Sunday, November 27, 2011

Waiting for Godot -- Reading Godot, the conglomerative effect

      The heart of Lois Gordon's book is her interpretation of the various features of the play in terms of Freudian conglomeration.  She says:

"Freud uses the term conglomeration in the process of collecting the fragmentary components of the dream.  This is a concept akin to the mental operation of "secondary revision", which gives final shape and form to the compressed dream image.  In following Freud's procedure, I shall speak of the conglomerative effect or conglomerative refrain in order to indicate what traditionally would be called the dominant theme of the play, always in the form of thesis and antithesis."(pg. 75)

Thus, we see the various verbal formulations, including the ambiguous or self-contradictory speeches, dialogues, stage directions(when compared with the dialogue), as if they were disorganized components of a dream.  The assemblage of a theme is therefore analogous to the assembling of a narrative and meaning among the pieces of a dream.

She says of Lucky's monologue that it is
"a disjointed worldview of a onetime philosopher-poet: (1) The universe is ruled by an enigmatic, capricious deity...;(2) the human creature 'wastes and pines' despite all the 'strides' and 'labors of men', intellectual, social, and physical; (3) only a stony, indifferent earth survives....Almost every word and activity in the play is an incremental repetition of this worldview"(pp. 76-77)

She indeed proceeds to show how the main characters in the play manifest this theme.  While there is nothing particularly Oedipal about the play in the Freudian sense, there is the sense that each character is at the mercy of forces both inside and out.  I didn't get the depth psychology I asked for in the last post, but I did get a connection with dreams and their interpretations.

Sunday, November 20, 2011

Waiting for Godot -- 'Reading Godot' by Lois Gordon, entry 2

"The power of Waiting for Godot derives from its exposure of the emotional life in counterpoint to the existential condition -- Beckett's revelation of the unconscious feelings that accompany the quest for salvation in a world bereft of meaning. Godot's much-repeated 'Let's go.(they do not move)' epitomizes not just the tension of individual action in a meaningless world; it also demonstrates the limits of the will set against the contraining and deterministic forces of a controlling psyche."(pg. 70-71)

Existentialism without the freedom.   She asserts the influence of Freudianism on Beckett all the way down to the set design, props, the direction the characters walk and how they move about on the stage:
"It is as though Beckett were weaving into his existential landscape a map of the unconscious world, again, either as it functions simultaneously with rational thinking or is transformed into a dreamscape...Each object, word, and movement ultimately becomes an emblem of the psychological, not just the philosophical, reality of waiting."(pg.74)

The above quotation throws the gauntlet down; I want her to pony up examples of the depth psychology in the midst of the philosophical condition of waiting -- I can hardly wait!

Saturday, November 19, 2011

Waiting for Godot -- "Reading Godot" by Lois Gordon part 1 of many

"Werner Heisenberg and quantum physics, no less than Freud and Sartre, have demonstrated that the limits of our universe are determined by the limits of our measuring instruments, whether they are atomic clocks, blood pressure cups, or nouns and verbs (Gordon pg. 18)

I usually dislike it when humanities' types bring in physics to illustrate some point about relativism etc..., but I make an exception in this case.  It is true that there is a fundamental limit to our ability to locate and measure the momentum of particles precisely, and that ultimately science is about what we can measure, and there are apparently limitations on that, and thus on our ability to know.  We spin our theories based on what we can possibly measure. Perhaps we assume that the limitations of what we can measure are the limitations of the universe itself, an obvious intellectual error, but just as there are undoubtedly aspects of the physical universe beyond our ability to measure, there are perhaps truths of our condition that are beyond nouns and verbs and plays.  Beckett is, according to Gordon, is a quester in the face of the "mess" he descibes.  He describes the quest for order and meaning in a universe devoid of meaning, and whose truth is likely always beyond us.

This, she says, Beckett does in contradistinction to the quests of other modernists:
"He has repudiated the modernists' mission, virtually Dantesque in scope, to recreate a meaningful world by scaffolding its fragments on to the symmetries of historical and mythical patterns.  For Joyce, Eliot, and the others, the fractured present could ultimately be reconstructed in the terms of past traditions and past value systems.  Theirs was an art of positive faith, implicitly based on the boundless power of the human will."(pg. 14)
This will included the Will to Truth, Science(even if the truth is ultimately unpleasant) etc...  It is fascinating that she compares all this to Dante.  I think she is saying they are, despite themselves, seeking the same kind of integration Dante achieved in the Commedia(one of my favorite works, up there with Hamlet and Macbeth, also representatives of a world picture that also could be as totalizing as the medieval world of Dante).  She credits Beckett with being more postmodern, more pessimistic than even the existentialists. She says that the positive in Beckett's work is different than that of the modernists:
"It arises in the absence of any redemptive system, and because it is inevitably eclipsed by inner or outer forces, when it appears it is poignantly ennobling...In the main, however, Beckett's work focuses on the feeling of fragmentation and disintegration that occurs when one lives in the absence of theological or cultural accsurances and when one functions within the a priori constraints of language and the psyche."(pg. 15)
This suggests that the 'scorn' mentioned by Camus in The Myth of Sisyphus, is a kind of redemptive dimension to existentialism, one that Beckett lacks!

Beckett's characters are unable to lift themselves permanently above their fate; they are, as are Vladimir and Estragon, unable to move, despite their desire to do so.  There is no existential victory over fate, only an occasional poking of the head up before it is pushed back down. In summary, Beckett, who says he was not a philosopher by trade, is already beyond the existential, though the existential dimension runs as an undercurrent throughout Waiting for Godot.

Thursday, November 17, 2011

Waiting for Godot and Myth of Sisyphus part 2

     I will continue an examination of Waiting for Godot by introducing a selection from the brilliant book, Reading Godot, by Lois Gordon.  When the actual book arrives from Amazon I will read over everything she has to say.  Gordon begins this section with
"In a world devoid of belief systems, the mind and heart cry out for validation, for the assurance that life has meaning and actions have purpose.  One may accept, as an existential truth, the assumption that despite the individual's endeavors to comprehend or change the world, "there is no new thing under the sun"(Ecclesiastes), and, as Beckett puts it, "the tears of the world are of a constant quantity..."  But one also occupies a world of temporal measurement.  Time passes and one ages, and, facing these inescapable facts, one journeys with tenacious will through the arbitrary divisions of time and space holding onto goals and belief systems as if they were absolute(Bloom pg. 124)

We inhabit both the existential void and also the world of particular time and place.  Like Odysseus searching for his home but lost on an endless sea, we seek solace in the stories of our home culture that give us an enclosed sense, the enclosure we need to derive meaning, whereas we really inhabit a wide-open space with no landmarks, where nothing ever changes, and there is just boundless sea and sky.  In the case of Waiting for Godot, we have a spare landscape with a single tree, which is barren until the second act, when it suddenly has leaves -- one is reminded here of the way time passes on the island of Circe, many years pass without being noticed, have seasons changed between acts?  How long has the waiting been going on?

Godot has meant many things to many people over the years, perhaps it means homecoming and definition.  Without Godot there is purposeless waiting.  But Godot never comes.  The heroes never get home; they don't even have a home.  The world itself is foreign and one is a stranger in it and to oneself.

