Socrates’ Theory of Definition

Definition

A Socratic definition is an answer to a question of the form, “What is F-ness?”. Plato represents Socrates searching for definitions of piety (Euthyphro), temperance (Charmides), justice (Republic I), courage (Laches), virtue (Meno), and beauty (Hippias Major).

The Importance of Definitions

Socrates find it important to find the answers to these questions because he accepts what has come to be known as the Priority of Definition (PD). PD encompasses three separate theses (PD1, PD2, and PD3):

PD1: If you don’t know what F-ness is (i.e., if you don’t have a definition of F-ness), then you don’t know, of any given thing, whether it is F.

Text: “Now we’ve done it, Lysis and Menexenus—made fools of ourselves, I, an old man, and you as well. These people here will go away saying that [we think] we are friends of one another— for I count myself in with you— but what a friend is we have not yet been able to find out.” (Lysis 223a)

What Socrates suggests here is that it is foolish for someone to claim to know that he is a friend (to someone else) without having knowledge of what friendship is. That is, knowing what friendship is (knowing the definition of friendship) is necessary for knowing, of oneself, whether one is a friend.

Text: “How will you know whose speech—or any other action—is finely presented or not, when you are ignorant of the fine?” (Greater Hippias 304e)

The claim here is that knowing what the fine is (knowing the definition of the fine) is necessary for knowing, of any action, whether it is fine. [Note: “fine” is one of the many English versions of the Greek word “kalon”. Other English translations include: “beautiful”, “noble”, “honorable”, and “admirable”.]

PD2: If you don’t know what F-ness is (i.e., if you don’t have a definition of F-ness), then, for any property G, you don’t know whether F-ness is G.

Text: “…when I don’t know what justice is, I’ll hardly know whether it is a kind of virtue or not, or whether a person who has it is happy or unhappy.” (Republic I 354b)

The claim here is that knowing what justice is (knowing the definition of justice) is necessary for knowing whether justice is a virtue and for knowing whether a person in possession of justice is happy.

Text: “I am so far from knowing whether virtue can be taught or not that I do not even have any knowledge of what virtue itself is…If I do not know what something is, how could I know what qualities it possesses?” (Meno 71a-b)

Here, PD2 is explicitly stated. And the following instance of PD2 is also stated: Knowing what virtue is (knowing the definition of virtue) is necessary for knowing whether virtue can be taught.

PD3: If you don’t know what F-ness is (i.e., if you don’t have a definition of F-ness), then you don’t know how to advise someone as to how to achieve F-ness.

Text: “Then isn’t it necessary for us to start out knowing what virtue is? Because if we are not absolutely certain [Better translation: if we don’t know] what it is, how are we going to advise anyone as to the best method of obtaining it?” (Laches 190b-c)

The claim here is that knowing what virtue is (i.e., knowing the definition of virtue) is necessary for knowing how to advise others as to the best way to become virtuous.

Conditions of Adequacy on Definitions

Every definition is of the following form: The F is the ABC (or: F-ness is ABC-ness). The acceptability of any definition

depends on the following conditions being satisfied:

1. Existence: There is such a thing as F-ness.

Texts: “Here’s a good first question: Is justice a thing or is it not a thing? I think it is.” (Protagoras 330c; see also Greater Hippias 287c)

“Suppose he questioned us further: ‘Do you also say there is a thing called piety?’ [Better translation: ‘Do you also say that piety is something?’] We would say we do, right?” (Protagoras 330d)

“Do you acknowledge that there is such a thing as folly?”—“Yes.”— “And diametrically opposed to it is

wisdom?”—“It seems so to me.” (Protagoras 332a)

“Is there such a thing as beauty?”— “Yes.”— “Is there any opposite to it except ugliness?”— “There is not.” — “Is there such a thing as goodness?” — “There is.” — “Is there any opposite to it except badness?”— “There is not.” (Protagoras 332c)

2. Causality: For Socrates, the F is whatever it is that makes F things F. So, for example, justice is whatever it is that makes just things just. Socrates sometimes puts the point by saying that it is by (or: through) the F that F things are F. If “the F is the ABC” is the correct definition of the F, it follows that the ABC is what makes F things F. So one condition of adequacy on defining the F as the ABC is that it be true that the ABC is what makes F things F.

