Wednesday, April 25, 2012

Overcoming the Problem of Mysticism in Logic

(Another recent post titled 'Man is the Animal that Speaks' is also related to some of the thoughts here.)

   Whenever you hear the complaint, or reassurance, that logic cannot be proved or is unjustifiable, you are hearing a mystic speak. Mystics speak of things that are closed off from normal discourse, and this accounts for the rather indirect and puzzling ways in which mystics speak. Properly understanding the mysticism of logic can go a great length in clarifying if its mystery is necessary or an accident of history. My intention here is not to avoid the mystery, but to better see it for what it is and to suggest a new beginning. I mean to move very rapidly and in a very aggressive mode.
   (If it is not immediately obvious why one may maintain that logic cannot be justified, here is the normal account put rather crudely: logic would require logic to justify itself, which is circular, therefore, impossible.)
   Let us look at a 'logical law' which apparently cannot be justified. When someone says "there is a square circle" nothing occurs that would indicate a contradiction, yet we recognize it. Ultimately, it is because we cannot imagine such a shape that we encounter this as a contradiction, but we do not even go through the effort to try since these terms conflict formally (symbolically) for us now.
   Why are the "contradictory" terms able to appear side by side with no complaint from reality? Put briefly, the words do not contradict absolutely, but only relative to their meanings in our attempt to imagine. If we were to substitute the meaning of 'red' for 'square' then we would no longer have difficulty imagining such an object. The process of being unable to imagine certain combinations of meanings has been generalized and formalized into logic of the sort that we encounter - and even worse, teach - as some sort of fundamental, unjustifiable, mysterious component of the 'rational'.
   Now, we may of course ask: why must such justification be in terms of logic? It certainly seems that formality itself should not demand a formal proof, and that the lack of such a proof is not a problem on the part of formality. Maybe the person who demands the proof should be charged with inconsistency? I agree, and the above was meant to show this to some degree.  However, it seems that the mystics have control over logic even in this counter complaint, and we should be very puzzled to find ourselves mystics ourselves as we oppose mysticism in logic.  
   The formalization of logic (possibly starting in Aristotle's Organon) did not intend to create a mystery cult, but only seemed to want to illustrate some of the existing norms for clear communication.
   A long standing project of mine is to establish logic anew, this time keeping logic more closely tied to 'discourse' (λόγος). I have a hypothesis that a great deal of disagreements are really misunderstandings - in fact, I would maintain that most disputes in Philosophy are purely misunderstandings. These disputes are held up from being completed by the mysticism of logic. What would it look like to overcome these hurdles in the mysticism of logic? Perhaps people will be able to pursue wisdom with each other rather than have to characterize each other under 'isms' so that they can fit a nice mutual exclusion in formal logic? Maybe people will notice that these isms aren't opposed as much as people may secretly want them to be (why? In order to be correct? We affirm ourselves at the expense of others quite frequently).
   As logicians we should be interested in clear discourse - discourse that serves its purpose of communicating, and helping people to get along and mutually benefit each other in cooperation. We should expect no way of showing that a person is correct or incorrect in what they say through any sort of process called logical, we can only interpret what we took it to mean, and how what it meant is something possible for us and the speaker.
   If someone says, "there is a cup on the table, and there is no cup on the table", the general impulse is to see a contradiction and to throw the red flag labeled 'false'. However, logic can never show what is correct or incorrect. The mysticism of logic has blocked us off from clarify what it means for this sentence to be problematic. How does logic pretend to do this? We take the statement "the cup is on the table" and assign it the character 'A', and then "the cup is not on the table" is taken to be "~A". Then we interpret the sentence, formally, as "A & ~A", which is a manifest contradiction. We then stop here, self-satisfied in our grasp of the clever method of formalizing these statements.
   If we do not wish to take the formal route, we can note that the meaning of the 'contradictory' sentence implies that if I look at the table I will both see and not see a cup there, and this is something that I cannot imagine. Perhaps this person intends to speak of two different tables, or two different cups? Perhaps the passage of time is left out or only implied in the sentence? There are other options for understanding the sentence, for who would say such a thing?
   Try to imagine a being for whom a cup could be and not be on a table at the same time. While we certainly could not imagine the way this being experiences, we can at least posit such an being. The discourse available between us and this entity is problematic, and it will be hard to know the proper way to act on the suggestions of such a being. Now, given that we can imagine such a being, we can see that we find the impossibility of the statement above to be grounded on a certain way of understanding the possibilities for the person who says it to us: we assume that, like us, the cup can either be or not be on the table, and not both. This is where we have a chance to discuss the role of logic.
   Logic will investigate the sorts of assumptions we have of other speakers and the ways in which beings like us can discuss things. Perhaps this is Aristotle's intention by his categories that illustrate basic kinds of determinations of objects. Logic can also have an empirical part which examines the ways in which people do tend to talk about things, and to this we can attach our formal apparatus (hopefully with some hesitation).
   Here I would like to break off and change topics to a brief discussion of the ancient Greeks. The word we translate as truth from the Greek is alethia (ἀλήθεια). This word more literally means 'un-covering'. In Greek the word we translate as false is pseudos (ψεῦδος) which more literally means dissembling (lying). We can recognize right away how different these words are from our casual usage of their translated counter parts.
   Plato, who did not have a science of logic, understood that the only thing convincing in discourse as what is true (what un-covers). Clearly he does not mean by truth here what we assign to propositions as a result of our formal process, or even correspondence; rather, Plato refers to how words are only understood on the basis of how things are un-covered for us (loosely, the way in which we can experience the world). Plato affirms that we cannot understand things in a way that is beyond our capacity to experience (except for negatively - by claiming our own finite nature). This is certainly something to meditate on as we try to found logic anew.

