Logical term for when an object is the same thing as itself

Question

I'm trying to see if there's a word for this in English and having some problems making a definition in my program.

I want to say that two objects are not only have identical properties/values but that these objects are in fact one and the same thing.

Not that they're equivalent, not that they are identical clones of each other, but in fact selfsame.

Would selfsame be the correct term? There is some term in philosophy for it I just can't recall it.

Let me clarify. I have a web page and 2 hyperlinks to that page. Clicking a hyperlink doesn't create 2 separate web pages that look similar and act similar, they in fact lead to a page that is selfsame. It's kind of like the difference between looking at a mirror of yourself and having a clone. If you change your reflection changes, if you change your clone does not change.

If you know about programming I'll tell you the exact thing that prompted my line of questioning. Problem 2.7 of Cracking the Coding Interview, page 221. I have two linked lists and the task is to find an intersection point between the two. Picture: https://i.sstatic.net/Mt4es.jpg

Answer 1

You said that you'd use identical if not for the following problem:

People use identical in conversation to mean that A and B's properties are indistinguishable. Like identical twins aren't one and the same person, they are just indistinguishable for the most part.

As it happens, and as you anticipated when you said that 'there is some term in philosophy for it', philosophers did run into this same problem. Their solution was to invent the concept of numerical identity. Here is the opening paragraph of the article 'Identity' from Stanford Encyclopedia of Philosophy:

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.

So, using the example of linked lists, suppose we have a linked list a consisting of nodes a1-a4, a linked list b consisting of nodes b1-b4, and let's suppose that the last two nodes are common to both lists. In other words, a3 and b3 corresponds to one and the same chunk of computer memory, and similarly for a4 and b4. Then philosophers might say that a3 and b3 are numerically identical, by which they mean the following. When you point to nodes a1 and b1 and ask the question, 'How many nodes am I pointing to?', the answer is 'Two'. But if you point to nodes a3 and b3 and ask the same question, the answer is 'One'. That's why they are said to be 'numerically identical': they are identical (even for) the purposes of counting.

Unfortunatelly, the term numerically identical probably won't work outside of philosophical contexts. The problem is that non-philosophers will be tempted to think that when we say that two nodes are numerically identical, all we mean is that they contain the same numerical values, which can happen if they correspond to different chunks of physical memory whose contents are bit-for-bit clones of each other. Probably in non-philosophical contexts you'd have to say something like nodes a3 and b3 denote one and the same chunk of computer memory.

Answer 2

There is a term in mathematics which distinguishes between two things that are not merely the same value but actually the same. We say they are Identical.

The super hero is not just very much like his everyday alter ego. He is identically equal to him, despite appearances. They are one and the same as frogyedpeas suggests.

We can say they are identical or identically equal.

Answer 3

The phrase that springs to mind is "One and the same".

This implies that not only are they actually the same object, all of their features in any instance you are talking about are the same as well.

one and the same

the same thing or person: I was amazed to discover that Mary's husband and Jane's son are one and the same (person).

Answer 4

Are the objects complex? If not use "same" or "equal".

Are the objects only equal to each other with respect some filter or point-of-view, then "equivalent" or if you want to be fancy you can also say "congruent".

Do the objects carry a lot of internal structure or data? Then in such situations I casually would use the word "isomorphic" borrowing its general usage in math.

Examples, "these two apples are the same!", "your steak dinner is nutritionally equivalent to my burger", "These two programming projects originate from isomorphic templates"

The last felt a bit contrived, but I've seen some of my more technical friends use it appropriately (it's an in the moment type of thing)

Answer 5

In the world of logic, if there is an object 'A' and and object 'B', such that everything true of A is true of B and vice versa, then A is identical with B. You can call it 'self-identity', but, looking online, the widest use of this word at the moment is associated with state, personal, cultural and social identity.

But maybe your 'objects' are 'objects' in the brogramming sense, in which you might programme a virtual object in different ways, such that, the object-programmes create the same 'object' - i.e. does all the same things and has all the same properties, even though the programming that creates them/it differs. So an app for an online bike hire company would have to have differences of programming for use on Apple or MS system. Yet they are in all other respects the same. But then, so long as the programming is different, there would be at least one statement that would be true of the object(s) as seen on an Apple device but not true of the object(s) as seen on an MS device. So they would not be strictly identical in logic.

But this depends on what is meant by 'object'. Is it 'objects' in the conventional sense (stuff) or virtual 'objects', in which case any identity might be much more like the identities that exist in language, called 'synonymity'?

Answer 6

I'd bet you're looking for tautology.

A phrase or expression in which the same thing is said twice in different words.

Definition courtesy of Oxford Dictionary.

Tautologies are exceedingly useful in proofs using symbolic logic, which is often part of the study of philosophy.