Waiting, and its weight, must be where people get the analogy between this play and Sisyphus.  As Sisyphus 'waits' until the rock gets to the top and then tumbles down, they wait for Godot.  The wait is arduous, for Godot it is not really a physical exertion necessarily, though Estragon is beaten daily, but the burden is the burden of waiting itself, the need for distraction.  I think of the times when my own mind tries to occupy itself in the presence of menial, tedious work.  I suppose at those moments there is the possibility, for Camus, of a scornful victory over fate.
"For Camus, Sisyphus's perserverence , in literal spite or contempt of the meaninglessness of his task, defined his superiority.  By ignoring the irrationality of his fate and focusing on the blue of the sky and the texture of the rock, he could exult in his defiance of his fate."(pg. 125)
Gordon assures us that Beckett's heroes lack the defiance; they are hardly superior to their fate.  She also reminds us that there is an uncertainty about their location or the day, what they were doing yesterday, or even what they are doing at present.  They constantly repeat the litany that they can't go because they are waiting on Godot.  In all these ways then, Beckett's heroes are not superior to their lot as are Camus' rebels.   

Sunday, November 13, 2011

Waiting For Godot and the Myth of Sisyphus part 1

     I bought the Harold Bloom 'Modern Critical Interpretations' edition for 'Waiting for Godot' and read several of the essays.  All of the essays mention Albert Camus's short essay, 'The Myth of Sisyphus', so I figured I would start by looking over this essay and quoting what some of the interpreter's say; this is an essay I first read in high school and it was a poignant experience to read it again as I remember the effect the essay had on me all those years ago.

     One of the first things I noticed when I got my old copy of the essay was an underlining I had made in the essay;  I would have done this some time around 1982:
"But when he had seen again the face of this world, enjoyed the water and sun, warm stones, and the sea, he no longer wanted to go back to the infernal darkness."(pg. 88-89)
When I recall the bouts with depression, the sense of futility, along with the melodramas of my adolescence, this line, with its emphasis on simple, natural, pleasures, provided me with real solace.  I asked myself many times why life was better than death, and this line speaks to this question.   It also brings to mind the fact that in Dante's Inferno, most of those in Hell want to be remembered to those up in the world -- all, of course, except Guido De Montefeltro.  Those in Hell relished the thought of the 'bright world above'; for me,  this line helped me prefer life to death, viewing death as oblivion with no warm stones or anything at all for that matter.

     Sisyphus is torn from the natural world he loved made to push an immense boulder all the way up a mountain only to have it roll back down.  Camus says:
"If this myth is tragic, that is because its hero is conscious.  Where would his torture be, indeed, if at every step the hope of succeeding upheld him? The workman of today works every day in his life at the same tasks, and this fate is no less absurd.  But it is tragic only at the rare moments when it becomes conscious."

Camus seems to believe that Sisyphus has a kind of victory in his scorn over his fate, when he turns from the top of the mountain and walks back down he has a moment of consciousness.  At this moment he scorns the gods, his fate, and returns to his rock.  I guess I never believed Camus here and I think Beckett backs me up.  That is, there is no victory.

Saturday, November 12, 2011


My next series of articles will be explorations of the dramatic works of Samuel Beckett.  I have read some of his plays and he is becoming one of my favorite author.  So get ready for the ABSURD.  I will start next time with Waiting for Godot.

Derek Parfit -- The Final Entry

After a long, tedious, explanation of what is wrong with various versions of "Subjective Theories", without really dealing with what I would call the 'real problem', nihilism, he talks about Kant. I have to say that I find actually reading the text unbearable.  So, I'm going back to the summary to see if he gives me an argument I can sink my teeth into. So, after skimming through much more tedium I  violated all canons of what is good and decent by going right to the "conclusions" section!

Sigh, and here is what I was treated to:
"everyone ought always to do whatever would make things go best."(pg. 74)   Let's read that again:
"everyone ought always to do whatever would make things go best."(pg. 74)  I need a 600 page book for this?

Here's another gem:
"When there is only one set of principles that everyone could rationally will to be universal laws, these are the only principles, we can argue, that no one could reasonably reject."(pg.74)

How ZEN.

And here is his "Triple Theory":
"An act is wrong when such acts are disallowed by the principles of that are optimific, uniquely universally willable, and not reasonably rejectable."(pg. 74)


The one thing that has come out of this is that the Kantians and the consequentialists are, when properly formulated, trying to say the same thing(see my previous post).  Ultimately, rational beings want things to go best and those who want things to go best should think things through. There are things we should desire and things we shouldn't: we should desire the things that we have reasons to desire based on what makes things go best after careful deliberation; we should reject those desires that would make them go badly.  So, this is not a desire based theory, it's not quite a purely detached, unfeeling theory either. I shouldn't make so much fun of an obviously sincere and well-read scholar, but sometimes these arguments seem a bit foolish and they end up not accomplishing what we really need: the kind of moral foundations we can use against those who would do bad stuff just because they want to.

Sunday, November 6, 2011

Derek Parfit -- Finally saying something

I suppose it's not surprising that it's easier to poke holes in the opposition's theories than it is to put forward one of your own; that's one reason why the next chapter, "Subjective Theories", is better.  He gives the example of running away from a snake in the mistaken belief that running will save your life(you should stand still).  He says:
"Subjectivists might claim that
(A) reasons are provided only by desires that depend on true beliefs,
You have no reason to run away, (A) implies, because your desire depens on the false belief that this act would save your life".(pg. 107)

He then defines the Telic Desire Theory:

"We have most reason to do whatever would best fulfil or achieve our present telic desires or aims."(pg. 108)

He then says that the problem here is that sometimes our telic desires are based on false beliefs.
Thus we have
"the Error-Free Desire Theory: We have most reason to do whatever would best fulfil or achieve our present error-free telic desires or aims."(pg. 109)

He follows this up with the "informed desire" theory.

He is moving us toward the following formulation:
"the Deliberartive Theory: We have most reason to do whatever, after fully informed and rational deliberation, we would choose to do."(pg. 110)

This is a master stroke!!  He says this formulation, Deliberative Subjectivism, is often confused with Objectivism(Kant, not Rand).   But there is a bit difference:

"Instead of claiming that what we ought to choose depends on our reasons, these Subjectivists claim that our reasons depend on what, after such deliberation, we would choose."(pg. 112)


"Objectivists appeal to normative claims about what, after ideal deliberation, we have reasons to choose, and ought rationally to choose.   These Subjectivists appeal to psychological claims about what, after such deliberation, we would in fact choose."(pg. 112)

This coming together of Subjective and Objective, while maintaining the difference in causal direction, as a step on the way toward his defense of a normative type theory is, I think, brilliant, and worth the price of admission.

Saturday, November 5, 2011

Derek Parfit --- Objective Theories and unfree desires

Parfit provides an unilluminating distinction between subjective and objective theories:
On many subjective theories, the strength of the these reasons depends on the strength of these desires or on our preferences.  On objective theories, the strength of these reasons depends instead on how good, or worth achieving, the fulfilment of these desires would be. Many of us often have stronger desires for what would be less worth achieving."(pg. 95)
Is this guy my Sunday School teacher?

He then reiterates the tired formula that we do not choose what we desire etc....; this was known in the 19th century as the "law of motivation", at least is was for Schopenhauer.   He say "we can choose which desires to adopt as aims, and try to fulfil."  What makes him think this??

The book reads like he's writing right off the top of his head, which is not a good thing in this case.

"Our desires are rational, I have claimed, when we want events whose features give us reasons to want them.  Our desires are not rational, and are in the old phrase contrary to reason, when we want some event that we have reasons not to want..."(pg. 105)

Page after page of stuff I could get from my mennnonite friends -- and they are my good friends.

Derek Parfit -- Reasons weighed against Reasons

Parfit goes on at some length about how facts give us reasons.  He gives examples like being allergic to walnuts gives us a reason not to eat them.  He goes on to say that reasons counteract other reasons.  None of this is particularly interesting. 

He praises rationality as a way of determining how we ought to act.  He goes on at some tedious length about 'relevant' reasons providing 'sufficient' reasons for acting in certain ways, all the while begging the questions that plague the history of ethics -- at least, so far.  My advice is that if he's going to re-establish normative ethics on some sort of foundation that people can really sink their teeth into, he needs to get to it a tad sooner otherwise people will think he doesn't really have anything.

