, I cannot think of two identical things. Even if two things were completely completely completely identical down to each atom, the two would not be identical because they cannot occupy the same space (thinking of solids here).


Every concept representss a shared identity, so for every concept there are identical things... The does not mean they are equal in every repsect... And the correct statement of idenitity is A is A...
kennethamy
 
  1  
Reply Sat 12 Jun, 2010 10:42 pm
@Fido,
Whether or not they usually identified as the same thing has absolutely nothing to do with whether they are the same same thing. And none of this has anything to do with what is called, the principle of identity, namely, if two things are qualitatively identical then they are quantitatively identical.
0 Replies
 
kennethamy
 
  2  
Reply Sat 12 Jun, 2010 10:46 pm
@Fido,
Fido phil wrote:

mister kitten wrote:

Yes of course.
x=x
the two, when separate, are (x) and (x). They both equal each other. If (x) is a shape, then it is not only equal but congruent to (x) as well.

Aside from math, I cannot think of two identical things. Even if two things were completely completely completely identical down to each atom, the two would not be identical because they cannot occupy the same space (thinking of solids here).


Every concept representss a shared identity, so for every concept there are identical things... The does not mean they are equal in every repsect... And the correct statement of idenitity is A is A...


As Wittgenstein said, we should not confuse "same" (equal in some respects) with identical (one and the same).
laughoutlood
 
  1  
Reply Sun 13 Jun, 2010 03:04 am
@mark noble,
Quote:
it's hardly believable that even two electrons can share exactly the same state


Oh goodness me, what if one electron is in two places at the same time, would that be half marks?
fresco
 
  1  
Reply Sun 13 Jun, 2010 03:17 am
@kennethamy,
Quote:
As Wittgenstein said, we should not confuse "same" (equal in some respects) with identical (one and the same).


Where did W say that ?... In the Tractatus which he later rejected ?
Fido
 
  2  
Reply Sun 13 Jun, 2010 07:25 am
@kennethamy,
kennethamy wrote:

Fido phil wrote:

mister kitten wrote:

Yes of course.
x=x
the two, when separate, are (x) and (x). They both equal each other. If (x) is a shape, then it is not only equal but congruent to (x) as well.

Aside from math, I cannot think of two identical things. Even if two things were completely completely completely identical down to each atom, the two would not be identical because they cannot occupy the same space (thinking of solids here).


Every concept representss a shared identity, so for every concept there are identical things... The does not mean they are equal in every repsect... And the correct statement of idenitity is A is A...


As Wittgenstein said, we should not confuse "same" (equal in some respects) with identical (one and the same).


Identical does not mean equal in all respects... All cats are equally cats, equal by identity, just as all humans are equally human... All rational thought would be impossible if we could not class like with like, and only in the comparison of like with like does difference become meaningful... When I run, I compete against others of my own age because it is a given that people younger will be faster and older ones slower just as it is a given the dogs are different from cats; so people do not compare them... Look at the great effort of philosophy in the middle ages the Syllogism... Is that not all about arriving at a prospective identity which than can be examined scientifically???

Identity is half the battle... In its other form, that of conservation we see identity in its scientific character, in recognition of the qualities that are stable, and those which change... The principals of conservation of mass, or of motion, are examples of identity.,. In fact, all concepts and quasi concepts are identities and are conserved... Consider, that when we talk of justice as a quasi concept, it is not the concept that is changed by every differeing example... The identity remains the same unless some significant change in values corrects the concept... If all cats began to grow two tails, eventually the identity and the concept would change
0 Replies
 
Owen phil
 
  1  
Reply Sun 13 Jun, 2010 07:40 am
@mark noble,
mark noble wrote:

Hi Everyone,
Can you think of any two things that are identical to one another in every way?
This is an ongoing research question, and all your answers will be gratefully received.
Thank you.
Mark...


No.
Only x is identical to x.
If there is some property that x has and y does not have then, x is not identical to y.

For physical objects, the uniqueness of space-time-location denies that any two different objects can be equal.

x=y, if and only if, they share all of their properties.

That x is in a different space-time location than y, shows that they are not equal.

engineer
 
  1  
Reply Sun 13 Jun, 2010 07:52 am
I suppose it would depend on the observer and how he values the objects being considered. Take two one dollar bills. One is new and crisp, the other a bit worn. To one person, the new bill has more ascetic value, being new and unwrinkled. To another, both are the same in that they confer the ability to purchase one dollar worth of goods, hence they are different, yet identical.
fresco
 
  1  
Reply Sun 13 Jun, 2010 08:02 am
@engineer,
Quote:
I suppose it would depend on the observer and how he values the objects being considered


Spot on ! Any analysis which fails to take the observer into account is waffle !
0 Replies
 
Owen phil
 
  1  
Reply Sun 13 Jun, 2010 08:05 am
@kennethamy,
kennethamy wrote:

Leibniz had two principles:

1. The indiscernability of identicals.
2. The identity of indiscernibles.

The first says that if (putatively) two things have the very same properties, then they are not two things, but really one (and the same thing). The second is the converse of the first. It says that no two things can have the very same properties. It is generally agreed that the first is true, and indeed, it is the definition of identity logicians accept (Leibniz's Law of Identity). The second is obviously controversial. Leibniz held it was true just as he held that the first was true, but although the first is intuitively true, Leibniz had to give (dubious) metaphysical reasons for the second. Of course, the second might be true (for all we know). But if it is true, it is clearly not a necessary (or intuitive) truth as is the first. And the issue is not whether the second is true, but whether it must be true as the first is not only true, but it must be true.


