Sorglose Nacht

This post is the inaugural element in what I plan to be an ongoing project into attempting to develop a framework for translating philosophical propositional calculus (PC) into terms that computer programmers can easily understand.

Personally, I find the confluence of factors that motivate this project incredibly interesting; but of course that’s because they’re largely about my life. The next section will talk about some of my motivations, as well as some of the sources I plan to draw on for this project. If you want to skip this section, you can click here.

Background

1. I told you before that my philosophical background is in the so-called continental tradition. What does this mean? Well, one thing that it means is that in my previous philosophical career, I never had to understand the sentential calculus. It’s just not a form of arugmentation that people in that tradition are prone to use.
2. At the same time, I told you that I was applying for PhD studies in American philosophy programs. Most of these programs are couched in the analytic tradition, which is a tradition that is deeply enamored of propositional logic as an argumentation tool. American analytic philosophy in the Russelian tradition - at least in some (admittedly much rarer now) cases - actually situates logic as first philosophy. This is quite a change for a person who comes very distinctly from a tradition that has historically situated everything but logic (i.e. metaphysics, epistemology, ethics) in the big chair.
3. Luckily, in addition to my philosophical interest, I have also been a computer programmer for ten years. This means that I have spent a lot of time negotiating symbolic logic, and as such I imagine or — at least hope — that there’s got to be a strategy to map these things together.

Pedagogy

When I was eighteen, I took a class called Formal Foundations of Computer Science, which was a symbolic logic class. I did rather poorly at this, which should confuse you, given the aforementioned. It confused the heck out of me for just long enough to be disastrous. Only recently, spurred by my partner Nick’s research project in programming pedagogy, did I understand this: the pedagogical model for teaching formal logic to computer programmers should be way more practical than it is (or at least was in my case).

Hence, the following attempt to make logic work. Throughout the following, I will be using the class notes and assignments most kindly provided by the Massachusetts Institute of Technology’s Open Courseware project. The syllabi will be provided courtesy of Prof. Vann McGee’s Logic I and Logic II classes in the MIT Linguistics and Philosophy department. The pedagogical materials will be provided courtesy of Delicious.com and Nicholas Senske of the University of Michigan.

Finally, expect this series to take some time to complete. Let’s get started.

Propositional Calculus for Computer Programmers: Part 1

Today’s course is easy. All we’re going to do is look at the basic syntax of the propositional calculus, and then the truth assignments for its basic operations. Really, nothing to it. I’ll be doing this using C-style syntax.

Syntax

You’ll notice that the last two rows above are logical operations that don’t have C operators. Programming languages usually handle these operations by selection statements. For brevity’s sake, I’ll be using the ternary operation.

function onlyIf(a,b)   { a ? (b ? return true : return false) : return true; }
function ifOnlyIf(a,b) { a ? (b ? return true : return false) : (b ? return false : return true); }

Now, you may remember from way back in your beginning CS career drawing truth tables. Well, that’s what we’re going to be working on now. A final note on my conventions is that you should just assume, from now on that 1 == true and 0 == false.

Truth Assignments for simple PC operations

One last thing to note that’s really convenient for programming types is that when you draw truth tables, an easy algorithm for mapping out your variable columns (in the above case, the first two columns: a, b), you just start from the bottom and count in binary (above: 00,01,10,11). This holds true for n variables.

So the plan is that in the next one of these, we’ll look at the axioms for the PC. I’m hoping that we can figure out ways to make this stuff feel more intuitive for the pragmatic programmer.

Overview

A Stranger, a student of Parmenides, will set out to define the Sophist. Upon reaching the conclusion that the Sophist is one who sells the appearance of wisdom, he will announce that in order to prove this conclusion, an investigation into the nature of non-Being will be required. This will be approached by an investigation into Being itself, which will be divided into five great kinds. By analyzing these, he will prove that the negation of not-being operates on the predicate being, not the subject. Further, negation simply implies difference, not opposition.

Background

This is a late Platonic Dialogue. After criticizing the Middle Period conception of the forms (the theory of separate, immaterial forms) in Parmenides. The Sophist and Statesman show the author’s increasing interest in mundane and practical knowledge.

The Setup

SOCRATES asks an Eleatic STRANGER to help him define the terms “statesman”, “sophist”, and “philosopher”. They start with Sophist. Socrates, remembering the method employed in Parmenides by its’ namesake, asks whether the stranger would like to proceed by Q&A. The Stranger indicates that he would, if someone would not give him a lot of sass-back, but just acquiesce to his points (qua young Aristoteles in Parmenides). Socrates proposes that THEAETETUS will do just that.

