Skip to main content

The Euthyphro Argument

  1. pious =df god loved. [Premise]

    “I’d say that the pious is what all the gods love… .” [9e]

    [‘god loved’ =syn ‘loved by the gods’]


  2. x is loved by the gods because the gods love x. [Premise]

    Principle endorsed at 10c:


    x is φ-ed by S because S φ-s x.


    “[I]t’s not because it’s a loved thing that it’s loved by those who love it; rather it’s because it’s loved that it’s a loved thing?”

    “Necessarily.” [10c]


  3. The pious is loved by the gods because it’s pious. [Premise]

    “So is [the pious loved by all the gods] because it’s pious or because of something else?”

    “No, it’s because it’s pious.” [10d]


  4. The god loved is loved by the gods because it’s god loved. [1, 3]
  5. But (4) is inconsistent with (2); moreover, it entails (6):
  6. The pious is pious because it’s loved by the gods. [1, 4]
  7. But (3) and (6) are inconsistent.

    “But, as it is, you can see that the two are related in the opposite way, as things entirely different from one another. For one of them is lovable because it’s loved [cf. 6], whereas the other is loved because it’s lovable [cf. 3].” [11a]


  8. Therefore, the definition at (1) fails. [7]

Evaluation: the argument is invalid, as the inference at 4 (and 6, for that matter) is no good.

Diagnosis: Socrates is employing a certain principle — the Substitutivity of Identicals — according to which one is permitted to replace one term with another whose reference is the same.

Example:

  1. Kassim went to the concert.
  2. Kassim is the oldest son of Sameer.
  3. Therefore, the oldest son of Sameer went to the concert.  [1,2 Subst. Ident.]

But the principle doesn’t work in all situations. Specifically, one isn’t permitted to make such substitutions in opaque contexts (so called because they are “closed”, in contrast with transparent contexts, which are “open”).

The word ‘because’ creates opaque contexts. To illustrate, suppose the following is true:

1. John was justly fired from McDonalds because he is the individual who left the store safe unlocked.

(We assume for this exercise that McDonalds has a zero-tolerance policy regarding night managers leaving the safe unlocked.)  If (1) is correct, then the following must be the case:

2. John = the individual who left the store safe unlocked.

Now suppose the following is also true:

3. John = the only vegetarian employee in the restaurant.

By the transitivity of identity, (2) and (3) jointly entail (4):

4. The individual who left the store safe unlocked = the only vegetarian employee in the restaurant.

By a legitimate application of the Substitutivity of Identicals, (1) and (3) jointly entail (5)

5. The only vegetarian employee in the restaurant was justly fired from McDonalds because he is the individual who left the store safe unlocked.

The substitution is permitted, because it occurs in a transparent context. (‘John’ is the grammatical subject of (1), but because the sentence is in the passive voice, ‘John’ is also the direct object of the verb in its active form, and ‘to fire’, as an extensional verb, creates transparent contexts.)

But do (1) and (4) entail (6)?

6. John was justly fired from McDonalds because he is the only vegetarian employee in the restaurant.

Surely not! If John’s dietary habits were unknown to his supervisors (which is something that we could stipulate), there is no way that those habits could have had any role in his supervisors’ decision to fire him; and even if they had, the firing would not in that case have been just!

This substitution occurs within the scope of ‘because’—an opaque context—and is therefore illegitimate.

But this is precisely what Socrates does, and it’s equally illegitimate there.

Questions: does Socrates (or Plato) recognize that the argument is fallacious? If so, why would he have employed it?