Texts: “Bear in mind then that I did not bid you tell me one or two of the many pious actions but that form itself that makes all pious actions pious, for you agreed that all impious actions are impious and all pious actions pious through one form, or don’t you remember?”— “I do.” (Euthyphro 6d)

“Then it is by virtue of temperance that [people who act temperately] are temperate.” (Protagoras 332a)

“And foolish behavior comes from folly, just as temperate behavior comes from temperance? [Better translation: And things done foolishly are done with folly, just as things done temperately are done with temperance?]”—“Yes.”— “And if something is done with strength, it is done strongly; if done with weakness, weakly?”—“I agree.”—“If it is done with quickness, it is done quickly, and if with slowness, slowly?”—“Yes.”—“So whatever is done in a certain way is done through the agency of a certain quality, and whatever is done in the opposite way is done through the agency of its opposite? [Better translation: So whatever is done the same way is done through the same thing, and whatever is done in the opposite way is done through its opposite.]”—“I agree.” (Protagoras 332b-c)

“Now then; that through which cowardly people are cowardly, do you call it cowardice or courage?”—“Cowardice.” (Protagoras 360c)

“For I don’t suppose that it’s by slowness that people act unjustly, but by injustice. Right?”—“Yes.” (Gorgias 520d)

“Is it not by justice that just people are just?…And by wisdom wise people are wise, and by the good all good things are good?…Then all fine things, too, are fine by the fine, isn’t that so?” (Greater Hippias 287c)

“…the fine itself by which everything else is beautified and seen to be fine when that form is added to it…” (Greater Hippias 289d)

“Aren’t you capable of remembering that I asked for the fine itself? For what when added to anything—whether to a stone or a plank or a man or a god or any action or any lesson—anything gets to be fine?” (Greater Hippias 292c-d)

“I thought we were looking for that by which all fine things are fine.” (Greater Hippias 294a-b)

“The same is true in the case of the virtues. Even if they are many and various, all of them have one and the same form which makes them virtues, and it is right to look to this when one is asked to make clear what virtue is.” (Meno 72c)

3. Commonality: For Socrates, the F (i.e., whatever makes all F things F) is something that all and only F things have in common. If “the F is the ABC” is the correct definition of the F, it follows that the ABC is something that all and only F things have in common. In other words, one condition of adequacy on defining the F as the ABC is that (i) all F things be ABC and (ii) that all ABC things be F.

Texts: “…is the pious not the same and alike in every action…?” (Euthyphro 5d)

“So try again to state first what is the courage that is the same in all these cases.” (Laches 191e)

“What power is it which, because it is the same in pleasure and in pain and in all the other cases in which we were just saying it occurred, is therefore called courage?” (Laches 192b)

“…the virtue of all is the same…” (Meno 73c)

“…I am seeking that which is the same in all these cases…” (Meno 75a)

“Then they have some thing that itself makes them be fine, that common thing that belongs to both of them in common and to each privately.” (Greater Hippias 300a-b)

4. Intersubstitutability: If the F is (correctly defined as) the ABC, then “F” and “ABC” are everywhere intersubstitutable salva veritate. In other words, if the F is correctly defined as the ABC, then substituting “F” for “ABC” or “ABC” for “F” in any sentence will not alter its truth-value (whether true or false). Socrates does not state this thesis in so many words, but the validity of some of his arguments depends on it. So it is reasonable to attribute to him acceptance of the thesis.

Texts: Euthyphro 7a-8b, and 9d-11a. The validity of both of the arguments in these passages depends on Intersubstitutability. See Handout (Euthyphro).

An Additional Socratic Thesis

As we’ve just seen, Socrates accepts that the F is that common thing that makes all F things F. In addition, he accepts what might be called the Transmission Theory of Causality:

5. Transmission: Whatever makes F things F must itself be F.

This theory was held by Socrates’ philosophical predecessors, most notably Anaxagoras who pointed out that whatever makes hot things hot must itself be hot.

Text: “And could a thing be good that does not produce good men? [Better translation: And could a thing that produces good men not be good?]”—“Of course not.” (Charmides 160e)

The claim here is that whatever produces good men (i.e., whatever makes good men good) must itself be good.

Consequences

The theses of Commonality, Causality, and Transmission have two important consequences: Oneness and Self-Predication.

6. Oneness: Socrates states in various places that the F is one (thing). This thesis follows from Commonality, the claim that the F is what all and only F things have in common.

Texts: “…all impious actions are impious and all pious actions pious through one form…” (Euthyphro 6d-e)

“…folly, which is a single [i.e., one] thing…” (Protagoras 333b)

“The same is true in the case of the virtues. Even if they are many and various, all of them have one and the same form which makes them virtues…” (Meno 72c)

7. Self-Predication: Socrates states in various places that the F is F. This thesis follows from Causality and Transmission. For Causality says that the F is what makes F things F and Transmission says that whatever makes F things F must itself be F. It follows directly that the F must itself be F.

Texts: “Then justice is the sort of thing that is just. [Better translation: Then justice is such as to be just.]” (Protagoras 330c)

“How could anything else be pious if piety itself is not?” (Protagoras 330e)

“How could we dare deny that the fine thing is a fine thing? [Better translation: How could we dare deny that the fine is a fine thing?]” (Greater Hippias 288c)

“I suppose the fine is always fine.” (Greater Hippias 292e)