1. DIAIRESIS: Since Sophists are slippery to define, the Stranger suggests that they begin by using their proposed method on something easier; say, an angler.
   1. Str. defines two classes of arts: productive (or creative) and acquisitive. Anglers belong to the acquisitive class, which can itself be separated into two: exchange and conquest. Conquest may be further separated into hunting and fighting. Hunting can be divided into animal hunting and the hunting of lifeless things. Animal hunting can be divided into by-land and by-water. By-water into fowling and fishing. Fishing into enclosure (fishing by nets) and striking (by spear). Striking into firing (by night) and barbing (by day). Barb-fishing into spearing and angling (by hook).
   2. This method of definition-finding is called diairesis. Now we’re going to try this method on the Sophist.
   3. The Sophist is acquisitive, and further is a hunter. And a by-land hunter at that.
      1. Hunting on land has two divisions: Hunting tame and wild animals.
      2. Tame animals into hunting with violence [piracy, tyranny], and hunting with persuasion [lawyer, orator].
      3. Persuasion into public and private.
      4. Private into receiving hire and bringing gifts (lovers).
      5. For hire into those whose reward is virtue and whose is money. The latter of these is the Sophist.
   4. Alternatively the Sophist could follow the path of exchange. Exchange divides into giving and selling.
      1. Selling into the sale of one’s own productions (retailers), the sale of others’ (merchants).
      2. Merchants into those who provide food for the body, and for the soul (music, paintings, marionette playing, knowledge).
      3. Food for the soul -> display and (n). (n) -> sale of knowledge of virtue and sale of other kinds of knowledge (art-seller). The former is the Sophist.
   5. A third alternative is that the Sophist follows the path of the fighting arts. This into competitive and pugnacious.
      1. Pugnacious into violent (bodily strength) and controversy (words). Controversey into forensic and disputation. Disputation into without rules and by rules (argumentation). Argumentation into wasting and making money. The later of which is Sophistry.
   6. Fourth, we run down this line: Let’s start with the arts of discernment. This can be split into a) arts that split like from like and b) those that split better from worse.
      1. The latter is called purification, which can be split into purification of living things and of inanimate objects. The former can be split into purification of bodies and souls. The latter can be split into: the purification of vice and of ignorance. (Alternatively the former can be split into gymnastic and medicine.)
      2. The purification of ignorance requires instruction, which can be split into admonition (resolves stupidity - ignorance which thinks it’s knowledgeable), and the dialectical remedy for plain ignorance. The latter of these is the domain of the Sophists.
   7. Thus the Sophist is determined to be:
      1. A paid hunter after wealth and youth (c).
      2. A merchant in the goods of the soul, a retailer of these wares (and one who manufactures them) (d).
      3. A hero of debate (e).
      4. A purger of souls, clearing away notions obstructive to knowledge (f).
2. COMBINATION: With five definitions in hand, they set out to find the common elements of contained within the five.
   1. The Sophist is a disputer, and teaches disputation. That is, the art of argumentation about anything. This means that the Sophists (otherwise they would be bankrupt) are assumed to have knowledge about everything. Thus, Sophists are in possession of a conjectural, non-truthful knowledge of all things.
   2. Sophists thus imitate wisdom, he is like a juggler. And the imitative art, like anything, can be split: a) likeness-making (painters) and b) appearance-making (that is, where one could not get a broad enough perspective on the reality to even understand if there is a likeness or not.
   3. And now, if the essence of the sophist is that he produces appearances, and more precisely false appearances. He imitates the wise man (Sophist 268b-c). But how can we make sense of this appearing but not being, this stating things but not true things? We have to contend once again with Parmenides’ old doctrine: “He who says that falsehood exists has the audacity to assert the being of not-being.”
3. THE RETURN OF PLATO’S BEARD:
   1. To define the sophist as an expert in deception, as someone who produces false appearances by means of statements, the Stranger needs to show that Parmenides was wrong; he needs to demonstrate that it is possible to say and to think that things that are not are, and to do so without contradiction.
      1. We can’t say “things which are not” nor “what is not” because in doing so we attribute singularity or plurality to non-Being, which is inapplicable.
      2. This is the basic Quinean position on Plato: by admitting things that aren’t, you are already contradicting yourself. (Note that this is what propositional logic theoretically resolves - contra term logic - via bound variables.)
   2. Parricide?
      1. We can’t make the “image”/non-being analogy, because the Sophist will show that
         by defining images, we predicate non-being.
      2. False opinion seems to think that things are not are, or vice versa.
      3. Hence, the Stranger will be forced to test the philosophy of Parmenides.
   3. Investigating Being: Number
      1. First of all, all previous theories of being may have taken the concept of “being” as lightly as Theaet. used to take non-being. Thus, let us investigate being first.
      2. Both the concepts of multiplicity and unity run into problems when you assert them of being. Starting with unity, we go through the standard Purity-F regimen:
         1. If Being is one then it is both being and one, and hence not one.
         2. Being can’t parts (a beginning, end).
         3. Yet, if being is not one, it lacks unity, and hence is not whole (everything). Etc.
      3. Hence, maybe we need to throw away the idea that Being is either one or two.
   4. Investigating Being II: Essence
      1. Let’s appeal to various notions of essence (essentially: materialist and Platonic notions).
      2. Starting with the materialists, Str. wants to suggest that being is that which has any power to affect another. Now the appeal is that given bodies (changing) and souls (unchanging; essential).
      3. Further, Being must contain both the movable (insofar as it contains mind, life, and soul) and unmovable (insofar as it contains sameness, etc).
      4. Which is a bit like the problems of (c) above, insofar as both rest and motion require predication, which is thus a third term.
      5. But if the many cannot be one, and the one cannot be many, how again will we attribute being to motion or to rest? In other words, we need an account of how one thing can be called by many names.
   5. Return to Participation: To show that one thing can be called by many names and that some names specify the object but mis-describe it, the Stranger introduces some machinery. He proposes that some kinds can partake of other kinds (these terms appear to be synonyms and to introduce an asymmetrical relation between an object and a property it has), whereas some kinds cannot blend with each other.
      1. Further, there are great kinds that enable the blending of kinds, much as vowels enable consonants to fit together. Even as some expertise is required to determine which letters can associate with which, so dialectic is required to determine which kinds blend and which do not, and which kinds hold everything together and make them capable of blending, and which are causes of division.
      2. The Stranger announces that there are five great kinds. He will ask two questions about them: (1) what are they like? and (2) what capacity do they have to associate with each other? The kinds to be discussed are: motion, rest, being, sameness and difference. Note that these five are not claimed to be exhaustive of all great kinds. Presumably, there are others, such as are discussed in the second part of Parmenides.
4. THE FIVE GREAT KINDS: TWO QUESTIONS
   1. The Stranger addresses question (1): What is each of the great kinds like? He distinguishes each of the five kinds from one another, starting with being, motion, and rest.
      1. Motion and rest, as opposites, do not associate with each other; but being associates with both, since both of them are. Being must be a third thing distinct from them:
      2. Similarly, sameness and difference are distinct from motion and rest. Furthermore, being is distinct from sameness. They have to be different, because if they were not, when we say that motion and rest both are, we could substitute the same, and motion would be the same as rest.
      3. Finally, the Stranger distinguishes difference from being. This argument introduces a crucial distinction between two modes of predication.
      4. Difference is distinct from being, because difference is always in relation to other things (pros alla) and more precisely in relation to something different (pros heteron), whereas being is both itself by itself (auto kath hauto) and in relation to other things (pros alla).
   2. Question (2): The Blending of Kinds
      1. The Stranger carries out the analysis for one great kind, motion, and argues very systematically that motion is non-identical with each of the other four kinds (motion is not rest, not the same, and so on), but partakes of three of the four - all but rest.
      2. The whole analysis is implemented with two relations: non-identity (F is not G, because F partakes of difference from G), and positive predication (F is G, because F partakes of G). Note that this leaves out negative predication - which is what one would think Plato would want to use to handle the problem of false statement.
5. NEGATION
   1. The Stranger made a serious mistake about negation in the last two (constructive) puzzles about not-being earlier in the dialogue. The mistake was to suppose that the negation in “not-being” indicates the opposite of being (opposites are polar incompatibles, and these include polar contraries, like black and white, which have some intermediate between them, and polar contradictories, like odd and even, and motion and rest, which do not).
      1. The opposite of being (its polar contradictory) is nothing. Parmenides was right to object that we cannot speak or think about nothing. If any speaking or thinking is going on, we are speaking or thinking about something. The Stranger showed in the first three (destructive) puzzles about not-being that any attempt to refer to nothing fails.
      2. But Parmenides was wrong to suppose that all talk about what is not is attempted talk about nothing.
      3. The problem of not-being is solved by recognizing two things: (1) the negation operates on the predicate, not the subject; (2) the negation need not specify the opposite of the item negated but only something different from it.
      4. Now, the negation appears to specify part of a wider kind which is determined by the positive term (e.g. large) that is negated (in this case size). Like varieties of applied mathematics, whose content is supplied by the domain to which the knowledge is applied, there are kinds of difference whose content is supplied by the objects differentiated.
      5. A kind of difference (say size) contains two parts, which are opposites (polar contradictories), such as large and not-large. Let us call this kind an incompatibility range.
   2. The Stranger distinguishes between names and verbs. A verb is a sign that is set over actions (or properties); a name is a sign that is set over the things that perform the actions (or have the properties). There cannot be a sentence that is simply a string of names or a string of verbs. A statement must fit a name together with a verb.
      1. The central idea is very simple. Statements are structured.
      2. For instance, “Theaetetus is sitting” is true, because “sitting” specifies something that is about Theaetetus, who is currently sitting. “Theaetetus is flying” is false, because “flying” specifies something different from what is about Theaetetus.
      3. As noted above (§4.b.ii), we need negative predication to explain the false statement: If “Theaetetus is flying” is false, it is false because the negative predication “Theaetetus is not flying” is true.
      4. The analysis of negative predication (as distinct from non-identity) is complex. This is what scholars of the Sophist talk about; which is a lot more detailed than we care to be.
6. MUTATIS MUTANDIS…
   1. The Sophist was left closed in the imitative art, which was a kind of creation. But now, we’re going to go back and note that creation is of two kinds: human and divine.
      1. Inside the human kind of creation, we have a split (again) between representational creation and appearance-based creation. Now, from above we remember that the latter was to partake of falsehood, it it could be shown that falsehood was a part of real being. We have now accomplished this, and thus, it is so.
      2. This diairesis continues until we come to our definition of a Sophist: “he…who…is an imitator of appearance, and is separated from the class of phantastic which is a branch of image-making into that further division of creation, the juggling of words, a creation human, and not divine-any one who affirms the real Sophist to be of this blood and lineage will say the very truth.”

