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Plato: An academic approach to concepts

Plato: An academic approach to concepts

Author: Sophia Tutorial
Description:

Apply basic philosophical analysis by demonstrating an understanding of necessary and sufficient conditions.

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Tutorial
what's covered
Plato was the most famous student of Socrates. Like his mentor, he was interested in clear and distinct concepts: they were the cornerstone of his approach to philosophy. After a brief introduction to Plato's philosophy, we will explore the basics of conceptual analysis and its application in one of Plato’s best-known works.

This tutorial examines Plato's academic approach to concepts in three parts:

  1. An Introduction to Plato
  2. Necessary and Sufficient Conditions
    1. Defining Necessary and Sufficient Conditions
    2. Determining Necessary and Sufficient Conditions
    3. Practice
  3. The Euthyphro

1. An Introduction to Plato

Plato, born circa 427 B.C.E., was Socrates’ pupil until Socrates’ was executed in 399 B.C.E. During their time together, Plato recorded dialogues between Socrates and various Athenians. It is as a result of these written records that we know the philosophy of Socrates.

After Socrates’ death, Plato wrote his own philosophical works, using the dialogue format that had been employed by his teacher. To honor Socrates (and to present his ideas in an unbiased way), Plato’s fictional dialogues involved Socrates, usually as the one pronouncing Plato’s philosophical views. As a result, Plato’s early dialogues include historical conversations of Socrates. In his mature work, however, Plato used fictitious Socratic dialogues to develop and defend his philosophy.

Roman copy of a portrait bust of Plato by Silanion for the Academia in Athens (c. 370 BC)
Roman copy of a portrait bust of Plato by Silanion for the Academia in Athens (c. 370 BC)

Plato founded a school of philosophy called the Academy.

did you know
Plato (which means “broad” in ancient Greek) was a nickname. His birth name was Aristocles. Plato founded the Academy in Athens, which was one of the first institutions of higher learning in the western world.

Although the Academy played a major role in the development of western philosophy, it is important to realize that much of what Plato wrote was intended to educate his students (i.e., they were philosophical texts to be read and discussed at the Academy). His books, including the Euthyphro, were teaching tools, used to impart important lessons.

The Euthyphro enables us to begin to realize the importance of clear and accurate concepts, and how we can identify them. In the Dialogue, Plato describes how Socrates engaged Euthyphro, an Athenian who charged his father with murder in a case that was far from black and white. Socrates was interested in what he could learn from this case regarding the essence of piety, or godliness.

term to know
Essence
What makes a thing what it is

An essence is a concept of metaphysics, not of language. An essence is more than a definition. For example, the essence of humanity is what makes a human, human. Whether or not an essence can be captured in words is irrelevant to the fact that every human must possess the human essence in order to be human. Plato was interested in essences, and they play an important role in philosophy. However, not every philosopher agrees that essences exist. Those who believe they do, sometimes disagree on the details. This was true of Plato and Aristotle, as will be discussed in other tutorials.

Why are essences so important to philosophy? Essences are not definitions because they are unchanging, even when language changes. That which makes a human a human will always do so. It is irrelevant whether “human” has been defined in different ways at different times. Essences are the grounds for truth and falsity. If I ask, “Why are Bob and Sheila humans?” I am seeking an answer that is deeper than a dictionary definition. Any claim that “Bob and Sheila are humans” is true will involve a human essence in some way. The same is true if we replace “human” with important philosophical concepts including "justice" and "goodness."

In order to identify and make use of essences, it is essential to use clear, accurate terms. To identify the essence of justice, we must make accurate claims of the form, x is just or y is unjust. We do not need to know much about philosophy to know that grading student work based on hair color is unjust, or that assigning grades based on merit is just. We don't need philosophical analysis in the easy cases. But what about the gray areas? Is it just to give an oral exam — one that is ordinarily given as a written test — to accommodate one student's disability? If we can accurately identify the essence of justice, we can eliminate gray areas and provide the correct answer. Essences are crucial to philosophy because they enable us to clarify gray areas and discover the truth.

EXAMPLE

Essences can help us to discover the truth in gray areas including the morality of abortion, capital punishment, and wealth inequality.


2. Necessary and Sufficient Conditions

2a. Defining Necessary and Sufficient Conditions
How can we identify essences? Examination of natural categories of how things are in nature is a good way to begin. For example, what is the relationship between dogs and mammals? This is not a relationship between words or statements, but between real things. When considering realities, there are two basic ways in which categories can be related.

