Possible Logical Error in Euthyphro?

Question

There is an argument near the beginning of Euthyphro that Socrates tries to make to Euthyphro in which I believe that Socrates makes a logical mistake. It's a pretty basic mistake, so rather than assume that Plato made such a simple error, I'd like to ask everyone here what they think. All quotations are taken from G. M. A. Grube's translation of Euthyphro in Plato's Complete Works, edited by John M. Cooper.

In 7b-d, Socrates says:

"What are the subjects of difference that cause hatred and anger? ...What subject of difference would make us angry and hostile to each other if we were unable to come to a decision? Perhaps you do not have an answer ready, but examine as I tell you whether these subjects are the just and the unjust, the beautiful and the ugly, the good and the bad. Are these not the subjects of difference which, when we are unable to come to a satisfactory decision, you and I and other men become hostile to each other whenever we do?"

Now, if we let D be the statement, "We disagree about goodness, justice and beauty" and let H be the statement "We become hostile to/at odds with each other," Socrates seems to be saying here that D causes H.

I interpret D causes H to mean if D, then H.

Then, in 7e, Socrates goes on to say:

"Then according to your argument, my good Euthyphro, different gods consider different things to be just, beautiful, ugly, good, and bad, for they would not be at odds with one another unless they differed about these subjects, would they?" (Emphasis mine)

This statement, I interpret to mean not H, unless D, which is the same as if not D, then not H, which, by contraposition, is equivalent to if H, then D.

The first and second quotations here thus lead to the following two statements, respectively:

1) if D, then H

2) if H, then D

But 1) does not entail 2)! Nor does 2) entail 1), for that matter. They are converses of each other. So how can Socrates make the claim in 7e that 1), which was established earlier, entails 2)? Clearly, 1) does not entail 2).

This seems like a straightforward error to me, but I don't feel comfortable accusing Plato of such a basic mistake. Perhaps I am misreading or misinterpreting something here? What does everyone else think?

Answer 1

I symbolize what happens in the passage roughly as follows (I've bracketed the subargument from 3-5):

1. Piety = Dear to gods "what is dear to the gods is holy and what is not dear to them is unholy" (6e-7a)
2. gods disagree about piety (7b)

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3. Some disagreements lead to discord (7b)
4. If a disagreement is empirically resolvable, it does not lead to discord (7b)
5. Disagreements about justice, truth, and beauty lead to discord (7d)

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6. Ergo, since the gods are in discord, they must substantive disagreements about justice, truth, piety, etc. (7e-8a)
7. Finally, 6 & 1 are contradictory so something must be wrong in the argument (8a)

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Starting from 6d-e, the argument is framed by Euthyphro's claim that what unifies the things we call holy (despite their differences) is

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The latter half of 7b which you quote in part is the beginning of a subargument:

But what things is the disagreement about, which causes enmity and anger? Let us look at it in this way. If you and I were to disagree about number, for instance, which of two numbers were the greater, would the disagreement about these matters make us enemies and make us angry with each other, or should we not quickly settle it by resorting to arithmetic? (7b-c) ... Then, too, if we were to disagree about the relative size of things, we should quickly put an end to the disagreement by measuring? ... weighing? (7c)

I take this line of questioning to mean that we don't waste our time disagreeing about minor things that we can simply or empirically resolve.

Conversely, Socrates and Euthyphro accept that we can wind up with

a disagreement [that] we could not settle and which would cause us to be enemies and be angry with each other (7c)

And that this would be about questions like:

Is it not about right and wrong, and noble and disgraceful, and good and bad? (7d)

= substantive disagreements would be about things like right/wrong and notably about things that are not empirically or simply resolvable are the sort of things that can lead to discord. In other words, it's things like the Forms (which makes sense considering this dialogue is about Piety).

Note that from 7b to the middle of 7d, Socrates is not talking specifically about the gods.

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At the end of 7d, he bridges it back to his main point by saying that gods would disagree about matters of import which are not resolvable by measurement or simple math. Moving to 7e, I don't think his point is the symbolization you suggest.

Specifically, I take the part at 7e to express "discord if and only if disagreement is about substantial things" -- i.e. I take it to express that the gods aren't in discord over something minor but rather they are in discord because they disagree about the nature of piety, etc. in a fundamentally irresovable way.

Why then does Plato make this argument (since he already said they were in discord)? I take it that the point is to block out the option of just saying "god A is correct for reason of knockdown argument B or reason of empirical fact C." Instead, it's point out that there's a fundamental incapacity to define piety by appeal to the gods -- since the gods are in discord and this means by definition that they do not agree for empirically and logically non-resolvable reasons about the nature of piety.

Answer 2

What are the subjects of difference that cause hatred and anger? ...What subject of difference would make us angry and hostile to each other if we were unable to come to a decision? Perhaps you do not have an answer ready, but examine as I tell you whether these subjects are the just and the unjust, the beautiful and the ugly, the good and the bad. Are these not the subjects of difference which, when we are unable to come to a satisfactory decision, you and I and other men become hostile to each other whenever we do?

I take this to mean that justice, beauty, and good are the subjects, ie, the only subjects, that disagreeing about would lead to anger and hatred. Perhaps in a more precise formulation, the only subjects, that disagreeing about could reasonably lead to anger and hatred; but even then, I would suppose that both Socrates and Euthyphro would assume that the gods, if they existed, would be reasonable beings, and, so, would only get angry at each others if they disagreed about justice, beauty, or good.

In other words, I interpretate the first quote as meaning

1) only if, D, then H

in which case "if H, then D" logically follows.

Answer 3

First, I don't believe your formulation is correct. If Socrates was claiming that D implies H, he would be excluding the possibility that H could be false when D is true. In other words, it would be interpreting him as saying that we can't help but becoming hostile with each other when such a disagreement arises. I don't believe that that's a fair interpretation of his words.

Second, even if that weren't the case, he never claimed that the assertions were equivalent or that one implied the other. Two statements may corroborate one another without being logically equivalent or involving implication, and there is no inconsistency unless you can demonstrate a contradiction. If your formulation were correct and Socrates was speaking inconsistently, then there would be no case in which the following were true:

(D → H) & (H → D)

However, both of the conditionals are compatible when both D and H are false or both are true. But again, I don't believe it's correct to interpret him as saying D → H.

Euthyphro believes that there is conflict among the gods:

"And do you believe that there really is war among the gods?"

Socrates is arguing that if that were the case, then it would be due to them disagreeing as to what is just and unjust. That argument only works if H → D. There's no reason to believe that that is inconsistent with his former statement in which he was only making a general observation about what sorts of things lead to conflict.

Answer 4

Going on the above extracts, we have Socrates saying in 7bd:

What are the subjects of difference that cause anger and hatred? ... these are the just and the unjust, the beautiful and the ugly, the bad and the good

Here Socrates is talking about men at odds amongst themselves, and he gives a reason why; Euthrypo agrees with this.

The later extract has Socrates saying:

Different gods consider different things to be just, beautiful, and good

Here he has the gods differing amongst themselves; and he offers in support of this statement the following:

For they would not be at odds with each other unless they differed about these subjects.

Which put in a conditional form is:

if they do not differ on these subjects, then they are not at odds.

Formally, taking the contrapositive, the sentence becomes:

if they are at odds then they do differ on these subjects

And since he takes the gods to be at odds, this backs up the conclusion he wants:

Different gods consider different things to be just, beautiful, and good