Overview

Socrates, on his deathbed, lays down four arguments for the immortality of the soul to his group of disciples and friends.

The Setup

Phaedo recounts the story of Socrates’ death. Socrates’ death took place so long after his trial because of an Athenian holy season, in which the city was not allowed to be “polluted by executions.” Many friends were present at Socrates’ deathbed, but Plato, apparently, was ill.

1. RHAPSODIZING

   1. The discussion starts with Socrates casually remarking on light things - the apparent attachment of pleasure to pain and why he’s suddenly taken to writing verse since he’s been in jail (he was told to in a dream!).
   2. Socrates then sends an envoy to the philosopher Evenus: Come along! Cebes, befuddled, asks Socrates why “a man ought not to take his own life, but that the philosopher will be ready to follow the dying”. Socrates claims that
      1. Our lives are the possessions of the Gods, and therefore we have no right to take them ourselves.
      2. However, a philosopher should not grieve at his death, as the rewards of the afterlife certainly make the experience of death a “far better thing for the good than for the evil.” He goes on to explain (c):
   3. Death is nothing but the separation of the soul from the body. Now, the philosopher should care not for the pleasures of the body, and hence, the wise man desires nothing more than to enact this very separation of the soul from the body.
      1. The senses deceive us when it comes to the quest for knowledge. The body is a hindrance, not a help.
      2. The philosopher gets the work of knowledge done best with the mind alone; the soul can attain truth best as revealed to her in thought.
      3. Further, our eyes cannot behold absolute (justice|truth|beauty|etc.) Again, our bodies hinder our souls’ progress toward truth. Thus, “either [absolute] knowledge is not to be attained at all, or, if at all, after death.”
      4. Hence, he who repines at death is hardly a philosopher. For at the end, all the vagaries of courage and temperance in the face of death (especially for the philosopher!) should be subsumed by the promises of wisdom in the afterlife.
   4. Cebes, thus, poses the question: “many arguments are required in order to prove that when the man is dead the soul yet exists, and has any force of intelligence.” Socrates is ready to respond.

2. THE FIRST ARGUMENT (THE CYCLICAL ARGUMENT)

   1. Socrates starts with an appeal to a Greek belief in reincarnation. However, in the same breath, he admits that there is no verification of this. So, he suggests starting with a broader appeal. Aren’t all opposites generated reciprocally? (aka. no good without evil).
      1. And this generation is actually “a passing from one to the other” - aka. heating and cooling, division and composition - that is, any opposites require an intermediate process.
   2. So, by analogy to sleep:waking, we are to understand death:life. The process of generation of sleep is falling asleep, and of waking is waking up.
   3. If this is true, by inference (and extension), we can believe in the birth of the dead to the world of the living. And hence the souls of the dead must continue to exist.

3. THE SECOND ARGUMENT (THE RECOLLECTIVE ARGUMENT)

   1. Cebes now offers that Socrates’ favorite doctrine of recollection seems to presuppose a previous time in which we learned what we can come to recollect. Cebes reminds us of the proof of this doctrine (from the Meno) of Meno’s slave remembering geometry.
   2. Socrates offers a second proof of this argument:
      1. If the image of one thing can bring to mind another (your lover’s garment, i.e.), and thus if recollection can be triggered either by things like or unlike.
      2. Extrapolating from here, if seeing particular pieces of wood and stone, and in identifying them as in some way equal, we are recollecting absolute equality, which we have never seen.
      3. Further, if things can only be understood sensually, we must have known about things like absolute equality before we were born, because we certainly haven’t seen/touched/smelled it in this lifetime. This implies absolutely that all knowledge is recollection.
      4. And the ability to access this knowledge implies an uninterrupted medium in which it was stored. This leads to only two possible conclusions. Either we had this knowledge since birth, and continued to know it throughout life, or else we received it after birth, and then lost it immediately, which doesn’t make any sense.

4. THE THIRD ARGUMENT (THE AFFINITY ARGUMENT)

   1. Now, everyone is sufficiently convinced that we’re born from the dead, but apparently not that when we die our souls don’t blow away in the wind and scatter. Socrates suggests here that it might be instructive to know something about the nature of the soul.
   2. Namely, Socrates wants to show that the soul is “uncompounded” and hence “indissoluble.”
      1. The aforementioned essences (Forms), it is agreed, must always be the same (unchanging). And the particulars that partake of Form F are contrawise always changing. Further, you can see and touch the particulars but not F.
      2. So, let’s assume that there are two sorts of existences, the seen and the unseen; these correspond to the changing and the unchanging.
      3. Now, if we are two parts, body and soul, and the body has a clear affinity to the changing/visible realm, meanwhile the soul is obviously unseen. The soul, we have argued, trapped by the body, only finds her home realm of the unchanging in wisdom. Hence, it seems that the soul has an affinity with the unchanging.
      4. Nature orders the soul to rule over the body, a nice analogy to the divine ruling over the mortal. Now, if all this is true, it must be admitted that the soul is “almost or altogether indissoluble.”
   3. This discussion now degrades into some crazy speculation about what kinds of animals the souls of the wicked will be reincarnated as. (Proportional justice: Drunkards as asses and pigs, etc.) Additionally, only philosophers are allowed to attain nirvana, with the Gods, and not be passed back into a new body.
   4. Cebes and Simmias both have some concerns with this line of argument, but are reticent to put them to Socrates. Socrates assures them that it’s cool. Simmias goes first. He poses the possibility that soul:body may be more like harmony:lyre. It seems to Simmias that if somebody cuts the lyre’s strings, it pretty much kills the harmony at the same time.
   5. Cebes then poses the problem that soul:body may be something like weaver:coat: That is, the soul may weave many bodies, and outlast them, but still it will die. He needs Socrates to prove that the soul is absolutely immortal to have any confidence.

