I’m currently reading The Myth of Morality by Richard Joyce. In the summery section of chapter three he presents a central argument thus:
1. If x morally ought to Ø, then x ought to Ø regardless of what his desires and interests are.
2. If x morally ought to Ø, then x has a reason for Øing.
3. Therefore, if x morally ought to Ø, then x can have a reason for Øing regardless of what his desires and interests are.
4. But there is no sense to be made of such reasons.
5. Therefore, x is never under a moral obligation. (p. 77)
This argument is not valid under a straightforward interpretation. However Joyce earlier clarified the structure of the argument. He stated that the form is:
1. If P, then Q
2. If P, then R
⊢ 3. If P, then (Q and R)
4. Not (Q and R)
⊢ 5. Not P. (p. 42)
However this does not correspond well to the words above. First, notice the wording in (3). It is “can have”, which expresses a possibility, not an actuality like (2) does; “has a reason”. (3) should be either reworded (probably the best solution) or the formalization changed to ◊R (“it is possible that R”).
Second, (4) does not correspond very well to the formalization at all.
Third, (5) contains the word “never” which is a temporal concept not found in any of the other premises. Indeed they don’t feature temporal words at all. Accordingly, the wording of (5) should be changed or the formalization changed (to something like GQ, using these formalization keys). If we ignore the word “never” in (5), then the argument is valid even though (3) is a about a possibility instead of an actuality. This is of course because (∀P), from P, ◊P follows. (P→◊P is a theorem of S5)
So, given the above, I think that Joyce is a bit careless. More careless than professional philosophers should be. Especially a professor!
Never isn’t temporal. It’s the opposite of “always”. The opposite of ∀x[P(x)] is ¬∃x[ P(x)]. If P(x, y) means “x is morally obligated to y”, then “x is never under a moral obligation” is ¬(∃x.∃y [P(x, y)]), i.e., there are no x and y such that P(x, y). Premise 4) is straightforward enough, if you deign to read what it says: such reasons are nonsensical. They’re either like “xcdghds” or like square circles and in neither case can they be coherently said to exist. 3) is obvious enough, since P entails possibly P.
There’s a reason philosophers usually write in plain text, rather than in logical formalism. It’s easier to read and write. Writing philosophy for machines rather than people to read, now that would be careless of a professional philosopher.
Regardless of formal validity and in plain text: Premise 1 sounds unsound to me. At least it’s not at all trivial.
best regards
Simen,
It is true that there are some cases where “never” and “always” are not temporal, but they are often temporal. Using the word where it is not clear which it means is sloppy/careless.
You may have got the formalism wrong. What does “opposite” mean? The negation of (∀x)(Px) is not ¬(∃x)(Px). The negation is ¬(∀x)(Px) which is l. equivalent to (∃x)(¬Px). See this for a ref:
https://emilkirkegaard.dk/en/?page_id=1807
Also note that his notation was in propositional logic, but predicate logic. Though it should have been in predicate logic.
If you read P4 literally, the argument is invalid.
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Søren,
Premises are not sound or unsound. Arguments are. For a justification of the premise, I suggest that you read the book, of course. :)
Emil,
If you intend to do academic philosophy, deliberately reading fellow philosophers uncharitably isn’t going to make you any friends. I think it’s quite clear what Joyce means, and I’m willing to bet most philosophers would also find the wording unobjectionable.
The opposite is not the same as the negation. Since you like absolute clarity, let’s put it this way: “none” is the antonym of “all”.
Søren,
If I recall correctly, Joyce spends some time justifying his premises. It’s just that Emil cut off the context, because he’s interested in the argument’s validity, not its soundness. The premise is intended to capture the idea that, say, if I happen to enjoy murder (and so have a reason to murder), murder is still morally wrong. If the moral wrongness of murder depends on whether I like murder or not, morality doesn’t amount to much. And if the moral wrongness of murder is not a reason not to murder, then morality, again, is pretty vapid. Moral realists, whom Joyce is arguing against, don’t want an amputated, inert morality that is incapable of motivating anyone. If X’s moral obligation not to murder depends on X’s desires, culture, beliefs, interests, goals, and so on, morality collapses into some kind of anti-realism or relativism; that means objective morality is a myth, and Joyce has proven his point.
Simen,
But then of course I am not deliberately misreading him. What he wrote is arguably badly written. That is my complaint.
“Opposite” is ambiguous and can mean many things like negation. I did not know what you meant. I don’t know what the relation between (∀x)(Fx) and (∀x)(¬Fx) is called, but let’s call it opposite then. Then you are right. Since ¬(∃x)(Px) is l. equivalent to (∀x)(¬Fx).
I agree with your summary of Joyce’s work (as far as I have read, anyway).
@Emil:
My bad, I’m not that used to arguing in English. Let me rephrase: Premise 1 sounds false to me. One sighted focus on formalism can sometimes shadow the philosophical substance, you know… If you’re interested in a debate on morality some day it would be cool ;)
@Simen:
Thanks. Your murder-example is obviusly intuitvely correct. But I think it’s a jump to conclusion from such an intuition to say that desires and interests are completely irrellevant to moral imperatives. Some (like me) would say that moral truths have to do with ideally informed interests from an impartial perspective. This would be a kind of realism much ad modum Railton. And such a model could easily contain your murder-intuitions, I think. Perhaps even explain them.
All best