Many people have said that we cannot derive an 'ought' statement from an 'is' statement. In one sense this is trivially true, in another it is straightforwardly a mistake in logic. I'll discuss this in relation to new natural law theory and the grounding of morality in metaphysics.
First the sense in which it is true. Obviously if the premises of your argument contain no 'ought' statements then you can't logically derive an 'ought' from them. At best you can conclude from the premises that some ought statement is plausible. However, I think most people who want to say we can derive an ought from an is would all agree with this rather trivial observation.
Now some discussion of natural law: On new natural law theory we immediately perceive certain states of affairs as to be pursued, and from this we determine what we ought to do; the states of affairs to be pursued are instances of the 'basic goods', which are immediately recognizable aspects of human flourishing. Now, new natural law theorists say we cannot derive an ought from an is. However, they also say that new natural law theory does not carry any commitments one way or the other as to what, metaphysically speaking, human flourishing consists in or is grounded in. After all, everyone can know the natural law in their hearts, and you do not need to be a metaphysician to gain insight into what's right and wrong. But by the same token on new natural law theory, it should be consistent with the theory to say the human flourishing is grounded or consists in something like, say, the perfection of the human form. New natural law should not rule this out.
What follows from this? Well, if this type of theory is possible on new natural law, then supposing it is true, every aspect of human flourishing will at the very least coincide with some aspect of the perfection of the human form. The details of this perfection aren't that important, since the main point of this post is supposed to be logical. So just take some arbitrary aspect of human flourishing A and some arbitrary aspect of the perfection of the human form P. A and P coincide just means that if one exists then so does the other. Now we can launch an argument:
(1) If P and A coincide then P is an aspect of the perfection of the human form if and only if A is an aspect of human flourishing. [by def.]
(2) P and A coincide [prem]
It follows logically that
(3) P is an aspect of the perfection of the human form if and only if A is an aspect of human flourishing. [from 1 and 2]
From this we can infer by the rules of logic that
(4) If P is an aspect of the perfection of the human form, then A is an aspect of human flourishing. [from 3]
(5) P is an aspect of the perfection of the human form. [prem]
Again by the rules of logic:
(6) Therefore, A is an aspect of human flourishing. [from 4 and 5]
(7) If A is an aspect of human flourishing, then instances of A are states of affairs that ought to be pursued. [by NNL]
(8) Therefore, instances of A are states of affairs that ought to be pursued. [by 6 and 7]
(1) just follows from the definition of 'coincide'. (7) is just what new natural law says. Given the premises the rest follows by the incontestable rules of logic. Now, one might question premise (2) and (5). However, it is at least possible for them to be true given new natural law theory. And if they are true then this argument shows one can derive an ought from an is.
Basically, to say we can derive some statement Q from some set S of premises {P1, P2, ... , Pn} just means that there is a proof of Q from S. This is Logic 101 stuff. Given all the premises and definition in our argument we can derive an ought, namely (8). Our premises, (2) and (5) are paradigm 'is' statements. This is why it is false to say we cannot derive an 'ought' from an 'is' statement.
Here's the upshot for natural law theory: If NNL is true, then it is possible for (2) and (5) to be true. If (2) and (5) are true there's a perfectly good sense in which we can derive an 'ought' statement from a set of 'is' statements. Hence, even if NNL is true, it is possible to derive an 'ought' from an 'is' in the precise logical sense of 'derive' above. The only other possibility is to either say aspects of human flourishing can't coincide with anything, which basically means NNL is inconsistent with certain metaphysical theories of flourishing (viz. all of them), or else we are using some other sense of 'derived' in saying an 'ought' can never be derived from an 'is'. As a person sympathetic to NNL myself I think we should go with the latter (or possibly drop the use of the phrase altogether).
