The Euthyphro Dilemma Reconsidered

Mike Arnautov, February 2007-December 2008

Synopsis

While in its original context of ancient Greece the Euthyphro Dilemma is fully valid, its status as a dilemma is far less obvious in other contexts. The main argument of this paper is that within the specific context of Christian beliefs, there is no such dilemma.

A disclaimer

In this paper I attempt to present an argument from a stand-point of a Christian believer. This should not be construed as representing my personal stand-point. I develop the argument in the spirit of "maximal charity", in interpreting doctrines of Christian belief in a way which seems to me make most sense.

I urge any readers to read the below in the same spirit.

Dilemma statement

The so-called Euthyphro Dilemma (further just Dilemma) is stated in Plato's Euthyphro dialogue as the question whether some action is

(S1) right because it is what the gods command or
(S2) right and therefore the gods command it

This is seen as a dilemma in that one and only one of these two alternatives can be correct.

Other Alternatives

While it is true within the confines of Greek theology that one and only one horn of the Dilemma can be true, I suggest that once we step outside those confines, we should entertain the other two logical possibilities: neither of the two horns being true, as well as both being true.

The first of these additional alternatives is trivially acceptable to an atheist. However, it simply denies the Divine Command theory, and thus cannot be discussed within the framework of the theory.

The status of the second alternative, that of both S1 and S2 being true, is less clear. It seems to me that from the point of view of a believer in the Christian God (just God in further discussion), it represents the actual state of affairs.

Some definitions and a clarification

For the purposes of this discussion I shall use the following definitions:

Ag is the set of all actions commanded by God

Ar is the set of all right actions.

We also need to clarify the expression "commanded by God". There is clearly no implication of God somehow manifesting himself in order to deliver an explicit command to a believer. When a believer says "God commands action A", he means "It is my belief (a justified belief, as far as I am concerned) that A is in accordance with God's will, whereas ¬A is not". Just how such a belief is justified (personally or collectively) in a religious context, is a much broader question, outside the scope of this discussion.

A formal restatement of the Dilemma

Given the above definitions, the two horns S1 and S2 of the Dilemma can be reformulated as follows:

S1: Ag ≡ Ar, i.e. Ar is defined as being synonymous with Ag.

S2: Ag ⊆ Ar, i.e. Ag is a subset (proper or otherwise) of Ar.

This formulation makes explicit the fact that S1 and S2 differ in their logical character. While S1 defines one of the two action sets by means of the other, S2 defines neither of them. In particular, S2 does not preclude Ag ≡ Ar without this effective synonymy obtaining directly by definition.

It is therefore incorrect to argue that asserting both S1 and S2 effectively amounts to asserting P and ¬P. The logical structure of the Dilemma is more complex than that.

Salient Christian doctrines

I base my assertions regarding the status of the Dilemma in the Christian context on three doctrines, which are taken as axiomatic by most Christian believers:

  • God is the ultimate summum bonum ('greatest good').
  • God is both the transcendent creator and the immanent God of his creation.
  • Time is a part of God's creation, and hence God stands outside time and is not himself subject to change.

Possible objections

As far as I am aware, to argue for the possibility of S1 and S2 being both right, I need to deal with three objections:

  1. In the context of S1, actions in Ag need not be necessarily right. God may command different actions in different possible worlds.
  2. In the context of S2, Ag and Ar may not be identical - Ag may be a proper subset of Ar. In other words there may be right actions which are not commanded by God.
  3. In the context of S2, If an action is objectively right, then its rightness is a sufficient justification for the action – God's command is irrelevant and can/should be dispensed with.

I hope to demonstrate that within the specific context of Christian belief none of these objections are valid.

Replying to Objection 1

A Christian believer must maintain that all action in Ag must be necessarily right, i.e. right in all possible worlds.

This is a tricky ground and great care should be taken with the exact meaning of the term "possible worlds", which is only too often conflated with the term "conceivable worlds". Blurring the distinction between the two can lead to much philosophical fun (be it intentional or not 1), but a belief in God implies some considerable constraints.

God is both the transcendent creator and the immanent God of his creation. In this his status is very different from that of Greek gods, who are simply usurpers in a pre-existing creation. Furthermore, as has been discussed by theologians over centuries, within the confines of his creation, God is bound by the logic of that creation.2

Furthermore, God is the sole source of all creation. The act of creation necessarily encompasses all that actually exists, existed and will ever exist, including this universe and its entire history, as well as any other universes that may or may not exist, including Heaven, Hell, Limbo, Purgatory and any other putative "planes of existence". The act of creation also creates time and is thus an act outside time. Like everything else, the distinction between right and wrong in that all-encompassing creation is simply an expression of God's nature.

Being by definition summum bonum, God could not have possibly created a world ruled by evil. Such a world may be conceivable in human imagination, but this does not make it actually possible. To assume otherwise, would be tantamount to admitting the possibility that the distinction between right and wrong is not fundamental to God, in which case incompatible ethical values may arbitrarily apply not just to different worlds, but to different continents (e.g. Aztec and Christian religions faithfully expressing the will of the same creator), to different countries, or indeed to individual human beings.

Hence for a Christian believer that which is right, is necessarily right in all existing worlds. This still leaves us with the question whether it is also right in all possible, but not actually existing, worlds.3 In other words, the question is whether God could have (but did not) create a "multiverse" based on ethical values incompatible with those built into the "multiverse" he actually created. It is hard to see how a believer in God could entertain this possibility, since it would flatly contradict the summum bonum nature of the unchanging, transcendent God.

