The is-ought gap is brought up numerous times in ethical discourse, especially against the likes of, say, natural moral realism. I think the way it is used against these positions is confused though, it doesn’t pose a unique problem to these positions and it’s of little salience. One does not even have to attempt prove you can get an “ought” from an “is”
Now there is no need to go too far into depth into the dilemma which I am sure we are all familiar with but in essence normative facts cannot be reduced to descriptive facts given the dilemma and we cannot go from a descriptive fact to a normative one without sneaking a normative premise in.
As Hume famously observed in A Treatise of Human Nature:
"In every system of morality... I have always remark'd, that the author proceeds for some time in the ordinary way of reasoning... when of a sudden I am surpriz'd to find, that instead of the usual copulations of propositions, is, and is not, I meet with no proposition that is not connected with an ought, or an ought not... [H]ow this new relation can be a deduction from others, which are entirely different from it." (3.1.1)
Here's the thing though, the challenge posed by Hume's is/ought for moral claims actually extends to a bunch of other claims we take ourselves to be justified in making.
The same way no set of nonmoral premises will alone entail a moral conclusion, no set of non-psychological premises will alone entail a psychological conclusion, and no set of nonbiological premises will alone entail a biological conclusion. the premises entail the conclusions only if (seemingly) psychological or biological premises, respectively, are introduced.
Yet we don't assume that in fields like psychology or biology justification is impossible there. While this analogy, of course, doesn't prove our moral claims are justified, it does show that acknowledging the inferential gap (between non-moral and moral facts) doesn't automatically negate the possibility of evidence for moral claims, or dismiss moral realism entirely.
More importantly though, it seems as if the is/ought problem is a trivial one. There are two major interpretations of the is/ought gap:
(1) The logical is-ought gap: One can’t validly infer a prescriptive conclusion from purely descriptive premises in a deductive argument.
E.g.
P1: It is raining
P2: I have an umbrella
C: Therefore, I ought to use my umbrella
(2) The natural is-ought gap: normative properties are totally unlike and non-reducible to natural/descriptive properties
When it comes to the logical is/ought gap, you need not argue that ought claims do indeed follow from purely descriptive premises. Because, similar to what was said before the gap works too well and extends beyond normativity.
Pigden gives the example of trying to argue that X is a hedgehog.
E.g.
P1: X has spikes
P2: X hibernates
P3: X is called sonic
P4. X is part of the Erinaceidae family
C: X is a hedgehog
The conclusion doesn’t deductively follow, as one can’t validly infer from hedgehog-free premises that X is a hedgehog unless you added in a hedgehog premise.
Here, Pigden isn’t saying you can derive an "ought" from an "is", but he’s saying we can also never derive X is a hedgehog from hedgehog-free premises.
According to Pigden, Hume’s is-ought gap observation is just a trivial observation about how deductive logic works rather than an indication of a deeper metaphysical truth, namely, that normative propositions aren’t synthetic. We do not believe that the inability to logically derive "X is a hedgehog" from hedgehog-free premises implies a metaphysical divide between "facts" and "hedgehogs." or that it has any deeper metaphysical implications about hedgehogs. The same is true for morality.
Further consider:
X: is a man
X: has a brother/sister
X: X’s brother/sister has a son/daughter
Therefore, it follows that X is…
???
You probably said it follows that “X is an uncle” but if you are an is-ought gap enthusiast you would know that this inference is illicit unless a hidden premise about uncle’s was contained within the argument
Remember the point is that every valid derivation introducing a new term requires an analytic bridge premise one that already contains that term/predicate (or an equivalent). e.g. an “ought” in the case of morality
In the case of the argument above it would be
P1: X is a man
P2: X has a sibling
P3: X’s sibling has a child
P(implicit): The term “uncle” means a man whose sibling has a child
C: Therefore, X is an uncle
The entire point is one of triviality when it comes to entailment, that is, it’s about whether their introduction in a conclusion requires prior appearance in the premises. So the semantic meaning of “hedgehog” or “good” is superfluous to the formal entailment rule. Even if “hedgehog” has a perfect analytic definition, you still need to include that definition or something equivalent as a premise (implicitly or explicitly) before the inference to “X is a hedgehog” or "x is an uncle" can go through.
Logic is Conservative. In a deductively valid argument, you cannot get out what you didn't put in. Logic doesn't know what a "hedgehog" is; it only knows symbols.
If your premises are about A, B, and C.
And your conclusion is about D.
The argument is invalid. It doesn't matter if D is "Moral Goodness" or "Hedgehogs" or "Batman." If the term wasn't in the premises, it cannot appear in the conclusion without a bridge.
The existence of the gap, then, cannot be used as evidence that moral facts are suspicious. If the gap prevented moral realism, it would also have to prevent "biological realism" or "hedgehog realism." (Yes, these are silly terms, but you get the point being made). Since we accept that biological facts are real despite the logical gap, we must accept that moral facts could be real despite the logical gap.
With that I rest my case
Stay Brilliant,
Remi Kojo
