Plato (5): Four principles of Socratic/Platonic reasoning.


  This essay is a critical reconstruction of a reasoning method found in Plato, capable of supporting the interpretation of Plato's Form theory presented in previous essays.  It describes the theory behind Socratic/Platonic method described in the previous "how-to" essay.

Click here for an example from Plato, a Socratic discussion of Courage presented in Plato's dialogue Laches.

I present the theoretical basis for this method in the form of four principles.


The first principle concerns the goal of this reasoning.

Critical reconstruction of Socratic/Platonic reasoning requires careful thought about the goals we expect it to achieve, and its function in the life of the ideal Platonist. Today so much of moral skepticism is due to overambitious and unrealistic expectations of what it is that moral reasoning can actually achieve. For example, if one thinks that the goal of Socratic reasoning is to bring all people everywhere to common agreement, this will lead to skepticism about Socratic reasoning itself when it proves unable to reach this goal. We must carefully define and limit our conception of the goal of this reasoning, to something that Socratic reasoning can actually be expected to perform.
    As a preview, here is a list of common goals that Socratic/Platonic reasoning should not be expected to achieve:
- It does not try to say what usually does happen, or what actually does motivate most people.
- It does not discuss whether we should generally follow some given rule such as "tell the truth"
- Its results would not be useful as a blueprint for widespread reform of society as a whole.
- It will not yield a set of rules determining what conduct is obligatory, allowable, or not allowable, in social interactions.
- It will not resolve moral dilemmas, or the many controversies stemming from these dilemmas.
- It will not yield "moral principles" from which one can logically deduce proper moral conduct.
- It cannot be expected to produce widespread agreement on a single particular set of virtue-definitions to serve as a single norm for judging all individuals in all cultures for all time.

Of course we cannot know for sure ahead of time that there are no virtue-concepts on which everyone everywhere will or should agree.  There is no reason to try to avoid agreement, or to think agreement is not a desirable outcome.

The main practical conclusion of the above observations are:

#1- Don't make transcending all cultural differences and reaching universal agreement the main goal of reasoning about virtues.  Even if there does exist such a reasoning method, it would be very different from any kind of reasoning we find in Plato.  When conducting a Socratic discussion about a virtue, don't worry about whether others would agree with you or not.  This is irrelevant.

#2- Don't regard Plato's failure to offer a way of transcending all cultural differences and reach universal agreement as a fatal weakness in Platonism, a reason for rejecting Platonism.

The central goal of Platonism is to formulate virtue-concepts perfect in their goodness.  "Perfect in goodness" means something completely different from "universal," or "obligatory for everyone," or "transcending all cultural differences."

    There are potentially thousands of virtue-Forms more perfect in their goodness than the imperfect virtue-concepts people usually use for self-evaluation and to model their characters on.  So there is no need for everyone to agree on their choice of which perfect virtue-concepts to adopt for these purposes.
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 Socratic reasoning does have a rather ambitious and difficult intellectual goal to try to achieve. A description of this goal has to start with the idea of a virtue, and the ultimate function that virtue-concepts need to perform in the concrete personal life of the ideal Platonist.
    A virtue is an admirable internal character-trait, not an action. Admirable character traits manifest themselves in visible external action, but are not themselves directly visible. (Plato says that the essence of what makes a person admirable can never be described in terms of anything directly visible to sense-perception.)

A character-trait is like a skill or a habit.  "Tennis-playing skill" is an ongoing part of a professional tennis-player's physical and mental makeup.  This skill remains part of her mental/physical makeup even when she is not actually playing tennis.  In the same way, "kindness" might be an ongoing aspect of my mental/emotional makeup, even when I am not at the moment engaged in kind behavior.  Particular tennis-playing skills have become "second nature" to the tennis-pro, so that they spontaneously manifest themselves when some situation in a tennis game calls for these skills.  The virtue of kindness is a character trait that has become second-nature in a genuinely kind person, and spontaneously manifests itself when some situation calls for kindness. 

This point is important because so many modern moral discussions revolve around behavior and behavioral rules.  If I am a genuinely kind person, then this kindness will be spontaneously activated in those situations calling for kindness, and manifest itself in that kind of admirably kind behavior appropriate in this situation.  Suppose there is a person who doesn't have this kind of spontaneous kind response -- because "kindness" is not really part of her personality -- but this person tries to act kindly anyhow, following a rule telling her how to do so, or imitating the behavior of genuinely kind people.  This might be admirable in itself, because acting kindly is perhaps better than nothing.  But acting kindly in this way does not make a person a kind person.  Whether acting kindly is admirable or not depends on motivation.  A cynical politician or terrorist can act kindly in order to gain people's trust to exploit them or harm them.  An admirable person is a person with admirable motivations.  Kindness as a virtue is a habit of mind consisting of certain motivations that spontaneously come into play when a situation calls for kindness.  For example, empathy seems one such possible admirable motivation.  Feeling another's pain as one's own is something that might motivate a person and manifest itself in acts of kindness, when certain situations call for it.  In this case, kindness as a habit of mind, might be partially defined by speaking of a person in whom empathizing with another's difficulty is part of her habitual mental makeup, an habitual way she responds to others in difficulty.

Plato does not discuss rules for behavior, but tries to define concepts, virtue-concepts in particular.  The function of specially defined virtue-concepts is to serve as models to model oneself on.  That is, it assumes an individual who is able not only to act differently, but able and desiring to improve her inner character, to bring about some inner fundamental change in her habitual personality. This cannot be done overnight, but seems to assume a long-term process of self-training. In the concrete, then, a Platonic virtue-Form should be imagined as something that will be used to guide the process of self-training, self-administered character-formation.

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So a "virtue" is a habit of mind that is spontaneously activated in situations calling for this virtue.

"Habit of mind" describes the kind of thing a virtue is (it is a habit of mind, not a behavior).  But since Plato is after virtue-concepts to serve as models to model one's character on, these virtue-concepts need to be a perfect as one can make them.  This is not necessarily connected to a realistic desire to become perfect.  It's only that, if I want to improve in anything -- say tennis-playing -- I want to model myself on the best models available to me.  If I take very imperfect tennis-players to imitate and model myself on, becoming more like them may or may not really improve my game.

This is the purpose of using Socratic reasoning to detect imperfections in my present concepts of virtue, and find ways of removing those imperfections to develop virtue-concepts to model myself on that are as perfect as I can make them.

