Identity is circular?

Question

SEP on identity says:

Identity can be characterised ... as the relation everything has to itself and to nothing else. But this is circular, since "nothing else" just means "no non-identical thing"

This seems to me both obvious and unacceptable.

That it is obvious is, well obvious!
That it is unacceptable follows from the fact that circular definitions dont 'work' to successfully define anything. Yet we use identity all the time in everyday life as much as in philosophy.

Clearly there is some other principle at play that makes identity work (mostly) that SEP is not saying (or I am not seeing).

If I say: This apple is the same as the one I left here last night,
I am relying on many secondary factors

• my trust in my own normal consciousness, last night and now
• my trust in my everyday intuitions of space-time (I left it here, then; it's still here, now)
• many other factors, eg. the relative stability of the setup (a tsunami didnt hit list night)
• etc

So there need to be two clauses

• Identity is hopelessly circular. Or else ...
• It is defined in terms of other models in which we put our trust tacitly

I am seeing the first in the above quoted SEP article.

Can someone point me to some authoritative source for (something like) the second?

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The question arises in the technical context of object-identity (and equality) in object-oriented languages (OOPLs). I strongly suspect this is ill defined. Related to my earlier question because

• If object identity is defined in terms of memory and pointers it defeats the claim to hi-levelness of the language
• Else (and that's the choice most OOPLs take) is to hedge and pretend that everyone knows what is the same means.

Note: I would like a philosophical answer! Not one explaining OOP etc please. [The other question I expressly asked in terms of multiple examples but all the answers were in terms of memory and pointers]

Answer 1

The issue is one of first-order logic, because identity is non-first-order-izable. Use second-order logic and the circularity disappears. I'm obliged to quote SEP on identity:

In fact, no condition can be stated in a first-order language for a predicate to express identity, rather than mere indiscernibility by the resources of the language. However, in a second-order language, in which quantification over all properties (not just those for which the language contains predicates) is possible and Leibniz’s Law is therefore statable, identity can be uniquely characterised. Identity is thus not first-order, but only second-order definable.

SEP also has an article on identity of indiscernables and Leibniz's Law. I'll restate the law in English for posterity: two objects are identical if every predicate either holds for both objects or holds for neither object. Note that "every predicate" is a second-order universal quantification.

Answer 2

Identity is not circular when it arises as the product of an unconscious process which Helmholtz describes as unconscious inference. We simply recognize the distinctions that arise. So one item is not the same as another item even if the two items share attributes or features that abstract away from the distinct items. I knew two beautiful young ladies who were identical twins and yet they were not identical or fungible items arising as the product of an unconscious process. I did not apply logic to comprehend their distinct attributes and I could tell them apart by respective appearance, subtle movements, and the sound of their respective voice.

When we discuss identity in the context of language and logic it becomes a question for evidence and logic. Paradox arises. See the Ship of Theseus and theories of the validation of evidence via human testimony.

Edit: OOP Identity

Long document 191 page pdf is the AVR Instruction Set Manual:

https://ww1.microchip.com/downloads/en/devicedoc/atmel-0856-avr-instruction-set-manual.pdf

Article on OOP from low level perspective (I have not tried to decode the technical or philosophical details in the examples given):

http://x86asm.net/articles/oop-from-low-level-perspective/index.html

In the context of low level operations Identity is just an machine operation that determines whether items are identical or distinct based on instructions provided by the Programmer. In a high level OOP language the compiler or interpreter transforms the program code into low level instructions and there is no identity problem related to the location of objects in memory. There is the problem of computer malfunctions where code or memory becomes corrupted and then the machine goes off the rails doing operations that have lost their intended meaning encoded by the Programmer.

Answer 3

You are conflating identity with other issues. You can split 'this is the apple I left here last night' into two different ideas. To see this, let's suppose every apple carried a unique serial number. You can then say, a) This is apple x; b) I left it here last night. The identity of the apple is defined by a). When you say the identity is dependent on things such as your memory, your understanding of spacetime, etc, you are really referring to b), which is not about the identity of the apple per se.

Answer 4

Identity is defined by Leibniz' law:

∀x∀y x=y → ∀F(Fx ⇔ Fy)

(if two objects are equal, they have all the same properties)

and

∀x∀y (∀F Fx ⇔ Fy) → x=y

(if two objects have all the same properties, they are equal).