5. THE FOURTH ARGUMENT: THE ARGUMENT FROM THE FORMS

   1. Socrates begins with Simmias: He takes umbrage starting with the idea that harmony is a compound. If “the soul is a harmony which is made out of strings set in the frame of the body,” it cannot be prior to the elements that compose it. But, granting (3) above, the soul must be prior to the body. Thus the analogy is false (harmony is made last and vanishes first).
      1. Additionally, harmony is absolute (not measured by degrees). So, if the analogy were true, souls would all be equally good (harmonious), as opposed to some being good, some being bad, etc.
      2. Finally, if the soul were a harmony generated by the physical, it wouldn’t caution us against the lusts of the bodily.
   2. So much for Simmias and Harmonia. Now on to Cebes and Cadmus. Socrates will argue from generation and decay. He will premise his argument on the existence of absolute beauty, goodness, etc. The Forms. He first attempts to set up his premises:
      1. He introduces the argument of Causality: Things that are F (other than the F) are F by virtue of partaking of the F. [Clearly stated, 100]
      2. He introduces the argument of Separation: The F is itself by itself, at least in the sense of being separate from, and hence not identical with, the things that partake of it. [end of 102]
      3. He introduces Impurity-S: Sensible things are impure inasmuch as they can (and, in fact, often do) have contrary properties. (Simmias is both tall and short.) This is also the corrolary to:
      4. Purity-F: Forms cannot have contrary properties. [74] (Whereas sensible things that are equal are also unequal, the equal is not unequal, and hence the equal is not identical to any equal sensible thing.)
      5. Also, Self-Predication: For any property F, the F is F. [100, 102] (Largeness)
   3. So, if all this is true, and things can reject a form completely, but not oppose it as such (3 rejects oddness), then G’s simple participation in F doesn’t necessarily mean that F is that whose inherence is essential to the being of G. So, since the soul brings life, as established above, it must participate in the Form of Life. And by Purity-F, this means that the Soul cannot participate in death. Now, the opposite of death is immortality, and if the soul does not admit death, then the soul is immortal.
      1. “The preceding argument shows that the soul will not admit of death…any more than three or the odd number will admit of the even, or fire…of the cold.”

6. CRAZY UNCLE SOCRATES’ GEOGRAPHY LESSONS

   1. Everyone is pretty happy with that, so now Socrates goes off on a wistful rant about the nature of heaven and earth. This includes:
      1. The earth is a round body in the center of the heavens.
      2. The earth is actually at the bottom of a sea of aether (the heavens), and we are deceived that we dwell atop the earth. If we could fly we could see the true earth/heaven.
      3. Rivers circle this true earth, going underground under the deserts, and this is purgatory.
   2. It is basically a charming overture to purity. After which, he goes to take a bath. Crito is sad. Socrates drinks the poison with good cheer. Everyone is sad.

Overview

Critical interpretation of this dialogue varies more widely than with any other. The general structure works like this:

1. Introduction / Socrates’ Speech
2. Problems with the Theory of the Forms (4, generally understood to be scathing)
3. How to Save the Forms: The (8) Deductions.

There are a lot of notes internally here. The gist of it is that Socrates is reliant on a middle period Platonic conception of the forms. Parmenides tries to save it. Critical assessment of his success and what this meant to Plato is noted in overview at the end of this outline.

The Setup

CEPHALUS arrives at Athens from Clazomenae with some of his countrymen. ADEIMANTUS welcomes him. They ask Adeimantus to take them to his half-brother, ANTIPHON, who they wish to recall a conversation which took place between a young SOCRATES, ZENO (40ish), and PARMENIDES (old, 65) many years ago.

Introduction

1. Zeno is giving a lecture in Athens. At the end of the lecture, Socrates asks Zeno to clarify, and Zeno maintains each division of his treatise is an argument to (negatively) prove the unity of Being: “if being is many, it must be both like and unlike, and that this is impossible.”
   1. Socrates notes that Parmenides (present) affirmed that “the All is one” positively, and Zeno echos his sentiment here negatively. “You affirm unity, he denies plurality.” Zeno affirms that he is defending Parmenidean monism to its many opponents.

Background

1. Socrates now, under the guise of asking a question, begins to articulate the distinction between the sensible (particular) things, and the Forms (universals).
   1. “Participate-things” (particulars) participate in both likeness and unlikeness. They (things) are both (like and unlike) by degree.
   2. This does not imply, though, that “…the absolute one [is] many, or the absolute many one…” - “if a person shows that such things as wood, stones, and the like, being many are also one, we admit that he shows the coexistence the one and many, but he does not show that the many are one or the one many; he is uttering not a paradox but a truism.”
   3. Parmenides now asks Socrates if he believes that there are particulars and also universals (ideas and things that partake in them).

Socrates’ objection is based on the theory of the Forms based on Plato’s Middle Dialogues.

The Arguments

1. ARGUMENT 1: The Paradox of the Singular Plural

   Overview: If particular things come to partake of the Form of Beauty or Likeness or Largeness they thereby become beautiful or like or large. Now each particular thing must receive either the whole of the Form of which it partakes, or a part of that Form. Either way, however, the Form becomes many - in the first case by multiplication, in the second by division - and thus will not still be one.

   1. Socrates affirms that there are absolute ideas of things like the Good, the Beautiful, etc. but not of things like hair, mud, and dirt. On the question of whether there is one for “man”, Socrates is undecided. He even wavers about dirt, etc.
   2. Parminedes confirms that Socrates is suggesting that particulars participate in universals (”partake of them”). Further, Socrates must admit, he thinks that each Idea is one, and is simultaneously apparently in each one of the many. Parminedes suggests that this is a paradox.
      1. (a)&(b) may also constitute a separate argument: “The extent of forms”.
   3. Socrates suggets that Ideas are more like the day, “is one and the same in many places at once, and yet continuous with itself.” They thus continue to discuss the potential for an Idea to be both whole and divided into pieces (as it’s found in particulars).
   4. Argument 1: The Paradox of the Singular Plural
      1. They confirm to themselves that these Ideas must be divisible, because it would be impossible for each particular to possess a whole Idea. This would imply that the Idea was multiple (multiply-instantiated). [Sail]
      2. They deny the possibility that things are (e.g.) great in virtue of possessing a framgment of the whole of the Idea. This would imply that the whole was multiple (divided and distributed). [Greatness, etc.]
      3. Socrates concedes that this is indeed a paradox.