 So the goal to strive for through Socratic/Platonic reasoning is to try to come as close as possible to answering the question:

That kind of V which I find admirable, how can I precisely articulate the essence of what I find admirable about it?
This essence would be a Platonic Form of V.
    If I were able to describe in a very precise way the essence of what it is that makes V admirable, a I could not have this essence and not be admirable. All other things being equal any increase in this essence would increase the quality of V, because I would be "participating in" the essence to a greater and greater degree.
    You should expect that a description of this essence will take the form of a description of some internal and invisible character-trait, describing such things as attitudes, motivations, value-priorities, and mental abilities.
    ("But how could you be sure that you have arrived a final and completely faultless description of such an essence?" You can't. The purpose of this description of the question to be asked and the goal to aim at is to keep Socratic discussion focused. Make everything you do in this discussion contribute to this goal, avoiding all kinds of other reflections and comment that will not contribute to this goal. Your realistic goal should be to make progress. A Socratic discussion is a good discussion if you end with a better virtue-concept than you began with. You can rationally know that you are making progress. You can never know you have reached a state where no further progress is possible. Note that, despite the claims of some scholars and scientists, this seems true of all fields of knowledge [with the possible exception of particular mathematical truths considered as pure theory-- it's hard to improve on 2+2=4 as pure theory, but actually in concrete life, two gallons of water added to two gallons of alcohol will not yield four gallons of liquid, since alcohol absorbs water].)

There are potentially thousands of virtue-Forms more perfect in their goodness than the imperfect virtue-concepts people usually use for self-evaluation and to model their characters on.  So there is no need for everyone to agree on their choice of which perfect virtue-concepts to adopt for these purposes.

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The Second Principle: The ultimate basis for all moral knowledge.

A cornerstone of this reconstruction of Socratic/Platonic reasoning is the assumption that we do have a reliable source of moral knowledge. This consists in personal perceptions of what is admirable and not admirable in the case of clear and unproblematic concrete stories.
    "Clear and unproblematic" is important here. There are many situations in which I am uncertain as to what is the best course of action, many situations in which I recognize there are good arguments on both sides (I'm unclear about the death penalty, because on the one hand I think it perpetuates brutality, but on the other hand society needs to make strong statement against some particularly brutal crimes).  These are moral dilemmas, un-clear, problematic, controversial cases, and they are not useful in Socratic reasoning.  Basing moral ideals on my perceptions in unclear cases, is like basing a scientific theory on uncertain data, gathered from unreliable thermometers or defective scales.
    It is true that concrete life presents us with many moral dilemmas. But if we want to, it is not too difficult to make up clear and unproblematic stories, stories in which it is very clear, not controversial, what is admirable and not admirable.
    One example Plato gives: Suppose a friend left weapons with me for safekeeping, subsequently went insane, and now comes wanting his weapons back. Should I return them? Most individuals will not regard this as a dilemma, presenting a problem for moral judgment. It is just obvious that one should not give weapons to an insane person, even if the weapons belong to him. This is an example of a "clear and unproblematic story."
    Clear personal perceptions of what is admirable and not admirable in the case of unproblematic stories are the most reliable source of moral knowledge, and form the ultimate basis for all moral judgments and ideas, including all knowledge of otherworldly Platonic Forms.

For example, a person might be tempted to add details to Plato's story in order to make it more problematic and controversial: I am uncertain whether the man is really insane, and whether he just wants to sell the weapons because he has run out of money. Further, there are enemy forces attacking the town and having his weapons is the only chance the man has to escape.  Such a story is useless in Socratic discussion, because these details make it uncertain whether giving the weapons back is admirable or not admirable.  (Using it would be like using data from a faulty thermometer in a scientific experiment.)  To make sure the story is useful, add details to make it ridiculously obvious that it is not admirable, as for example: The man has been acting insane for months, there is no enemy he needs the weapons to defend himself from, he is dragging his little daughter behind him saying he wants the weapons to kill her.

("But there will not be 100% agreement even on apparently clear cases like the person insane wanting his weapons back." There will always be some individual, perhaps a sociopath, who disagrees."  Yes.  But critical reconstruction makes this irrelevant, because this is self-critical self-exploration by individuals, so universal agreement is not essential.  What is important is:

(1) that the individual not base her discussion on dilemmas where she herself is unclear as to what is admirable and not admirable.  If you find yourself discussing pro's and con's, whether some given action is admirable or not admirable, you know you are on the wrong track.

(2) that individuals think up clear and unproblematic stories that undermine their own beliefs, not stories that illustrate and support their beliefs.  Don't use stories as an occasion to assert and support some favorite principles that you know to be controversial.  This will be explained in principle #3 below.)

("But everyone's personal perceptions are subjective, and colored by socialization, particular cultural concepts and assumptions, and individual personal life-experiences.  If this reasoning is based on such subjective and culturally conditioned perceptions, it cannot possibly provide objective and universally valid knowledge free of individual subjectivity and cultural conditioning."  Yes.  But critical reconstruction renders this objection irrelevant, because such objectivity and culture-free universality is not the goal to be achieved by this reasoning. This principle states really nothing beyond what most people assume in leading their everyday lives.  Many fairly clear cases present themselves to us, and hardly anyone seriously doubts that all of their subjective and culturally conditioned moral perceptions are unreliable.)

This principle assumes that personal perceptions of what is admirable and not-admirable have a kind of "soft objectivity." That is, they do not have the kind of hard objectivity characteristic of scientific data gathered by scientific instruments.  (Only human subjects have moral perceptions.)  Nonetheless they have a kind of "objectivity" in the sense that a given individual either perceives some action to be admirable, or doesn't perceive it -- perceiving something to be morally admirable is not a matter of arbitrarily choosing to label it "admirable."  "Soft objectivity" is explained in more detail in Appendix 1 below, and some relevant fundamental philosophical problems are discussed at considerable length in another essay Why is this not Relativism?

This second principle, proposing perceptions of what is admirable/not-admirable in concrete cases as the ultimate basis for knowledge of Platonic Forms, is partly derived from passages in Plato's Republic chs. 5-7, suggesting how knowledge of abstract Forms can be derived from such concrete perceptions.  This is explained in another essay Key Passages in the Republic on the Forms.  This aspect of the present critical reconstruction of Plato's thought differs completely from a common interpretation among philosophers today, who think Plato believed that knowledge of the Forms is a priori knowledge, arrived at by pure reason with no basis at all in what we perceive with our senses.  I explain the reasons for this departure in Appendix 2 below.

