In order to define a notion of "good" and "evil" which is not personal or cultural, one which is transferable and agreed upon by different people, one finds that one needs to introduce a concept which is sufficiently close to the notion of God that it might as well be identified with it. In order for the decisions which comprise the absolutely good actions to be self-consistent in all possible circumstances, and to be consistent with mutual pre-recognition of the existence of an ethical universal, the strategy in the game must be that which maximize a utility function. God can be defined as the entity whose utility is this function.
This conclusion follows from the assumption that the absolute morality is complete--- so that every circumstance has a best-action associated to it, that it is transitive, so that if outcome A is preferable to outcome B in game 1, and B is prefered to C in game 2, then A is always preferred to C, and that the morality is continuous--- so that mediocre is a probabilistic mixture of better and worse. These axioms guarantee that there is a consistent rational utility associated to all games, which means that one might as well imagine that the preferences of the absolute ethics reflect the desire of a perfectly rational being.
the point here is that rational entities with a consistent aximoatic utilitarian ethics (imagine a planet Vulcan populated with Spocks), free of empathy for others, emotional instincts regarding ethics, or ability for transcendence or revelation, can still formulate a notion of God just from their own personal utilities and the superrational strategies they devise to maximize their utility. This needs a long argument, because the notion of utility plus the notion of self-interest (as maximized through superrationality) is not at all intuitive, and conflicts with other notions of rationality which do not make decisions which can be consistently intepreted as the desires of a consistent super-entity. The appropriate super-entity defined in this way is, excluding miracles, meddling, and universe-creation, identical in the logical positivistic sense to the God that religious people identify.
This definition makes God a meta-entity, a construction belonging to mathematical ethics, which has as much power to influence the world as the number π. The number π can't smite you for mis-measuring the circumference of a circle, but in some abstract way, it ensures that this circumference is consistent with the diameter, and if you don't use the right value, you will be in trouble.
The definition above means that God's utility is maximized when humans act absolutely goodly. It is minimized when humans act absolutely badly. The existence of a consistent utility is the sign of a rational entity, and the perfection of this entity, the omniscience, is due to the self-consistency requirement of rationality. This notion lives outside of space and time, it is in the same Platonic realm in which the number π lives. Whether you choose to believe in the existence of this realm or not is logically positivistically meaningless, the consistency of the absolute ethics is either there or not, and the property of "existence", either of God of of Pi, does not change the outcome of the reasoning which uses these concepts.
Once you understand the divine ethics, you can choose to live by these ethics, or you can choose not to. Nothing is compelling you. But I think it is very silly, and inhumanly evil, to consistently choose not to.
I don't want to use loaded words here, so I will distinguish between different conceptions of God.
- Supernatural God: This is an entity which performs miracles, violates the laws of nature. For example, "I prayed to Supernatural God, and my cancer went away!".
- A Demiurge: will be an entity which is given responsibility for creating the universe.
- Ethical God: will refer to a decision making entity whose utility function is absolute good.
The traditional monotheistic religions identify the last two concepts with one all-powerful supernatural God. This makes faith a tough pill to swallow, because the notion of supernatural events is not compatible with scientific rationalism, and the idea of a creator is not compatible with logical positivism.
I will ignore the notion of Demiurge, because I cannot give any logical positivistic meaning to the statement "X createdthe universe". I cannot see how to reduce it to sense perception, or to mathematics, or to anything at all, so it just sounds like a gibberish statement which you are free to believe or disbelieve, since it doesn't change anything about anything.
Regarding Supernatural God, I will follow scientific convention and take it for granted that there are no supernatural events. It is not reasonable to rationally accept supernatural events, since a simple probabilistic evidence should convince one that any evidence for supernatural events, including evidence of one's own eyes, is practically infinitely more likely explained through misperception or deception, rather than by any deviations from natural law. If you have ever seen a magic show, you will know what I mean.
But neither the Demiurge nor the Supernatural God as particularly important when discussing the practical implications of religion. So I will try to focus on the ethical God, to see to what extent this concept is meaningful in light of logical positivism, and to what extent it is a correct conception of an ethical absolute.