2. ARGUMENT 2: The Third Man Argument

   Overview: Socrates’ reason for believing in the existence of a single Form in each case is that when he views a number of large (for example) things, there appears to be a single character which they all share, viz. the character of Largeness. But consider the series of large things: x,y,z, Largeness Itself. If all members of this series partake of a single Form, it must be the Form Largeness Two. Similarly, x,y,z, Largeness and Largeness Two must all partake of a further Form, Largeness Three, and so on ad infinitum. Hence, instead of there being one Form in every case, we are confronted with an indefinite number.

   1. Parmenides begins by apparently introducing a dialectic in which:
      1. He suggests that inductive reasoning leads Socrates to his conclusions about Ideas. Socrates sees great things, and their common greatness helps him to reason that they participate in one absolute Greatness.
      2. However, Parmenides suggests, when you combine the Absolute Greatness above with the particulars which participate in it, it seems that their unity constitutes a greatness even greater than Absolute Greatness.
      3. This seems to introduce an infinite regress.
   2. Socrates responds that “the ideas are, as it were, patterns fixed in nature”. That is, they aren’t thoughts, per se. Things “assimilate” to them.
   3. Parmenides then says that if Ideas are discernable in things via some “assimilation”, then Ideas must at least resemble the things that assimilate to them. This is what would provide the condition of recognizability.
   4. But this co-likeness between Ideas and things assimilating them again suggests a “higher” likeness, which again leads to an infinite regress.
      1. Assuming non-contradiction of Forms, this infinity contradicts Oneness.
      2. (c)&(d) may also constitute a separate argument: “The likeness regress”.

3. ARGUMENT 3: Animism versus the Empty Thought

   Overview: To the suggestion that each Form is a thought existing in a soul, thus maintaining the unity of the Form, Parmenides replies that a thought must be a thought of something that is a Form. Thus we still have to explain the participation relation. Further, if things share in Forms which are no more than thoughts, then either things consist of thoughts and think, or else they are thoughts, yet do not think.

   NOTE: Chronologically, This argument takes place between (3a) and (3b) above.

   1. Socrates tries to suggest that Ideas are simply mental states (not things - they are without “proper existence”).
   2. Parmenides tells him that all thoughts are thoughts of something (which is a singular form or nature, and thus apprehended as one).
   3. And this would entail that everything was thinking, or that there were thoughts with no object. Both of which seem wrong to Socrates.

4. ARGUMENT 4: The Separate Domains Argument

   Overview: The gravest difficulty with the theory of Forms arises as a consequence of the assertion of the separate existence of the Forms. Forms do not exist in our world but have their being with reference to one another in their own world. Similarly, things of our world are related among themselves, but not to Forms.

   All our knowledge is such with respect to our world, not to the world of the Forms, while ideal Knowledge is knowledge of the things not of our world but of the world of the Forms. Hence, we cannot know the Forms. What is more, the gods who dwell in the divine world, can have no knowledge of us, and nor can their ideal mastership rule us.

   1. Parmenides now cites his greatest difficulty, “If an opponent argues that these ideas, being such as we say they ought to be, must remain unknown, no one can prove to him that he is wrong…” (note that this seems to mirror the problem of arguing against Kant).
   2. Socrates must agree that in order for Ideas/essences to remain absolute, they cannot exist in us. This would make them finite.
   3. Parmenides’ example: A master and a slave. “Mastery” and “slavery” are only meaningful in relationship to one another - as abstract ideas. They have nothing to do with the two men, at least not absolutely.
   4. Which is to say that:
      1. We can’t have access to the absolute Ideas. We can’t know “the nature of the beautiful in itself, and of the good in itself, and all other ideas which we suppose to exist absolutely.”
      2. Parmenides also suggests that since the converse is true: “the ideas are not valid in relation to human things; nor human things in relation to them; the relations of either are limited to their respective spheres.”
         1. No terrestrial master is master of Slave itself, and no terrestrial master-slave relation has any relationship to the ideal Master-Slave relation. And so it is with knowledge.

         Thus, the idea that their is a relationship of exclusivity between the two denies God knowledge.

   5. Further, the inaccessibility of Formal knowledge eradicates the possibility of any real success in philosophy. (I think this is actually Hegel’s critique of Kant’s moral philosophy as well - “all formalisms are empty.”)

The Exercise

5. Parmenides now recommends that Socrates try an exercise. Here, it seems clear that although
   Socrates has failed to prove his doctrine to Parmenides’s satisfaction, Parmenides buys it
   anyway, and thinks that Socrates is just too young to argue it correctly.
   1. He suggests that Socrates attempt to disprove Zeno’s argument negatively (as opposed
      to positively - see [2] above) - that is, to extrapolate the consequences to the one
      and the many in relation to themselves and each other on the opposite of “the
      hypothesis of the being of the many”. [Presumably here, the hypothesis of the being
      of the one.]
   2. Socrates demurs, and reciprocates the request. Parmenides says he’s too old, then
      Socrates asks Zeno, who asks Parmenides again, who now agrees. Parmenides will
      demonstrate this technique based on his own hypothesis - the being of the one. He
      will extrapolate the consequences of affirming and denying this hypothesis.
      Parmenides will dialogue now with Aristoteles.

The Deductions

These all run similarly, and they’re all dry, so after the first deduction, we’re just going
to paste the conclusions in from the SEP.

6. THE FIRST DEDUCTION

   (D1) If the G is, then the G is not F and not con-F (in relation to itself and in relation to the others).

   1. The if the One exists, it can’t be a part or a whole (wholes necessitating parts and vice versa) - which means also that it would be infinite in time (beginning, end, etc. being parts).
   2. The One is thus unlimited by time, and for similar reasons unlimited by space (reminiscent of Kant’s ‘container’ hypothesis in the trancendental deduction of space).
   3. Further, then, the One cannot “move”, which is to say, it cannot come into being (this being a process constrained by space and time). It is immovable, and it is nowhere. Since it is nowhere, it is not “in the same”, since it can’t be anywhere, and hence it is likewise never in the same place. This implies that it is never at rest. One “is neither rest nor in motion.”
   4. Neither will it be the same (with itself, another) nor other (than itself, another). The second part of this gets handled first, and then the first: “Neither will it be other than other, while it remains one; for not one, but only other, can be other than other, and nothing else.” Which is to say, I guess, that its oneness would be divided by the relationship to any other. Further since anything that becomes the “same” with the many, becomes many. Hence, if there were no difference between oneness and sameness, this would violate the Purity of Forms hypothesis. (Oneness would be both oneness and sameness.)
   5. Thus we have determined that: the the one is not different from itself, the one is not the same as another, the one is not different from another, the one is not the same as itself, the one is not like another or itself, and the one is not unlike itself or another.
   6. Continuing, we find that the one cannot be equal or unequal to itself or others, nor can it be greater or less than itself or others, nor can it be older, younger, or the same age as itself or others.
   7. Finally, the one - since it cannot partake of being (be the subject of predication) cannot be in time. Thus it neither comes to be nor ceases to be, and hence does not partake of being. Thus the one is not, and it is not one. Hence, the one is not named, expressed, opined, known, or perceived. However, this cannot be.