There are potentially thousands of virtue-Forms more perfect in their goodness than the imperfect virtue-concepts people usually use for self-evaluation and to model their characters on.  So there is no need for everyone to agree on their choice of which perfect virtue-concepts to adopt for these purposes.
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The Third Principle: The negative use of unproblematic stories in Socratic Questioning.

Here we get to the actual technique of Socratic reasoning. This is based on a few deceptively simple ideas:
    What we are after is some general concept of moral goodness that I can know to be only and always admirable. (This is what would make it deserving of my unreserved commitment, deserving to serve as a norm for self-evaluation.)
    Think of some general concept such as "tell the truth." If I can tell a clear and unproblematic story in which a person "tells the truth" but in my perception is clearly not admirable, this shows that the phrase "tell the truth" does not represent something always admirable (assuming again that personal perceptions of what is admirable and not admirable in clear concrete cases are a reliable source of knowledge).
    One possible story: Sue tells some malicious gossip about what Liz did long ago, for the purpose of stealing a promotion which Liz deserves but Sue does not. This story is a "counterexample" to the phrase "tell the truth." If we accept clear and unproblematic stories as a reliable source of moral knowledge, this counterexample proves that the phrase "tell the truth" does not represent something only and always admirable.
    This counterexample proves that it would be a mistake to take the rule "tell the truth" as an invariable norm for self-evaluation, thinking that no matter what the circumstance I can be proud of myself for telling the truth (even if it is malicious gossip), and I should feel guilty if I say something that is not the truth (even if it is just telling a white lie to get my friend to come to a surprise birthday party).
    Since personal perceptions of what is admirable and not admirable in clear concrete cases is the ultimate basis of all moral knowledge, whenever such concrete perceptions (it's right to lie to a murderer to protect his intended victim) conflict with general principles ("always tell the truth"), priority should be given to the concrete perceptions. Such conflicts always show a weakness or ambiguity in the general principle.
    This use of counterexamples constitutes "Socratic questioning," and is a way of proving that some particular concept or verbal expression does not precisely represent something only and always admirable.  A counterexample shows that some given concept or principle does not qualify as a "Platonic Form."
    It also suggests a procedural definition for what would qualify as a Platonic Form: A Platonic Form is a virtue-concept that would withstand the most strenuous Socratic questioning by means of counterexamples.
    Socratic questioning resembles modern scientific method. In science also, if empirical data contradicts some general theory, this is taken to show a weakness in the theory, needing remedying by refining the theory.  The difference is that science relies on completely objective data, whereas the "data" that Socratic questioning relies on consist in non-controversial but still "subjective" human perceptions (such as the wrongness of returning weapons to an insane person), which will not show up on any scientific measuring instrument, meeting the requirement of completely "objective" scientific data.

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    Two further comments must be made about this Socratic mode of critical reasoning.
    First, it must be a self-critical examination of the beliefs of a single individual, based on objections also recognized as valid objections by this same individual. It is basically a method of uncovering conflicts and contradictions within a single individual's beliefs and perceptions. (I might think I believe in the principle "always tell the truth" but I also think it is OK to deceive someone to get them to come to a surprise party. My perception in this particular case conflicts with the general principle I thought I believed in.) This makes Socratic reasoning different from a combative argument or debate between two people, a competition between the beliefs of two people with different beliefs and perceptions.
    Secondly, good Socratic questioning requires a sincere and strenuous attempt to discover or make up counterexamples that reveal such internal contradictions and conflicts within an individual's own thought, and so undermine this individual's confidence in her own beliefs. This is contrary to the normal habit in which a person tends to make up and want to consider only stories that support her beliefs.
    (In Plato's dialogues, Socrates plays the part of the one bringing up counterexample-objections. But it is important that the person he is talking to agree to the point of the objection, acknowledging this as a contradiction within his own thought, not a conflict between his views and Socrates' views. This means there is no reason why a person cannot engage in this kind of self-critical self-exploration by herself, provided she is willing to engage in strenuous attempts to think up counterexamples undermining her confidence in her general beliefs.)
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  Socratic questioning proves an amazingly powerful negative tool.
    One thing it easily demonstrates is the Platonic principle that pure goodness can never be represented by any rule for concrete visible behavior. To show this, think of the example of a terrorist who hires the wisest moral philosopher to tell her how to behave on every occasion in order to appear to be an admirable person. She does this for the purpose of gaining the confidence of her neighbors so she can blow them up. No matter how good the rules or advice you gave this terrorist, if it is advice regarding external visible behavior, she could do it for evil reasons.

To put this in most general terms: External behavior can always be counterfeited. Admirable visible behavior can be done for bad motives. In Plato's language, visible external good behavior is always the "appearances" of admirable virtue, not the "essence" of admirable virtue itself.
    Socratic questioning relies on something most of us experience in everyday life, the conflict between general rules ("tell the truth") and our perceptions of what is right/wrong in individual situations (it is OK to tell Jane a "white lie" to get her to a surprise birthday party). Our customary response is to just "fudge" our way through these situations, leaving our belief in simple general rules intact, but feeling justified in breaking the rules in exceptional circumstances, with perhaps only a vague tinge of guilt. Plato's Socrates is not content with such fudging on "exceptional" occasions, but goes about systematically undermining people's confidence in the general rules, by actively seeking out or making up cases in which clear perceptions in individual cases contradict the general rules. Plato also is not content with fudging, but seeks out a way of resolving these contradictions, arriving a general moral norms for self-evaluation that can survive the severe tests of Socratic questioning. These norms take the form of pure and perfect virtue-concepts that constitute "Platonic Forms."
    Anyone who seriously tries to practice Socratic questioning even for a short time soon discovers how amazingly difficult it is to give a verbal description of a virtue-concept that will withstand strenuous Socratic questioning.  (All of Plato's "Socratic dialogues" end inconclusively.)  It is not just a matter of hitting on some ready-made familiar concept or set of words that will fit the bill. Rather, it is a creative process of trying to articulate something exceedingly difficult to articulate. Doing this well requires developing some particular mental skills, particularly the ability to think in abstract and unusual concepts separate from anything concrete or visualizable

("But this means that this reasoning sets itself an unrealistic goal, a goal that can never be finally achieved."  Yes. If you want a realistically achievable goal, think of the realistic goal as continually improving your moral ideals.  You can realistically expect that, if you do this reasoning well, you will end up with moral ideals better than the ones you began with.  But of course you achieve this realistic goal of continual improvement by trying to get as close as you can to the more distant goal of arriving at a virtue-concept that could survive all Socratic questioning.  It's apparent that this distant goal is very difficult to achieve, and we can never be absolutely sure we have achieved a absolutely final answer, and no more improvement is possible.  [Is this true of any knowledge outside of mathematics?]  We can't know for sure ahead of time that this distant goal is definitely unachievable.  I propose that the essence of romantic love described at the end of the "How to" essay comes very close.  But this doesn't essentially matter.  The exercise is morally useful if it improves your moral ideals.)