To not hide the conclusions, I believe that the ethical notion of God is meaningful positivistically, and one can be reasonably certain that it exists, in the same way one is certain of the existence of π, and that it is essential in guiding ethical actions to make use of this concept.
Without this notion, or something equivalent, one cannot give meaning to right and wrong, beyond the meaning of aesthetic quality or of pleasure and pain, which are the philosophies found in nietzsche, or earlier expounded by Sadian villains.
It is impossible to study physics without the idealized frictionless plane, nor to study mathematics without counting. Likewise, to analyze ethics, one must start with idealized simplified situations which are maximally enlightening.
Consider a prisoner's dilemma with payoffs as follows: if the two players cooperate, they get a large reward ($1,000,000 dollars). If one player cooperates and the other defects, the cooperating player gets nothing, and the defecting player gets a miniscule addition reward for defecting (d gets $1,000,001, c gets nothing). If both defect, both get a miniscule reward (both get $5).
Under these circumstances, as in any prisoner's dillema, there is a unique Nash equilibrium, which is to defect. Each player is better off defecting holding fixed what the other player does. Assuming neither player cares about the other (so that the other person's reward does not affect your utility), the economic solution is defection.
That this solution is not reasonable is obvious. It is manifestly ridiculous to assume that anyone would want to press the button in this circumstance, rather, they would not press in the hope that the other person would not too. This type of behavior is consistent with magical thinking--- it suggests that the player who does not press thinks that this will lead the other to not press too. This means that using magical thinking, you can argue that one should not push the button, and two magical thinkers will outperform two cold rational economists in this situation. This shows that there are situations where it is advantageous for both parties to be magical thinking.
But the action does not require magical thinking to be sensible, and this is important, because magical thinking is incompatible with scientific rationalism.
The prisoner's dilemma is fundamentally ill-posed. One cannot know the "right" answer to maximize your payoff without knowing something more about the situation and your hypothetical opponent, because your actions can be correlated with your opponent's, without any causation, just from their mutual rationality. You can't know the answer in this case without knowing the extent that rational decisions can be correlated without causation, and to what extent one is supposed to take this into account in the decision.
Rational decisions regarding a specific mathematical problem are usually 100% correlated. If you perform a multiplication, say 18*96 and another person in another room performs the multiplication too, you can know that your two answers are very likely to be the same without knowing what the answer is. If you extend this to a symmetric game situation, you can know that the result of your mental calculation regarding the prisoner's dilemma above is going to be the same as your opponent's, even without knowing what the answer is.
But knowing that the two answers are the same, you can then ask: which of the two answers maximizes my utility, assuming that it is known in advance that the two answers are going to be the same? The answer is to cooperate. The assumption that one should maximize the utility after first assuming that the answer will be the same in a symmetric situation is called "superrationality" by Hofstadter, and it defines a second self-consistent mode of behavior in a symmetric game.
I will call the standard Nash-equilibrium rationality used by economists "Nash rationality".
In order to determine the superrational strategy in a prisoner's dilemma, one must know something about your opponent. If the opponent is Nash-rational, the superrational strategy is to defect (since this maximizes your payoff, assuming all superrational players play it--- which tells you nothing about your Nash-rational opponent). A superrational player playing against an irrational button avoider (a really stupid person who just miscalculates the payoffs, or something like that) will also defect. But a superrational player playing against a superrational opponent will cooperate.
If the opponent has probability p of being superrational, and you are superrational, and further, you know that you had a probability 1-p of being replaced by a Nash-rational person, then as long as p>.000001, the superrational strategy is to not push the button.
Suppose that you play a symmetric game which is not a prisoner's dilemma. There is a button in two rooms, if you both push the button, you both get $5. If you both don't push, you both get $10. If one of you doesn't push and the other does, the button-pusher gets $1,000,000, the other gets nothing. What is the superrational strategy?
In this case, the superrational strategy is to flip a coin and push the button with probability 50%. This maximizes your payoff assuming the strategy is correct.
When there are N players, and the huge reward goes to the one who pushes the button only under the condition that this person is alone in doing so, the superrational strategy is to push with probability 1/N. Again, the solution is probabilistic, even when the game is determined.
I will assume for the remainder of the discussion that the superrational strategy is the absolute ethical one for a perfect symmetric game, and that there is no other mode of behavior which is acceptable, not even Nash rationality.