7. THE SECOND DEDUCTION

   (D2) If the G is, then the G is F and con-F (in relation to itself and in relation to the others).

   1. If the one is, then the one partakes of being, the one is not the same as being, the one is a whole, being and the one are parts of the one, the one is infinitely many.
   2. The argument from one admitting all numbers: the different is not the same as the one, the different is not the same as being, the one has parts, the one is a whole, the one is limited, the one is unlimited.
   3. Then (”can anything be a whole without these three?”) the one has a beginning, a middle, and an end. Which implies that it has a shape. And, in containing its parts, it is thus in itself (and thus not nowhere) and thus in another [the whole is not in the parts]. Since in itself and in another, the one is always both at rest and in motion.
   4. And by these relations, the one is the same as itself, the one is different from itself, the one is different from the others, the one is the same as the others, the one is like the others, the one is unlike the others, the one is like itself, and the one is unlike itself.
   5. Further, being in itself it cannot touch others, but being in others, it can. Since the one cannot be next to itself (be two), however, it cannot touch itself. And since its other cannot be it (one), consequently, they cannot have number, which means that the one is alone, and cannot touch an other
   6. Now, by Purity-F, greatness and smallness cannot be in oneness, but also, everything must either be in the one or the others (one of these must contains them). In consequence, the one is equal to itself, the one is equal to the others, the one is both greater than and less than itself, the one is unequal to itself, the one is both greater than and less than the others, the one is unequal to the others, the one is more than, less than, and equal to itself in number, the one is more than, less than, and equal to the others in number.
   7. Further, the one must partake of time (being must be predicated of it), and from that: 1) The one comes to be older than itself, the one comes to be younger than itself, the one always is older than itself, the one always is younger than itself, the one is the same age as itself, the one is neither older nor younger than itself, the one neither comes to be older nor comes to be younger than itself. 2) The one is older than the others (as their condition), the one is younger than the others (them being its condition), the one is the same age as the others (being contained in each one), the one is neither older nor younger than the others, the one neither comes to be older nor comes to be younger than the others (materially), the one comes to be younger than the others (relatively), the one comes to be older than the others.
   8. Finally, since the one partakes of time past, future, and present, the one is and comes to be, was and was coming to be, and will be and will be coming to be. And thus it could be named and spoken of, as well as be the object of an account, knowledge, perception, and opinion.

8. THE APPENDIX TO THE FIRST AND SECOND DEDUCTIONS

   “The function of the Appendix is to show that the Conclusions of D1 and D2 together entail that, for a range of properties F, if the one is, then there is a moment outside of time (the so-called ‘instant’) at which the one changes from being F to being con-F.”

   1. If the one is, then there are times T1 and T2 such that T1 is distinct from T2 and the one partakes of being at T1 and the one does not partake of being at T2.
   2. There is a definite time at which the one comes to be, and there is a definite time at which the one ceases to be, there is a time at which the one ceases to be many, there is a time at which the one ceases to be one, there is a time at which the one is combined, there is a time at which the one is separated, there is a time at which the one is made like, there is a time at which the one is made unlike, there is a time at which the one is increased, there is a time at which the one is decreased, and there is a time at which the one is made equal.
   3. There is something (call it “the instant”) that is in no time at all and
      1. at which the one changes both from being in motion to being at rest and vice versa, and at which the one is neither at rest nor in motion
      2. at which the one changes both from not-being to being and vice versa at which the one neither is nor is not
      3. at which the one changes both from being one to being many and vice versa and at which the one is neither one nor many
      4. at which the one changes both from being like to being unlike and vice versa and at which the one is neither like nor unlike
      5. at which the one changes both from being small to being large and vice versa and at which the one is neither large nor small.

9. THE THIRD DEDUCTION

   (D3) If the G is, then the others are F and con-F (in relation to themselves and in relation to the G).

   1. If the one is, then the others are not the one, the others have parts, the others are a whole, the others are one, the whole and the part of the others are many, the whole and the part of the others are unlimited in multitude, the whole and the part of the others are unlimited, the whole and the part of the others are limited, each of the others is like itself, each of the others is like each of the others other than itself, each of the others is unlike itself, and each of the others is unlike each of the others other than itself.

10. THE FOURTH DEDUCTION

    (D4) If the G is, then the others are not F and not con-F (in relation to themselves and in relation to the G).

    1. If the one is, then the others are not one, the others are not many, the others are not a whole, the others do not have parts, the others are not like, the others are not unlike, the others are not both like and unlike, the others are not the same, the others are not different, the others are not in motion, the others are not at rest, the others are not coming to be, the others are not ceasing to be, the others are not greater, the others are not equal, and the others are not less.

11. THE FIFTH DEDUCTION

    (D5) If the G is not, then the G is F and con-F (in relation to itself and in relation to the others).

    1. If the one is not, then the one is different from the others, we have knowledge of the one, the one is different in kind from the others, the one partakes of something, that, and this, the one is unlike the others, the others are unlike the one, the one partakes of the unlike (i.e., has unlikeness) in relation to the others, the one partakes of the like in relation to itself, the one is like itself, the one is unequal to the others, the others are unequal to the one, the one partakes of the unequal in relation to the others, the one partakes of the large, the one partakes of the small, the one partakes of the equal, the one partakes of being, the one partakes of not-being, the one is in motion, the one is not in motion, the one is at rest, the one is altered, the one is not altered, the one comes to be, the one ceases to be, the one does not come to be, and the one does not cease to be.

12. THE SIXTH DEDUCTION

    (D6) If the G is not, then the G is not F and not con-F (in relation to itself and in relation to the others).

    1. If the one is not, then the one in no way is, the one in no way partakes of being, the one in no way comes to be, the one in no way ceases to be, the one is not altered in any way, the one is not in motion, the one is not at rest, the one does not partake of the small, the one does not partake of the large, the one does not partake of the equal, the one does not partake of the like, the one does not partake of the different, the others are not like the one, the others are not unlike the one, the others are not the same as the one, the others are not different from the one, none of the following (namely, of that, to that, something, this, of this, of another, to another, time past, time future, time present, knowledge, perception, opinion, account, and name) is applicable to the one, and the one is in no state at all.

