You are going to say that about any argument that has any premises - so, you know, all arguments. Any argument for anything whatsoever - no matter how profound and important that argument - all you are going to do is point out that it has assumptions.
All. Arguments. Make. Assumptions. The issue is whether those assumptions can reasonably be denied.
In the case of my argument, they can't. Which is, you know, kinda significant.
You talk about intrinsic value. So, er, 'moral' value, then! My argument is about what that value is - what it is made of. I know that some things are intrinsically morally valuable. Where have I denied that? I am showing what it is made of, not denying its existence.
For something to be intrinsically morally valuable is for it to be being valued for its own sake. There still needs to be a valuer. And the valuer is demonstrably not me or you. Same argument. Same conclusion.
Imagine I have said that cheese is made of milk. You say "ah, but Edam is cheese". Yes. I know. And it is made of milk.
You then say "ah, but those who deny that cheese is made of milk will deny that it is made of milk"
Yes, but I have this evidence that it is made of milk - it is demonstrably made of milk.
You: yes, but those who deny that cheese is made of milk will deny it.
on and on.
Anyway, you don't get to speak on behalf of others. Why assume that an objectivist will reject my argument?
two points.
A) why think they will? If they're proper philosophers and they cannot refute the arguments I have presented, then why think they'll stubbornly stick to their original thesis? You're assuming they're all like you. That is, so wed to their original view that they won't give it up for love nor money. But they may not be.
I used to be an objectivist about moral value. Then I discovered the arguments I have presented above. I could not refute them. I concluded that moral value is therefore subjective and that I had quite the wrong view about it.
Why think that objectivist moral philosophers won't do that?
B) Obviously - obviously - an objectivist must deny a premise of my argument. I mean, that's why the argument disproves objectivism!
Which one and on what basis? Don't just keep telling me about what an objectivist will or will not do. Put some skin in the game. Challenge a premise.
And don't think you're doing that by just mentioning intrinsic value. Again, intrinsic value is a kind of moral value and my argument is about every kind - every kind - of moral value.
Which premise do you deny?