In this post I would like to discuss several objections to two axiological arguments: one axiological argument for the existence of God and a related axiological argument against naturalism. I would like feedback regarding my thinking on these arguments and my objections to them.
Here are some relevant links:

https://en.wikipedia.org/wiki/Axiology

https://structureoftruth.wordpress.com/2018/05/26/the-axiological-argument-ii/

https://structureoftruth.wordpress.com/2018/06/09/the-axiological-argument-iv/

Let us first examine an axiological argument for the existence of God. The argument is axiological because it contains a premise about values—namely, that there are objective values that we can know to be objective—and argues that from that and a second premise it follows that God exists. The briefest form of the argument appears as follows:

1. If God does not exist, then we cannot have moral knowledge.
2. We can have moral knowledge.
3. Thus, God exists. (1, 2 MT)

The argument is valid. If the conditional statement, “If God does not exist, then we cannot have moral knowledge,” and the statement, “We can have moral knowledge,” are both true, then it must also be true that God exists, by modus tollens. However, the argument does not appear to be sound, since both premises are questionable. The first premise is questionable because the existence of God is not the only condition on which it is possible to have moral knowledge. There is no contradiction in thinking that there is an objective moral code that we can know, despite there being no God. Thus, it does not follow that without a God there can be no moral knowledge. The second premise is questionable because it appears either to equivocate with respect to premise 1, or it is simply unsupported as a claim about objective moral knowledge. While premise 1 seems to hold that, without God, no objective knowledge is possible, premise 2 might be taken simply to mean that we have knowledge of our own moral beliefs, which might be purely subjective. In other words, there is room for skepticism about the objectivity of moral beliefs in premise 2. Thus, the two premises have different senses of the words “moral knowledge.” If premise 2 is taken to mean that we have objective moral knowledge, then skepticism is still possible, since we have yet to establish that we have objective moral knowledge. Again, we may know with certainty that we hold certain moral beliefs to be objectively true, but our feelings of certainty do not guarantee that such beliefs are objectively true. Thus, the argument appears to be unsound.

A second, related axiological argument concludes that naturalism is false. A brief version of the argument is the following:

1. If naturalism is true, then either there are no objective moral values or we cannot know that there are objective moral values.
2. There are objective moral values, and we can know them.
3. Thus, naturalism is false. (1, 2 MT)

This argument is also valid: if it is true that if naturalism is true, then either there are no objective moral values or we cannot know that there are objective moral values, and if it is true that there are objective moral values, and we can know them, then it must also be true, by modus tollens, that naturalism is false. However, the argument appears to be unsound, since premise 2 is objectionable. First, the claim that there are objective moral values is unsupported. Again, just because we can know with certainty that we have moral values that we believe to be objective, it does not follow that they are objective. Even if it is true that everyone in the world holds the same moral values, it does not follow that those values are objectively true. In other words, just because one—or even everyone—is a moral realist, it does not follow that moral realism is true. One, or everyone, can still be wrong. Second, even if there are objective moral values, it does not follow that we know what they are, even if everyone holds the same opinion regarding which values are objective and which are not. Again, everyone in the world can simply be wrong about which moral values are objectively true. Thus, because premise 2 is unsupported, the argument against naturalism appears to be unsound.

I would like to receive feedback regarding my objections to these two arguments. Thanks.