Both are necessarily true, ie. [](x=y <-> ∀F(Fx ↔ Fy)), is a theorem.

Stanford: The Identity of Indiscernibles

The Identity of Indiscernibles (hereafter called the Principle) is usually formulated as follows: if, for every property F, object x has F if and only if object y has F, then x is identical to y. Or in the notation of symbolic logic:

∀F(Fx ↔ Fy) → x=y.
This formulation of the Principle is equivalent to the Dissimilarity of the Diverse as McTaggart called it, namely: if x and y are distinct then there is at least one property that x has and y does not, or vice versa.

The converse of the Principle, x=y → ∀F(Fx ↔ Fy), is called the Indiscernibility of Identicals. Sometimes the conjunction of both principles, rather than the Principle by itself, is known as Leibniz's Law.
----------------------------------------------------------------------
(x=y) ↔ ∀F(Fx ↔ Fy), is a theorem of Principia Mathematica ..Russell and Whitehead.
fresco
 
  1  
Reply Sun 13 Jun, 2010 08:13 am
@Owen phil,
Waffle !

What the guys fixated on formal logic fail to understand is that the first level of measurement is the nominal i.e the "naming of a thing", or "counting one of.."

I challenge them to explain what that requires without considering aspects of the "namer".
0 Replies
 
kennethamy
 
  1  
Reply Sun 13 Jun, 2010 08:18 am
@fresco,
In the Investigations.
0 Replies
 
Owen phil
 
  1  
Reply Sun 13 Jun, 2010 08:18 am
@engineer,
engineer wrote:

I suppose it would depend on the observer and how he values the objects being considered. Take two one dollar bills. One is new and crisp, the other a bit worn. To one person, the new bill has more ascetic value, being new and unwrinkled. To another, both are the same in that they confer the ability to purchase one dollar worth of goods, hence they are different, yet identical.


There are no things that are "different yet identical".
To be different and identical, is contradictory.

Two different dollar bills are clearly not identical.
If we can demonstrate that one of the dollars has a property that the other dollar does not have, then they are not identical.
0 Replies
 
Fil Albuquerque
 
  2  
Reply Sun 13 Jun, 2010 08:19 am
As I mention earlier no two things can exactly have the same background.
The exact same background who shapes them to be what they are in an enlarged epiphenomena hardly boundary objective...one should bare in mind that the entire process is dynamic and not static regardless of our conveniences, so as far as my logic can go, nothing on this Universe can exactly have the same property´s of anything else.
0 Replies
 
kennethamy
 
  1  
Reply Sun 13 Jun, 2010 08:23 am
@Owen phil,
Owen phil wrote:

kennethamy wrote:

Leibniz had two principles:

1. The indiscernability of identicals.
2. The identity of indiscernibles.

The first says that if (putatively) two things have the very same properties, then they are not two things, but really one (and the same thing). The second is the converse of the first. It says that no two things can have the very same properties. It is generally agreed that the first is true, and indeed, it is the definition of identity logicians accept (Leibniz's Law of Identity). The second is obviously controversial. Leibniz held it was true just as he held that the first was true, but although the first is intuitively true, Leibniz had to give (dubious) metaphysical reasons for the second. Of course, the second might be true (for all we know). But if it is true, it is clearly not a necessary (or intuitive) truth as is the first. And the issue is not whether the second is true, but whether it must be true as the first is not only true, but it must be true.


Both are necessarily true, ie. [](x=y <-> ∀F(Fx ↔ Fy)), is a theorem.

Stanford: The Identity of Indiscernibles

The Identity of Indiscernibles (hereafter called the Principle) is usually formulated as follows: if, for every property F, object x has F if and only if object y has F, then x is identical to y. Or in the notation of symbolic logic:

∀F(Fx ↔ Fy) → x=y.
This formulation of the Principle is equivalent to the Dissimilarity of the Diverse as McTaggart called it, namely: if x and y are distinct then there is at least one property that x has and y does not, or vice versa.

The converse of the Principle, x=y → ∀F(Fx ↔ Fy), is called the Indiscernibility of Identicals. Sometimes the conjunction of both principles, rather than the Principle by itself, is known as Leibniz's Law.
----------------------------------------------------------------------
(x=y) ↔ ∀F(Fx ↔ Fy), is a theorem of Principia Mathematica ..Russell and Whitehead.




http://www.unc.edu/~jfr/II-STR.htm
0 Replies
 
kennethamy
 
  1  
Reply Sun 13 Jun, 2010 08:34 am
@fresco,
fresco wrote:

Quote:
As Wittgenstein said, we should not confuse "same" (equal in some respects) with identical (one and the same).


Where did W say that ?... In the Tractatus which he later rejected ?


In The Investigations. But how would that matter, anyway? It could be true even if it happened to be in the Tractatus. I am not citing Wittgenstein as an authority on identity.
 

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