It is generally assumed we are the same person throughout our lives. Moreover, there is a study that asserts the continuity of self remains stable throughout our lifetimes. Nonetheless, a simple argument, which I'm going to present next, suggests otherwise.

The argument

Let's consider a person called X, who exists in the present moment. If we also consider only the present moment is real (nor the past nor the future exist), then past X (eg: X from one year ago) and future X don't exist. Since it is impossible that the same person exists and does not exist, we conclude present X and past X are different persons.

Why this argument might be wrong

This is my first post, so feedback on this issue is specially welcomed and appreciated. Below I give what I thought about this.

First, with the above argument we could think our identity changes at each instant. However, it only asserts present X is different from past X and future X, but not that X from any two different points of time are not the same person.

Second, the argument presented relies on the assumption that only the present moment exists, and only present entities exist. This is philosophical presentism. Stanford Encyclopedia of Philosophy presents a valid argument against presentism:

(1) If a proposition is true, then it exists.
(2) <Socrates was wise> is true.
(3) <Socrates was wise> exists. (1, 2)
(4) If a proposition exists and has constituents, then its constituents exist.
(5) Socrates is a constituent of <Socrates was wise>.
(6) Socrates exists. (3, 4, 5)
(7) If Socrates exists, then presentism is false.
(8) Presentism is false. (6, 7)

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