Thursday, April 19, 2012

Socrates and the Rejection of the Majority

   Plato portrays Socrates as alienating himself and his interlocutors from the majority of people by suggesting that you should not consider the opinions of the many. There is a lot of insight that can be gained from a more appreciative interpretation of Socrates treatment of the many, for while it is easy to see the rejection of the opinions of the many as elitism, it may make more sense to see this alienation as serving a number of other purposes. Three of these interpretive candidates are as follows: first, in rejecting the many, Socrates' means to show his interest in considering things in principle; second, this habit is a part of a broader tactic for bringing people together in discussion rather than opposition in debate; third, we should notice that the many are continually outstanding, that is, whoever Socrates speaks with is not counted as unworthy, and rather is put on an equal footing. I wish to explore some of my thoughts on these briefly here, but first I will spend a moment addressing what I think of some hints of elitism in Plato.
   It is certainly fair to consider a complaint of elitism regarding Plato, but many of the points where one finds such a concern may be avoided. For example, above the entrance to Plato's academy was inscribed, "Let None But Geometers Enter Here". This could certainly be seen as intellectual elitism, but I have my doubts since in the Meno Geometry is shown to be among the things that all people know regardless of their station in life. There is also accusations of elitism directed at Plato in what is considered his division of the perfect state in the Republic. This accusation also seems suspect, since the elite class in the Republic would be those who were best suited to sacrifice themselves for the state, not an elitism of intellectuals. The Philosopher King is not a creative intellectual free to do what he wishes, but rather someone who only serves the interests of the state which can be determined by its end, while the guardians must have the capacity to unfailingly follow orders that are in the interests of the state. For these sorts of reasons I would at least like to leave it an open question if we must see elitism as playing a clear role in Plato's thought. (Note: I don't wish to rule out any reading here, but only to raise the bar on what should be considered an informed reading if we are to accuse Plato of elitism.)
   Socrates' rejection of the many seems to have some roots in his youth, as it was part of a lesson given by Parmenides (in the dialogue of that name by Plato). In this lesson, Parmenides asks Socrates if he only considers the forms in relation to the virtues, and other ideas of that caliber, or if he also considers if there are forms of things like mud. Socrates answers that he is worried to consider the later without falling into absurdities, to which Parmenides replies that he will learn not to care what the many think of him, and that then he will be able to think about these other forms that are more mundane. (This advice from Parmenides looks forward all the way to Heidegger's Being and Time, which spends a great deal of effort in discussing the average and mundane. This will come up again later.) With this we can move to my first suggestion.
   The first of the options I suggested for interpreting Socrates' habit of holding the majority at a distance was his interest in considering things in principle (possibly inherited from Parmenides) in order to truly understand them. The dialogue Euthydemus shows two men, Euthydemus and his brother Dionysodorus, giving eristic arguments. At the end of the dialogue Socrates has the following exchange with Crito to close off the dialogue:

SOCRATES: Dear Crito, do you not know that in every profession the inferior sort are numerous and good for nothing, and the good are few and beyond all price: for example, are not gymnastic and rhetoric and money-making and the art of the general, noble arts?

