Identity and identicality are two different things. I may have an identical twin who shares all of my physical characteristics, and yet who is not me. We are different persons. I have one identity, and he has another. However, is my twin identical to me in every way? Do we share every attribute? For instance, are we in the same place at the same time and share all characteristics in common? If so, I have no twin. There is only one of me. Exact identicality seems to always entail identity. People can identify me (mark my identity) based on my exact identicality with myself (if that even makes sense). If I look like a duck, swim like a duck, taste like a duck, etc., I must be a duck.
On the other hand, identity cannot always be said to entail identicality. I am not always identical with myself. For instance, I changed my clothes this morning, my mind this afternoon, and my haircut this evening, yet I remain me. I can be non-identical with myself at a different point in time. In fact, being in a different time means that I am now different than myself yesterday, even if everything else about me remained exactly as it was yesterday (if that were possible) because I am in a different time (a non-identical attribute)—I am different relative to the external world. Even though my brain cells change (for instance through learning/growing, through new cell growth, and through loss of cells), I can continue to be me. I hold on to my identity through change.
So I can be identical with myself (I am), and non-identical with myself (for instance, myself from a different point in time) and continue in my identity.
This idea might be fruitfully applied to our understanding of the Trinity. In the three persons of the Trinity, we have God the Father, God the Son, and God the Holy Spirit. God the Father, God the Spirit and God the Son all have the identity of being God, yet are not identical (they do not share all attributes in common). Many of the attributes of God are enjoyed by all of the persons of the Trinity, such as being eternal, but some others are specific to specific persons. For instance, Jesus underwent death. The Father did not (he is a spirit). In this they are not identical. This does not mean they are not one. It also does not mean that they are mere modes of one thing (or are parts of one thing). Jesus is all God. He is the exact representation of the Godhead bodily. When we see Jesus physically, we see the Father. Yet no man has seen God (that which is identical with God). Nevertheless, Jesus, who is said to sit at his right hand, has seen the Father (he who has the identity of God), and testified of him, revealing him to the world through his own person. In this, Jesus can change, and yet God does not change. Jesus is identical with Jesus, and is non-identical with Jesus (himself from a different point in time/space or with differing attributes), and he continues in his identity as Jesus. Jesus is also non-identical with God the Father, non-identical with the Holy Spirit, yet continues in his identity as God the one and only. So being God is not the same as being identical to God (because God can be non-identical to God). In this way Jesus can empty himself of the glory of God through kenosis, and yet be God. He can live in time and be timeless. Jesus in time is not identical with Jesus that is timeless, but Jesus is the timeless God, and Jesus is God in time.
The distinction between identity and identicality might also help us to understand ourselves. I am me (I share the same identity with myself, if that even makes sense). I am not always self-identical though, as we discussed above. Further, my spirit is me. He (me) is the spirit of Bob. My spirit is not identical with me (we do not share all properties in common, such as having material substance and dying in the future). I do have material substance and will likely die in the future. Yet my spirit is me. My spirit is fully Bob (it is me, my identity). The same goes for my physical body, which is me, is not a part of me (it is wholly me), is not identical with my spirit, and yet is truly me. When you point at my body, you can truly say “You are Bob”. My body has the identity of Bob. My body is not a part of Bob (a part of my identity), my body is Bob (it is my identity, though it is sometimes non-identical). If my body dies, I die. I cannot be said to die if my body is not me. If my spirit lives on, I live on. I cannot be said to live on after death if my spirit does not live on. If my body is resurrected, I live on bodily. I cannot be said to live on bodily if my resurrected body is not me.
The differentiation of identity and identicality helps us solve several other major metaphysical puzzles, for instance, Zeno’s paradox of motion, the cat and its fur (fuzzy identities) and identifying a cloud (where does it start and where does it end?).
One puzzle presents itself in this analysis: how different can a being be from itself before it is not itself? Well, we might answer (tongue in cheek) that a being can be as different from itself as possible and still be itself. It does not cease to be itself through loss of identical attributes. Or does it? If a shovel has had the handle replaced multiple times, the wood stem replaced several times, and the scoop replaced several times, and has had different owners, is it the same shovel as when first created? Most would agree that it is not identical to the original shovel. Does it keep its identity through all of these changes, or is there a point (for instance, when the last remnant of the original is replaced) that it ceases to be itself, and something else is there (for instance, a new shovel)? If it is still called a shovel, it retains at least one attribute of the original. Perhaps to make the original shovel not be, it must cease to exist in totality (no attributes shared with the original). If this is the case, is it even possible for things to lose their identity? (Can’t things always be said to retain at least one attribute that is identical?)
In admitting that identity might be lost only through loss of every identical attribute, are we still holding on to some form of “identity equals identicality”? Because in this, we seem to be saying that identity requires at least some identicality (though not necessarily total identicality).
