0. **Introduction**

In the *Treatise of Human Nature*, Hume outlined the ‘is-ought’ problem, sometimes referred to as ‘Hume’s Guillotine’. The idea is that it is not possible to argue validly from ‘descriptive’ statements (about how things *are*) to ‘normative’ conclusions (about how things *ought to* be).* *

Hume describes how he often notices a change that takes place when he is reading certain passages on moral philosophy:

“I am surprised to find, that instead of the usual copulations of propositions,

is, andis not, I meet with no proposition that is not connected with anought, or anought not. This change is imperceptible; but is, however, of the last consequence” (Section 3.1.1)

Examples of this switch include the move from 1 to 2 in the following examples:

A)

- X makes people happy
- Therefore, people ought to do X

B)

- God commands people to do X
- Therefore, people ought to do X

If we want to turn A) into a valid argument, we would naturally want to add another premise, as follows:

- X makes people happy
- People ought to do what makes them happy
- Therefore, people ought to do X

Now the argument is valid. But now the conclusion follows from a set of premises which are not *all* descriptive. Our new premise 2, needed to make the argument valid, is normative (because it is about what ought to be the case, not just what is the case). Therefore, it is not a case of getting ‘an ought from an is’; but of getting ‘an ought from *an ought and an is*‘. Hume’s point is that without the addition of a normative premise, like 2, an argument like A or B cannot be made valid.

We can state the is-ought problem as follows:

*There is no valid argument such that the premises are purely descriptive, and the conclusion is normative*.

A counterexample to this would be a valid argument with purely descriptive premises and a normative conclusion.

1. **A counterexample to the is-ought problem**

Consider the following example:

- The conclusion of this argument is true
- Therefore, we ought to do X

This inference is valid; there is no way the premise could be true without the conclusion also being true. After all, the premise says that the conclusion is true; so the only thing that makes the premise true is the conclusion being true.

The premise is seems to be quite clearly descriptive. It doesn’t include the word ‘ought’ or any synonym of the word.

On the other hand, the conclusion clearly is normative, involving the word ‘ought’ quite explicitly.

This means we have a valid argument with purely descriptive premises and a normative conclusion. This makes it a counterexample to the is-ought principle as stated above. In some sense, it shows that it *is* possible to derive an ought from an is, after all.

Cute, but not actually a counterexample. The reason is that the argument is self-referential. When we try to parse “the conclusion of this argument is true” we have to look at the conclusion; the premise then is “it is true that we ought to do X” and is no longer merely descriptive.

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Reblogged this on jtveg's Blog.

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Hello, Alex. I just finished listening to your conversation with David Smalley, and wanted to offer what I believe is a solution to the is-ought conundrum for you to contemplate. It is not based on “flourishing” or “well-being”, but is perfectly natural. Let me know if you are interested.

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Interesting post. But isn’t this argument exploiting a type of self-referential paradox? Specifically, I think it’s a

, since it’s logically equivalent to the Curry-type sentence:Curry-type paradox“If this statement is true, then F”(where in this caseF := “we ought to do X”).As I understand it, a Curry paradox is self-undermining in that it can be used to simultaneously “prove” any proposition and its negation in ill-founded logics that allow for such paradoxes. This means that a Curry paradox can be used to “prove” any falsehood in any such ill-founded logic (

i.e.,it “trivializes” logics which admit it). For example:“If this statement is true, then China is on the moon and all numbers are odd.”I think that when we make arguments using propositional logic, we assume either (a) that the logic which we’re relying upon is well-founded (

i.e.,it doesn’t suffer from paradoxes which would allow an argument to prove anything, including any falsehood), or (b) that we stay away from such paradoxes by, for example, not resorting to self-referential classes of arguments (which could prove anything, including any falsehood). Otherwise, an argument using propositional logic could be essentially useless.At most, what this “counterexample” demonstrates is that

“an ‘ought’ can be obtained from an ‘is’ “ifwe use an ill-founded logic or a self-referential (and possibly paradoxical) argument. So, it seems that Hume’s is-ought problem remains quite safe in the face of this “counterexample,” provided that we stay clear of self-contradicting logics or statements.Perhaps a statement that overtly avoids these problems (instead of charitably granting to Hume that he was already counting on logical well-foundedness) would make for a more robust Hume guillotine as follows:

“An ‘ought’ cannot be obtained from an ‘is’ in well-founded (non-trivial) logics or in statements that avoid self-referential paradoxes.”To continue with structureoftruth’s line of thought, a Curry-type argument “trivializes” any logic that admits Curry-type paradoxes, by self-referentially asserting a conclusion, so that in order to determine the soundness of a Curry-type argument, one must evaluate the truth value of its conclusion (consequent) independently of the truth value of its asserting proposition (antecedent):

T = T.

In the case of the “counterexample,” the argument is reduced to evaluating the truth of a normative conclusion only, since the premise (antecedent) trivially asserts the conclusion (consequent).

Finally, a possible defeater of the “counterexample” can also avail itself of a Curry-type argument:

1. The conclusion of this argument is true.

2. Therefore an “ought” cannot be obtained from an “is,” regardless of counterexamples.

Or equivalently:

“If this statement is true, then an ‘ought’ cannot be obtained from an ‘is,’ regardless of counterexamples.”As an aside, I wonder if the theistic

omniproperties incur Curry-type paradoxes? Would logics that resolve these paradoxes leave God’s existence in a state of indeterminacy?LikeLike

I agree with structureoftruth and Miguel, but here is a truly valid counterexample:

1. If P is rational, then it is true. (Fact)

2. Value judgement X is rational. (Fact)

3. Therefore, X.

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I can see objections to both premises.