Thus, general equality x=y is founded on logical equivalence A ⇔ B, which we can take as a more primitive notion.

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In actual practice, we call a lot of things "the same" when they are not exactly "the same." For example, we may say I am "the same" person I was yesterday, even though today I am older than I was yesterday, and not at the same temperature, and wearing a different shirt.

What this usage is about is equivalence for a certain purpose rather than exact identity. I am not exactly the same person I was yesterday - but for tax purposes (among other purposes) I might as well be! So it is useful (in some but not all contexts) to speak as if I am the same person today as I was yesterday.

Equivalence for a certain purpose can often be modeled as level sets of a function. Two objects x and y may not be exactly equal, but if we have some function f of interest, and f(x) = f(y), then we may speak as if x and y were the same, provided we are only interested in the output when we feed different values into f. f maps x and y to a domain where they happen to be the same.

For another example, if we are building a brick wall, all of the bricks may be "the same shape" in terms of building the brick wall, in that each of them is interchangeable with any other as we build the wall. In truth, no two bricks are exactly the same shape; they are simply close enough for our purposes.

We might try to formalize this in the style of Leibniz' law by saying that two things are "roughly the same" if they are logically equivalent on all properties that we care about. e.g. if C(F) denotes that we care about the property F, and ~= denotes rough equality, then:

∀x∀y (∀F C(F) → (Fx ⇔ Fy)) → x~=y

Answer 5

It is unacceptable, except in artificial situations, such as in mathematics when we provide artificially equivalent forms of language such as in precising definitions. Frege may be responsible for advocating truth-semantic logical equivalence as a means of settling questions of identity as noted in this response, but logical operations are not the only way for solving questions of identity.

You say:

I am relying on many secondary factors... my trust in my own normal consciousness, last night and now... my trust in my everyday intuitions of space-time (I left it here, then; it's still here, now)... many other factors, eg. the relative stability of the setup (a tsunami didnt hit list night)

Consciousness, intuitions of space-time, and other physical factors are indeed important to explaining why a=a is insufficient for real-world identification of things. The traditional view that beyond propositions something is required is part of empiricism, where what we know, including the identity of things, is from direct apprehension of our senses. Consider this passage from the SEP's article on Concepts:

empiricists have argued that all concepts derive from sensations. Concepts were understood to be formed from copies of sensory representations and assembled in accordance with a set of general-purpose learning rules, e.g., Hume’s principles of association (Hume 1739/1978). On this view, the content of any concept must be analyzable in terms of its perceptual basis. Any purported concept that fails this test embodies a confusion.

Certainly Leibnitz's Law of Identity is useful for resolving questions of coherence of propositions. To reduce an equation to a=a in algebra, for instance, can affirm that our propositions, say of an equation and a point that it includes, are consistent and true. But clearly questions about the truth of identity of physical objects is much more than reducing language to a=a. It requires a relationship between a reference and the state of affairs in the physical world. When we walk down the street and an angry dog runs at us, our minds are hardly greeted by the thought 'An angry dog is an angry dog!'.

So, consciousness, the intuitions of space and time, those are widely held under the physicalist programme to originate with the body, which is the very purpose of positing and defending embodied concepts (SEP). Going back to the SEP's article on embodied cognition:

Despite the unpopularity of verificationism (though see Dummett 1993, Wright 1989, and Dennett 1991), a growing number of philosophers are attracted to modified forms of empiricism, forms that primarily emphasize psychological relations between the conceptual system and perceptual and motor states, not semantic relations. An example is Lawrence Shapiro’s defense of the claim that the type of body that an organism has profoundly affects its cognitive operations as well as the way that the organism is likely to conceptualize the world (Shapiro 2004).

Thus, while the semantics of a=a are a powerful intuition, the wider scope of identity rests in psychological, not merely logical relations. And those psychological relations, and those relations themselves are inherently fallible. For if identity is more than merely logical, and psychology is pluralistic since it is subjective, then a notion of absolute identity might not be tenable. This was the position of Geach. Consider the SEP's article on Relative Identity:

The philosopher P.T. Geach first broached the subject of relative identity and introduced the phrase “relative identity”. Over the years, Geach suggested specific instances of RI (a variant of the case of Oscar and his tail is due to Geach 1980) and in this way he contributed to the development of the weak view concerning relative identity, i.e., the view that while ordinary identity relations are often relative, some are not. But Geach maintains that absolute identity does not exist.

