You can't step into the same river twice

Not only because the river is constantly changing, "YOU" are constantly changing too, hence the title.

If some philosophers are correct (namely the 4-dimensionalists), then you are not the same person as the person a year ago. Nor are you the same person an hour ago. Not even a second ago.

I know what you are thinking. You are thinking: of course I am not the same person I was a second ago. I have changed, slightly, from moment to moment. Compare the you 10 years ago and the you now, there will have been differences in terms of physical states and beliefs and desires. If we assume that the changes take place along a continuum of time, gradually and smoothly, then there will be changes however imperceptible every second. (At the very least, each breath you take will cause chemical changes throughout your body, resulting in minute changes at every moment in time.)

But that's not what those philosophers meant. You are not the same person not because you are a changed person at every following second. You are not even a changed person from the previous second because the previous "you" are not even you AT ALL.

Now what does that mean exactly, to say that the previous "you"-s are not even you at all? In layman terms, it means that a second ago, there is a person who looks almost exactly like you, who shares nearly all of your beliefs and desires, and wants to do almost nearly everything that the current you is doing. But that person is not you. He looks like you, acts like you, thinks like you; he thinks he will be you, and you think you had been him, but he is not you, neither are you him.

You are not the same person as the person who started reading this page. Nor are you the same person as the person who started reading this sentence. You exist only at an instant. For the length of reading this page, an infinity of you would have existed and flickered out, each thinking (naively) that they have existed all along with a history of, say, 20 odd years, and will continue to exist for quite some time yet.

How do we explain the appearance of personal history that we appear to be able to call up in our memories? Each of the instantaneous you possess an entire set of beliefs, desires, and memories, each largely coherent with the preceding you. For example you at time T would possess the memories of having sat down at the table and the current experiences of sitting down at the table; you at time T+1 would possess the memories of sitting down at the table and the current experiences of reading this post; you at time T+2 would have the memories of reading this post, and the current experiences of trying to remember all the memories you have since childhood in order to prove this post wrong; you at time T+3 would have the memories of trying to remember all the memories you have since childhood in order to prove this post wrong and the current experiences of doing that some more., etc.

All the memories are merely apparent memories. They are real memories, but only in the sense that they appear to be of the current you doing certain things in the past. But you never did those things, your previous selves might have, but they weren't you.

In fact, you don't need to have the previous selves in order to have those memories. They could simply have appeared in the repertoire of the current you's mind without there being any previous beings having done whatever you thought you have done in those memories.

You could simply be an instantaneous being who appeared and disappeared, thinking that it has lived for quite some time, and will live for some time yet, and there being no other instantaneous you-s before or after you.

You are thinking: now this surely is absurd. I reflect now, and I can just feel it. There is a whole history stretching back from me. I remember me doing all those stuff. Look, I am touching my cheek now. I shall vividly remember this feeling. 2 seconds later, I am pretty sure that it is the same me who did that cheek-touching; I have that experience in me now, even. Surely I am not mistaken about that!

But you are, if those philosophers are correct. You only think that you are the same person who did the cheek-touching. Maybe there has been a person who really did the cheek touching, but that person is not you, even if the details of the memories you have now is almost identical to the experiences that person has while touching his cheek.

Up till this point, I have not yet given any reasons for thinking this account of you surviving time is correct. But how do you know that it isn't?