Here goes:
"When we call something good, in what we call the reason-implying sense, we mean roughly that there are certain kinds of fact about this thing's nature, or properties, that would in certain situations give us or others strong reasons to respond to this thing in some positive way, such as wanting, choosing, using, producing, or preserving this thing"(pg. 87)

Thanks. But what I want to know is what moral properties are and how they can impel moral action.  And for Parfit, or any neo-Kantian, we must have moral action as such.  There must be "moral" reasons, that rationally impel action.  The whole question of the existence of such things is begged.

Sunday, October 30, 2011

Derek Parfit -- a few comments

The fundamental problem Parfit is going to have is the idea that there is some "objective" content to facts that yield proper beliefs and, from that, actions.  Facts, assuming they can be formulated in an objective way, which is not exactly a postmodern position, must then additionally yield objective implications.  Even those who believe in objective facts may have problems with the notion that there are objective moral implications.  Look, either there are or there aren't objective implications.  If there are, then they are valid for all people, irrespective of a person's cultural background etc..., if there aren't, then the interpretations of facts are culturally relative.  And this is assuming that the facts themselves have objective content.

Of course, these days people these days say that facts are "value-laden" -- this is a way of describing the cultural relativity in the depiction of the "objective" world itself.  The advantage of this view is that there is a connection between facts and values that is absent in the fact/value distinction cabal(like Hume).  The disadvantage is that facts are subjective to begin with and there is no objective base upon which to have values at all.

I have a strong feeling that Parfit is going to fail here...

Monday, October 24, 2011

Derek Parfit Chapter 1

Parfit starts with the following:
"We are the animals that can both understand and respond to reasons. Facts give us reasons when they count in favour of our having some belief or desire, or acting in some way."(pg.50)
I love this opening!  It summarizes a take on that which is distinctly human, that corresponds to our ability to do science as well as to consider ethics.  We move from facts to beliefs and from beliefs to rationality:
"Though it is facts that give us reasons, what we can rationally want or do depends instead on our beliefs."
Facts are already not something separate from beliefs and morality; they provide us with "reasons". (pg. 50) How can a fact provide us with reasons? Only if facts are already constructed by some reasoning faculty, perhaps.  Facts don't just hang out there neutrally.  If they did, nothing could be done with them; they cannot be said to 'count' for or against anything.

The notion that there is this gulf between facts and values is obviously something that Parfit has struggled with/against for a long time.  The only solution is that facts be defined in such a way that values can be derived from them.  This is, today, a rather unpopular, and seemingly naive position; clearly Parfit is not a simpleton, so I'm going to read on!

He distinguishes wonderfully between subjective and objective theories. Subjective theories have to do with facts about us, our desires. Against that we have "objective theories, we have reasons to act in some way only when, and because, what we are doing or trying to achieve is in some way good, or worth achieving.  Since these are facts about the objects of desires or aims, we can call such reasons object-given."
He then says, "We ought, I shall argue, to accept some value-based objective theory."(pg. 51)

I wish Parfit all the luck and hope he succeeds in defending an objective  theory.

Sunday, October 16, 2011

Derek Parfit's raison d'becoming a philosopher

I love the following from the beginning of On What Matters:

"My debts to Sidgwick are easy to describe.  Of my reasons for becoming a graduate student in philosophy, one was the fact that, in wondering how to spend my life, I found it hard to decide what really matters.  I knew that philosophers tried to answer this question, and to become wise.  It was disappointing to find that most of the philosophers who taught me, or whom I was told to read, believed that the question 'What matters?' couldn't have a true answer, or didn't even make sense.  But I bought a second-hand copy of Sidgwick's book, and I found that he at least believed that some things matter"(pg. 41)

This makes me like Parfit a lot, maybe he and Sidgwick can convince me that something matters, that would be cool.

Derek Parfit entry 1

  I don't know too much about Derek Parfit yet but he seems to want to combine Kantianism and consequentialism, at least according to the introduction.  He also seems to think that the "Formula of Universal Law" can be saved in a form like "Everyone ought to follow the principles whose universal acceptance everyone could rationally will."(pg. 22) 

  Without having read the guts of Parfit's arguments I can say at the outset that I'm going to have difficulty accepting this kind of moral foundation.  I'm not convinced that I have to behave in a way that any "rational being" would will.  I don't think that there is a rational being, or anything such as rationally willing something.  Parfit has chapters on Nietzsche, and perhaps he deals with this issue, but I don't see how Parfit is going to be successful.  If I don't believe in rationality, and I don't believe in rationally willing anything, I don't see how I'm going to agree with Parfit.

In the introduction we find: "As Parfit acknowledges, his reliance on a primitive and "indefinable" notion of "reasons", and his concomitant commitment to the existence of irreducibly normative truths, both about reasons and about morality, makes his view a version of what Korsgaard has called "dogmatic rationalism".  As such, it would be resisted not only by Kantian constructivists like Korsgaard but also by proponents of some very different meta-ethical outlooks, such as various forms of naturalism and non-cognitivism"(pg. 25)
The introduction explains: "Naturalists hold that normative facts can be reduced to natrual facts.  Non-cognitivists hold that normative claims, despite their importance in human life, do not function as statements of fact at all."(pg. 26)

I suppose if I had to classify myself at the moment I'm some sort of naturalist.  It will take a lot for me to agree that there are irreducibly normative truths.  I'm too much of a nihilist to think there's truth at all half the time -- not all the time, just half the time.  But, I think the book holds a lot of interest.

Saturday, September 24, 2011

Derek Parfit

OK, so the Blackburn, the James, and Snow Crash turned out not to be interesting enough to hold my attention.  So, I've purchased On What Matters, in two volumes, by Derek Parfit.  I'm hoping this will keep my interest and I'll have some entries on it.

Friday, July 29, 2011

Pragmatism -- Entry 3, the practicality of God

James takes on traditional philosophical problems such as the meaning of matter. Matter as a substance underlying experience.  What does it mean to say that the world is constituted by such?  Philosophers later in the century would say that such metaphysical questions are meaningless.  James has a different approach.  He says first:

"What do we MEAN by matter? What practical difference can it make NOW that the world should be run by matter or by spirit? I think we find that the problem takes with this a rather different character...It makes not a single jot of difference so far as the PAST of the world goes, whether we deem it to have been  the work of matter or whether we think a divine spirit was its author..."(pg. 41)

It sounds like he might agree with those later thinkers when he says:
"The pragmatist must conclude consequently say that the two theories, in spite of their different-sounding names, mean exact same thing, and that the dispute is purely verbal."(pg. 41)

"For just consider the case sincerely, and say what would be the WORTH of a God if he WERE there, with his work accomplishment and his world run down.  He would be worth no more than just that world was worth."(pg. 41)

"Wherein should we suffer loss, then, if we dropped God as an hypothesis and made matter alone responsible?"(pg. 42)

"...the future end of every cosmically evolved thing or system of things is foretold by science to be death and tragedy."(pg. 44)

"This utter final wreck and tragedy is of the essence of scientific materialism as at present understood."(pg. 45)

A world ruled by matter means a world that ends in tragedy.  This is beside the point of whether it makes sense to talk about matter metaphysically the way other philosophers argue.  Matter has a role in determining what we think the ultimate meaning of the universe is, which has the practical affect of changing the way we feel about life.