CRITO: Certainly they are, in my judgment.

SOCRATES: Well, and do you not see that in each of these arts the many are ridiculous performers?

CRITO: Yes, indeed, that is very true.

SOCRATES: And will you on this account shun all these pursuits yourself and refuse to allow them to your son?

CRITO: That would not be reasonable, Socrates.

SOCRATES: Do you then be reasonable, Crito, and do not mind whether the teachers of philosophy are good or bad, but think only of philosophy herself. Try and examine her well and truly, and if she be evil seek to turn away all men from her, and not your sons only; but if she be what I believe that she is, then follow her and serve her, you and your house, as the saying is, and be of good cheer.

   This exchange is not the first time that Socrates turns Crito away from the many in order to consider something itself. In the dialogue named after Crito, Socrates summons up the laws of Athens themselves and holds a conversation between the three of them (while he also speaks for the laws). (Crito particularly seems to get lost on the mores of the many and to be forgetful of these talks with Socrates. Near the end of the Phaedo, Crito asks what Socrates wishes be done with him when he has died, forgetting or ignoring the contents of the conversation that has just occurred. Socrates reply is, "Catch me if you can.")
   It seems that Plato's emphasis on considering things in principle regards how to govern oneself by principles, and that this has a great deal to do with being wise. Much more could be said about this, but I will instead continue to my second consideration of Socrates attitude of towards the many.
   Socrates seems to want to avoid conflict in his discussion and rather favors a common pursuit where everyone benefits. Socrates employs this tactic in variety situations and in a number of ways. In the later part of the Protagoras, Socrates attempts to work with Protagoras by giving an external complaint from the many who hold a common opinion about the nature of good and evil. Socrates is able to answer the many along with Protagoras as a comrade, which is in sharp contrast to the earlier part of the dialogue when Protagoras' combativeness almost brings the dialogue to an early end. The example from the Crito where Socrates summons up the laws as a third party to the conversation with Crito can also serve here. In many other places where Socrates is confronted with a difficulty from one of the interlocutors it is common for him to call on another (and often younger and more beautiful) party present at the discussion to help him through a dialectic. We find such a tactic used in the Phaedo when Socrates asks for help from Phaedo when he is confronted by the problems of both Simmias and Cebes. (Also, in this crucial moment he mentions the dangers of misology that can occur from encountering bad arguments, and rejecting reason giving from particulars. This is much like the end of the Euthydemus.)
   Socrates' technique is not always shown as working out successfully, however, and can upset interlocutors from time to time because Socrates ends up looking evasive, and not wanting to take a stand and debate (which may be the whole point). In the first book of the Republic, Thrasymachus has a reaction of incredible outrage to Socrates attempt to be evasive. There are a number of options available for interpreting what Plato means to say through encounters such as the one with Thrasymachus, but that can be held off on for another time as I proceed to discuss the third and last interpretive suggestion.
   This may be the most subtle of the suggestions, but potentially the most revealing and interesting for me as an interpreter of the history of Philosophy. The many that Socrates so often insists on ignoring are never actually present in the dialogues. No matter who Socrates meets he is always willing to speak to them as equals (and often as unequals, as Socrates will be interested in learning whatever wisdom he can from those who claim to have it). The reason why I find this to be such an interesting suggestion, is that in some sense it means that Socrates is considering the many in principle, or as a sort of idea that every human has, and that can be used as a contrast to really understand ourselves, and the world, in principle. Once again, this theme seems to suggest what Heidegger is doing in considering the average in his Being and Time, as well as the themes of the authentic and inauthentic. As a philologist, seeing how Plato and Heidegger can be mutually informative for each other on this matter is a delight to consider. What other ways of thinking about this problem of the average can Plato open up for us in seeing how the tradition follows after Plato's treatment of the many? There seems to be a great deal of potential here that will only come after much more work.
   While I clearly do not read Plato as an elitist, there is, in fact, a great risk of intellectual elitism which comes along with inheriting Socrates as an idol of sorts, and in using this idol as a way to instruct others. This risk is what I hope to help avoid and criticize. The typical example of it is to use questioning as a means of provoking an interlocutor to think for themselves while you keep the answer you are looking for to yourself. This sort of deceit is something that is often interpreted as the motive of Socrates. I see this as a mistake, since Socrates almost always speaks to the contrary of this, and is always upset by the idea of wisdom being withheld from him. Instead, if we must assign such a motive, we must assign it to Plato. I often refer to this as a sentimental approach to Socrates, and perhaps Plato was the first in a long line of sentimental, Socratic philosophers. However, part of Plato's genius seem to be in writing in dialogue form so he can produce the effect he wants (this sentimental motive) while having a character that is sincerely ignorant. Hopefully we can all aspire to loving wisdom, and not instead just loving holding wisdom over the heads of others - something that may result in Aesop's fable regarding sour grapes.