And this is what you are looking for when you frame the problem of identity much wider than circular and analytic definitions. Identity has an empirical and psychological component, a view Frege would seemingly been at odds with given his views on logicism and anti-psychologism. Today, however, given modern notions of the philosophy of mind, where neural correlates of consciousness strengthen the notion that the mind and body are not necessarily fully disconnected metaphysically (read property dualism), it seems reasonable to accept that identity has logical and empirical aspects.

Answer 6

I go with chapter "10. Are there philosophical problems about identity?" (and the authoritative sources mentioned there) of the SEP page you quoted in your OP.

This chapter is very informative. The answer is clearly "no". There are no philosophical problems about identity. Everything is identical with itself. If you have two things, then they are not one thing (i.e., identical). If you have one thing, it is not two things.

The rest is my personal interpretation:

All of the (verily non-trivial) problems on the SEQ page and in your question boil down to valid philosophical problems, but they are not about identity per se, but about other things (closely related to identity, or maybe to your individual definition of identity).

For example:

• Naming/labeling/referencing things introduces many interesting problems (these will be very relatable to you in OOP settings, even if you asked us not to mention OOP in our answers). For starters, it should be very clear that a name, label or reference to a thing is not the thing, and thus all questions regarding identity which relate to these topics can be culled immediately. If you confuse twins and use the wrong name when addressing one of them, then the issue is not their identity, but your not recognizing the individual.
• Temporal changes introduce problems, mostly of definition (i.e., whether one accepts infinitesimal incremental change to "update" the definition of the object and thus let it keep its identity; this may make sense in some cases, and not in others). The solution to the paradox of small changes which accumulate over time (i.e., a fresh, yummy apple today vs. the same apple wrinkled and old, in a week) is to accept that the dimension of time is simply out of scope regarding (or at least orthogonal to) identity. For individual cases, you can always update your definition of identity, or your perception of the thing you are studying to fit your use-case. Having a general, abstract definition ("everything stays the same for one second at a time, after which it becomes something else") is unnecessary.
• All the problems you mentioned (about your own sanity, the question whether a tsunami moved the apple, or whether quantum mechanics allowed all molecules of the apple to let it swap places with a different apple) have nothing to do with identity; they are just bogus scenarios. The question is "did a tsunami hit the apple", not "is this apple the same as the one I placed there yesterday".
• As the SEP page clearly states, all its points are about numerical identity, not qualitative identity: "Things with qualitative identity share properties, so things can be more or less qualitatively identical. [...] Numerical identity is our topic." This means other semantics of "identity" (i.e., identifying with a gender or other attribute, for humans) are out of scope here.

(Interestingly, you can map all these bullet points onto OOP objects just fine and find the parallels. I'll spare us the time.)

Why is this all so difficult?

My suggestion is that we find so many interesting problems because the way our brains are made is simply quite fuzzy (in a value-neutral way). Our brains clearly have a built-in mechanism of working with identity of objects surrounding us; our brains clearly can work with reference and referents; our brains clearly can handle temporal issues just fine, as relating to everyday questions. Our brains clearly are very good indeed at classifying (literally: associating individual objects with "classes" like in your OOP example, but with a class hierarchy on steroids...). Our brains have no issue attributing properties to concepts or classes, not only to individuals. Our brains clearly can sometimes slightly update the impression of an object and keep its identity, but sometimes also break the object into separate objects, clearly identifying the new parts as separate identities while recalling that they were once one.

But our brains are also flexible enough not to let us freeze to figure out a philosophical enquiry when in the heat of the moment - when the lion attacks it is just not relevant whether it is the same as the one yesterday; it is enough to know that the vague class of "big mammal with long fangs" is a reason to start running right now. When your neighbour from the cave next door grabs your rock chisels and slightly damages them before you go over to grab them back, you are not confused by a small nick that wasn't there before.

