Mental 00: Identity, Part 00: The Problem

    Recently, I got into an argument with a good friend of mine about the nature of identity. She said that my idea was interesting, but that it lacked substance, i.e. it required more evidence. A Google chat conversation is not the best place to lay out well-thought, detailed arguments, so I promised her I would write a blog post about it, and invited her to comment on it publicly or talk to me in private about it. I know I've said that my first Mental post would be about Un-arguments, but this may serve as a good introduction to my view about reality, and how we experience it.

    A quick look a Wikipedia shows me that I must clarify what I mean by "identity." I am not referring to social identity. Social identity is a "self-concept derived from perceived membership in a relevant social group," which can be based on sexuality, ethnicity, socio-economic status, country of birth, etc. Philosophical (or mathematical) identity is much simpler: when are two things the same thing? This is an important concept: the idea of identity is a certain kind of relationship between things. We call this an identity relation.

    A mathematical identity relation must satisfy three conditions. These are:

1. Reflexivity. Given some x, x is identical to itself.
2. Symmetry. Given some x and y, if x is identical to y, then y is identical to x
3. Transitivity. Given some x,y, and z, if x is identical to y, and also if y is identical to z, then we have that x is identical to z

     All very cute, but not very interesting. So, what's the problem with identity in the Universe?¹ Well, nothing if you take a freeze frame. If I could somehow take a 3-dimensional photograph, I could point to any object and easily say it's identical to itself. Identity relations can also be looser: I could use the identity relationship of "in the same room." Then, I would have all three properties satisfied: my keys are in the same room as themselves; if they're in the same room as my water bottle, then my water bottle is in the same room as my keys; and, if my keys are in the same room as my bottle, and my bottle is in the same room as me, then I'm in the same room as my keys!

Exciting, right?

    The problem may or may not become apparent to you when we factor in time, so we now turn the the famous "Ship of Theseus" paradox. This is stated by Plutarch as follows:

"The ship wherein Theseus and the youth of Athens returned [from Crete] had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place, insomuch that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same."
—Plutarch, Theseus

     Simply put, if I take a ship, and over the course of time slowly replace old planks with new planks, after a certain amount of time the ship is made only of planks which it did not have when I began. So in what sense is it the same ship? If you argue it is, consider the possibility that I remove planks before they become unusable, and instead perfectly preserve them some way. When all the planks are removed, I build an exact model of the ship of Theseus from these planks. Now I have two ships, each with rather strong claims to being "The Ship of Theseus". If your answer is, "'The ship of Theseus' is whichever one he owns," then you're just mincing words. We are just interested in the object itself, not the nature of it's verbal description.

    If our identity relationship is strictly physical, then of course these objects are not the same. However, choosing that identity relationship is problematic, because objects are always changing. The molecules change their arrangements, the wind and the waves erode the wood and cause it to be caked with salt and minerals, bacteria which eventually cause the planks to rot slowly germinates, etc, etc. It's clear that based on what we know about the laws of physics, from moment to moment nothing is ever exactly physically identical to itself a moment ago.

This problem is summed up nicely in the following quote (taken from the Stanford Encyclopedia of Philosophy, attributed to Irving Copi):

1. If a changing thing really changes, there can't literally be one and the same thing before and after the change.
2. However, if there isn't literally one and the same thing before and after the change, then no thing has really undergone any change.

    Do objects persist through time, or are brand new ones just popping into existence moment to moment? This becomes increasingly important when we talk about the identity of people, for in a way we are also like the Ship of Theseus - many (thought not all, I'm told) of our cells die and are replaced by cells which came from outside sources, like food. We are never exactly physically identical to ourselves a moment ago, and yet we have this strong intuition that we are in fact the same self. Are we wrong, and the identity of the self through time simply doesn't exist, or is there something meaningful to our intuition? I believe it's the latter of these two, and I will explain why in later posts.


1. It's for another post to describe how I view the structure of persuasive argument. Suffice for now to say that there's no argument if there's no problem, which can be either tangible or conceptual in nature.