On the other hand, identicality of some attributes does not equal identity (you are not me just because you are also human). Loss of all attributes that are identical might mean loss of identity, but this would also require loss of being, since one of the attributes of the original identity would include being. I suppose it should come as no surprise that if a thing ceases to exist entirely it also ceases to retain its identity.
I don’t actually believe in the existence of attributes or properties of objects as things in themselves. How might this change the conversation? I believe that what we describe as attributes or properties of objects are actually merely “the way the thing exists”, in its relative relationship with other things and itself. “Being” is not part of the way a thing exists. While “being” could be construed to be a property of a thing (that which makes it exist), I don’t believe in properties. Instead, in my framework “the way the thing exists” presupposes the thing’s existence in order to describe it. So if (as in the previous paragraph) a thing suddenly ceased to exist completely, we could not speak of “the way it exists,” since it does not exist any longer. So, in reiterating our previous thesis, identicality of some “ways a thing exists” does not equal identity (though identicality of all the ways a thing exists does entail identity). For a specific object, loss of all the ways of existing that are identical ways of existing might mean loss of identity (though not necessarily loss of existence). It would take a loss of all ways of existing (even those that are non-identical) in order to lose existence entirely. Why would existence cease when ways of existing ceased? If a thing does not have any way that it exists, it should also be said to not exist. For example, there is no way of walking for the person who does not walk. And if a person loses all ways of walking they should be said to not walk. Similarly, if a person loses all ways of existing, they do not exist.
This might be applied to hermeneutics as well. The meaning I get from a text might share the identity with the meaning of the original author, though it might not be identical with the author’s meaning (it might not share everything in common with it). The meaning I get might share some (though not all) identical ways of being with the author’s meaning, and as such retains its identity as the original meaning, while not requiring identicality with that meaning. I can understand without fully understanding.
Similarly with perception. I perceive the way a thing is (outside of me), and I believe it is a certain way (the way I just perceived it). For instance, I perceive the cake is hot (I see steam rising from it), and I am thereby justified in believing the cake is hot (in the absence of defeaters). I perceive the way the cake exists (hot), and I believe it is a certain way (hot). But in this case, let’s say that the cake is actually cold, and there is a hot cup of coffee behind the cake that is letting off steam (because it is hot). I mistakenly think the cake is hot, but I might still be justified in thinking the cake is hot. The reality of the cake (that it is cold) is not exactly identical with what I perceive (that it is hot). Yet my perception matches the identity of the cake with the cake in the external world (and the way it exists). How? The cake looks brown to me, and the cake actually does let off a brown hue in this light (my perception in this case is identical with how the cake exists). Something of my perception is identical with the way the cake actually exists, meaning the identity of the cake is perceived, even though my perception (and resulting belief) do not identically match the state of the world that is external to me. So the statement “the cake is hot” is false (it does not correspond with external reality—the cake is actually not hot), but I am still referring to the same cake nevertheless (though it is not identical with what I believe or what I perceive). As long as some one way of existing crosses the boundary from the external world to my perception, I have (at least imperfectly) perceived the identity of the thing (because I have perceived one of the ways that it exists).
This last example presents an interesting problem. What if I perceive a way of existing for the cake that is not possible for cakes? What if the identity of the thing is irreconcilable with one of the ways of existing that I perceive (and I go on to believe this perception)? For instance, I perceive that the cake is alive and walking around. It is not possible for a cake to be a real cake and also to be alive and walking around. That’s not a possible way of existing for cakes (at least, for what we mean when we say “a real cake”). In that case, the identity is broken. A real cake cannot be alive and walk, but I perceive a cake that is living and walking, and therefore I do not perceive a real cake. The identity of the real cake is lost entirely, not as the result of missing all identical ways of existing (as before), but only by the perception of one way of existing that is not possible for that identity. For instance, a human being cannot turn into a cloud. If that is true, then my identity as “human” is lost if I suddenly become a cloud (in other words, “I” do not become a cloud—rather, a cloud is where I once was, or in some other way shares identical attributes with me, though it is not me).
To sum up, identity and identicality are different things, and an appreciation (and analysis) of how they differ helps us to understand ourselves, our God, philosophical puzzles, hermeneutics, perception, and even cakes. Exact identicality entails identity (if it quacks like a duck…). Identity does not entail identicality (I can be different than myself). Some identicality is necessary for identity (there must be something that is the same). Loss of all identicality entails loss of identity (loss of every identical attribute entails loss of identity), but difference of identity does not entail the absence of identicality (two different persons may have many things in common). And finally, there are essential identical ways of existing that, if absent, entail absence of identity (for instance, there are some ways of existing that are not possible for humans).