At no point in time was there an evolutionary benefit in being able to succinctly discuss these topics and analyze all the mechanisms explicitly, in language, and mapping all the concepts out in an ultimately non-contradictionary way (which there may or may not be any!). Hence our fascinating discussions about these things.

Answer 7

In short, identity is circular when we argue that the initial causes of things (metaphysics) are irrelevant. For example, if I were to be within a paradigm, a circular paradigm, I could identify as something that I am not. Thus, I could constantly wipe the circle clean, start over, and even convince myself, ideally others as well, that I have always been what the new circle entails. On the flip side, if we are to reject the circle even existing, we would see that all the variations of identity have to be understood properly. Once this is done, we start to see the changes that are essentially just manipulations. The metric I use for distinguishing manipulations is one of nature. This is understood more so in depth below, via Chapter 7-The Metaphysical in my book The Cosmosis: How The Metaphysical and Physical Merge:

"Metaphysics deals with initial principles, while utilizing concepts such as knowing, being, cause, substance, time, identity and space. Aristotle provides two descriptions of this first philosophy:

1. The study of “being as such”, pertaining to the nature of being or what it is for a thing to be or exist.

2. The study of “the first causes of things”, pertaining to the original or primary causes.

While the answers to these descriptions, that is what exactly quantifies the descriptions aforementioned, may vary per individual, it is incredibly obvious that there are objective quantifiers that aid in understanding the two descriptions provided by Aristotle. One argument against this claim would be understanding the identity that quantifies physical objects. Identity is defined as the fact or being who and what a person or thing is, while having a resemblance to said fact, especially in a physical manner. Some may try and scramble this definition, however, it is incredibly straightforward. If something is, by nature, then it will always be what it is. You may attempt to manipulate what something is by nature, however that does not make it other than what it has always been, rather it makes it a manipulated variation of what it is.

“How can you manipulate something by nature?” It’s incredibly simple, we know that nature has a direct cause and effect relationship with itself. Humans are apart of nature, we are nature, therefore any affect a human has on ourselves or any other aspect of nature, is a direct display of nature affecting nature. It is important to note that there are natural consequences of nature affecting nature and there are unnatural consequences of nature affecting nature. Let’s undergo a quick thought experiment, that has been utilized since the ancient times.

There is a statue that is formed via pouring molten gold into a particular mold. After the statue has been poured and solidified, it is immediately melted down and the re-molted gold is poured into the same mold it was previously poured into. Just like the initial pour, it is allowed to cool and solidify. The question is, does the resulting statue hold the same identity as the original? There are individuals that would argue that this example is not relevant to either of the descriptions Aristotle outlined. That the question at hand has nothing to do with either being as such or the first causes of things. This is an incredibly false claim, that negates the determined nature of existence itself.

The truth is, the aforementioned example has everything to do with both being and the first causes of things, it simply requires a big picture perspective that utilizes the law of cause and effect, while also acknowledging the universal application of determinist philosophy. The statue would not exist without the existence of the gold utilized to create the statue. While statues can be made out of other materials, the statue defined in this example would not exist if gold did not exist. Therefore, for the golden statue to exist, gold itself must exist. For gold itself to exist, minerals and metals must exist. For minerals and metals to exist, our beautiful world must exist. For our world itself to exist, the universe must exist. For the universe itself to exist, the cosmos must exist.

This implies that the statue may only be, so much as gold must be. Gold may only be, so much as minerals and metals must be. Minerals and metals may only be, so much as our beautiful world must be. Our beautiful world may only be, so much as the universe must be. The universe may only be, so much as the cosmos must be. This is the essence of understanding being itself, it requires a causal understanding to comprehend the determined nature of existence, for everything exists because something before it allowed for it to exist. Nothing is spontaneous, nothing is naturally chaotic, and nothing is what it is without acknowledging why it is what it is.

It is true that the statue would not be, if an individual did not decide to melt gold into a liquefied state, so that it may be molded into said statue. When the individual molds the first statue, then melts the statue down to then form the same statue out of the same material, it is true that the second statue does not hold the same identity as the first statue. Yes, both statues were created utilizing the same amount of material and even the same exact material. The most important thing to understand about identity is that it is indeed perishable, just like the ego, our identities tend to be depleting and false senses of what is true. The moment the solid gold is melted down, it is no longer identifiable as solid gold, rather it is melted gold. The moment the melted gold is poured into the mold, it is molding gold. Once it has dried and solidified, then and only then, can it be known as the statue.