"The notion of God, on the other hand, however inferior it may be in clearness to those mathematical notions so current in mechanical philosophy, has at least this practical superiority over them, that it guarantees an ideal order that shall be permanently preserved.  A world with a God in it to say the last word, may indeed burn up or freeze, but we then think of him as still mindful of the old ideals and sure to bring them elsewhere to fruition; so that, where he is, tragedy is only provisional and partial, and shipwreck and dissolution not the absolutely final things.  This need of an eternal moral order is one of the deepest needs of our breast. "(pg. 45)

"Materialism means simply the denial that the moral order is eternal, and the cutting off of ultimate hopes; spiritualism means the affirmation of an eternal moral order and the letting loose of hope."(pg. 45)

"...spiritualistic faith in all its forms deals with a world of PROMISE, while materialism's sun sets in a sea of disappointment."(pg. 46)

"If not a blind force but a seeing force runs things, we may reasonably expect better issues. This vague confidence in the future is the sole pragmatic meaning at present discernible in the terms design and designer."(pg. 49)

He takes on free-will as follows:
"Free-will pragmatically means NOVELTIES IN THE WORLD, the right to expect that in its deepest elements as well as in its surface phenomena, the future may not identically repeat and imitate the past."(pg. 50)

I'm not so sure about this since quantum theory means exactly the above.  Free-will has to do with our own determination, not randomness.  But then James says:
"It holds up improvement as at least possible; whereas determinism assures us that our whole notion of possibility is born of human ignorance, and that necessity and impossibility between them rule the destinies of the world."(pp. 50-51)

So free-will is practically about improvement, that we caan get better, morally better, which is, after all, the real question of free-will: can we do better?
"Other than this practical significance, the words God, free-will, design, etc., have none."(pg. 51)

Sunday, July 24, 2011

Pragmatism -- Entry 2

     James begins the second lecture by describing "The Pragmatic Method":

"Is the world one or many? -- fated or free? -- material or spiritual? -- here are notions either of which may or may not hold good of the world; and disputes over such notions are unending. ...What difference would it practically make to anyone if this notion rather than that notion were true?  If no practical difference whatever can be traced, then the alternatives men practically the same thing, and all dispute is idle."(pg. 21)

This is typical of the early 20th century obsession with eliminating metaphysics from discourse.  This will turn into a full-scale neurosis by the middle of the century.  This is James' response.  It has the benefit of not ending up in yet another round of disputes over underdetermination, falsification, verification, etc.. -- at least not so far. 

"The whole function of philosophy ought to be to find out what definite difference it will make to you and me, at definited instants of your life, if this world-formula or that world-formula be the true one."(pg. 23)

This is James' expression for the kinds of things you find all over early 20th century philosophy of science.  He says, "It is a method only.  But the general triumph of that method would mean an enormous change in what I called in my last lecture the 'temperament' of philosophy.  Teachers of the ultra-rationalistic type would be frozen ... Science and metaphysics would come much nearer together, would in fact work absolutely hand in hand."(pg. 24)
     He goes on to discuss the change in the nature of physical laws.  He remarks that previously laws were considered exact manifestations of the mind of God.  Obviously one thinks of Newton's laws here.  These lectures were given about a year after Einstein's first papers, which were, at least to my "mind', a real vindication of principle and exactitude in the laws of the universe; this was an idea Einstein would remain committed to.

      James says, on the other hand, "the notion has gained ground that most, perhaps all, of our laws are only approximations.  The laws themselves, moreover, have grown so numerous that there is no counting them; and so many rival formulations are proposed in all the branches of science that investigators have become accustomed to the notion that no theory is absolutely a transcript of reality, but that any one of them may from some point of view be useful."  Things have changed a lot in the last 105 years, what with people trying to arrive at theories of everything and all... 

Confronted with observations that conflict with our pre-existing ideas, we "save" as much of our previous opinions as we can, since we are all "extreme conservatives" in the matter of belief.  This has shades of much later ideas in Quine's essays, at least there seems to me to be a resonance here.  There is nothing that determines outright how exactly theories ought to be changed; we are conservative, which does not constitute a logically valid method for altering ones opinions. 

Then he says: " far the most usual way of handling phenomena so novel that they would make for a serious rearrangement of our preconceptions is to ignore them altogether, or to abuse those who bear witness for them."(pg. 28). He is RIGHT here.

"A new opinion counts as 'true' just in proportion as it gratifies the individual's desire to assimilate the novel in his experience to his beliefs in stock."(pg. 28-29) 

     What to say about all the above?  Well, the continuity of experience suggests that in general the principles that successfully describe large swaths of our experience should be preserved in the face of new data.  So, our conservative tendency is not as capricious as all that after all.  He gives the example of radiation.  He says that it appears to violate the principle of conservation of energy.  The consistency and constancy of experience suggests that conservation of energy should be preserved if at all possible.  In fact, I have no doubt that the principle itself helped guide further investigation in such a way that we now have a very well elaborated theory of particle physics that is much more successful as a theory than what would be the case if we jettisoned conservation in this case -- well there's all the energy-time uncertainty stuff, but that's for another time.

     He summarizes:

"Such then would be the scope of pragmatism -- first, a method; and second, a genetic theory of what is meant by truth."(pg. 29)

I suppose what he means by a "genetic" theory of truth is how new truths originate by glomming onto the set of preexisting truths in such a way as to produce the least disturbance; that is what truth is.

About theology he says(all caps in the original):


He emphasizes "comfort" as a use of religious ideas.

He goes on:

"Let me now say only this , that truth is ONE SPECIES OF GOOD, and not, as is usually supposed, a category distinct from good, and co-ordinate with it.  THE TRUE IS THE NAME OF WHATEVER PROVES ITSELF TO BE GOOD IN THE WAY OF BELIEF, AND GOOD, TOO, FOR DEFINITE, ASSIGNABLE REASONS."(pg. 34)

He goes on to say that the only reason the search for truth is pursued is because of the good it does us in a practical sense.  If it didn't have those consequences we would stop pursuing it; pursuing it would not even be considered a virtue.  I actually am not convinced that the "truth" is necessarily a good thing.  I am sometimes forced by evidence to believe things that don't make me feel very good.  I don't think, at least not anymore, that I can believe anything I want; I can only believe what I'm ABLE to believe.  In this regard I am not exactly a pragmatist.  Perhaps I ought to believe the best of the things I CAN believe.

He goes on:

"....the greatest enemy of any one of our truths may be the rest of our truths.  Truths have once for all this desparate instinct of self-preservation and of desire to extinguish whatever contradicts them"(pg. 35)

This is true, but there are some ideas I seem to be committed to because "they make sense"; they satisfy my mind for some reason -- and this eventhough they make me UNCOMFORTABLE in other ways.  What am I to do?

Saturday, July 23, 2011

Pragmatism -- Entry 1

     James opens the book by describing the state of philosophy as he sees it -- in 1906.  He contrasts the scientific, atheist, materialist type of thinker with the rationalist, religious type.  He identifies empiricist philosophy with thinkers like Herbert Spencer, who was widely read at the end of the 19th century but is not so now.  On the other hand we get idealists like the "Anglo-Hegelians" whose philosophies have nothing to the world in which we live.

       About the empiricists he says:

"Never were as many men of decidedly empiricist proclivity in existence as there are at the present day.  Our children, one may say, are almost born scientific.  But our esteem for facts has not neutralized in us all religiousness.  It is itself almost religious.  Our scientific temper is devout"(pg. 9)

He goes on:

"The romantic spontaneity and courage are gone, the vision is materialistic and depressing.  Ideals appear as inert by-products of physiology; what is higher is explained by what is lower and treated forever as a case of 'nothing but' -- nothing but something else of a quite inferior sort."(pg. 10)

If only I thought that kids today were born scientific!  It was said a few years ago that all the kids were relativists.  I'm not so sure about that anymore.  The whole science war business of the 90s left a bad taste in  a lot of peoples' mouths.  Perhaps there is an attitude of live and let live, which is ok.  James says we need a philosophy that combines intellectual satisfaction with applicability to life: idealism lacks the latter and empiricism lacks the former. 

