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In a preceeding question I have asked about the foundations of rational reasonning. It seems the concept of identity plays a key role. However "identity" is not observed in the real world: our mind creates identities.

For example if you see a simple blue pencil, turn your head and go back to the pencil, you say "these are the same". If the pencil has changed a little bit when you turn your head back you might think it is a different pencil or just forget about the difference and keep thinking it is the same. The reason why and the condition in which you should foreget about the difference in the second case is the purpose of my question:

when and why would you say that two things are the same?

Side Note: It seems to me that the identity is created to connect two events that we percieve. This creation is made possible because the identity is not modifying our system of representations. Creating identities is always a reduction, a simplification of the objective truth but it is very important to create identities to fit the real world into our mind and make it possible to think about.

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    I think that the question's title is a bit misleading and needs an edit. I'm leaving it for now, in the hopes that the OP will do so. – vanden Jun 11 '11 at 17:05
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    @robin, I have reformulated your question somewhat, mostly changing the reference to 'identity principle' to 'law of identity' which is the more common term. Hopefully I've enhanced your chance to get an answer, but please let me know if I've misrepresented the intent of your question. – Joseph Weissman Jun 11 '11 at 22:26
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    I think it would be great if someone went on to discuss the Identity of Indiscernibles, i.e. "two or more objects or entities are identical (are one and the same entity) if they have all their properties in common." Then also how that principle fails. – boehj Jun 11 '11 at 22:56
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    I really wish I had a better sense of what was being asked here so I might try to answer it... – Ami Jun 13 '11 at 3:16
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    @robin, this question is still really difficult to understand. – Joseph Weissman Jun 13 '11 at 23:01
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The law of identity provides a logical expression of the notion that a thing (x) is the same entity as itself (x=x). It establishes a simple two-way relationship of equality that serves as a basic presupposition of any formal logic.

My understanding is that the law of identity is somewhat more technical than simply a rule for calling two things "the same"; in fact the law of identity is really an axiom, a tautological expression indicating a single object "is itself."

Furthermore, I think things get significantly more complex when we need to talk about the identity or equality of two distinct objects, even if it is ultimately the same object simply referred to in different ways. (I believe in particular there are implications for epistemology and the theory of reference.)

Finally I might suggest that identity is not a trivial characteristic; is the candle the "same" object after it has melted into a lump of wax? Perhaps, but even so it has undergone some kind of transformation. Since at an energetic level everything is effectively continuously transforming, identity is as you suggest -- a common notion, an axiom, but not something reflective on an underlying truth.

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    I'm giving this +1. I appreciate that someone answered a question, the content of which is fairly hard to determine. Regarding the last para, Leibniz held that "that no two distinct things exactly resemble each other." However, we can find such objects in both a) thought experiments, see: Black, and b) in the 'real world' of quantum physics. – boehj Jun 13 '11 at 6:25
  • Two distinct things aren't going to be identical in the sense that the OP is discussing, precisely because they would be distinct. – shane Mar 10 '14 at 12:23
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    The modern discussion of this, with dramatic impact on foundations, is given in homotopy type theory ncatlab.org/nlab/show/… . – Urs Schreiber Mar 10 '14 at 15:25
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Two things are never the same.

Even the words that "labeled your thought" when you asked this question point to something in the past, something that was and no longer is. Having the same label but addressing two separate times is precisely the issue with impermanence and "naming." Really, nothing exists independently, so everything is the same [thing].

If you assume that every moment is a different set of sensory inputs, thoughts, sounds, tastes, smells, sights, physical sensations (touch), then perhaps you may say: that re-experiencing an identical set of sensory inputs is a repeated situation, or "the same," however, you (the general "you") are a biased observer, and the conditions in which you are observing occurrence #2 are all dependent on you having observed occurrence #1. By virtue of labeling this moment "the same" you have made it different; by assuming a separateness of moments rather than a continuous feed of moments, one may say that the principle of "sameness" exists, that is, that each moment is a separate "slice" of time;" but all experience points to the opposite -- the continuity of information rather than discontinuity.

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    Had I more reputation I would downvote this. You say, "Two things are never the same." I'd agree if you had instead said, "Two distinct things are never the same." To argue that two things are never the same would entail that 42 is not the same as 42. – Michael McGowan Jun 15 '11 at 21:21
  • @Michael McGowan, that is precisely what I'm trying to say. Context is constantly in flux, so they are indeed Not the same because they occur in different context. They are inseparable from the context in which they occur, so they are different, i.e. not the same. – sova Jun 16 '11 at 18:32
  • @sova So, just so we are clear, is 42 the same as 42? – Michael McGowan Jun 16 '11 at 18:41
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    @sova Sorry if you perceived aggression in my response; it was not my intention. I think there may have been some subtleties in your post that caused me to disagree. I think I might agree for those "things" for which time matters, so the thing at timestamp 1 is not the same as the thing at timestamp 2. – Michael McGowan Jun 17 '11 at 14:40
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    @Michael: what are you referring to when you say "42" the first time, and the second time? Because word are not what they are referring to. Saying that both are referring to the exact same object is fine, but you have no absolute proof that this object exist. Russel for example tell that number are logical fictions. – psychoslave Jan 19 '14 at 21:22
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I'm not sure if this is slightly off-topic, but I think the world of object-oriented programming in computer science offers an interesting perspective.

