I don’t see how an infinite chain arises under my proposal that there exists a supreme value (a second-order one). On the contrary, I think that if you don’t assume the existence of such a supreme value, you won’t be able to explain how values sometimes conflict with one another. For example, a religious value that conflicts with a moral value. In order for such a conflict to arise, we must assume a common basis that makes it possible. That basis is universal, and it can be formulated like this: God wants human beings to carefully clarify their different values, weigh them, and in the end decide in favor of only one of them (in the case of a conflict).
On the other hand, the supreme value is logically prevented from falling into such a regress, for the simple reason that it is singular and cannot conflict with other supreme values (which would require third-order values).

A conflict between values doesn’t require any common basis. The conflict arises because of the situation in which value A instructs me to do X and value B instructs me not to do X. There doesn’t have to be anything shared between A and B other than the fact that both of them have instructions about what to do in the given situation.
I thought you were claiming that subordination itself to a value system requires a supreme value. That isn’t correct, as I wrote in the previous message.

Now I’ve lost you. Isn’t commitment to God a value in your view?

I lost you a long time ago. I don’t understand how this question is relevant.
Commitment to God is a meta-value. Like commitment to morality. It is artificial and almost absurd to say that there is a supreme value of commitment to morality from which commitments to specific moral values are derived. This is not a process of deriving one thing from another, but of specification. Commitment to morality is itself the commitment to all the commands of morality. The same is true with regard to the commands of the Holy One, blessed be He.

The word “commitment” in everyday language (you can also check the way you yourself use it in your writings) is logically bound up with the concept of “values” or with the idea of evaluative choice. Therefore commitment even to what you call a “meta-value” *is itself* an evaluative choice, that is, a second-order value system. I don’t understand why that is “artificial” or “absurd” in your eyes. At most you can say that there is dialectical thinking here, except that in this case it is required.

What you call “specification” is in fact derivation. For example, Reuven and Shimon agree between themselves that commitment to God is the basis for values (a meta-value), but their mode of derivation, that is, the application, is not the same: Reuven thinks that male homosexual intercourse is forbidden by Jewish law in a categorical way (no matter what its “moral” price is), and that this is God’s true will; and Shimon thinks the opposite (that there is room for leniency sometimes). Each one of them “derived” the practical implication differently from the same supreme value (“meta-value”) on which they had already agreed.

We’re entering into sophistry that is mainly semantic.
In my opinion, there is no point in speaking about commitment to morality as a value in its own right, because if you do, it itself requires yet another value to justify it, and so on — “turtles all the way down.” Commitment to morality is self-understood and does not need to rest on anything else. Commitment to specific moral commands is a specification of the general commitment to morality, not something derived from it. Exactly as the claim that Socrates is mortal is not derived from the fact that all human beings are mortal, but is rather a specification of it (a particular case of it).
The same is true regarding commitment to God. In my view, it is not based on a prior value; rather, the commitment is self-understood. Its specification is all of His specific commands.
Think, for example, about the prohibition against violating one’s word in a vow (“he shall not profane his word”). Suppose I vowed not to eat bread. Is my prohibition against eating bread derived from the prohibition “he shall not profane his word”? No. It is a specific application of the prohibition, not another prohibition derived from the original prohibition. This is connected to what in my writings I have often called specification versus branching off (you can search the site).
The fact that there is a dispute about God’s will is irrelevant to the discussion. There is a dispute about what God wants, but both of us are committed to what He wants. Just as there could be a dispute about what exactly I vowed, but we would both agree that I am forbidden to violate what I vowed. It is the same value itself, and we are not dealing here with the ‘derivation’ of one value from another except in a very artificial sense. This may be derivation in the logical sense (as with Socrates), but the derivation merely reveals the content of the original value. It is not a value that stems from another value, in the sense that these are two different values.
I do not see where this discussion is going.

So we disagree. But notice the significant change in your position in the last two sentences (in your latest reply): now you already agree that this is “derivation,” even if it is only a derivation of specific content (“in the logical sense”).
I already explained at length what the meaning of “derivation” is and how it requires a completely different worldview from the one you present on this specific issue.

There isn’t the slightest change in my position. I merely clarified that you are apparently speaking about derivation in its logical sense, which I call specification, and I wrote my opinion about its meaning.