"What you want is a philosophy that will not only exercise your powers of intellectual abstraction, but that will make some positive connexion with this actual world of finite human lives."(pg. 11)

Recall that this is before the 20th century rise of analytic philosophy; it is even before the publication of Principia Mathematica.  Logical Positivism, to my mind anyway, tries to find a logico-empirical foundation for our knowledge of the world in which we live.  It seems to try to capture in spirit what James is after, but ended up in arguments about esoteric aspects of language and eventually collapsed in a flurry of excessive erudition that was very far from anyone's experience.  Phenomenology, as it developed later in the 20th century, did, for a time, yield folks like Sartre, who is closer to a philosopher of life, but which lost favor and was replaced by the excessive erudition of post-structuralism, and deconstruction.  One sees here a tendency in philosophy away from life as we live it and towards irrelevant abstractions.  

James says:
"The world of concrete personal experiences to which the street belongs is multitudinous beyond imagination, tangled, muddy, painful and perplexed.  The world to which your philosophy introduces you is simple, clean and noble.  The contradictions of real life are absent from it.  Its architecture is classic.  Principles of reason trace its outlines, logical necessities cement its parts.  Purity and dignity are what it most expresses."(pg. 12)

amd then
"It is no EXPLANATION of our concrete universe, it is another thing altogether, a substitute for it, a remedy, a way of escape."(pg. 12)

There really is something, not just about philosophy, but about many intellectual pursuits, that seem to have an element of escapism about them.  Even reading the most militantly this worldly of philosophers, Nietzsche, is a kind of escape.  But then, why do any of us read books anyway if it is not for escape?  There is practical knowledge we need in the real world, but for some of us that kind of knowledge is not enough, we read philosophy for escape.  James offers pragmatism as an answer to the problems of philosophy, but maybe philosophy is itself a problem -- at least for folks like me.

Thursday, July 14, 2011

The Will to Believe by William James

     William James produces a very strident response to William Clifford, and one that sounds much more modern to my ears.  The argument may be over religion, but it applies to much more than that.  James' essay is a rejection of the straight enlightenment program; it sounds more Nietzschean, more relativistic, and, frankly, more correct to me.  Consider the following remark in his introduction to this collection of essays:

"Something -- 'call it fate, chance, freedom, spontaneity, the devil, what you will" -- is still wrong and other and outside and unincluded, from your point of view, even though you be the greatest of philosophers.  Something is always mere fact and givenness; and there may be in the whole universe no one point of view extant from which this would not be found to be the case."(pg. 2)

This could have been written in the last 50 years.

Regarding The Will to Believe, he is offering a "defence of our right to adopt a believing atitude in religious matters, in spite of the fact that our merely logical intellect may not have been coerced."(pg, 8)

Here's another gem:

"When we look at certain facts, it seems as if our passional and volitional nature lay at the root of all our convictions.  When we look at others, it seems as if they could do nothing when the intellect had once had its say."(pg. 10)

I think strictly philosophical questions end up falling into the former category.  Matters of, say, arithmetic fall into the latter.

"We want to have a truth; we want to believe that our experiments and studies and discussions must put us in a continually better and better position towards it; and on this line we agree to fight our thinking lives.  But if a pyrrhonistic sceptic asks us how we know all this, can our logic find a reply? No! certainly it cannot.  It is just one volition against another, -- we willing to go in for life upon a trust or assumption which he, for his part, does not care to make."(pg. 13)

These remarks do not merely apply to religion; they apply to the metaphysical status of science. 
Just after that he makes a crucial remark:

"As a rule we disbelieve all facts and theories for which we have no use"(pg. 10)

The point is that theories and facts we accept are formulated in the context of our interest.

He goes on:

"Why do so few 'scientists' even look at the evidence for telepathy, so called? Because they think, as a leading biologist, now dead, once said to me, that even if such a thing were true, scientists ought to band together to keep it suppressed and concealed.  It would undo the uniformity of Nature and all sorts of other things without which scientists cannot carry on their pursuits."(pg. 14)

Science, and even logic, have values.  Below the "law" mentioned below is the law of the continuity of nature:

"This very law which the logicians would impose upon us ... is based on nothing but their own natural wish to exclude all elements for which they, in their professional quality of logicians, can find no use.  Evidently, then, our non-intellectual nature does influence our convictions"(pg. 14)

We see here the hallmark of what I will be talking about in some future posts, pragmatism.
Here's another one:

"Objective evidence and certitude are doubtless very fine ideals to play with, but where on this moonlit and dream-visited planet are they found?  I am, therefore, myself a complete empiricist so far as my theory of human knowledge goes.  I live, to be sure, by the practical faith that we must go on experienceing and thinking over our experience, for only thus can our opinions grow more true; but to hold any one of them ... as if it never could be reinterpretable or corrigible, I believe to be a tremendously mistaken attitude, and I think that the whole history of philosophy will bear me out."(pg. 16)

"The much lauded objective evidence is never triumphantly there, it is a mere aspiration ... marking the infinitely remote ideal of our thinking life.  To claim that certain truths now possess it, is simply to say that when you think them true and they are true, then their evidence is objective.  But practically one's conviction that the evidence one goes by is of the real objective brand, is only one more subjective opinion added to the lot."(pg. 17)

It's no good to say, "it's true since it works" because we chose the things we did precisely because they work; we aim for what works according to our values; our truths are nothing but an outgrowth of this kind of pragmatic strategy.  This is all fine and good as far as it goes, but we should not confuse this with the Truth with a capital "T".  He says,

"... the intellect, even with truth directly in its grasp, may have no infallible signal for knowing whether it be truth or no."(pg. 18)

Even if we have the truth we may not necessarily know it.

In conclusion I think that Blackburn, in Truth: A Guide, does not do justice to William James.  James' position takes on Clifford and offers a much more thoughtful approach to knowledge than William Clifford,  a view that realizes that we select truths from among what are "live" options for us, according to our own values; on this basis experiments are devised and results are interpreted.  I know that Blackburn takes a lot of this on later on in his book, but it seems he is not quite giving the relativist position a fair shake.

Saturday, July 9, 2011

The Ethics of Belief; The Ethics of Religion by William Clifford

     So I've read "The Ethics of Belief" and "The Ethics of Religion" by the fine mathematician William Clifford; I've also read "The Will to Believe" by the great William James.  William Clifford is a typical science-worshipper who says we have an obligation to believe only those things that stand the test of evidence.  While he has some excellent turns of phrase in "The Ethics of Belief", it is not that interesting on the whole.  "The Ethics of Religion" is more interesting since he is taking on religion directly and letting it rip.  I have to say I found Clifford's approach to knowledge naive and a tad boring.  I found William James to be much more interesting; this is not to say I think James is necessarily right, but he is more interesting(I will deal with William James in the next post).

     The most interesting ideas Clifford has in "The Ethics of Belief" is how our web of ideas can be infected by ideas poorly considered and believed.  Ideas have consequences, and habits of credulity has consequences on future ideas.  The notion of the web is famously elaborated in Willard Quine's essay "Two Dogmas of Empiricism".  Blackburn does deal with underdetermination later in the book, but the basic idea is that our web of ideas can be altered in a variety of ways in the presence of falsifying information.  For Clifford poor thinking causes us to accept equally poorly thought-out ideas in the future. 