The first is a sufficient condition:

term to know
Sufficient Condition
A is a Sufficient Condition for B, if membership in A logically guarantees membership in B

Note that a sufficient condition is a relation, like saying “taller than.” It always applies to two things, not one. Since this is so, think of a sufficient condition as a logical guarantee. For example, getting caught stealing is a guarantee that you were breaking the law. Therefore, getting caught stealing is a sufficient condition for breaking the law.

What other types of things are logical guarantees? Recall the previous example of dogs and mammals. Being a dog is a sufficient condition for being a mammal. In general, any subclass is a sufficient condition. Being a square is a sufficient condition for being a quadrilateral, etc. Other examples involve a special type of subclass. Being Sacramento is sufficient for being a state capital. Being Socrates is a sufficient condition for being a philosopher. Being Socrates guarantees membership into the class of philosophers.

The other type of basic relation that may occur in the world is a necessary condition.

term to know
Necessary Condition
X is a Necessary Condition for Y if membership in X is logically required for membership in Y

Think of a necessary condition as a logical requirement. Completing your coursework is a necessary condition for receiving your degree. What kinds of things are logical requirements? First, a supertype is a rarely-used word that means the opposite of a subtype or subclass. Being an animal is a necessary condition for being a starfish. Another type of necessary condition is the “part of” relation. This can be a physical part (e.g., having a spine is a necessary condition for being a human), or a conceptual component (e.g., fairness is a necessary condition for justice).

2b. Determining Necessary and Sufficient Conditions
If this is confusing, there is a simple procedure for determining whether either of these relations exists between two things:

step by step

Step 1: Set up the question as follows:

(1) is a (blank) condition for (2), where (1) and (2) are the two objects, concepts, etc. that you are relating.

Step 2: Ask two simple questions:
Question 1: "Are all cases of (1) also cases of (2)?”
  • If you answer yes, then (1) is sufficient for (2).
  • If you answer no, then (1) is not sufficient for (2).

hint
Note that this first question only determines sufficiency. To determine necessity, change the order.

Question 2: “Are all cases of (2) cases of (1)?”
  • If you answer yes, then (1) is necessary for (2).
  • If you answer no, then (1) is not necessary for (2).
Step 3: Determine conditions. Note that this produces four possible answers relating any two categories:
  • (A) Sufficient, not necessary
  • (B) Necessary, not sufficient
  • (C) Both necessary and sufficient
  • (D) Neither necessary nor sufficient

The whole of reality has just become a multiple choice question, because one of these four possible relations must always exist between any two things.

The following table categorizes the four possibilities based on the answers to the above questions.

(1) is a (blank) condition for (2). Sufficient Condition:
Are all cases of (1) also cases of (2)?
Yes No
Necessary Condition:
Are all cases of (2)
also cases of (1)?
Yes Both Sufficient
and Necessary
Necessary,
not Sufficient
No Sufficient,
not Necessary
Neither Necessary
nor Sufficient

2c. Practice
Return to the examples of sufficient conditions above, and see how they all come out as option (A), sufficient, not necessary.

Next, try all of the previous examples of necessary conditions and see how they come up as option (B), necessary, not sufficient.

So we have seen some examples of relations that fall into the category of sufficient, not necessary and others that are necessary, not sufficient. But what about the last two categories?

To answer (D) (i.e., neither necessary nor sufficient ) that there is no logical relation between two entities. For example, being a pirate is neither necessary nor sufficient for being a ninja. This is an example of no relation at all. Note that statistical relationships fall into category (D) as well. For instance, being tall is neither necessary nor sufficient for being a professional basketball player. Why? There are tall people who are not basketball players, and there are basketball players who are not tall. Being tall is neither a requirement nor a guarantee for being a basketball player.

The most important category in conceptual analysis is (C) (i.e., both necessary and sufficient). What kind of things are both necessary and sufficient? Cases of identity fall into this category. Being Socrates is both necessary and sufficient for being Plato’s mentor. More important, however, are two things of interest to philosophy: good definitions (linguistic) and essences (metaphysical). Being a bachelor is both necessary and sufficient for being an unmarried male who has reached the age of consent. Using necessary and sufficient conditions is a simple way to begin using conceptual analysis.

try it
Try the following six problems:

Problem Answer Explanation
Being furniture is a (blank) condition for being a chair. Necessary, not sufficient Being furniture is a necessary, not sufficient condition for being a chair because not all cases of furniture are chairs, but all cases of chairs are furniture.
Being a good driver is a (blank) condition for having a driver’s license. Neither necessary nor sufficient Being a good driver is neither necessary nor sufficient for having a driver’s license. There are good drivers who do not have a driver’s license and there are plenty of people with a driver’s license who are not good drivers.
Being a regular quadrilateral is a (blank) condition for being a square. Both necessary and sufficient Being a regular quadrilateral is both sufficient and necessary for being a square. This is a case of identity. When you do the test, one is trivially all so you answer yes, yes.
Having a heart is a (blank) condition for being a human. Necessary, not sufficient Having a heart is a necessary, not sufficient condition for being a human because not all cases of having a heart are being a human, but all cases of being a human are having a heart.
Eating Thanksgiving dinner is a (blank) condition for being full. Sufficient, not necessary Eating Thanksgiving dinner is sufficient, not necessary for being full because if you eat Thanksgiving dinner, you will be full. However, you just being full doesn't guarantee that you ate Thanksgiving dinner.
Being enrolled in this course is a (blank) condition for being a student. Sufficient, not necessary Being enrolled in this course is sufficient, not necessary for being a student because your enrollment guarantees you are a student, but being a student doesn't necessarily mean you are enrolled in this course.


3. The Euthyphro

Though the terminology used for these categories did not exist during Plato’s time, Plato taught his students many of these concepts (and a few more) in the Euthyphro. In that dialogue, Socrates asked what is the essence of piety (i.e., holiness or goodness). He therefore asked Euthyphro for the necessary and sufficient conditions for piety. In the dialogue, Euthyphro presented six unsatisfactory definitions. Plato’s students learned the fundamentals of conceptual analysis from Socrates’ rejection of the unsatisfactory answers. We will examine some of them briefly.

The first definition Euthyphro proposed is that piety is to do what he was doing, that is prosecuting the wrongdoer.

Socrates quickly pointed out that this was merely an example, or to use our terminology, sufficient, but not necessary. There are other ways of being pious, so an example, while helpful, does not grasp the essence of piety. (Imagine that someone asked you what it meant to be human and, in response, you pointed at a passerby.)

Euthyphro next stated that piety is what is loved by the gods. Socrates replied that this wouldn’t do, because the gods disagree (which probably makes it neither necessary nor sufficient). What is loved by Aphrodite, goddess of love, is different from what is loved by Ares, god of war. The important lesson is that, when dealing with concepts, say what you mean (i.e., say what you are willing and able to defend), nothing more, nothing less.

EXAMPLE

Consider this claim: “Abortion is wrong.” Does this mean all abortions are wrong? What about cases of rape? What about cases in which continuing the pregnancy will kill the mother? Surely it was not intended to include cases in which continuing the pregnancy will kill the mother and the fetus. Only claim what you are willing to support.

The third definition, therefore, is that piety is what is loved by all of the gods. Things which satisfy these conditions may exist, (the Greek virtues of courage, wisdom, justice, and moderation, for example), but there is a problem, which has come to be known as the Euthyphro Dilemma: Is a thing pious because the gods love it, or do the gods love it because it is pious? The former makes piety arbitrary and uninteresting. The latter means we must look beyond the gods to isolate the concept.

This is what Euthyphro tries to accomplish in presenting his fourth definition: piety is part of justice, and all that is pious is just. Once more, however, the “part of” relation is incomplete (recall that “part of” is necessary, not sufficient). In this instance, Euthyphro tried to define a tricky concept by introducing a trickier concept, which is unhelpful.

Euthyphro moved on to another religious definition of piety: piety is doing what is required by the gods or care of the gods. This is vague. Care how? We have not adequately defined the concept.

Euthyphro clarifies this in his sixth (and final) definition: piety is service to the gods. This is also vague. Even worse, we can remove the vagueness. We serve the gods by doing what they wish, but this is the same as saying "doing what pleases them." Euthyphro has simply restated his third definition.

The results of the dialogue were not all failures, however; Socrates provided a positive notion of what the essence of piety may be (i.e., the virtue of living in a way that fulfills one’s duties to humanity, and to the gods). What is important to realize is how to approach precise philosophical concepts, while avoiding standard pitfalls, and why precision matters.


summary
Philosophy is a pursuit of truth, but this means we need to identify the truth-makers of categories — essences. A good way to do this is to learn necessary and sufficient conditions: logical guarantees and requirements that relate categories of being. In Plato’s Euthyphro, he taught his students in this way, using the concept of piety. By doing so he emphasized the importance of precise concepts.
Attributions
Terms to Know
Essence

What makes a thing what it is

Necessary Condition

"X" is a Necessary Condition for "Y" if membership in "X" is logically required for membership in "Y."

Sufficient Condition

 "A" is a Sufficient Condition for "B" if membership in "A" logically guarantees membership in "B."