The Memory Theory: Logical Worries.

After some modifications, we have stated the Memory Theory as:

The Modified Memory Criterion:

x is the same person as y
if and only if
(i) x and y are person-stages, and
(ii) x remembers x’s doing something that y did.

Gretchen points out a "circularity problem with this theory", but here I want to focus on some logical worries that we might have with the theory, as stated above.

Logical Features of Identity

First, let me explain some basic logical properties of identity. These are properties that are supposed to hold of identity in general and not just personal identity.

Identity (=) is:

(i) Reflexive. For all objects a, a = a. (Every object is identical to itself).
(ii) Symmetrical. If a = b, then b = a. (If a is identical to b, then b is identical to a). For example, 2+2 = 4, so 4 = 2+2. (Contrast this with the relation of "admiring". I might admire someone, but that doesn’t automatically mean that they admire me.)
(iii) Transitive. If a = b and b = c, then a = c. (If a is identical to b and b is identical to c, then a is identical to c.) For example, 2+2 = 4 and 4 = 1+3, so 2+2 = 1+3. (Contrast this with the relation of "being a friend of". I might be friends with Jack and Jack may be friends with Jill, but that doesn’t automatically mean that I am friends with Jill.)

The Memory Theory.

The Memory Theory is supposed to be a theory of personal identity. It is a theory that attempts to spell out when person A is identical with person B. (More officially, it is a theory that attempts to spell out when two person-stages are part of the same person.)

But notice that, as it stands, the Memory Theory fails to satisfy symmetricality and transitivity. (It does, however, satisfy reflexivity.)

Symmetricality.

Let’s start by looking at an example which shows that this account of personal identity fails to be symmetrical.

I am the same person today that I was last Wednesday. Let’s see what the above Memory has to say about this.

First, let x be the person-stage of Ben-today and let y be the person-stage of Ben-last-Wednesday.

I can remember doing, thinking and feeling what I did last Wednesday. This means that x (Ben-today) can remember doing something that y (Ben-last-Wednesday) did, so it follows that according to the above Memory Theory x is identical to y.

But trivially, last Wednesday I didn’t have any memories of things I did today. (I don’t have memories of what I’ll do in the future. So y (Ben-last-Wednesday) can’t remember doing anything that x (Ben-today) did. So it seems to follow from the Memory Theory that y is not identical to x.

But this is a violation of symmetricality. x is identical to y, but y is not identical to x.

Transitivity (The Brave Officer Objection)

To see that transitivity fails on the above theory, consider the "Brave Officer" objection (discussed in Think on pp. 131-2) that Reid raised against Locke.

A young boy was flogged for robbing an apple orchard. (Let’s call this person-stage A)

This boy grew up to be an officer and took a standard from the enemy in his first campaign. (Let’s call this person-stage B.)

Later in life, he was made a general. (Let’s call this person stage C.)

As the case is described, B can remember performing A’s robbery of the orchard. And C can remember performing B’s taking of the standard. But C can’t remember doing anything that A did.

Given these details, it looks like the above memory theory will say that:

C is identical to B.
B is identical to A.
But C is not identical to A.

And this is a violation of transitivity.

These logical worries are somewhat troubling. A defender of the Memory Theory would need to either revise her theory, in order to preserve symmetricality and trasitivity, or would need to argue for the (very implausible) claim that when it comes to people, identity is not symmetrical or transitive.

I’ll leave it as an open question how a defender of the Memory Theory could best respond to these worries:
Can you see how we might restate the Memory Criterion to deal with these logical worries?