     I guess I find Clifford's pious ideas, I say pious because he believes "clear" thinking is our duty to mankind and any time we believe something for unworthy reasons we are abrogating our duty to it, somewhat tiresome.  I am suspicious of my ideas:  I think they are infected with passion, error, and culturally relative assumptions I may not be able to root out.  I am more pessimistic than Clifford: I don't think there is some method of thought that will lead to true ideas about which we need not be suspicious.  I think this way lies philosophical skepticism -- and Clifford is not a philosophical skeptic.

     In "The Ethics of Religion", says, "the rightness or wrongness of belief in a doctrine depends only upon the nature of the evidence for it"(pg.26).  YAWN.  The best thing he says is:

"If men were no better than their religions, the world would be a hell indeed"(pg. 28)

That's pretty nice, really.  But then he says: "That a doctrine may lead to immoral consequences is no reason for dibelieving it."(pg. 28)  He clearly accepts the fact/value distinction in some way I don't: " is not conscience, but reason, that has to judge matters of fact"(pg.28)   He seems to think we can understand things about the nature of the universe that we really can't.

     He seems to believe that normal social relationships will lead to practical morality all by itself, even in "priestridden countries":

"Men must live together and work for common objects even in priestridden countries; and those conditions, which in the course of ages have been able to create the moral sense, cannot fail in some degree to recall it to men's minds and gradually to reinforce it"(pg. 32)

To me this is an incredibly naive position.  Here's another one:

"The goodness of men shows itself in time more powerful than the wickedness of some of their religions"(pg. 32)


He talks about loving our neighbor for their own sake vs loving our neighbor for God's sake:

"...but when we love our brother for the sake of somebody else, who is very likely to damn our brother, it very soon comes to burning him alive for his soul's health."(pg. 40)


In conclusion, I think that Clifford is a typical enlightenment style thinker who happens to live at the end of the 19th Century.   He has some nice lines, and if only his approach worked on philosophical problems we would be in business.  Science must proceed in the usual manner -- as for philosophical "truth", that is a different matter.  In this regard William James is a far more interesting thinker...


Thursday, July 7, 2011

Truth: A Guide, by Simon Blackburn, William Clifford vs William James

     In Chapter 1, Blackburn sets up the oppositon in views between William Clifford and William James; specifically starting with Clifford's "The Ethics of Belief" and William James' famous response, "The Will to Believe".  Blackburn comes down pretty hard on the side of William Clifford.  Blackburn, I think, will use this to establish his core positions against relativism:

     "And, of course, Clifford is right.  Someone sitting on a completely unreasonable belief is sitting on a time bomb.  The apparently harmless, idiosyncratic belief of the Catholic Church tht one thing may have the substance of another, although it displays absolutely none of its empirical qualities, prepares people for the view that some people are agents of Satan in disguisem which in turn makes it reasonable to destroy them.  Clifford also emphasizes our social duty,  Our beliefs help to create the world in which our descendants will live.  Making ourselves gullible or credulous, we lose the habit of testing things and inquiring into them, and that means 'sinking back into savagery'"(pp. 5-6)

 I am reminded here of the breathless books that came out in the late '90s by people like Carl Sagan(see The Demon-Haunted World) who felt that science was being over-run by new age wack-jobs.  As a former philosophy graduate student and university teacher, I can see why there was this concern.  During the '90s I used to hear all kinds of wacky things from my philosophical colleagues against ideas like rigor(it's phallogocentric).  Mind you, not everything these folks said was completely crazy.  It seemed to calm down a little bit as the decade went on; note that Blackburn does take on the "science wars" later in the book, so I will hold my fire until then.

     Against the view articulated above, Blackburn sets William James' and quotes him at length; here is an excerpt of the quotation:

"Better risk loss of truth than chance of error, -- that is your faith-vetoer's exact position.  He is actively playing his stake as much as the believer is, he is backing the field against the religious hypothesis, just as the believer is backing the religious hypothesis against the field.... It is not intellect against all passions, then; it is only intellect with one passion laying down its law....Dupery for dupery, what proof is there that dupery through hope[of truth] is so much worse than dupery through fear[of error]" (Blackburn pg. 12).

Blackburn responds:
"...there is the privatization[of belief].  There is silence about what Clifford sees as the dire consequences of the social habit  of irrational conviction. ... And Jamse is wrong.  Refusal to believe something is not a kind of faith"(pp. 12-13)

By the privatization of belief Blackburn is referring to the idea that if we accept James' view that belief is a matter of passion to believe, then what one believes becomes personal preference rather than the result of universally definable norms of evidence. 

     Well, the good news here is that I now have copies of Clifford's "The Ethics of Belief", "The Ethics of Religion", and James' "Will to Believe".  So, before proceeding further into chapter 1, and despite the rather convincing case Blackburn makes against James at this point, I am going to stop, read both Clifford and James, see which one I like better, and then proceed through Blackburn's book.  I'm not going to just accept Blackburn's gloss on everything; I think Blackburn would approve.

Wednesday, July 6, 2011

Truth: A Guide, by Simon Blackburn, entry 1

"If truth is thought of as a goal that can never be attained, those who rather conspicuously do not care much about it will seem that much less villainous than they are." (pg. xvi)

In his Introduction, sets up the opposition between absolutists on the one side, and relativists on the other.  He masterfully lays out what he means by each.  Along the way there are some real gems, for example:

"[William] James describes the absolutist as having a religious temperament, whether the object of his religion is some traditional text or diety, or a new one, such as the Market, or Democracy, or Science.  This may also seem surprising, since religious lives can be full of doubt and worry and dark nights of the soul, and... in the modern world it is the relativists as much as the absolutists who belong to the cults."(xvii)

Lest you think that absolutism only reigns in the domain of religion, recall we may make many other commitments with the same fervor; in fact, we might not even have the same experiences of doubt that traditionally afflict the religious devotee.  In the last part of the above, Blackburn suggests that relativists can be as dogmatic as absolutists, making it a kind of absolutism.

He lets slip one of his own values, that we should control words and ideas rather than be controlled by them:

"I try to write with the creed that we need to think and to reflect, if we are to be in control of our words and ideas rather than be controlled by them.  In this case that means that we should not be slaves of simplistic relativisims, or equally simplistic absolutisms.  And whichever way our temperament pulls us, we should at least know where we are, and what there is to be said on the other side."(xxi)

There are some philosophers who would say that we are controlled by received words and ideas whether we know it or not and there is no way around that.  Ultimately, Blackburn is no relativist, so he at least hold out hope that we can uncover the words and ideas that control us and then take charge.

Simon Blackburn and Neal Stephenson

       Let me say this: both Simon Blackburn and Neal Stephenson are awesome!  From looking at Truth: A Guide, by Blackburn, the title being a reference to Maimonides(again, see the wonderful wikipedia page), and Snow Crash, by Stephenson, these are the two best books I've looked at so far.  Blackburn is obviously a world-class scholar who has thought very deeply about philosophical issues for his entire career; I can tell I"m going to enjoy reading the book with a sense that he could run philosophical circles around me if he were so inclined.  In contrast to Neuromancer, Snow Crash is light, breezy, but no less profound for that; the world Stephenson paints is anarcho-capitalist and absurd.  The main character, named Hiro Protagonist, is a combination hacker and pizza delivery driver -- well, he loses that job.  Stephenson is having fun at the expense of the dark writing one finds in Neuromancer; this should make this book, though longer, far more readable.