("But why is it necessary to do this?  A person can be a very admirable person without going through this rational process.  Further, why is it necessary to want to become a more admirable person in the first place?"  Yes, it cannot be rationally shown to be necessary to want to be moral at all.  There is no relevant other reason to want to be morally admirable.  A desire to be morally good for its own sake is what makes a person morally good.  Wanting to be good for some other reason does not make a person a good person.  This method will only be useful for a person who wants to become a more admirable person, for its own sake.  And yes, later essays will argue that early Buddhists and early Christians developed extremely admirable moral ideals without the use of systematic critical reasoning.  This can be true of many other individuals and groups.  It is overambitious to claim that this is the only way of improving one's moral ideals or becoming a more admirable person, or even that this is the only rational way of doing this. [How could I know this?]  "Putting on the Socratic hat" requires pretending for the moment at least that you are a person who wants to improve her moral character for its own sake, and who wants a rational way of dealing with the many problems involved in developing higher moral ideals.)

There are potentially thousands of virtue-Forms more perfect in their goodness than the imperfect virtue-concepts people usually use for self-evaluation and to model their characters on.  So there is no need for everyone to agree on their choice of which perfect virtue-concepts to adopt for these purposes.

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The Fourth Principle: The use of positive unproblematic examples to arrive at Platonic Forms.

This fourth principle has to do with the positive relation between concrete examples and abstract Platonic Forms. It can be stated in two parts:
    A- Concrete examples and easy-to-understand concepts of goodness are our only direct source of knowledge of virtue. They are most readily accessible to understanding, but also imperfect in their ability to represent something only and always admirable.
    B-Platonic Forms are pure and precise representations of what is only and always admirable, but they are hardest to grasp, and least readily accessible to understanding. We only come to know them by using concrete examples and familiar concepts as starting points. The way we come to know them is by generalization from, and refinement of, our perceptions of concrete admirable examples.
    Some analogies will help here:
    - Pure silver exists in silver ore, but it exists there in an impure way, mixed with other things. We get pure silver by starting with impure silver ore and refining it to extract the pure silver from the rest of the materials in the ore. In the same way, it can be said that pure goodness exists in our perceptions of goodness in concrete cases. But no particular concrete case represents something purely, only and always admirable. Platonic reasoning is a process of mentally extracting pure and perfectly refined concepts of goodness from these imperfect concrete representations.
    - Suppose I want to make rose perfume, "rose essence." The fragrance I want exists in rose bushes, but it exists there in a diluted form mixed with many other things. Distilling rose essence requires somehow isolating just that liquid in the rose that contains the fragrance, separating it from everything else in rose bushes, and distilling it down so that it has this fragrance in its most pure and concentrated form. Then I would have rose-scent in its most intense form, more intense than it actually occurs in roses.
    In the same way, the Platonic Form of Courage, a Platonic "essence" of Courage, exists in our perceptions of particular concrete visible examples of courage -- a soldier standing at his post, a fireman saving someone from a burning building. But no particular visible example of courage represents something only and always admirable. We come to know the Platonic Form of courage by mentally extracting a pure concept of courage from such concrete examples.
    This point can be put in another way by thinking of precise "articulation." As an example, in Plato's dialogue Laches, Socrates asks the Athenian general Laches "What is courage?" Laches answers, "It is standing at one's post and not running away." Socrates poses some counterexamples, for instance a case in which an army's strategy is to fake withdrawal for the sake of an ambush. In this case "standing at one's post" would not represent admirable courage. This shows that the phrase "standing at one's post" does not represent something only and always admirable.
    But Laches was not completely wrong when he started by reaching into his memory for a concrete visual image of a courageous person. Concrete examples of courageous actions are our only source of knowledge of the virtue of courage. Laches' problem was a problem of inadequate articulation. He was right to admire soldiers he had seen standing bravely at their posts. It's just that "standing at their posts" did not articulate in a very precise way what it is that he actually admired. If it did, then he would admire everyone who stands at their post under any circumstances, which he really does not.

In Plato's language, "standing at one's post" represents the external "appearance" of courage, not its inner and invisible "essence." This essence of courage lies buried somewhere in his perception of visible courageous actions. Verbalizing this essence would mean articulating in a very clear and precise way what it is that he actually did admire. Later in the dialogue, Laches actually makes some progress in this more precise articulation when he revises his definition and says "courage is a certain tenacity of soul." Under further Socratic questioning, this proves to be not fully satisfactory, but it is a step in the right direction. "Tenacity of soul" clearly remedies the weakness and ambiguity that earlier counterexamples had revealed in the phrase "standing at one's post." One can also note that "tenacity of soul" articulates something more internal, invisible, and abstract than "standing at one's post."
    Using the concept of "articulating" to clarify this aspect of Socratic/Platonic reasoning highlights its creative character. Coming to know the Platonic Form of some particular virtue is not a matter of surveying already-clear, familiar, ready-made concepts and words, and just hitting on the right one. It means trying to find creative ways of articulating something very difficult to articulate. Paradoxically, a Platonic Form is something one already knows, but is most difficult to know. That is, it is paradoxically something one already knows, and something most difficult to know -- i.e. something one already knows intuitively in a vague and confused way, but something very difficult to articulate in a very clear and precise way.
    Plato's favorite way of representing this relation between concrete perceptions and abstract Platonic Forms is to say that concrete reality "participates in" the abstract Forms. A courageous action on the part of a particular soldier is not itself the pure Platonic Form of Courage, but this concrete courageous action "participates in" the Platonic Form of Courage.

A concrete example of courage gives us access to knowledge of pure and perfect Courage, because it "participates in" this pure and perfect Courage. But participation also explains how the ideal Platonist as an individual concretely existing in this world relates to the transcendent otherworldly Platonic Forms. She never expects to concretely realize the full perfection of the Platonic Forms in her own being, but tries to approximate or "participate in" them as much as she can in her inevitably imperfect concrete individual existence. In my terms, when she considers who-I-am for purposes of self-evaluation, she does not measure herself in terms of any prescriptions for external behavior, but in terms of how well she approximates the pure and perfect virtue-Forms she has come to know through Socratic/Platonic reasoning.