As to Premise 1, I’m not sure what P is, but I would assume that its being both “rational” and “true” means that it is the conclusion of a full-blown argument within some propositional logic under which it can assume a truth value. But a rational argument does not necessarily lead to a true conclusion (think validity yet unsoundness). For example, it may have been rational for ancients to believe that the earth was flat given the information at hand.

Premise 2 is even more problematic as it assumes that value judgments are subject to rationality (i.e., subject to propositional logic and truth values). But this is question-begging, even if one rehabilitated Premise 1 to the tautology

“If P is sound, then its conclusion is true.”For example, is it rational (sound) to push the large man off the bridge to divert the trolley and save 5 people? Is it rational for the doctor to sacrifice a healthy patient without her consent to harvest her organs in order to save 5 other patients? Is it rational for a woman to abort one hour before labor?Hume’s maxim remains safe, I think.

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Yeah, you might be right. By “rational” I probably meant something like “reasonable”. So here’s a rephrased version of Premise 1:

1. If P is reasonable then it tends to be true.

As for Premise 2, about your examples, I would say it depends on whether they are reasonable.

So here’s a rephrased version of my argument which is inductive:

1. If P is reasonable then it tends to be true.

2. X is reasonable.

3. Therefore, X.

(P.S On a sidenote, why is your blog private? Did you get my invite request?)

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Thank you for your response.

You say:

“I probably meant something like ‘reasonable’.”OK, but it seems to me that since it is, after all, your statement, it is you who knows best exactly what you meant (not “probably”) and can make it clear to those of us who read it.I still see possible objections to the rephrased version. You’ve defined “reasonable” as something that “tends to be true,” or is probably true. So again, “reasonable,” just like “rational,” refers to alethic truths. Changing the degree of certainty doesn’t change the nature of the truth value from alethic to normative.

Granting both premises would get you to “X tends to be true,” which means that X tends to have (or probably has) a given alethic truth value. But Premise 2 is again the most problematic. X is a “value judgment,” so can a value judgment be “reasonable” without appealing to value judgments? In other words, how can a value judgment have an alethic truth value (obtained from propositional logic)?

The aim here is to “get an ought from an is” and it seems to me that Premise 2 presupposes that value judgments can have an alethic truth value via being “reasonable” (i.e., more likely than not to be “true”). But this is an unsubstantiated assertion and makes the argument circular.

“…about your examples, I would say it depends on whether they are reasonable.”But that’s precisely the rub, isn’t it? I claim that none of those examples are “reasonable” or “rational;” they are normative value judgments which, to the extent that there’s even agreement on them (there isn’t), cannot be derived using strictly rational processes without resorting to normative “truths.” That’s why they’re “value judgments.”What you have done here, when switching “rational” to “reasonable,” is change the possibility of the truth value of a proposition from certain to probable, but you have not changed the nature of said truth value. It is still alethic and you have done nothing to move the needle towards normative by decreasing the likelihood of the alethic truth value from certain to probable.

In other words, you still cannot “get an ought from a probable is” nor a “probable ought from a probable is” any more than you can “get an ought from an is.” Or if you prefer, you still cannot “get a probable ought from a reasonable is.”

P.S.: Yes I did receive your invite request, thank you for your interest. The reason it’s private is that I don’t have much content worth reading yet, it’s a slow work in progress due to lack of time. Once I think it’s ready to share, I can certainly invite you in for your input.

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>”You say: “I probably meant something like ‘reasonable’.” OK, but it seems to me that since it is, after all, your statement, it is you who knows best exactly what you meant (not “probably”) and can make it clear to those of us who read it.

I still see possible objections to the rephrased version. You’ve defined “reasonable” as something that “tends to be true,” or is probably true. So again, “reasonable,” just like “rational,” refers to alethic truths. Changing the degree of certainty doesn’t change the nature of the truth value from alethic to normative.”

Ok, how about this: reasonable = that which is supported by an argument with evidently or experience or seeming-based well-defined premises.

> “Granting both premises would get you to “X tends to be true,” which means that X tends to have (or probably has) a given alethic truth value. But Premise 2 is again the most problematic. X is a “value judgment,” so can a value judgment be “reasonable” without appealing to value judgments? In other words, how can a value judgment have an alethic truth value (obtained from propositional logic)?

The aim here is to “get an ought from an is” and it seems to me that Premise 2 presupposes that value judgments can have an alethic truth value via being “reasonable” (i.e., more likely than not to be “true”). But this is an unsubstantiated assertion and makes the argument circular.

“…about your examples, I would say it depends on whether they are reasonable.” But that’s precisely the rub, isn’t it? I claim that none of those examples are “reasonable” or “rational;” they are normative value judgments which, to the extent that there’s even agreement on them (there isn’t), cannot be derived using strictly rational processes without resorting to normative “truths.” That’s why they’re “value judgments.”

What you have done here, when switching “rational” to “reasonable,” is change the possibility of the truth value of a proposition from certain to probable, but you have not changed the nature of said truth value. It is still alethic and you have done nothing to move the needle towards normative by decreasing the likelihood of the alethic truth value from certain to probable.”

Ok, so it seems, if I understand you correctly, your objection is to Premise 2 for presupposing that value judgments can be “reasonable”. (As in, using propositional logic?) Are you thinking of, like, cognitivism vs. non-cognitivism?

P.s Fair enough on the blog thing.

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