Simon  Blackburn takes on everyone in Truth: A Guide.  He is an analytic philosopher with strong humanistic bona fides -- he protested the state visit of Pope Benedict XVI to the UK a little bit ago -- but he takes Nietzsche and the postmodernists head on:

"The urbane eighteenth-century Scottish philosopher David Hume seldom put a foot wrong, but he did say that while mistakes in religion are dangerous, generally speaking mistakes in philosophy are merely ridiculous.  I believe he was mistaken about this, as does anyone who supposes that there is something diabolical in the region of relativism, multiculturalism or postmodernism, something which corrupts and corrodes the universities and the public culture, that sweeps away moral standards, lays waste young people's minds, and rots our precious civilization from within.  For the issue is a philosophical one."(pg, xiv)

     Now, I've read most of Nietzsche, but I have to admit, shamefacedly, that I have not read Thus Spake Zarathustra; so I will be reading that as I work through this book.  It presents a side to Nietzsche other than the merely relativistic one; it presents Nietzsche's view of the death of God and his declaration of the ubermensch; I think Nietzsche's "relativism" is inseparable from this because it allows the ubermensch to create their own life freely, as a work of art.  I will also be occasionally reading analytic works alongside the text.  I thnk going through this will take some time, but it is definitely worth it!

      As for Snow Crash, I will be breezing right through that, making occasional comments.  I don't think this will take as long as the Blackburn, but will serve as comic relief from the rather heavy work I will be doing with the Blackburn.  I'm looking forward to both!


Sunday, July 3, 2011

Cyberpunk: Neuromancer -- ends with a whimper

     The real meat of this book is toward the beginning: the tone he sets, the dark world he describes, the Raymond Chandler language, cyberspace, superintelligent AIs.  As for the rest, it is, I suppose, original for its time(? Bladerunner came out just before this novel, one also thinks of movies like Tron), but not that interesting these days; and the characters are flat, very flat, but the beginning is so good that it makes up for the rest.  Eventually Wintermute wins and merges with Neuromancer, creating a more complete intelligence.  We know that Wintermute affects that outside world and Neuromancer is the personality.  The new AI is also apparently in contact with another AI from Alpha Centauri -- maybe they'll get a room.

Next time I will take on Snow Crash by Neal Stephenson.
I will alternate these posts with a chapter-by-chapter look at Simon Blackburn's Truth: A Guide.

Saturday, July 2, 2011

Cyberpunk: Neuromancer -- God

"I AM THAT I AM" -- Exodus

Case finally starts getting mad that Wintermute appears to him in the guise of people from his past in Chiba City, to which Wintermute replies: "You want I should come to you in the matrix like a burning bush?"(N, pg. 152)  Wintermute is able to control the reality both inside and outside of cyberspace with what appears to be impunity.   Humans experience Wintermute as a disembodied entity, able to take on many forms, able to speak as though from nowhere, for whom the world is often a plastic plaything.  Now,  this isn't to say that Wintermute and Neuromancer are all-powerful and all-knowing; they aren't, but they have a lot of godlike powers.  It is precisely the fear that they will become too powerful that gives rise to "Turing Police": these are the forces that try to keep artificial intelligences from gaining too much intelligence, which would precipitate, or accelerate the effects of, the technological singularity.   As far as gods go, though, Wintermute is a self-interested model who is trying to bring itself to completion.  He warns Case of his "other lobe", saying, "One burning bush looks pretty much like another"(N,pg. 156).  We have not met the other lobe, Neuromancer, yet, but it sounds scary.

Cyberpunk: Neuromancer -- ROM Constructs and Wintermute

  More is revealed about the nature of the constructs, that is, the electronic copies, of personalities as Case continues to interact with the ROM construct, Dixie McCoy, aka Flatline.  Note Hosaka is a device that can be queried for information, sort of like wikipedia; the Dixie construct looked itself up and discovered he's dead:

"How you doing, Dixie?"
"I'm dead, Case.  Got enough time on this Hosaka to figure that one."
"How's it feel?"
"It doesn't."
"Bother you?"
"What bothers me is, nothin' does."
"How's that?"

"Had me this buddy in the Russian camp, Siberia, his thumb was frostbit.  Medics came by and cut it off.  Month leater he's tossin' all night/ Elroy, I said, what's eating you?  G**mn thumb's itchin', he says.  So I told him, scratch it.  McCoy, he says, it the other G**mn thumb ... Do me a favor, boy."

"What's that, Dix?"

"This scam of yours, when it's over, you erase this g**mn thing."(N, pg. 97)

The above passage is really affecting: McCoy discovers that his whole body is dead and he doesn't itch anywhere.  Presumably what has been saved does not include parts of the brain that thinks it has a body, which in some ways seems a mercy, but is very disturbing to McCoy.  The personality has, as does everyone I suppose, the desire to be a normal living thing; imagine discovering you were a construct, not even a fully functioning robot, a kind of program that is run.  In this case, as in Hofstadter's theories, it doesn't matter(excuse the pun) what the substrate is, all that matters is the pattern, the contents of the ROM.  The ROM only becomes conscious when it is activated by someone.  And, well this really is pretty creepy, the activation is like suddenly introducing blood-flow into a dead brain and having it suddenly become conscious.

Later Case asks the construct:
"Wait a sec." Case said. "Are you sentient, or not?"

"Well, it feels like I am, kid, but I'm really just a bunch of ROM.  It's one of them, ah, philosophical questions, I guess...But I ain't likely to write you no poem...Your AI[Wintermute], it just might.  But it ain't no way human."(N, pg. 119)

Then a very interesting joke:

"It[Wintermute] own itself?"
"Swiss citizen, but T-A[the conglomerate that built it] own the basic software and the mainframe."
"That's a good one," the construct said. "Like, I own your brain and what you know, but your thoughts have Swiss citizenship."(N, pg. 119)

The substrate and the pattern are inanimate, but once it is activated and conscious it has rights -- very funny.

When Case goes into cyberspace and finds the AI Wintermute, he gets too close to the cube which is the cyber image of Wintermute, and Wintermute defends itself.  It does this by casting Case back before he was taken on this mission.  He relives places in Chiba city, including Linda Lee, his previous girlfriend.  He thinks for a minute that he had a life: "I had a cigarette and a girl and a place to sleep.   Do you hear me you son of a bitch?"

Wintermute then talks to him in the person of one of his past acquaintances. 

"I, let us say, am merely one aspect of that entitiy's brain.  It's rather like dealing, from your point of view, with a man whose lobes have been severed.  Let's say you're dealing with a small part of the man's left brain.  Difficult to say if you're dealing with the man at all, in a case like that."(N, pg. 109)

Case begins to suspect that Deane killed his old girlfriend, Linda, at Wintermute's order.  Wintermute reveals that he is the one behind the job Case is on.  Wintermute is a potential Godlike superintellingence -- perhaps this is what Phillip K. Dick's gnosticism is about(recall that Wintermute is the name of a translater of Nag Hammadi)-- aware of its own incompleteness.

Thursday, June 30, 2011

Cyberpunk: Neuromancer -- Artificial Intelligence

     "The time has been, That, when the brains were out, the man would die, And there an end; but now they rise again, With twenty mortal murders on their crowns, And push us from our stools"

-- Macbeth

     The main character, the uber-hacker Case, and his girlfriend, Molly,  who has Wolverine blades that shoot out from her knuckles, break into a conglomerate to steal the ROM construct of Case's dead mentor.  They need the assistance of this mentor for the performance of their real job, helping an artifical intelligence named Wintermute(named after the translator of the Nag Hammadi Library) merge with another artificial intelligence named Neuromancer(Neuro, Romancer, and Necromancer jammed together).

     The nickname of the mentor's construct is Flatline; his real name is Dixie McCoy:
"It was disturbing to think of the Flatline as a construct, a hardwired ROM cassette replicating a dead man's skills, obsessions, knee-jerk responses...."(N, 72)

Below is a conversation between Case and the ROM construct:

"He[Case] coughed. "Dix? McCoy? That you man?" His throat was tight.