In an object-oriented programming language such as Java, there is the concept of a structure called an "object" which has a number of properties. If I have variables for objects A and B, A and B are really references to the bytes in memory to hold those objects. A and B are considered identical if they actually reference the same physical bytes in memory; in Java this means the operation A == B is true. There is a separate notion of "equality" that a programmer is free to define depending upon the type of object. Oftentimes this equality comparison is done by inspecting all of the properties of A and B; if all of the properties of A equal all of the properties of B, programmers generally declare that A equals B. In this way, although object identity implies object equality*, oftentimes objects are equal without being identical. Note also that if A and B are equal, I might later change a property of A without changing the corresponding property of B, resulting in A no longer equaling B.

Interestingly, Java also has the notion of "primitive values" that are mostly used for basic numeric values. These primitive values have an ethereal sense about them and the distinction between identity and equality is lost (and of course 42 == 42 is always true).

*In Java this implication is by convention; a rogue programmer is free to declare that A is not equal to A, but that breaks the contract of the "equals" method and is frowned upon.

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"identity" means "sameness." Two say of two things x and y that they are identical is just to say that the name "x" and the name "y" are two different names for the same object. Mark Twain is identical to Samuel Clemens because "Mark Twain" and "Samuel Clemens" are just different names for the same guy. "The only even prime" and "the second square" are just two different names for the same number, viz. 2.

Note that in our definition above we said, "two things x and y" and NOT "two distinct things x and y". This is because difference, or distinctness is the opposite of sameness/identity. If x and y are distinct, then they are not identical by definition.

Here are two logical principles that seem to many philosophers to be an intuitive part of what our concept of sameness amounts to.

  • The indiscernability of identicals: If x and y are identical, then every property of x is a property of y and vice versa.
  • The identity of indiscernables: If every property of x's is also a property of y's and vice versa, then x and y are identical.

Now, if you like those two principles, then you can understand identity as a binary relation, and think about it having the same kind of properties as other binary relations. And if so, then you're likely to note that identity has the following three properties:

Reflexivity: x = x. Symmetry: x = y iff y = x. Transitivity: if x = y and y = z, then x = z.

On this view, you'd say something like: "Identity is the reflexive, symmetric, transitive relation that everything bears only to itself."

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Practical:

This question to be specifically can be related to artificial intelligent. As i am working on project, creating logical framework for artificial intelligent, and i found an obstacle that had the sameness as represented by this question. This question can be related to artificial intelligent. But philosophically it can be related to epistemology.

Why we can identify (by seeing) whether something is changing its position or changing in any way without loosing our target (something itself)?

It's because we perceive difference through the minimum necessity that can be provided by eyes to identify a changing of something, so we can identify the sameness of the two things, whenever it's changing.

First, we have to understand what is aware of something.

We are aware of something it's because we perceive difference. We perceive something as different to others.

The minimum necessity for our eyes to identify something are:

  • Ability to identify the wide area of the same color. The same color is not always an exactly the same one to another, but there is continuity from one color to another color.

    • Just for the illustration: between white and blue color there is no continuation, but between blue and soft blue, there is continuation. there is smooth gradation.
  • For specific area as mentioned above, there is movement with activity that can make a distinction to others with lower activity or higher activity as an opposite to the target.

Less or more ...

The Essence:

But, if we define for how the two things can be considered the same at the essential level, then it's strictly can be asserted as "there is something on the first thing that exist within the second thing". The more the same for the two things each other, the more the same completeness in between the two each other.

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The purpose of defining temporal identity of material objects is to reason about resources, such as planning for the future, or detecting causations.

In many daily situations a simple matter-bound definition is sound and the ideal solution to solve a problem, giving optimal results in the shortest amount of reasoning time.

The most useful definition to me seems: 2 things in time are equal to a person if the person declares them equal. This subjective rule can be extended to any number of people like this: 2 things in time are equal to n persons if the persons all declare them equal.

People informally agree on identities usually by giving names (people, countries, cities), addresses, and ownership.

If you look for an objective (physical) definition that is philosophically sound for all circumstances, you are on a fools errand.

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It depends on what you mean by "the same". In computer programming for instance, you could say two objects are the same if their Value is the same, e.g. two dates. You could also say two objects are the same if the same operation is applied to both and yields the same result. And finally, two objects can be "the same" if there are many references to the same physical object. Think of it as either having many copies of Lord of the Rings you lend to friends, which would be "the same" or having one copy which you lend to all your friends, meaning everyone gets "the same" book.

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