What do I mean by "morality isn't logical"? I mean in the same sense that mathematics is logical but literary criticism isn't: the "reasoning" we use to think about morality doesn't resemble logical reasoning. All systems of logic, that I'm aware of, have a concept of proof and a method of verifying with high degree of certainty whether an argument constitutes a proof. As long as the logic is consistent (and we have good reason to think that many of them are), once we verify a proof we can accept its conclusion without worrying that there may be another proof that makes the opposite conclusion. With morality though, we have no such method, and people all the time make moral arguments that can be reversed or called into question by other moral arguments. (Edit: For an example of this, see these posts.)
Without being a system of logic, moral philosophical reasoning likely (or at least plausibly) doesn't have any of the nice properties that a well-constructed system of logic would have, for example, consistency, validity, soundness, or even the more basic property that considering arguments in a different order, or in a different mood, won't cause a person to accept an entirely different set of conclusions. For all we know, somebody trying to reason about a moral concept like "fairness" may just be taking a random walk as they move from one conclusion to another based on moral arguments they encounter or think up.
In a recent post, Eliezer said "morality is logic", by which he seems to mean... well, I'm still not exactly sure what, but one interpretation is that a person's cognition about morality can be described as an algorithm, and that algorithm can be studied using logical reasoning. (Which of course is true, but in that sense both math and literary criticism as well as every other subject of human study would be logic.) In any case, I don't think Eliezer is explicitly claiming that an algorithm-for-thinking-about-morality constitutes an algorithm-for-doing-logic, but I worry that the characterization of "morality is logic" may cause some connotations of "logic" to be inappropriately sneaked into "morality". For example Eliezer seems to (at least at one point) assume that considering moral arguments in a different order won't cause a human to accept an entirely different set of conclusions, and maybe this is why. To fight this potential sneaking of connotations, I suggest that when you see the phrase "morality is logic", remind yourself that morality isn't logical.
I'd split up Eliezer's view into several distinct claims:
A semantic thesis: Logically regimented versions of fairness, harm, obligation, etc. are reasonable semantic candidates for moral terms. They may not be what everyone actually means by 'fair' and 'virtuous' and so on, but they're modest improvements in the same way that a rigorous genome-based definition of Canis lupus familiaris would be a reasonable improvement upon our casual, everyday concept of 'dog,' or that a clear set of thermodynamic thresholds would be a reasonable regimentation of our everyday concept 'hot.'
A metaphysical thesis: These regimentations of moral terms do not commit us to implausible magical objects like Divine Commands or Irreducible 'Oughtness' Properties In Our Fundamental Physics. All they commit us to are the ordinary objects of physics, logic, and mathematics, e.g., sets, functions, and causal relationships; and sets, functions, and causality are not metaphysically objectionable.
A normative thesis: It is useful to adopt moralityspeak ourselves, provided we do so using a usefully regimented semantics. The reasons to refuse to talk in a moral idiom are, in part thanks to 1 and 2, not strong enough to outweigh the rhetorical and self-motivational advantages of adopting such an idiom.
It seems clear to me that you disagree with thesis 1; but if you granted 1 (e.g., granted that 'a function that takes inequitable distributions of resources between equally deserving agents into equitable distributions thereof' is not a crazy candidate meaning for the English word 'fairness'), would you still disagree with 2 and 3? And do you think that morality is unusual in failing 1-style regimentation, or do you think that we'll eventually need to ditch nearly all English-language terms if we are to attain rigor?
RobbBB probably knows this, but I'd just like to mention that the three claims listed above, at least as stated there, are common to many metaethical approaches, not just Eliezer's. Desirism is one example. Other examples include the moral reductionisms of Richard Brandt, Peter Railton, and Frank Jackson.