Once that initial statue is destroyed via re-melting the statue, it is no longer identifiable as the statue, rather it is melted gold that is a result of re-melting the material, which is what the statue is comprised of. The moment the re-melted gold is re-poured into the mold, it is known as re-molding gold. The moment that re-molding gold is solidified, it is re-molded gold that is identifiable as the statue. Even if the statue is made of the same material, it is indeed the second statue created. It is even true that the quantifiers for the second statue differ from the quantifiers for the initial statue. Simply because the initial statue was destroyed, that does not mean that the initial statue did not exist.

It did in fact exist, therefore any statue that is derived from the initial manifestation of the statue must logically be separate from the original statue. This can be understood in how clothing is manufactured as well, when an individual designs a shirt, they are not making the literal same shirt every single time. The variation of the shirt, in this variance pertaining to the design of said shirt, may very well be identical, however, the shirts that are produced after the very first shirt is brought into manifestation, must be considered the second, third, fourth, fifth and so on. One does not simply manufacture a quantity of 300 shirts, while logically being able to quantify 300 shirts under the first, single shirt produced. You must acknowledge that any shirt produced after the first, is indeed not the first produced shirt.

Utilizing the second description, it is indeed true that we know the first causes of the thing, that thing being the statue. It is already outlined in the previous paragraphs. The cosmos exists, therefore the universe exists, we know this by definition. Since the universe exists, we know that the world and worlds themselves exist. Knowing that worlds themselves exist, it is true that life exists, as biological life requires a plane of inhabitance. Since biological life requires natural products such as minerals to create things, it is true that minerals such as gold exist. Gold can indeed be manipulated by different temperatures, therefore it is true that when gold undergoes extreme application of heat, it liquefies.

Since a gold statue can indeed be molded, it is true that the melted gold can be utilized to fill the mold for the statue. Knowing that gold only melts under extreme heat, it is true that it will solidify once the application of heat is ceased. Once the gold is fully solidified in the mold, the statue exists. It is incredibly obvious that the primary cause for the existence of the statue, is the existence of the aforementioned. If we want to get incredibly simplistic in understanding this, because the cosmos exists, everything that requires the cosmos to exist, also exists. This simple acknowledgment quantifies the original and primary causes that allow for the statue to exist.

It is obvious that individuals that task themselves with understanding the aforementioned example, do not necessarily have the intent of acknowledging what is known, rather they only attempt to question why we know things. While this can be beneficial, there is a fine line between valid questions and perpetual questioning of what is indeed knowledge. These individuals claim that the two descriptions outlined by Aristotle, do not allow for the understanding of abstract questions such as change, time, composition and identity. On the contrary, the two aforementioned descriptions incorporate all of these aspects in an incredibly simplistic manner, while also allowing for the questions to exist and be directly correlated to logical solutions that are known.

Negating the two descriptions does nothing but prove that the negator fails to see how the pieces individually fit into the puzzle that is existence. It is required that we think clearly and consistently about both the abstract questions and the simplistic questions. As previously mentioned, there is a duality to simplicity and complexity. They may both exist in equilibrium, all that is required for this to manifest is the acknowledgment that what appears to be complex, need not be complex once it is known, for then and only then can it simply be knowledge. This allows for the perpetual manifestation of seemingly complex questions. I posit that with every complex question, that is inevitably answered simplistically, another complex question emerges. This is not spontaneous, rather the emergence of another complex question is a direct result of a previously complex question becoming simplistic."

While this text is lengthy, I truly understand this as an argument that shows identity as being capable of being circular, however, such a thing is not necessarily reasonable. Thus, identity itself is depleting, not impermeable via being circular, in turn allowing for a proper understanding of changes via identity. Even within this, we must understand that the argument of essence and existence can be utilized to show that our identities are fixed in essence yet can be easily contradicted via existence. If we are to aim for equilibrium, we must merge essence with existence via reverence to essence preceding existence. This is unfortunately a hard pill to swallow for many.