There are potentially thousands of virtue-Forms more perfect in their goodness than the imperfect virtue-concepts people usually use for self-evaluation and to model their characters on.  So there is no need for everyone to agree on their choice of which perfect virtue-concepts to adopt for these purposes.

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This idea of the positive relation between imperfect concrete reality and perfect Platonic Forms is best represented in the image of a mental "ladder" in Plato's Symposium.  It formed the basis for a later Christian tradition concerning the possibility of knowing God, known as the doctrine of "Analogy."  For example, God's love is thought to be completely perfect, unlike the imperfect love we are familiar with in human life.  But the imperfect love easily accessible to human understanding is analogous to God's perfect love, and so we can come to understand God's perfect qualities by using imperfect human examples as starting points, then imagining what these qualities would be at their most perfect.  This is a way of climbing a mental ladder from imperfect concrete reality to perfect transcendent reality.

I will call this fourth principle "The Principle of Analogy and Participation," or "Plato's Ladder," and will make extensive use of this idea in subsequent treatment of early Buddhist and early Christian ideas.

 

Here is the Symposium passage describing "Plato's Ladder":

[To learn about beauty, one should] start when young by pursuing beautiful bodies. First... he will love one beautiful body... then he must realize that the beauty attached to one body is kin to [the beauty] attached to another body, so if it is necessary to pursue beauty in Form, it is great folly not to regard as one the Beauty found in all bodies. Realizing this he must make himself a lover of all beautiful bodies...

After this he must realize that the beauty in souls is of much more value than the beauty in the body, [so that] if there is a soul with a little bloom [of beauty] beginning in it, he will love and care for it...

Contemplating [many specific] beautiful things rightly and in due order... he will suddenly have revealed to him something wonderful...

This [the Form of Beauty] is something always-being, not coming into being and perishing, not increasing and decreasing... It is not partly beautiful and partly shameful, nor now [beautiful] now-not [beautiful], nor in some respects beautiful and in some respects shameful... Nor will the beautiful appear to him as a face, or hands, nor any other part of the body... nor something existing in something else... but always being something single-formed having its own being with itself in itself... All other beautiful things participate in this, in such a manner that, while these other things come into being and perish, this thing becomes neither greater nor lesser...

Beginning from those beautiful things, always ascending upward for the sake of The Beautiful, like someone using the steps of a ladder, from one to two, and from two to all beautiful bodies, and from beautiful bodies to beautiful institutions, and from institutions to beautiful learnings, and from beautiful learnings... to that learning which is none other than the learning concerning The Beautiful...

What would you think if it happened to someone to see The Beautiful, exact, pure, unmixed... [What if] he were able to see unique Divine Beauty? Does it seem to you a trifling life for a man to lead, looking ‘over there,' contemplating it the way it should be [contemplated]?...

Seeing The Beautiful through what is visible, [he will] bring forth not images of virtue [aręte], since he is in touch not with images [of virtue] but with true [virtue]... When he has brought forth and reared true virtue he is destined to become God-pleasing.

(Note that whereas the English word "beauty" has strong associations with visual beauty, the Greek word Plato uses is kalos, which also has a broader meaning of "fine," "noble," or "refined."  This is why Plato can refer to "beautiful laws and institutions," and also regard "beauty" (to kalon) as a personal "virtue" (arētē). ML)

There are potentially thousands of virtue-Forms more perfect in their goodness than the imperfect virtue-concepts people usually use for self-evaluation and to model their characters on.  So there is no need for everyone to agree on their choice of which perfect virtue-concepts to adopt for these purposes.

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The theoretical basis for this kind of reasoning.

So far as reasoning is concerned, the present critical reconstruction consists mainly in a theory derived from Plato about the complex relation between the concrete, visible, familiar world around us, on the one hand, and pure and perfect, "otherworldly" Platonic virtue-forms on the other. 

Socratic/Platonic reasoning is a reasoning method based on this theory. Another essay, Key Passages in the Republic on the Forms explains the textual basis for this theory.

The essential elements of this theory are as follows:

1- Our perceptions of the concrete, visible, familiar world around us are ultimately the only basis for moral knowledge, and so constitute an indispensable starting point for knowledge of perfect Platonic Forms ("bottom rungs" on Plato's ladder).  "Perceptions of concrete visible reality" here consist in personal perceptions of concretely visualizable human behavior in the case of clear concrete stories.  We only acquire knowledge of admirable courage, for example, by being exposed to visualizable concrete behavior exhibiting admirably courageous behavior.  (We cannot directly intuit "the essence of courage," by trying to examine concepts somehow present in the mind independently of such concrete experience.)

My critical reconstruction of Socratic reasoning relies at this point on a concept of what might be called "soft objectivity." explained in an Appendix below.

2- The intellectual mistake people commonly make is to stick with images of concrete visible reality when they try to define moral ideals as bases for self-evaluation.  Because of concrete-mindedness, they remain on the bottom rungs of Plato's ladder, refusing to try to climb higher mentally, to more perfect virtue-concepts at the top of the ladder.  Concrete reality, whatever can be represented in concrete, visualizable imagery, and all concepts simple and easy to understand, are inevitably imperfect, not worthy of unreserved commitment and loyalty.  (This negative aspect of concrete reality (more exactly of concrete-mindedness), is represented in Plato's Parable of the Cave [see Excerpts from Plato #8].  Concrete-minded people are confined to a cave, seeing only shadows cast by realities in the Real World outside the cave.  The "Real World" is the world of Platonic Forms, cave-shadows are visible reality that imperfectly participate in the Forms but are not the perfect Forms themselves.)

3- As to living one's life, an individual person cannot expect to actually and fully become perfect as the Forms are perfect.  All concretely existing individuals, and all concrete human life and conduct, belong to the imperfect world "here below."  It would be a mistake to try to live in the other world of perfect Forms.  But it's also a mistake to take the concrete visible achievements, or the concrete norms of society, as an evaluative context for defining one's moral identity, allowing one's self-esteem to depend on these.  Perfect Forms are alone deserving of unreserved loyalty and commitment, and alone deserve to be taken as norms for self-evaluation and for defining one's moral identity.  The ideal Platonist keeps her mental eyes fixed on the perfect Forms and tries to make her life "participate" in the Forms as much as possible.