13. THE SEVENTH DEDUCTION

    (D7) If the G is not, then the others are F and con-F (in relation to themselves and in relation to the G).

    1. If the one is not, then the others are, the others are other, the others are different, the others are other than each other, the others are infinitely many, each of the others appears to be one, each of the others is not one, the others appear to be infinitely many, some of the others appear to be even, others odd, none of the others is either even or odd, among the others there appears to be a smallest, each of the others (even the other that appears smallest) appears large in relation to its parts, each of the others appears to come to the equal, each of the others appears to have no beginning, middle, or end in relation to itself, each of the others appears unlimited in relation to itself, each of the others appears limited in relation to another, each of the others appears to be like itself and each of the others, and each of the others appears to be unlike itself and each of the others.

14. THE EIGHTH DEDUCTION

    (D8) If the G is not, then the others are not F and not con-F (in relation to themselves and in relation to the G).

    1. If the one is not, then none of the others is one, the others are not many, the others cannot be conceived to be either one or many.

Potential Interpretations

1. Parmenides’ criticisms are no more than a “record of honest perplexity”.
2. Plato means us to understand that Parmenides’ criticims are false in this way:
   1. The form of the deductions is always “in relation to G and in relation to F”)
   2. These qualifications, properly understood, reveal that subject-predicate sentences (of the form “X is F”) are ambiguous: to say that X is F is to say either that X is F in relation to itself (i.e., pros heauto) or that X is F in relation to the others (i.e., pros ta alla).
   3. This entails that Plato meant us to understand that self-predicational sentences (”The F is F”) are ambiguous. If this is the case, the Third Man Argument and the Greatest Difficulty are equivocal. However, it is provably false that even given a-c, the TMA always comes out fallacious.
3. Plato puts the reader in the position to recognize that Parmenides’ criticisms are effective only on the wrong-headed supposition that forms are fundamentally similar to the sensible, material things that partake of them. The point of the dialogue, on this view, is to help the discerning reader see the forms for what they really are, transcendent beings that should be accessed by reason rather than with the help of categories drawn from sense experience. [Problem: There’s no textual evidence to support this.]
4. What Parmenides’ criticisms reveal is that, whether combined with the Pie Model conception of partaking or with Paradigmatism, Plato’s middle period theory of forms is internally inconsistent. It turns out that there are three principles the abandonment of which would eliminate all inconsistencies apart from the Greatest Difficulty: Purity-F, Uniqueness, and No Causation by Contraries. Careful logical analysis of the second part of the dialogue then reveals that the Deductions establish not only that the forms posited by the middle period theory exist, but also that Purity-F, Uniqueness, and No Causation by Contraries are all false. It is then reasonable to suppose that Plato meant the reader to recognize that the proper way to save the forms is by abandoning these three basic assumptions. And, importantly, this can be done without abandoning the most important principles at the heart of the middle period theory, namely One-over-Many and Separation. The aptly-named Greatest Difficulty is then left as a challenge for future work.

Overview

Meno wants to know how virtue is learned (by teaching, practice).

Context

1. Platonic: The Meno is an early-Middle Platonic dialogue. It’s question, how - if at all - virtue is learned, is also addressed in Protagoras, with opposite results.

2. Contemporary: The Meno is also an important historical precedent with regard to the question of the Value of Knowledge. After all, if a true belief about the correct way to Larissa is surely of just as much practical use as knowledge of the way to Larissa — both will get us to our destination (7, below) — why do we find it so much more valuable?

   Plato’s thought seems to be that knowledge, unlike mere true belief, gives one a confidence that is not easily lost, and it is this property that accounts for the distinctive value of knowledge over mere true belief.

Outline

1. Socrates suggests that we’d have to know what virtue is before we know how it can be learned. He asks Meno to explain to him what he thinks virtue is.
   1. Meno says:
      1. A man’s virtue is his duty to the state, to help his friends and himself, and harm his enemies.
      2. A woman’s virtue is her duty to the house, and to obey her husband.
      3. Virtues are limitless, and each is relative to who we are (”actions and ages”).
   2. Socrates notes that this is no kind of definition of what “virtue” is. It is just a list of virtues. (Bees, health, strength analogies) He prods Meno tell him “a common nature” which makes virtues virtues.
   3. Meno feels that virtue is a special case.
2. Socrates lures Meno in with a plausible-sounding common denominator: “…can either house or state or anything be well ordered without temperance and without justice?”
   1. Forced into providing one definition, Meno suggests that, “virtue is the power of governing mankind.”
   2. Socrates: “Is virtue the same in a child and in a slave, Meno? Can the child govern his father, or the slave his master; and would he who governed be any longer a slave?”
   3. Socrates then suggests that perhaps “the power of governing justly” is the right track.
   4. Meno, ever thick, goes back to reciting virtues: Justice, temperance, magnanimity, which Socrates compares to (particular) shapes and colors: roundness, whiteness.
   5. Now, Socrates agrees to define his analogy (figure), if Meno will define virtue. He suggests that figure is “the limit of solid.”
   6. Meno now stalls; he demands Socrates define color before he (Meno) defines virtue.
      1. Socrates defines color as “colour is an effluence of form, commensurate with sight, and palpable to sense.” This is derivative from Gorgias and Empedocles, it is “orthodox”.
      2. Socrates finds it worse than his definition of a figure; Meno, inured to orthodox thinking, finds the opposite. (*Clarifying why may be instructive.)
3. Mutatis mutandis, Meno offers a quote from “the poet”, “Virtue is the desire of things honourable and the power of attaining them.”
   1. Socrates notes that this implies that some men desire good, and some desire evil. He asks Meno whether all men don’t desire good. Meno replies in the negative.
   2. Meno admits that some men mistakenly desire evil, thinking it is good.
   3. Meno must also admit that those who desire evil unmistakenly seem to be desiring to be miserable and ill-fated. (Evils being “hurtful to the possessor of them”). He must admit it seems unlikely that anyone would desire to be miserable and ill-fated.
   4. Socrates now notes that, the desire of good being common to all, Meno’s definition of virtue is reduced to the power of attaining good.
   5. Socrates now seems to equivocate between “the good” and “goods”. He asks Meno if the power of acquisition of goods by unjust means is virtuous, to which Meno must reply again in the negative.
   6. Socrates can now say that if Meno wants to keep his definition of virtue, he’s going to require some additional criteria: justice, temperance, etc. And with that, we’re back where we started.
   7. Actually, though, Socrates takes the tack that since we’ve already understood these to be parts of virtue (figures, e.g.): “can any one who does not know virtue know a part of virtue?” (Can we understand the universal simply by means of appeal to the particulars?) To which again Meno must reply no.
   8. Meno is now exhausted, and Socrates is ready to begin his positive investigation. Before that though, Meno introduces a question to Socrates, which we call:
4. Meno’s Paradox: “how will you enquire, Socrates, into that which you do not know? What will you put forth as the subject of enquiry? And if you find what you want, how will you ever know that this is the thing which you did not know?”
   1. Socrates then notes that Meno is occluding all possibility of enquiry, as if one knows something, one has no need to enquire, and if one doesn’t know something, one can’t know the subject for enquiry. Meno, needled to the point of witlessness by Socrates, will take this. But of course, Socrates won’t let him.
   2. Socrates appeals to those who speak wisely of divine matters, and further of an immortal soul in which all knowledge is already immanent, if nascent - enquiry and learning then, for Socrates, are matters of recollection.
   3. Meno isn’t buying it, and asks Socrates to prove it. Socrates calls over one of Meno’s (unlearned) attendants, and goes over some geometry, prodding the boy to do some deductions and teaching him terminology, during which he claims the boy is remembering pre-learned geometry, and not learning it. “Without any one teaching him he will recover his knowledge for himself, if he is only asked questions?”
      