Replying to Objection 2

The above discussion also provides the ground-work for my response to the second objection.

I have already dealt with a somewhat frivolous form of that objection, namely that God may arbitrarily choose not to command some actions which are right. There is no expectation on a believer's part that God would actually say what should or should not be done. God's commandments are generally understood as being apprehended by believers in some way – either as individuals, or as a part of a community of believers.

In its serious form this objection assumes that it is possible for an action to be right without it being desired by God. But as already argued above, this contradicts the status of God as the transcendent creator of all that is and/or of his axiomatic (to a Christian) summum bonum nature. in fact, we can now see that in the Christian context the first two objections are in fact one and the same.

Replying to Objection 3

On the face of it, this objection is the most serious one. It seems very hard to argue against its logic: if some action is right in itself, God commanding it would indeed seem to be quite superfluous. However, this logic is based on an unstated assumption, which on examination does not appear to be sustainable. The objection assumes that we can by some unspecified means discover or deduce all right actions without recourse to a divine revelation of some sort.

Let us be honest, even those of us, like myself, who believe that it is possible (at least in principle) to uncover a naturalistic basis for our sense of morality and ethics, have to admit that this is very much a work in progress. We can invoke evolution (both genetic and memetic – or if you prefer biological and cultural), but we cannot be sure that this meta-Darwinian basis can be used to underpin our sense of right and wrong in its entirety. The boundary between right and wrong is notoriously "fractal" ("infinitely complex") in its nature, as a consequence of the non-monotonic character of real-world logic. 4

To a believer there is no such problem. Our sense of right and wrong is given to us (is commanded) by God. Irritating as this is to an atheist, believers are quite sincere, and within their world-view entirely justified, in being convinced that only God can be the ultimate source of that sense. Yes, the distinction between right and wrong is objectively valid, but we are not equipped to perceive this distinction without God's explicit or implicit assistance. This is no more controversial than an architect, having designed a bridge with a particular load-bearing capacity, subsequently acting as a consultant in the matter of unavoidable load-bearing limits of the bridge.

A thought experiment

Here is a thought experiment which may help to clarify my response to the third objection.

Imagine that the Bible also contains an 11th commandment: "Thou shalt know the Continuum Hypothesis to be true". Since the Continuum Hypothesis is known to be an undecidable proposition5, its status cannot be deduced from prior mathematical principles, but this does not preclude the possibility of somebody constructing or discovering an example of an infinite set with the cardinality higher than that of natural numbers and lower than that of real numbers, thereby disproving the hypothesis in practice.

However, if the Continuum Hypothesis is necessarily true (which may be the case) and if its truth happens to be somehow morally meaningful, then what we have is an objective moral truth, which must also be commanded by God in order for us to be aware of it.6

Conclusion

In summary, while Socrates was entirely correct in postulating the dilemma (as reported by Plato) within the Greek cultural context, I believe that once we step outside that context, two solutions become possible:

An atheist simply rejects both horns of the dilemma as being mistaken.

A Christian believer can justifiably claim that there is no dilemma, because its putative horns are for him entirely compatible.

- o O o -


1 E.g. philosophers often wrongly assume that the Many Worlds Hypothesis would imply the existence of all conceivable worlds. Even such an astute thinker as Daniel Dennett makes a related error in considering the notion of "nearby" possible worlds, in "Freedom Evolves", by explicitly assuming that the Big Bang event could be rearranged to result in any arbitrarily minimal change in a particular set of events.

2 One should not oversimplify this issue, too often exemplified by self-contradictory constructions, such as, e.g., four-sided triangles. Since the definition of a triangle is context-dependent, there is no difficulty in exhibiting such a "paradoxical" figure by simply stepping outside of its usual Euclidean context. Such demonstrations should not be dismissed as mere trickery – they point to fundamental issues in these matters, ultimately rooted, I believe, in the dichotomy of the Platonic and the Aristotelian conceptions of the world.

3 Remember, "existing worlds" are not restricted to our singular universe, but encompass everything in God's creation, including, e.g., the infinitely many worlds of the Many Worlds Hypothesis, should that hypothesis turn out to be true.

4 Stanford Encyclopedia of Philosophy ( http://plato.stanford.edu/entries/logic-nonmonotonic/): 'The term "non-monotonic logic" covers a family of formal frameworks devised to capture and represent defeasible inference, i.e., that kind of inference of everyday life in which reasoners draw conclusions tentatively, reserving the right to retract them in the light of further information. Such inferences are called "non-monotonic" because the set of conclusions warranted on the basis of a given knowledge base does not increase (in fact, it can shrink) with the size of the knowledge base itself. This is in contrast to classical (first-order) logic, whose inferences, being deductively valid, can never be "undone" by new information.'

5 See Standard Encyclopedia of Philosophy: http://plato.stanford.edu/entries/continuum-hypothesis/

6 Interestingly enough this thought experiment also demonstrates why the unchanging, transcendent moral reality of God may unfold in our world as a process in time. The Continuum Hypothesis commandment is meaningless without Cantor's conceptual framework of cardinalities. So if the set of all actions commanded by God happens to contain actions not applicable to us (but applicable to any or all of angels, archangels, thrones and principalities), this may be simply because we do not yet have the means to comprehend them, and as such they have no bearing on the Euthyphro Dilemma.


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Mike Arnautov (23 December 2016)