Wednesday, April 4, 2012

Man is the Animal that Speaks

   (I do not care to contend that language is exclusive to human beings, nor do I want to argue for any particular physical form that a human being must take. I wish to use this particular definition of man from Aristotle as an experimental starting point.)

   Certainly there is communication in many diverse ways in the animal kingdom, and humans certainly have their own unique sort of communication, but if we treat speaking as something special to man, then it cannot simply mean any generic communication. A compelling suggestion I have encountered in the past involves poetry.  In class, Professor Michael Gelven would reply to claims that animals speak by asking: "Where is the animal Shakespeare?" While this suggestion is powerful, I wish to take a different route that may be able to provide a better basis for grappling with Gelven some time in the future.
   Briefly: speech reveals in a way that is only possible between 'human beings'. Allow this seeming assertion to stand as rather a starting point for exposition. This claim is grounded in how things (conceived broadly) are revealed to any individual human in a certain way (how we 'see' them). This claim involves how, in speech, this common way things are revealed is assumed as at least possible in all parties participating.
   Animals certainly see (visually speaking) things that we see, and whether or not they 'see' (broadly) them in the same way as we do is indeterminate. However, when we speak, or do not speak, to certain things, then we find out just what we think are possible for those them. Things that we speak with as if they are of a kind with ourselves I will term 'human beings'.
   (I do not wish to raise the question of how to 'identify a human being' here. Sometimes we may speak to an animal, e.g. a pet dog, as if they are 'human beings'. This is not taken to be a refutation of the above, but rather to extend the term 'human being' to those things at those times. However, usually we find large differences in our 'talks' with animals and inanimate objects. For example, we do not expect a reply; in fact, we would be quite shocked, scared or confused by a reply from the chair we just stubbed our toe on, or our pet goldfish in response to being fed.)
   In using the word 'revealing' as what grounds our speech, I mean to refer to the Greek word that we translate as 'truth': ἀλήθεια (alethia). (A-lethia is literally 'un-hiding', and is the privative of lethe (λήθη) which means 'oblivion'.) In speech, man sets about a different kind of revealing; a sort of indirect sharing of what is revealed. The one who encounters the speech as speech understands it in its character of revealing indirectly, even if what is revealed is unclear. Because things are directly revealed to each 'human being' in the same way (problematically), the same possibilities of speech's revealing are opened up between any 'human being'. In this way, humans speak in a way that uniquely identifies them as equals: equals in their access to what is revealed, through an indirect revealing.
   Truly - or I should say - it is revealed, or manifest to us that if we are equals with something else, the most important way is through our capacity to share the revealed (I do not mean revelation), and this is done through speech.
   From here, we can afford a moment to turn a glance back to Gelven's suggestion which I will put in the following manner: man is the animal with poetry. How should this be interpreted? Is it that 'poetry' is a better name for what I have called 'speaking'? Is this definition more fundamental than 'man is the animal that speaks'? What sort of thing does poetry reveal? Can we gleam anything in Gelven's knowing speech from the relationship of 'poetry' to its origin in Greek (ποιέω)?