Socratic Definitions

I. The “What is X?” Question

  1. Socrates asked a simple kind of question that revolutionized philosophy: “What is it?”
  2. Usually raised about significant moral or aesthetic qualities (e.g., justice, courage, wisdom, temperance, beauty).
  3. Such questions are the central concern of the “Socratic” (early) dialogues of Plato.
  4. A so-called “Socratic definition” is an answer to a “What is X?” question.
  5. Socratic definitions are not of words, but of things. Socrates does not want to know what the word ‘justice’ means, but what the nature of justice itself is.
  6. A correct Socratic definition is thus a true description of the essence of the thing to be defined. I.e., definitions can be true or false.

II. The Importance of Socratic Definitions

A. They are objective.
  1. Socrates was opposed to the moral relativism of the Sophists.
  2. He believed that there were objective moral standards; that they could be discovered; that there were right and wrong answers to moral questions that went beyond mere opinion and popular sentiment.
B. They are fundamental for knowledge.
  1. Socrates claims that until you know what a thing is, you can’t answer any other questions about it.
  2. So any inquiry into any moral question presupposes an answer to the relevant “What is X?” question. Not just that there is such an answer, but that the inquirer is in possession of it.
  3. E.g., in the Meno, Socrates claims that you cannot answer a question about virtue (“Can it be taught?”) until you have answered a more fundamental question: “What is it?”
  4. In general, he thought that a person’s having knowledge involving a concept, X, depends upon his knowing the correct answer to the “What is X?” question.
C. They are fundamental for morality.
  1. He thought that the possibility of morality (moral character, moral behavior) depended on knowledge of definitions.
  2. Virtue is knowledge: if you know what is right, you will do what is right. Knowing a Socratic definition is thus (apparently) necessary and sufficient for moral behavior.

III. The Objectivity of Definitions

A. Objective fact vs. opinion
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.
B. The Euthyphro
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.

C. The Zsa Zsa Gabor paradox
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.

IV. Faulty Definitions

There are two ways definitions can go wrong: problems with form, and problems with content.
A. Problems with form: why enumerations can’t be definitions
Socrates insists that merely citing an instance, or a list of instances (rather than giving a general formula, or description) is inadequate.
1. Examples
Euthyphro 6d: piety is doing what I am doing now.

Meno 74c-d: defining shape as roundness, or color as white or as white + a list of other colors.

2. Practical Objections
Trying to list all the instances of the definiendum is likely to be practically unworkable.

E.g., you can’t expect to define ‘brother’ by listing all the brothers in the world. And even if you were presented with a such a list, how could you tell what one thing they are all instances of? You might not even have time to go through the entire list.

3. Theoretical objections
a. A complete list of instances is not always possible.
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.)
b. A complete list of instances is not necessary.
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.)
c. A complete list of instances is not sufficient.
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 with all of the instances.
B. Problems with content

The most common problem that Socrates finds with the content of a definition (although not, as we will see, the only kind of problem) it that the proposed definition fails to pick out the right things. A definition may be formally correct but still go wrong if it does not capture the right class of instances. The description may be

1. Too broad
2. Too narrow

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).

Example at Meno 73d: the ability to rule is both too broad (includes tyrants) and too narrow (excludes children).

V. Conditions for a Correct Definition

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.

A. The “application” requirement

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 every instance of X has characteristics ABC, and everything that has characteristics ABC is an instance 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.

B. The “explanatory” requirement

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 every instance of X is so because it has characteristics ABC.

These two necessary conditions are probably jointly sufficient:

X =df ABC iff
(1) every instance of X has characteristics ABC, and everything that has characteristics ABC is an instance of X, and
(2) every instance of X is an instance of X because it has characteristics ABC.

VI. The Relations between Definitions and Instances

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.)

VII. The Search for Definitions: the Recognition Problem

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,” to which we now turn.

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Copyright © 2004, S. Marc Cohen