[The main claim] Normative judgements do not have the certain epistemic profile which is necessary for them to be about non-natural properties. This does not necessarily imply that normative judgements are not beliefs. They may be beliefs, but not about non-natural properties.
Epistemic Profile for Normative Judgements?
The Thetic Direction of Fit: Judgement with content P is cognitive if (and only if??) it would tend to go out of existence in case one takes oneself to have decisive accepted evidence that not-P
* Some people think the thetic direction of fit thesis is a necessary or conceptual truth about belief, such as Michael Smith. But Bedke thinks such a strong claim is not true.
Weak Dispositoinalism: If a type of judgement systematically fail to have the thetic direction of fit, this is very good evidence that the judgement is not belief
If normative judgements are beliefs, we expect that they should be at least consistent with Weak Dispositionalism. Especially, if normative judgements are about non-natural properties, they should have tendency to be not held in cases where the evidence concerning the existence of non-natural properites is absent.
Two Arguments against the predicted evidence-sensitivity of normative judgements:
The Arugment from Error Theoretic Reactions
If normative nihilism is true, we always have no decisive evidence for our normative judgements.
Level One: do our normative judgements go out of existence if we embrace nihilism?
→ Many error theorists say no to this issue, on the basis of their own experience. The reason may be this: normative judgements are sensitive to natural features (the cat is being romented, it is experiencing pain, the boys enjoy this fact), not metaphysically suspicious non-natural features.
→ There are some possible answers to both the revisionist and abolitionist reactions.
The Argument from Normative Discovery
The presence of non-natural properties do not have any impact on our normative judgements. But non-naturalists have to hold this view: if one could directly cognize non-natural properties, then one would be disposed to change one's mind to align with whatever is revealed by that direct cognition, regardless of the natural facts, one's attitudes, etc.
A thought experiment: God reveals all the non-natural properties which are exhibited in this world. In this case, we have the direct cognition of non-natural properties. Then, do we change our normative judgements? Bedke thinks we do not, so non-naturalism is false.