There are potentially thousands of virtue-Forms more perfect in their goodness than the imperfect virtue-concepts people usually use for self-evaluation and to model their characters on.  So there is no need for everyone to agree on their choice of which perfect virtue-concepts to adopt for these purposes.

 

Possible topics for discussion:

Compare and contrast the Socratic reasoning described here with other kinds of reasoning you are familiar with.  What are its distinctive goals, its basis, the assumptions it is based on, or its methods?

How can this kind of reasoning support Plato's otherworldly worldview?

How is this related to Plato's picture of Socrates as someone who combines fundamental questioning of all moral ideas, with extreme moral idealism?

Describe the complex relation between concrete visible reality and transcendent abstract concepts implied in this reasoning method (concrete visible reality is our only basis for moral knowledge; but moral knowledge will always be imperfect and full of contradictions as long as we try to think n concrete images).

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The next essay assigned after this will describe how this works in practice.  If you want a preview, you can look at:

A Socratic discussion of patience (This is based on a paper written by a former student, and will give you an example of how Socratic discussion works in practice.  Giving a Socratic discussion of a virtue of your choice will be one option for the first graded paper.)

 

Appendix 1: Soft Objectivity

 The basis of Socratic reasoning, in personal perceptions of what is admirable in the case of concrete stories, is more subjective than the hard data relied on today in the physical sciences.  Only humans have perceptions of what is morally admirable and not admirable -- this is not something that will register on a scientific instrument.  But these perceptions are not "subjective" in the sense that a person can make them be whatever she arbitrarily decides she wants them to be.  In this sense, "admirable" is like "funny."  Only humans perceive jokes to be funny -- "funniness" is not a fully objective characteristic of a joke in the way that the force of gravity is a fully objective characteristic of material objects.  But I can't make myself perceive a particular joke to be funny just by arbitrarily labeling it "funny."  Given the kind of person I am, I either I perceive it to be funny or I don't.  "Funniness" has this kind of "objectivity," a "soft objectivity" in contrast to the "hard objectivity" of the force of gravity. 

"Interesting" is a similar concept.  Either I find something interesting or I don't.  If I don't, I can try to see it from some different perspective that will make it interesting to me.  But again there are often limits to what I can do in this regard -- try as I may, there are some things that will not appear interesting to me, no matter what I do.  It clearly is not just a matter of applying some intellectual judgment and arbitrarily labeling something "interesting."

This is why I use the word "admirable" throughout these essays.  It seems to be a word easily understood to have roughly the same kind of soft objectivity as "funny" and "interesting."

This is a crucial issue for the present reconstruction of Socratic reasoning.  Consider again the Republic passage about the weapons-owner gone insane.  Socrates whole argument in this passage depends on uncovering a contradiction between a general principle Polemarchos wants to uphold ("rightness consists in giving to each what belongs to him"), and his actual personal perception that it would be clearly "not right" to return weapons to a man gone insane.   Socrates' argument depends on Polemarchos treating this latter perception as having a certain kind of objectivity, i.e. his perceiving it as something "not right" is something he cannot arbitrarily control.  The point of the argument is that this perception stands in opposition to a general principle "give to each what belongs to him," and that this conflict reveals an inadequacy in the general principle.  This assumes two things:

(1) Perceptions are to a great degree independent of the conscious general principles Polemarchos thinks he believes in (like "give to each what belongs to him").  Conscious beliefs like this are subject to his control -- he could choose to believe in, or not believe in, the principle "give to each what belongs to him."  Perceptions, on the other hand, have a kind of objectivity (soft objectivity), independent of such conscious choice.  If perceptions were not to some degree independent of consciously held moral principles, there could be no conflict between them (Polemarchos could simply declare that it is right to return weapons to an insane person, because this is what his consciously held principle declares to be right.)

(2) Perceptions are more reliable as sources of moral knowledge than general principles -- this is why conflicts between perceptions and general principles show that there is something faulty about the general principles, not that there is something faulty about the perceptions.

Some will object, of course, that the moral perceptions of individuals have always been ultimately shaped by cultural conditioning some time in the past, i.e. by some teaching about consciously held moral principles taught them by their parents and their society.  This is why I speak of "soft objectivity."  Cultural conditioning is necessary to become fully human, and different cultures produce different kinds of cultural conditioning.  Nonetheless, given the culturally conditioned person that I presently happen to be, conditioned in some particular culture, some jokes will appear funny to me and others will not.  If I had been raised in a different culture, my sense of humor might well be different from what it is, and I would perceive different jokes to be funny.  But actually I am currently the particularly-conditioned person that I am, and being this kind of person puts perceptions of funniness beyond the control of my present conscious decision-making. 

The same is true of moral perceptions, perceptions of what is admirable and not admirable in concrete cases.  All these perceptions have been shaped by particular cultural conditioning.  But being the particularly-conditioned person that I am, puts perceptions of admirable/not-admirable beyond the control of my conscious decision-making.

In this critical reconstruction of Socratic reasoning, then, this is an "empiricist," "inductive" mode of reasoning -- deriving general virtue-concepts by generalization from concrete observations.  (This is in contrast to "deductive" models, which take general moral principles to be the most reliable basis for moral knowledge.)   Socratic method thus resembles method in the physical sciences, which derive general principles from concrete observations, and regard general principles as always subject to possible revision in the light of newly discovered observations.

The big difference is that the physical sciences rely on hard data, having a kind of "hard objectivity," i.e. data which are as much as possible independent of human subjectivity.  For example, dipping one's finger into water to find out how hot it is is too "subjective."  Scientists put thermometers in the water and observe more objectively the interaction between the water and the mercury in the thermometer.  But no scientific instrument will register and measure "morally admirable" or "morally not-admirable."  Only culturally conditioned humans have such perceptions.

From the point of view of modern philosophy, this proposal that personal perceptions of what is admirable and not-admirable are the most reliable source of moral knowledge, is probably the most controversial proposal in this critical reconstruction of Socratic/Platonic thought. This is because, ever since Hume and Kant, modern philosophers have only recognized two valid bases for knowledge of any kind: (1) purely objective "hard data", of the kind the physical sciences are based on, or (2) Self-evident, "necessary" truths, of the kind that mathematics is traditionally based on.  This explicitly excludes perceptions based on the subjective perceptions of culturally conditioned individuals -- the whole intent of modern philosophy has been to overcome the supposed narrowness and particularity of culturally-conditioned particularity, which the present critical pluralist Platonism fully accepts and embraces.

