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TheOtherDave comments on A wild theist platonist appears, to ask about the path - Less Wrong
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What a great question! Traditionally, the operations performed on a god are:
None of these, except the last one, could be performed on a god-as-a-mathematical-like-entity, I think.
Well, I can certainly ask the number two for goods and services, so if that's a useful operation to perform, there ya go.
My chances of receiving those goods and services won't increase if I do so, but that's something else again.
Similarly, I can ascribe mysterious feelings and special mind states to the influence of a mathematical structure, thank it for the blessings of existence, base my feelings of security and purpose in life on it, and (as you note) invoke it to avert metaphysical questions.
I admit, I don't quite understand how to ground morality on a mathematical structure, but then I don't quite understand how to ground morality on a traditional god, either. (I recognize that many people claim to do this.)
I've never quite understood how grounding morality on a traditional god is supposed to work.
Well then, you could also multiply gods by constants and add them together, producing a vector space over a divine basis.
Grounding morality works straightforwardly, I think: God said thou must not kill, love thy neighbour, etc.
Well, yes, I understand that various commands, preferences, etc. are ascribed to gods, and that followers of those gods attempt to obey those commands and satisfy those preferences.
I've just never understood what morality has to do with any of that.
I mean, sure, presumably a suitably knowledgable (let alone omniscient) god is capable of giving moral commands, in that it would know what the moral things to do are, in the same sense that it is capable of telling me what stocks to purchase in order to maximize my earnings, or how most efficiently to breed cows. But to conclude that therefore wealth, morality, or cow-breeding is grounded on god (in a way that poverty, immorality, and cow-genocide, for example, are not) has always seemed odd to me.
(Divine command theory, where you obey God because He's God as such (and not because He's God and He commands things because they're good), is not the most popular way to tie God into your meta-ethics, and it has various semantic problems. In better-justified meta-ethics God is useful as a necessary final cause of existence but it's not immediately derivable what properties He has that make Him a justified final cause, nor how we as creatures should orient our actions towards Him—these are matters of ethics that are somewhat decoupled from "grounding" morality in God in a higher level sense. God is used in such meta-ethics in a way similar to how an oracle machine is used in theoretical computer science, that is, He's an important part of a larger interconnected framework. One can't evaluate theistic meta-ethics without knowing what the other parts are.)
Yeah, the better-justified version you describe strikes me as, if not necessarily better justified, at least more intelligible.
That said, now that I think about it a bit more, I'm enough of a consequentialist to have serious difficulty thinking straight about what it even means for a choice to be moral in the presence of a force capable of, in practical terms, divorcing my actions from their consequences. (Of course, not every theistic theory posits such a force, and it is possible to be in that position in a nontheistic context as well.)
I might quibble about your use of "popular" above, though, unless you really do mean it advisedly.
That is, it seems likely to me that Divine command theory is indeed the most popular approach, in the same sense that the most popular theory of ballistics predicts that when I drop a rock as I walk down the sidewalk, it will hit the ground a step or two behind me even though no halfway serious student of ballistics would predict any such thing. (Modulo extreme winds, anyway.)
But I'd love to be wrong about that.
I don't know what meta-ethics are held by the Christian masses—does it actually come up very often?—but Catholic doctrine tends strongly towards Thomism, which isn't divine command theorist, and Catholicism is the largest sect of Christianity. I suspect that most Catholics would be dimly aware that divine command theory isn't quite right, upon considering the issue. I don't think that my "average Catholic" friend has ever considered meta-ethics in a detailed enough way such that she could distinguish between divine command theory and some alternative meta-ethical theory. After all, in all theistic meta-ethics morality stems from God in some sense, it's just the exact way in which it does so that is contentious. The sort of distinctions that are necessary to make are I believe quite beyond the philosophical competencies of your average Christian.
I think it goes something like this: (1) God created morality and cow-breeding, and (2) put the knowledge of it into humans [or, alternatively, the knowledge of morality was the result of eating the apple and knowing Good and Evil, I'm not sure], and (3) one of the important points of morality is that humans should have free will, and so (since God is moral) they do, and thus (4) they are free to practise immorality and cow-genocide.
If game-theoretic principles (like Nash-equilibrium) are mathematical structures and contractarianism (such as Gauthier's ethical theory) is true, then mathematical structures "ground morality".
Morality consists of courses of action to achieve a goal or goals, and the goal or goals themselves. Game theory, evolutionary biology, and other areas of study can help choose courses of action, and they can explain why we have the goals we have, but they can't explain why we "ought" to have a given goal or goals. If you believe that a god created everything except itself, but including morality, then said god presumably can ground morality simply by virtue of having created it.
Yeah, that is the dominant view, but Gauthier actually attempts to answer the question "why be moral?" (not only the question of "what is moral?") using game-theoretic concepts. In short, his answer is that being moral is rational. I don't remember whether or not he tries to answer the question "why be rational?"; I haven't read Morals by Agreement in years.
There are (at least) two meaning for "why ought we be moral":
I can imagine answers to the second question (it could be that explicitly replacing X with Y results in achieving X better than if you don't; this is one driver of extremism in many areas), but it seems clear that the first question admits of no attack.
An entity without goals would not be reading Gauthier's book.
Well, look at things like TDT/UDT for starters.
Though TDT and UDT weren't designed to be moral as such; it just turns out that non-self-defeating behavior seems to necessitate some degree of something like morality, largely because self-ness is a slippery idea.