I apologize, you’re right, I wasn’t clear enough. What I meant was: is it possible to keep the commandments only because we were commanded to, and without believing in reward in this world and in the World to Come? Does that not contradict belief in individual providence or in recompense?

What do you mean, “is it possible”? Again, you’re not answering me. Why would that contradict belief in individual providence or in recompense? If you don’t clarify what you mean, I’m done.

As for belief in recompense: from what I understood, that belief means that God gives good reward to the righteous and bad to the wicked. So if I do not believe in reward and punishment, neither in this world nor in the World to Come, that could contradict my belief in recompense, no? Because if I do not believe in reward and punishment either in this world or in the World to Come, then the belief in recompense—that God gives good to the righteous and bad to the wicked—is also uprooted, isn’t it? (As for individual providence, I wanted to ask you whether there could be a contradiction, because personally I don’t see one.)

But my main question was whether there is any point in observing the commandments, both positive commandments and prohibitions, without believing in the reward said to exist for those commandments in this world and in the World to Come, but only by virtue of their being a direct command from God.

That is, I observe them only because they are a direct command from God, and not because I believe in the reward for those commandments in this world and in the World to Come.

We’re starting to get closer to a reasonable formulation, although I still don’t really see a question here.
It does not seem likely to me that there is recompense in this world, because in my opinion God is not involved (or is almost not involved). The Sages also say that there is no reward for a commandment in this world. As for the World to Come, I have no idea. I’ve never been there. But whether there is recompense or not, what does that have to do with serving God for its own sake? I can serve for its own sake whether I believe in recompense or whether I do not. Maimonides already explains at the beginning of chapter 10 of the Laws of Repentance that although there is recompense in the World to Come, one should not serve God for its sake.
So why serve? Simply because He commanded, and there is an obligation to fulfill His commands. (And presumably that is also the right and beneficial thing in some sense. It is unlikely that He commanded for no reason.) I referred you to Column 120.

Sorry for the audacity, but does the Rabbi wear a small tallit?
If so, why?! As I understand it, modern clothes do not fall under the category that requires fringes—so there is no command.

If you say that there is a commandment that does not apply to you, but you choose to bring yourself into a state of obligation (that is, to buy a special four-cornered wool garment and then place fringes on it and then fulfill a commandment), because why not…
Then why not chase after every commandment like that—buy a field just in order to observe the commandment of the Sabbatical year, eat an olive-sized piece of bread every half hour in order to perform hand-washing, and so on…

It feels to me that we have some additional motive for observing commandments—some kind of cost-benefit consideration—and we assume there is a benefit.

Yes, because it became customary to wear a small tallit. What’s the problem with that?

There’s no problem, but that’s not what you argued.

I don’t want to harp on this, and sorry that I’m piling on you, but…
If you perform a commandment only because there is a command, it’s not clear why to wear fringes, and indeed I argued that there is an additional motive.
So you find another motive and broaden the argument and say that you also perform a commandment because that’s the custom (folklore / emotion / God commanded us to persist in custom—whichever answer is right), fine, but it comes out that one does not perform a commandment *only* because there is a command.

Where did you get this nonsense from? A commandment is only because of a command. This act is a commandment only because there is a command to place fringes on the garment.
The act of wearing the garment itself is not a commandment, because there is no command about it. Exactly as eating is not a commandment, but reciting a blessing if you ate is a commandment.