I saw him do that vs I remember him doing that

[Charlie Bernstein]

That's makes sense to me, as long as you remember that sometimes they do mean practically the same thing, e.g: Here, let me hold that for you. / Here, allow me to hold that for you.

In cases like that, the only difference is that one has a more formal tone.

[jutfrank]

I wouldn't say these patterns are synonymous. "Let me know if you need anything" isn't equal in meaning to "Allow me to know..." The former doesn't mean asking for permission and considers the hearer the direct source of information, while the latter makes the hearer an intermediate link just allowing to know but not necessarily giving information as such.

Okay, yes, but I was talking specifically about permission, as in your example in post #3.

Anyway, I've been considering the different patterns used after see/remember as per your main question. This is what I've come up with:

I saw him arrive
I saw him arriving

These sentences are both good and show the difference in meaning nice and clearly: The infinitive expresses a complete action whereas the participle expresses an action in progress.

Let's now put these in the present tense:

I (can) see him arrive
I (can) see him arriving

The infinitive doesn't work here because it doesn't make sense. Unlike with the first two examples, the moment of utterance is contemporaneous with the action. And since the experience of perception is ongoing at the moment of utterance, there cannot be any sense of a complete action.

I remember him arrive
I remember him arriving

This difference here is identical to the difference in the previous pair. Although the action is in past time, the experience of remembering is happening at the same time as the utterance, and so for the same reason the completion expressed by the infinitive does not make sense.

We have to remember that episodic memory is really just a special kind of perceptual experience. When we remember past events, we're really just reliving those events in an imagined actuality.

I hope this explanation makes sense. It does to me, but I'll be happy if anyone can point out where I might have gone wrong.

[Alexey86]

I (can) see him arrive
I (can) see him arriving

The infinitive doesn't work here because it doesn't make sense. Unlike with the first two examples, the moment of utterance is contemporaneous with the action.

What if I change the sentence a little bit: I see people arrive every day. Does it make sense?

I remember him arrive
I remember him arriving

Although the action is in past time, the experience of remembering is happening at the same time as the utterance, and so for the same reason the completion expressed by the infinitive does not make sense.

Can we move the experience of remembering to the past: I remembered him arrive/I remembered people arrive every day?

[jutfrank]

What if I change the sentence a little bit: I see people arrive every day. Does it make sense?

Yes, it does. Good example. Here it works because the experience is not dependent on the action being in progress. Every day you see the complete action.

Can we move the experience of remembering to the past: I remembered him arrive/I remembered people arrive every day?

Great question. This is exactly what I was expecting you to ask next. Look:

I remembered him arrive
I remembered him arriving

Although the second sentence is an odd thing to utter, and probably sounds quite unnatural to most, it is still possible whereas the first one is not, for reasons I've already mentioned—the experience of remembering must be contemporaneous with the action, as it is in the latter. The former doesn't work because there it isn't.

[Alexey86]

the experience of remembering must be contemporaneous with the action

We're dealing with two experiences here: seeing the action and remembering it. The first one is obviously contemporaneous with the action, but the second always comes after it, doesn't it?

What if I I remember only the fact of arriving without seeing it? For example, somebody could tell me, "He arrived." Would "I remember that he arrived/remembered that he had arrived" be the only options?

[jutfrank]

We're dealing with two experiences here: seeing the action and remembering it. The first one is obviously contemporaneous with the action, but the second always comes after it, doesn't it?

No. I'm saying precisely the opposite—that the remembering and the action are contemporaneous. When you remember something in your episodic memory, it's like you're reliving the past perceptual experience in your mind. The action is happening again, but in your imagination.

What if I I remember only the fact of arriving without seeing it? For example, somebody could tell me, "He arrived."

That's very different. You're not talking about episodic memory here. Your episodic memory would remember the action of someone informing you of this information, but not the fact itself.

In my view, this isn't really 'remembering' at all. It's just a certain kind of propositional knowledge. The relationship between memory and knowledge is treacherously murky and can lead one down all sorts epistemological rabbit holes. If you want to talk about this, that's fine with me but it's going to be very hard.

Would "I remember that he arrived/remembered that he had arrived" be the only options?

Yes, those sentences are correct. (I'm not quite sure what other options you may be thinking of.)

[Alexey86]

No. I'm saying precisely the opposite

You're right. Sorry for being inattentive. Would "I remember (the fact of) seeing him arrive" as a rewording of "I remember that I saw him arrive" be also incorrect?

If you want to talk about this, that's fine with me but it's going to be very hard.

I'm not ready to dive that deep yet.

Yes, those sentences are correct. (I'm not quite sure what other options you may be thinking of.)

I was wondering if the shift in the meaning of "remembering" from a perceptual process to propositional knowledge allowed us to use the infinitive: "I remember the fact of his arrival -> I remember that he arrived -> I remember him arrive. If the infinitive is still forbidden, then there must be some other reason for that than the contemporaneity of remembering and action because there's no real remembering (recollection) of the action in this case.

[jutfrank]

Would "I remember (the fact of) seeing him arrive" as a rewording of "I remember that I saw him arrive" be also incorrect?

Yes.

I was wondering if the shift in the meaning of "remembering" from a perceptual process to propositional knowledge allowed us to use the infinitive: "I remember the fact of his arrival -> I remember that he arrived -> I remember him arrive.

Unfortunately not.

If the infinitive is still forbidden, then there must be some other reason for that than the contemporaneity of remembering and action because there's no real remembering (recollection) of the action in this case.

I don't quite follow. Could you explain your line of reasoning a bit more?

[Alexey86]

Could you explain your line of reasoning a bit more?

As I understand it, remembering as recollecting/reliving an event is an ongoing/incomplete process. And since remembering in this sense is always contemporaneous with the event, the latter must also be incomplete. Let's call this Contemporaneity Restriction (CR). Then, if somebody tells me, "He arrived," all I can recollect is this phrase/my awareness of this fact, not the event of arriving itself, which means we can rule out CR, but we still can't use the infinitive. So, there must be some other reason for that.

Let's take another example:
- I saw him cross the street.
- Are you sure?
- I clearly remember seeing him crossing the street.

The last utterance isn't synonymous to the first one because it implies incompleteness of the action. It really means, "I'm only sure I saw him crossing the street." And I can't change it to, "I clearly remember seeing him cross the street." If I want to confirm the first utterance, I can say, "I clearly remember that."

Now, let's add "every day":
- I saw him cross the street every day.
- Are you sure?
- I clearly remember seeing him cross the street every day.

The first and the last utterances are the same in meaning, and the infinitive works well. Am I correct?

[jutfrank]

Let's take another example:
- I saw him cross the street.
- Are you sure?
- I clearly remember seeing him crossing the street.

The last utterance isn't synonymous to the first one because it implies incompleteness of the action. It really means, "I'm only sure I saw him crossing the street." And I can't change it to, "I clearly remember seeing him cross the street." If I want to confirm the first utterance, I can say, "I clearly remember that."

Okay.

Now, let's add "every day":- I saw him cross the street every day.
- Are you sure?
- I clearly remember seeing him cross the street every day.

The first and the last utterances are the same in meaning, and the infinitive works well. Am I correct?

Yes.