Title of article: Why Our Children Don't Think There are Moral Facts

[St_Francis]

I don’t think that anybody is going to claim to hold such a position, because it is too weak. Maybe this deserves a separate thread. You could put forward that position for consideration, not as something that you believe, but as something that somebody might believe.

Then we can look for the simplest and clearest examples of problems with that position. We can formulate questions for anybody who might hold that position. Somebody might take the devil’s advocate position and attempt to do what will be very difficult: give plausible answers to those questions.

Well, I agree that people would probably not admit to holding such a position when put that way, but all those who say they don’t believe in concepts, or those who say that different people can have different moralities, etc.

 

[PseuTonym]

There are no moral axioms.

This is a conclusion that you reached, but it seems to be based on your claim about qualifications.

It’s both 1 and 2.
As regards #2, you are correct in that it must not contain a qualification in the first instance. And you have not included a qualification in either of your examples.

If you were to say: ‘Every non-empty set of positive integers has a smallest element if…’ then whatever comes after the ‘if’ is a qualification.

The above seems to be nonsense. There seems to be reliance upon some assumption about the meaning of the term “non-empty.” In other words, there is no principle here, and there is simply reliance upon the authority to arbitrarily assert that the distinction between the empty set and non-empty sets is not put into the category “qualification.”

After all, we can define the concept of a Goldbach set as follows:
S is a Goldbach set if and only if (Goldbach’s conjecture is true and S is not empty).

Consider the following statement that we shall call Q (for Qualification):
Q: “Every non-empty set of positive integers has a smallest element if Goldbach’s conjecture is true.”

It is alleged that Q includes a qualification.

However, Q is logically equivalent to the following:

UnQ: “Every Goldbach set of positive integers has a smallest element.”

Let us see why Q is logically equivalent to unQ.

Case 1: Goldbach’s conjecture is false

If Goldbach’s conjecture is false, then Q is automatically true, because Q asserts merely a conditional and the condition is that Goldbach’s conjecture be true. If Goldbach’s conjecture is not true, then Q does not make any claim at all, so in that case, Q cannot be making a false claim.

For UnQ to be false, there would have to exist a Goldbach set of positive integers that does not have a smallest element. In particular, for unQ to be false, there would have to exist a Goldbach set of positive integers.
However, if Goldbach’s conjecture is false (and that is what we are considering in case 1) , then there does not exist a Goldbach set of positive integers. So if Goldbach’s conjecture is false, then unQ is true.
Thus, in case 1, Q is true and unQ is true.

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Case 2: Goldbach’s conjecture is true

If Goldbach’s conjecture is true, then the condition in the statement Q is satisfied. Thus, in this case Q is equivalent to the following: “Every non-empty set of positive integers has a smallest element.”

If Goldbach’s conjecture is true, then S is a Goldbach set if and only if S is non-empty.
So, if Goldbach’s conjecture is true, then we are entitled to replace “Goldbach” with “non-empty”.
Now, remember what unQ is:
UnQ: “Every Goldbach set of positive integers has a smallest element.”

Thus, if Goldbach’s conjecture is true, then unQ is equivalent to …
“Every non-empty set of positive integers has a smallest element.”
which is equivalent to Q.

Thus, in case 2, Q is equivalent to unQ.