I attempt a full discussion of the very fundamental philosophical issues surrounding culturally conditioned "soft objectivity" in a different lengthy essay "Why is this not relativism?."  This essay develops the thesis that "morally admirable" is one kind of significance that human beings perceive certain actions and certain character traits to have.  It discusses the "soft objectivity" of moral perceptions in the context of a broader discussion of significance.  "Funny" and "interesting" are also kinds of significance.  "Significance" is always relative to particular "subjective" human concerns, and to certain culturally-particular interpretive categories that shape the experience of individuals.  But for any given, particular individual, significance has soft objectivity, something an individual perceives, not a matter of how she consciously and arbitrarily decides to label things.

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Appendix II (for Philosophers):

The Question of A Priori Knowledge of Platonic Forms

The Socratic "midwife" principle asserts that gaining knowledge of virtue is not a matter of teaching someone something they do not know, but a matter of drawing out of an individual something they already know.  One passage in Plato's Meno illustrates this principle by having Socrates "draw out" of an uneducated slave-boy the knowledge of a not-very-obvious abstract theory in geometry, by a series of small observations of figures Socrates draws in the sand, each of which is obvious to the boy who has no previous knowledge of geometry-theories.  Plato then goes on to connect this example to a particular Pythagorean belief in the pre-existence of an disembodied soul, by claiming that this example shows that the uneducated boy must have known the theory in question when he was a disembodied soul.   The Phaedo also shows Plato trying to make a connection to Pythagorean theories about the pre-existence of an immortal soul, adding that knowledge of abstract Platonic Forms is only fully possible when the soul is in a disembodied state, so that Reason can operate free of interference by the senses.

Subsequent philosophical commentators have connected these passages to an idea developed by subsequent philosophers, of a priori knowledge, knowledge gained by "pure reason," operating prior to and independent of any knowledge of the concrete world perceived by the senses.  For many centuries, Euclidean geometry served as the paradigm of such a priori knowledge, since it rests on five "self-evident" axioms, such as the axiom that "the shortest distance between two points is a straight line."  The truth of this axiom is obvious and unavoidable to anyone who knows the meaning of the terms "shortest," "distance," "points," and "straight line."  This truth is so obvious to reason that it can be known independently of any actual experiments measuring the length of various lines connecting two points.  We can be absolutely certain ahead of time that we will never in the future encounter a case in which the  shortest distance between two points is not a straight line.  (The Latin phrase "a priori" means roughly, "from the first," i.e. we fully know this statement is true just by looking at it, "prior" to any further experiments to see if we can find a case where it is not true.)

But there are several problems with the idea virtue-Forms can be known a priori, and that Plato himself thought this.

The main problem is that, for subsequent philosophers, the idea of a priori knowledge was tied to a particular epistemology, a rational method by which one could come to know certain truths.  This is especially evident in Kant's Critique of Pure Reason, which consists of a long critical inquiry into the question concerning what we can and cannot know by "pure reason," i.e. about possible epistemological bases for knowledge of a priori truths.

By contrast, Plato's idea that knowledge of abstract geometry-theories and abstract virtue-Forms are innate in disembodied souls, is connected to no epistemology whatsoever.  Plato never makes this idea the basis for any rational method which a person in a present embodied existence could use to arrive at knowledge of abstract truths.  (Appendix III below explains the differences between (a) a priori knowledge, (b) the Socratic method of drawing on ideas presently "innate" to already socialized adults, and (c) the modern idea of innate knowledge "hard wired" into all infants at birth, prior to socialization.)

It is very striking that, even though the Meno passage uses geometry as an example, it proceeds in a way completely opposite to the Euclidean method of first positing five abstract truths as axioms known a priori, then proceeding to deduce theorems by from these axioms.  The theory that the boy arrives at is recognizable as what came to be called the Pythagorean Theorem in Euclidean geometry.  What's remarkable is that the actual method by which the uneducated boy arrives at this theory has nothing to do with deduction from self-evident axioms known a priori.  It is rather an "inductive" method based on abstractions from a series of sensory observations of visible squares and triangles that Socrates draws in the sand (in philosophical terms, methodologically, the boy's knowledge has been gained not a priori, but a posteriori, after ("posterior" to) making many factual observations about concrete figures drawn in the sand.)

(Euclid was a pupil in the Platonist Academy after Plato's death, and it is not even completely certain that the full text and system we know as Euclid's Geometry was actually written by this person.  It is also not certain that Pythagoras discovered the so-called Pythagorean Theorem, and if he did it is highly  unlikely that he arrived at it by deductions from the so-called Euclidean axioms developed several centuries later.)

Secondly, is it even remotely plausible that perfect virtue-concepts could be known a priori, in the same we know that 2 + 2 = 4?  It's hard to see how any person with half a brain could think that there is some specific definition of courage or love at their most perfect, that would be as obvious and unquestionable as 2 + 2 = 4.  Plato certainly never attempts anything like a rational demonstration of this kind.

Kant's comments on Plato in this regard are very interesting.  On the one hand, he thinks Plato must have been trying to found his theory of otherworldly Forms on truths known a priori by pure reason.  On the other hand, he clearly recognizes that Plato actually has no viable theory of a priori knowledge.  Consequently, in his Critique of Pure Reason, Kant compares Plato to a flying dove. The dove sees that friction with the air is impeding his flight, so he imagines that if he flies up higher and higher where there is no air, he will be able to fly much more easily. The moral: Plato saw that the necessity of finding rational support for his beliefs was an obstacle to holding the idealistic and otherworldly beliefs he wished for, so he decided to "fly higher" to develop knowledge unrestricted by the need for rational evidence. But of course just as the high-flying dove lacked air to support his flight, Plato also left the realm where his knowledge could be supported by any rational method.  Plato becomes for Kant a kind of paradigm of all those unfounded claims to a priori knowledge against which his Critique of Pure Reason was written.
    Here is what Kant says:

The light dove, piercing in her easy fight the air and perceiving its resistance, imagines that flight would be easier still in empty space. It was thus that Plato left the world of sense, as opposing so many hindrances to our understanding, and ventured beyond on the wings of his ideas into the empty space of pure understanding. He did not perceive that he was making no progress by these endeavors, because he had no resistance as a fulcrum on which to rest or to apply his powers, in order to cause the understanding to advance.
It is indeed a very common fate of human reason first of all to finish its speculative edifice as soon as possible, and then only to enquire whether the foundation be sure. Then all sorts of excuses are made in order to assure us as to its solidity, or to decline altogether such a late and dangerous inquiry. (I. Kant, Critique of Pure Reason. tr. Max Mueller. New York: Doubleday. 1966, p. 6.)