Different forms of superrationality
suppose that one considers a community of players that know the concept of "superrationality", but call it by a different name. Say they call it "holy-righteousness". They will not defect in a prisoner's dilemma when playing against another holy-righteous player, because they are confident in the shared superrationality of the super-righteous.
Suppose that there is a second community of players, the divine-action players, who also cooperate against each other. However, the two communities are not sure that the two strategies are actually the same between the two communities, because the two have different metaphysics for their ethics.
Under these circumstances, it is possible for players in communities to cooperate with each other, but not with other players in other communities, whose rationality mode is not compatible in certain ways. This is a breaking of symmetry, and when the symmetry is broken, even the existence of the superrational strategy is not so clear.
Simple asymmetric superrationality.
In order to generalize the concept to asymmetric games, I will define a religion.
A religion will be defined as an algorithm which gives you an consistent set of instructions regarding the correct play in all possible games, given the utility and payoff outcomes for the players. I will assume that the utilities come from the individual, and so are not influenced back by the religion, and this makes the definition somewhat different from the traditional colloquial idea. In the colloquial sense, a religion doesn't only tell you how to play, but what to want while you are playing.
A supperational religion is one which dictates cooperation in a symmetric prisoner's dillemma against other players of the same religion. The predictions of a superrational religion are those of superrationality regarding all symmetric games.
The first example of a religion is Nashism:
- Nashianism: play at the Nash equilibrium, and expect all other players to do so.
Nashism is not a superrational religion.
The strategies of a superrational religion R will be assumed to obey some consistency axioms, which are parallel to those of the Von-Neuman Morgenstern utility theorem. If there is a game G with N players, each with M options apiece, the outcomes of MN possible plays can be rank ordered by R, by asking what is the preferred strategy when (an arbitrary) one the players can choose between two of the outcomes. Since R is the universal strategy for all the R-players, the outcome should be the same no matter which player has the choice. The order of preferences of the outcomes defines the utility order of R.
Further, you introduce the Von-Neumann Morgenstern axioms for the utility of R, so that R can order two probabilistic options consistently, and you find that any consistent superrational religion R associates a real-valued utility with each decision, so that it makes sense to say R prefers outcome A twice as much as outcome B.
So this is the ethical gods proposition, a trivial corollary of Von-Neumann Morgenstern utility theorem.
If the preferences of R satisfy:
- Completeness: any two outcomes A and B either A is preffered to B, B is preferred to A, or A and B are equally preferred.
- Transitivity: if A is preferred to B and B is preferred to C, A is preferred to C.
- Probabilistic balance/Continuity: if A is preffered over B, which is preferred over C, then there exists a unique probability p such that A with probability p and C with probability 1-p is equally preferred to B.
Proposition: Any religion R has a utility function for all circumstances which is maximized when all players play according to this religion.
The entity whose utility is maximized by R will be called the R-god. The R-god has wants and desires, the same as a person does. It is important to note that while humans can behave irrationally, the gods of superrational religion can be perfectly rational, as they are Platonic idealizations.
Natural R-gods are utilitarian strategies, defined by a Rawlsian symmetrization of any given game, so that the players are equally likely to play in any position. This strategy will maximize the strict sum of the utility of the players, normalized by some measure, which defines how you make the Rawlsianism precise. The identity of superrational Rawlsianism and sum-utilitarianism is not obvious, and leads to many fascinating questions.
Nashian strategies are not superrational, and do not need to maximize the utility of anything.
Gods and God
The gods now have interactions with each other, in that there are games which involve gods playing games. These circumstances arise when a class of players of religion R play against a class of players of religion S. In these circumstances, one can argue that the Gods themselves, if acting superrationally, should play in accordance with higher Gods.
The definition of God is the ultimate limit of all the Gods, the entity whose utility is maximized when all the players in every game play ethically. This idea is not completely precise as stated, because the notion of God also feeds back to demand the utility of the players themselves should be modified, to take into account the utility of God.
But the basic idea is that rational ethics is religious ethics, at least in the logical positive way, excluding miracles.
I have left out Rawlsian considerations for symmetrizing asymmetric games (by altering your role), and many counterintuitive examples, but this is the basic idea.