      This is the diagram Socrates draws and uses to get the boy to remember his geometrical theorems.
   4. Now, Socrates implicitly compares the intellectual enrichment the boy just underwent at Socrates’ puzzling him to Meno’s own, and presents his apology for the Socratic method:
      

      …that we shall be better and braver and less helpless if we think that we ought to enquire, than we should have been if we indulged in the idle fancy that there was no knowing and no use in seeking to know what we do not know;- that is a theme upon which I am ready to fight, in word and deed, to the utmost of my power.

5. Agreed to sally forth and enquire into the nature of virtue, Meno once again sets forth his initial question, and this time, Socrates reticently concedes to discuss it without knowing first the essence of virtue.
   1. Socrates hypothesizes here that knowledge alone is taught, so only if virture is knowledge will virtue be taught.
   2. The minor premise of Socrates’ syllogism here is that virtue is good. To which Meno agrees. This leads Socrates to the conclusion that “if knowledge embraces all good,” then virtue must be knowledge.
   3. Then by a piece of rather dubious argumentation, Socrates suggests a second syllogism: p1) that virtue makes us good, p2) that all good things are profitable, so c) virtue is profitable.
   4. Socrates notes that many of the things we think of as being profitable (health, strength, beauty and wealth) may also sometimes lead us to harm. Further the “goods of the soul” (temperance, justice, courage, quickness of apprehension, memory, magnanimity, etc.) can equally be both profitable and hurtful - depending on whether they are practiced under the guidance of wisdom or folly.
   5. “If then virtue is a quality of the soul, and is admitted to be profitable, it must be wisdom or prudence” (e.g. that thing that tempers the goods of the soul). “And thus we arrive at the conclusion that virtue is either wholly or partly wisdom”.
   6. Unfortunately for Meno, Socrates now suggests that a) the good are made good by instruction, and b) if “virtue is knowledge, there can be no doubt that virtue is taught”, and c) that to be taught something needs teachers. Socrates’ experience doesn’t suggest that these teachers exist.
6. At which point, Socrates brings ANYTUS (whose father is a paragon of Greek virtue) into the conversation.
   1. Socrates asks Anytus whether it makes sense to send someone looking to learn a skill to one who professed to teach it (an apprenticeship). Anytus agrees that it does.
   2. Socrates now then reminds us that those who profess to teach virtue are called the Sophists. Anytus recoils: “By Heracles, Socrates, forbear!”
   3. Socrates here plants the idea that “Of all the people who profess that they know how to do men good, do you mean to say that these are the only ones who not only do them no good, but positively corrupt those who are entrusted to them, and in return for this disservice have the face to demand money?”
   4. Now Socrates and Anytus engage in a coversation about THEMISTOCLES, a man they agree was a virtuous man. They end up agreeing (in that Socratic way) that his son was not quite the man his father was, despite his apparent capacity. Other examples are cited. Particular note is made that while these good men teach their sons things like music, gymnastics and horseback riding, they don’t seem to be able to teach them virtue.
   5. Socrates concludes thus that virtue cannot be taught. But, paradoxically, virtuous men appear to have knowledge of right and good action. At any rate, they must /perform/ right and good action, definitionally.
7. Socrates suggests that the answer to this problem is that “true opinion is as good a guide to correct action as knowledge.” (Example of the guides to Larissa). Further, he suggests that knowledge is just right opinion, but bound through recollection (anamnesis) - that is, giving an account of its truth. It is in this way that knowledge attains its “stabilizing” character (contra true belief).
   1. They now just agree (with no argument) that right opinion is not given by nature (is not innate).
   2. Now, all his arguments established, Socrates delivers his opinion:
      1. Virtue is not knowledge since it can’t be taught.
      2. Since it’s not knowledge, it must stem from right opinion.
      3. Right opinion doesn’t come from nature.
      4. Thus, virtue comes neither from nature nor is it acquired, rather, it seems to be “divined” - that is, given by God to the virtuous.

Now you are going to get a confessional, because all of a sudden everything here is going to change:

After some time working for an interesting little startup company (a story which you should be pleased to be spared), I have been preparing this year to return to my studies in Philosophy, this time to earn my PhD.

One gets rusty after some time, and knowing that this was the case, some months ago I started a project of going back and reading some of the key texts of the Western Philosophical tradition, trying to (and here allow me a little of that good old theraputic Heideggerian argot) re-comport myself to the doxa.

This fact has two material consequences for SN:

1. First, during this period, I have been making more or less detailed outlines of the argumentation of more than a few significant historical philosophical texts, which I am now planning on sharing with you; probably once a week, maybe up to twice a week.
2. Second, I haven’t had any time for months to post any of these sort of "bloggy" observations about paintings or comic books or philosophy. This should be expected to continue indefinitely.

This is all to say that, into the foreseeable future, “fragments for the reading life” is to become “outlines for the reading life.” Which, unfortunately, probably means that you’re no longer interested in SN. Alas: This is the announcement of a significant theme change. So to you, my stragglers, apologies! And bon voyage. And now for some bureaucratic notes.

Three bureaucratic notes

1. First, sometimes the articulations of particularly complex arguments are more or less aped from the Stanford Encyclopedia of Philosophy. I am trying to read the Encyclopedia articles as I go, and, while almost always their articulation is better than mine, sometimes it is so much better that I flat-out supplant mine with theirs. Caveat lector.
2. Second, comments are not open. If you want to argue about any particular piece of my rendition of an argument, please just send me an email. You can get my email address at my personal launch page.
3. Third, these are “straight out of the notebook” so-to-speak, and as such will almost certainly be populated by meandering notes, comments, and questions, misspellings and solecisms, and the occasional irate outburst (see Outline for De Anima, forthcoming).

So with no further ado, and starting very nearly at the beginning, here’s my outline of the argument and plot of Plato’s Meno.