I agree completely that Plato offers absolutely no rational grounds capable of showing that Plato's virtue-Forms are categories of "pure understanding," known a priori by "pure reason."  My critical reconstruction of Platonism draws the conclusion that we should not interpret Plato's Form theory in this way at all, but should find some other way of interpreting it that has nothing to do with ideas developed by subsequent philosophers concerning a priori truths or pure reason.  I find the basis for an alternate interpretation mainly in some passages in the Republic chs. 5-7, presented with commentary in another essay, Key Passages in the Republic on the Forms.  This essay argues that, from an epistemological point of view, these passages assume that all moral knowledge is inductive, ultimately based on generalizations from what Plato calls aisthesis, "sense perception," which for him includes perception of what is right and not right, admirable and not-admirable, in concrete cases.  Noesis, the mental capacity to grasp abstractions, is the opposite of aisthesis.  But noesis is not "pure reason" in Kant's sense, a way of knowing self-evident truths that is completely separate from and independent of aisthesis Noesis is called upon to resolve problems unresolvable by aisthesis, but would never arise if one did not have a basic trust in the deliverances of aisthesisNoesis can be thought of as a kind of "pure reason" in that it is a grasp of abstractions that have become separated from anything audible or visualizable.  But these are abstractions derived by mentally separating abstract concepts from concrete sense-perceptions.

As to Plato's way of connecting knowledge of the Forms to belief in soul capable of existing without the body, from the present perspective this is due to Plato's attempt to connect his Form theory to some beliefs of Pythagoreans, an ascetic religious group Plato admired when he met some of them on his trip to Sicily.  These beliefs have become a liability rather than an asset to Platonism today, and should be allowed to fall without bringing the entire Platonist edifice down with them.

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A final note on the idea of self evident-truths as "necessary" truths: For centuries, Euclidean geometry was regarded as the paradigm of an Absolutely Certain and Universal science, which had shown itself to be the one and only true geometry.  This is because it rests on five "self-evident" axioms, and a large set of theorems that follow by strict logical deductions from these five axioms. 

This claim to be the one and only true geometry turned out to be based on a confusion between (1) claiming that some truths are a "necessary" truths because they are self-evident, and (2) claiming that Euclid's five axioms are the one and only  necessary choice of axioms that everyone must use as a basis for a system of geometry. 

The reason this is a confusion: Knowing that one particular set of truths (like Euclid's five axioms) is self-evident is different from knowing that there are no other truths that are equally self-evident.  Morris Kline's history of mathematics, (Mathematics: The Loss of Certainty) is partly the history of the loss of certainty that there is one and only one true geometry, due to the development of non-Euclidean geometries.  This is due to the discovery that changing the definitions of some concepts in geometry will yield a different set of fundamental axioms that are equally self-evident, and that can provide a basis for an entirely different system of geometry.  This does not deny that Euclid's axioms are self-evidently true, it just denies that these are the only axioms that are self-evidently true.

This does not result in complete "relativism" in mathematics, where truth in geometry consists in whatever anyone arbitrarily declares to be true.  It results rather in something like critical pluralism in mathematics: There are potentially many logically consistent mathematical systems, but not just any mathematical system is logically consistent.  This is what I claim for Platonic virtue-Forms.

(This analogy between pluralism in modern geometry to critical-pluralism in moral and religious theory is explained in a 1988 essay I published in the Journal of the American Academy of Religion, "Radically Pluralist, Thoroughly Critical: A New Theory of Religions".  It relies partly on some discussion in Stephen Barker's book The Philosophy of Mathematics. Englewood Cliffs,
N.J.: Prentice-Hall. 1964, p. 25.)

 

There are potentially thousands of virtue-Forms more perfect in their goodness than the imperfect virtue-concepts people usually use for self-evaluation and to model their characters on.  So there is no need for everyone to agree on their choice of which perfect virtue-concepts to adopt for these purposes.

 

Appendix III

On So-Called "Innate Ideas"

Ever since Jean-Jacques Rousseau popularized the idea that civilization corrupts people rather than improves them, Western thinkers have been fascinated by the task of trying to find out what impulse or knowledge is "innate" to all infants prior to being socialized and enculturated into particular societies and cultures.  Often this project is driven by Rousseau's assumption that this universal human nature that makes us all the same at birth is the best state of human beings before society corrupts them, or that the moral knowledge "hard-wired" into all infants is the most reliable kind of moral knowledge.

This might seem superficially similar to the Socratic "midwife" principle, which basically says that moral reasoning needs to start by drawing out and articulating the moral knowledge that is already inside of us, rather than learning "correct" ideas from some outside source.   But Socrates is speaking to adults in his society, drawing out intuitive knowledge that is "innate" to these already-socialized Athenians.   Even though he toys with the idea that they had knowledge of the Forms in some previous disembodied existence, this has no effect on the Socratic method of inquiry. 

As to method, Socrates invites individuals to articulate whatever ideas they happen to have concerning particular virtues, and test those ideas by whatever reactions they happen to have to the counterexamples Socrates uses to uncover unsuspected ambiguities and conflicts in their moral thinking.  He does not invite them to speculate on whether these moral intuitions or perceptions were innate in them as infants, or were something imposed from without by cultural conditioning.

Note also that, when it comes to method, the philosophical concept of a priori truths is completely different from the concept of "innate ideas," understood as what infants are born with.  Discovering what knowledge infants are born with requires examination of factual evidence -- either facts about actual infants, facts about evolutionary history, facts about neurobiology.  In philosophy, knowledge gained by investigation of factual evidence is called knowledge "a posteriori," the exact opposite of knowledge "a priori."  The truth that 2 + 2 = 4 is obvious "from the beginning" (a priori), prior to any further factual investigation, counting different objects.  One can be sure from the beginning, just by understanding the formula, that one will never be faced with a case in which 2 + 2 does not equal 4.  The opposite kind of knowledge, a posteriori, is knowledge that one can only know after ("posterior" to) examining facts.   Traditionally, it is thought that a posteriori knowledge can never attain the certainty attained through a posteriori investigation of facts.  No matter how many facts I have investigated and based my theory on, I can never be certain that there are no further facts that will contradict my theory.