At the start of the dialogue that he presents the philosophical question seems to be the following.
Can someone do the right thing without knowing what is the right thing?The Tim character maintains an affirmative answer, but Socrates cross-examines him. Socrates wonders if Tim (or anybody for that matter) could be mistaken about what they believe is the right thing. This is sloppy (Anderson is frequently philosophically sloppy). Here's what I mean. In raising the very question, "can someone do the right thing without knowing what the right thing is?" you're supposing there is a right thing. The asker of this question and the one being questioned (call them the evaluators) had better have it as common ground (for the purposes of the discussion) that there is at least something that is the right thing to do. Otherwise, the question just doesn't make sense. Once we've fixed on something like that, for instance, that donating money to a reputable charity is the right thing, then we can ask of a third-party say, Billy-Bob, whether he could in theory donate to charity (so as to do the right thing) while not being aware that it is the right thing to do. And the answer to that question is an obvious, yes. Now, it might not count in Billy-Bob's favor that he has done the right thing, because maybe he did it by accident or because he mistakenly thought it would do harm to the recipient. That is to say, there's a separate question about whether a person who does the right thing (without knowing what is the right thing) is in some way worthy of admiration. But that's an entirely distinct matter.
So, Tim answers affirmatively that a person (say Billy-Bob) could, in principle, do what is right without himself (Billy-Bob) knowing what is right. Okay, so far so good. But then it doesn't really make sense that Anderson's Socrates in turn asks Tim whether he (Tim) might be mistaken about his beliefs concerning what is right. It doesn't make sense for two reasons. As noted above, where Tim and Soc (the evaluators) are talking about whether or not a person could do the right thing without knowing what is right, they are presupposing that there is a right thing to do and that they (Tim and Soc) know that this is so. Again, without this assumption, the question at the start becomes unintelligible (i.e., "can someone do what is right without knowing what is right?" presupposes as common ground that there is at least something we--the people having this conversation--can take for granted as right.) So it makes no sense or at least is moving into a very separate line of inquiry for Soc. to ask Tim whether he knows what's right or whether he could be wrong about what is right.
But the second and perhaps more substantive problem with Soc. line of questioning is that it shows nothing. Tim can have it both ways. That is, Tim can consistently believe that 1) people sometimes disagree and are sometimes wrong about what they believe to be right and 2) people do what is right without knowing what is right. There's nothing incompatible about the conjunction of 1) and 2). The problem that Anderson seems to be trying to get at is based on a confusion about the subject matter of the conversation.
What I suspect Anderson is trying to get at is that there are metaethical theories (in this case concerning moral epistemology) about how we know what is right. And on one family of views, we know by way of intuition (aptly named "intuitionism"). And yes there is a worry that there will be disputes that go unresolved or that if intuitionism is true, there isn't an independent way for us to verify when our intuitions are correct.
I want to say two things about this. First, this point is irrelevant to the very opening question that Tim and Soc. are supposed to be addressing. That question isn't at all about how a person like Billy-Bob can know that something is right. In fact, the question asks us to assume that a third party is ignorant (doesn't know) of what is right. So this metaethical stuff is really orthogonal.
The other thing is that every metaethical view has difficulties. Anderson and Gangadean have a very naive way of doing philosophy. They suspect that if any theory has any problems, then it is a bad theory--not worth accepting or believing. But that standard is both ignorant and entirely unfair and where consistently held, leads to skepticism.
It's important to keep in mind at this point that Anderson (and Gangadean) have their own metaethical views about how we can know what is right or good. What Anderson and Gangadean either fail to see or are just being dishonest about is that their own view also has serious problems. In fact, I will argue that a version of the very problem which Anderson intends to point out for Tim's view (the intuitionist view) exists for Anderson and Gangdean's view about how we know what is right/good!
On Anderson's view, right is a function of the good. So the right thing to do is to do what is good and the good for a thing is entailed by the nature of that thing. The problem of course is this. How do we know what the nature of a thing is? Well, according to Gangadean, we have some mysterious ability to grasp the essences of things--that's just what it is to "have" a concept. What's important here is that there is a standard of correctness. My particular concept of a chair might fail to reflect the essences of chairs and in that way it would be a concept gone awry (maybe Gangadeanians would rather say that in such a case I don't have a concept of a chair, properly). However, they choose to characterize what is going on when say I've got a concept of knowledge that differs dramatically from the concept of knowledge that Gangdaean has, so that one of us has got it wrong, a problem looms. Let me express this by way of a conversation.
Soc. How do you propose that we know what is good?
Andy. You can just reflect on the nature of things and good (for a thing) is according to the nature of a thing.
Soc. But might you be mistaken about the nature of a thing? After all, people disagree about the nature of humans, the nature of right, or even the nature of knowledge, for instance. So how do you determine which belief of yours about natures is correct and which is incorrect?
Andy. Think transcendentally. If we assume that we cannot know the nature of things, then thought and talk are not possible. But thought and talk are possible so, we can know the nature of things.
Soc. You're being thick headed and cutting things with a butcher knife when what you need is a razor blade. Let's suppose what you have said is true--all that gives me is a very general claim that for some natures, we can know them. That doesn't tell me which of my beliefs about the nature of things in particular, is in fact, correct. Here's an analogy. I want to find a good babysitter for my children and ask you what criteria I should use to distinguish the good from the bad. You respond with, "well, it must be the case that we can know that some are good and others are bad." You will not have answered my question in the least.
Andy. Okay, we can distinguish our correct beliefs about the nature of things from our incorrect ones by thinking presuppositionally--from the less basic to the more basic via good and necessary consequences.
Soc. You tire me with your vague pronouncements. Must I really do all the work? Show me exactly how "thinking presuppositionally" answers my particular question. What about presuppositional thinking brings you to your definition of 'man' as 'rational animal' or even your own definition of 'rational'? I don't see how thinking basically gets us there.
And while you're at it, how do you know when you're actually thinking presuppositionally as opposed to falsely believing that you're thinking presuppositionally? After all, it seems possible that you might be mistaken. Relatedly, how do you identify something as more basic vs. less basic? What method do you use to adjudicate disputes about what is more basic. And whatever is that method, Andy, do tell me how you know that this method is to be trusted or authoritative.
Andy. It's just obvious--if you just think about the nature of man, you will discover him to be a rational animal.
Soc. So in other words, it's something like an immediate apprehension which you can't prove.
Andy. Yes, at the very basic level, we have immediate knowledge of things.
Soc. But could in theory be mistaken about even those judgments, right? You might be mistaken about what the essence of a human is (after all, people disagree, so somebody has got to be wrong). If so, then you're no better off than Tim (the intuitionist). You're calling it something else, but basically you're resting your case on an intuition which you can't independently verify as reporting to you truth. And if you're tempted to just flat-footedly respond that you simply can't be mistaken about the claim that the essence of humans is to be rational, then I wonder why Tim can't do the same about some of his own beliefs about what is right or about the reliability of his moral intuitions? Either way, your view suffers all the same problems as Tim's, it just took a little work to see that. All of this is starting to smell like "knowledge without proof" which is what you were riding Tim about.
Soc. Oh and before I go, notice you didn't answer a number of my questions about what method or faculty you use to determine that you are in fact, thinking presuppositionally (or determining something to be more basic than another)---and about how you know that you're not mistaken!
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