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The definition of a moral quality is not a matter of what people think. You cannot determine what goodness, or justice, or piety, is by conducting a poll. Consequently, whether something or someone has a given moral quality is also not a matter of mere opinion. Whether an act or a person is good, or just, or pious, for example, is not to be settled by a vote.
The Euthyphro gives us a good example of Socrates' belief that moral qualities are real, not conventional.
Euthyphro suggests that piety can be defined as what the gods all love (9e). Socrates objects. Even if all the gods agree about which things are pious, that doesn't tell us what piety is. (Even a poll of the gods is just a lot of opinions.) He gets Euthyphro to admit that it is not because they are loved by the gods that things are pious. Rather, they are loved by the gods because they are pious.
So piety cannot be defined as being god-loved. For if it were to be so defined, since Euthyphro admits that:
the gods love pious things because they are pious
he would also have to accept (substituting 'god-loved' for 'pious') that
the gods love pious things because they are god-loved.
But this Euthyphro rightly denies. For it would lead to circularity. The gods cannot love things because they love them. That would make their love whimsical and without foundation. If the gods love something because it is pious, then its being pious must be something independent of their loving it - something independent of opinion - something objective.
Another way of putting the point: moral qualities are not like such qualities as fame or popularity. A thing is popular just because people like it. If you ask them why they like it, they may have their reasons: because it's bright, or flashy, or durable, or economical, or beautiful, etc. But someone who answers "I like it because it's popular" is making some kind of mistake. For he seems to have no reason for liking it other than the fact that most other people like it. But what reason do they have?
If their reason is the same as his, they may all be making a huge mistake. They all agree with one another in admiring it, but there's nothing about it they admire. If they have some other reason, then his reason seems to depend on theirs. His liking it because they like it is rationally justifiable only to the extent that their reason for liking it is a good one.
Euthyphro's proposed definition leads to something like (what I'll call) the Zsa Zsa Gabor paradox:
Zsa Zsa is famous. She appears on talk shows, and everyone knows who she is. But what does she do? What is she famous for? As the joke goes, she's famous for being famous.But that's just to say that there really isn't any reason for Zsa Zsa to be famous. We're all making some kind of mistake to pay any attention to her. Likewise, if piety were being god-loved, the gods would all be making a mistake in admiring an act for its piety. For they would be admiring nothing other than their own admiration.
There are two ways definitions can go wrong.
Giving a description that does not capture the right class of instances. The description may be
Note that a definition may be both too broad and too narrow, i.e., it may admit instances that it should exclude, and exclude instances that it should admit. E.g., defining "brother" as "unmarried sibling". This condition is neither sufficient for being a brother (it includes some sisters, who should be excluded) nor necessary for being a brother (it excludes married brothers).
Some jargon. We'll call the term to be defined the definiendum, and the term that is offered to define it the definiens. We can then reserve the term definition for the whole formula defining the definiendum in terms of the definiens. Thus, in the definition 'A brother is a male sibling' (or, 'brother =df male sibling'), 'brother' is the definiendum and 'male sibling' is the definiens.
This requirement is simply that the definiens neither be too broad nor too narrow. The definiens must provide (materially) necessary and sufficient conditions. I.e., the proposed definiens should apply to the right things, viz. exactly the things that the definiendum applies to. To use some logical jargon: the definiens should be extensionally equivalent to the definiendum:
X =df ABC only if all instances of X are instances of ABC, and all instances of ABC are instances of X.
Most definitions found faulty in the dialogues fail the application requirement - the proposed definiens turns out not to be extensionally equivalent to the definiendum. But extensional equivalence by itself is not enough.
At Euthyphro 11a-b Socrates agrees that piety is loved by all the gods, and that what all the gods love is pious, but still objects to defining piety as what all the gods love. His objection is that it is not because it is loved by the gods that a pious thing is pious.
This suggests an additional requirement, that the definiens should in some way explain the definiendum:
X =df ABC only if all instances of X are so because they have characteristics ABC.
These two necessary conditions are probably jointly sufficient:
X =df ABC iff (1) all instances of X are instances of ABC, and all instances of ABC are instances of X, and (2) all instances of X are instances of X because they have characteristics ABC.
How does one arrive at a definition? Socrates' method is to examine particular cases, reworking his definition as he goes, until (if ever) he gets it right.
But how can he tell, in a particular case, whether he actually has an instance to which the definition applies? For he maintains that you cannot know anything about, e.g., virtue, until one knows what virtue is. But if I know that reading War and Peace is virtuous, don't I know something about virtue, viz., that reading War and Peace is an instance of it?
This is a problem for Socrates: how can one recognize an instance of X as such when one doesn't yet know what X is? Call this "The problem of recognizing instances." (It's the first half of the general recognition problem, of which more below.)
To list all the instances of the definiendum might produce something practically unworkable.
E.g., suppose you were presented with a list of all the brothers in the world. How could you tell what one thing they are all instances of? You might not even have time to go through the entire list.
E.g., try to define "even number" by enumeration. You can't give a complete list.
What about a partial list, with dots . . . . ? E.g.: 2, 4, 6, 8, . . . .
But what tells you the right way of continuing the enumeration? We all "know" that the next number is 10. But that's because we infer that the principle behind the enumeration is to list all the even numbers. Still, why can't the next number be 2? A fuller enumeration might be:
2, 4, 6, 8, 2, 4, 6, 8, . . . .
(Cf. Wittgenstein on "knowing how to go on", Philosophical Investigations, §§151-155.)
It is possible to know the definition without being able to produce a complete enumeration of its instances. (E.g., you know what it is to be a brother even though you don't know who all the brothers are.)
Even a complete enumeration of instances may not determine a single definition. That is, there may be two or more logically distinct definitions, incompatible with one another, but each of which is compatible will all of the instances.
This is an epistemological problem, similar to the problem of recognizing instances. This time, the problem is:
how can you recognize when a proposed definition is the correct one?
This is the problem of recognizing the correct definiens. The correct definiens is the one that applies to all and only the instances of the definiendum, and for the right reason. So to recognize the correct definiens, we have to be able to recognize the instances. But we can't do this, according to Socrates, until we know what the definition is.
Plato is aware of this problem. It arises in the Meno at 80d-e, in the form of "Meno's Paradox", or "The Paradox of Inquiry".
The argument can be shown to be sophistical, but Plato took it very seriously. This is obvious, since his response to it is to grant its central claim: that you can't come to know something that you didn't already know. That is, that inquiry never produces new knowledge, but only recapitulates things already known. This leads to the famous Doctrine of Recollection, to which we now turn.
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