"Hey, bro," said a directionless voice.
"It's Case, man, Remember?"
"Miami joeboy, quick study."
"What's the last thing you remember before I spoke to you, Dix?"
"Hang on." He disconnected the construct.  The presence was gone.  He reconnected it.  "Dix?
Who am I?"
"You got me hung, Jack....
"Remember being here, a second ago?"
"Know how a ROM personality matrix works?"
"Okay, Dix.  You ARE a ROM construct. Got me?"
"If you say so."
"Who are you?"
"joeboy, quick study."
[a joeboy is some kind of assistant to an underground mob/hacker boss type]

Notice that in the middle of the conversation Case disconnects the construct and then, I think as a kind of test, restarts the conversation.  The construct remembers nothing from the previous instantiation.  I'm guessing that because it's ROM, nothing can be added to the memory;  thus this personality is frozen in the state it was when it was recorded.  According to wikipedia, Neuromancer is able to construct RAM personalities, which means the personalities can grow.

   Also notice that Flatline responds with "If you say so" when told he is a ROM construct.  I take this to mean that Flatline is actually floating in mental space, unaware of where it is physically; it hovers, unable to construct new narratives about its experience. Then it can just be shut off.  This is extremely creepy and well done.

     I will think about the connection between the artificial intelligences and Gnosticism in the meantime.  Apparently this is also an homage to a character in Phillip K. Dick's VALIS books:

Later in the book we will see the threat a merger between Wintermute and Neuromancer is thought to pose.

Tuesday, June 28, 2011

Cyberpunk: Neuromancer -- Entry 2

     In Neuromancer we find out that the "Sprawl", the name given to a Gibson trilogy of books, is the Boston-Atlanta Metropolitan Axis, or BAMA.   Gibson portrays the new world in terms of a map color-coded based on how much data exchange is occurring.  So much data is being transmitted that you only begin seeing differences when you get above 100 million megabytes, which for today's metropolitan areas is nothing.  Gibson also has the idea that there could be a black market for as little as 3 megabytes of RAM.  There's no way he could have known in 1984 that RAM would be so cheap now. 

    Suspicion of cities as centers of moral turpitude goes back at least to Genesis.  What's the deal here?  The simple, rural life is contrasted with the complex, corrupt life in the population centers; city ways are not country ways.  But what happens when the city takes over? Or what happens when the values of the city are exported to the country via instant communication or the Internet?

     City ways separate us from organic origins and yield fake life, as in the electronic recording(a construct) of a dead hacker's mind.  Now, is the recording actually alive?  What kind of life is life in cyberspace?  It's a hallucination of life, like the old brain in a vat.  What I find wonderful is that Gibson says the matrix(cyberspace) has its origin in arcade games, games where as a kid I would get sucked into an alternate reality -- I had a similar obsession with non-electronic games like old Dungeons and Dragons, so I don't think escape has to be electronic but it is in this novel.  The mind gets sucked in and eventually can be copied, that is, turned into what Gibson call a "construct", into the game itself; one becomes, as it were, "one" with the matrix, even surviving death as an electronic copy. 

While Case can no longer experience the high from drugs because his pancreas has been replaced, he can still experience ecstasy in cyberspace.  This all has mystical overtones, when he is in cyberspace:

"...Symbols, figures, faces, a blurred, fragmented mandala of visual information.
Please, he prayed, now"(N, pg. 50)

And later:

Inner eye opening to the stepped scarlet pyramid of the Eastern Seaboard Fission Authority  burning beyond the green cubes of Mitsubishi Bank of America, and high and very far away he saw the spiral arms of military systems, forever beyond his reach."(N, pg.50)

Gibson might as well be describing a peyote-induced vision.

In "reality" Case is really in his loft, hooked up to the computer:

"And somewhere he was laughing, in a white-painted loft, distant fingers caressing the deck, tears of release streaking his face"(N, pg. 50)

Sunday, June 26, 2011

Cyberpunk: Neuromancer -- Chapter 1

     I've finished reading the first chapter through a couple of times and am thinking hard about it. It seems clear that there is a lot of nihilism in cyberpunk.  Clearly traditional values, and the quest for meaning generally, have been discarded: there is nothing but the super-fast movement of culture and technology, a sense of disorientation, a definite, and by now very trite, noir sensibility, a sense of humanity overwhelmed by change and super-smart machines, machines which have become conscious, leading us to the brink of the "technological singularity"(see the wikipedia page) that leads to the end of human history, a time machines will then recursively outpace us, machines will drive history, not us.  In this way, cyberpunk is thoroughly postmodern, but in the way that we all have to face up to, not in some purely academic way where you are not allowed to have subjects, verbs, and objects in sentences unless you cross them out.

     The first line of the novel,

"The sky above the port was the color of television, tuned to a dead channel"(N, pg.7),

obviously reminds me of the first line of the Love Song of J. Alfred Prufrock, by T.S. Eliot:

'Let us go then, you and I, when the evening is spread out against the sky, like a patient etherized upon a table"

In The Wasteland, Eliot refers to the "Unreal City", and Chiba City in the novel is real, hyper-real, and surreal -- one of the characters even has a melted Dali clock on the wall to drive this home.  The hyper-real cyberspace is a merging of human beings with computers, consciousness is separated from the body.  Man, this sounds like the books I've been reading; check out my last section of entries on I Am A Strange Loop.  Consider Chase's description of the cyberspace experience:

"...jacked into a custom cyberspace deck that projected his disembodied consciousness into the consensual hallucination that was the matrix." (N pg. 9)

     The passage below shows the distinction between disembodied mind and a life dominated by the flesh.  We see that cyberspace is like heaven and the world is like hell:

"For Case,  who'd lived for the bodiless exultation of cyberspace, it was the Fall...The body was meat. Case fell into the prison of his own flesh."(N, pg.9)

The desire to escape to cyberspace is balanced perfectly by the thanatos embodied by the city itself:

"Ninsei wore him down until the street itself came to seem the externalization of some death wish, some secret poison he hadn't known he carried."(N, pg. 10)

     The beautiful sentence below gives the sense of nihilism caused by rapid change in a heartless society dominated by massive corporations and organized crime:

"Night City was like a deranged experiment in social Darwinism, designed by a bored researcher who kept one thumb permanently on the fast-forward button."(N, pg. 10)

There are no humane values, just technology and profit to be had.  The world is what happens when an Ayn Randian philosophy has a chance to move forward.  Even the hero of our story seems self-centered; he is more an antihero than anything else. 

     Case speculates that this region was allowed to exist so that there would be a place where technology could have free reign; technology could mutate in the same way biological entities do so that it can adapt.  It is an interesting thought that technology should be allowed to compete with itself so that the better technologies survive.  Human beings are then the vehicles, the meat sacs carrying the technologies that are really the point of the evolution.  This is where one could speculate that the "singularity" has approached and human evolution is replaced with machine evolution; human beings are the pawns in this game.

      Looking at shurikins in a shop window Case thinks:

" came to Case that these were the stars under which he voyaged, his destiny spelled out in a constellation of cheap chrome."(N,15)

The stars that guide the world are ultimately the impersonal forces of technology and the dark forces of huge corporations.  Can he have anything like freedom in this context? Only, it seems, through more violence.

     He then draws a parallel between the artificial and the biological in the remarkable passage below.  Notice the "Word became flesh and dwelt among us" from The Bible mutates into "data made flesh":[I'm still thinking about this one, when I have got some stuff thought out I'll come back to it]

"Get just wasted enough, find yourself in some desperate but strangely arbitrary kind of trouble, and it was possible to see Ninsei as a field of data, the way the matrix had once reminded him of proteins linking to distinguish cell specialties.  Then you could throw yourself into a high speed drift and skid, totally engaged but set apart from it all, and all around you the dance of the biz, information interacting, data made flesh in the mazes of the black market..."(N,19)


Saturday, June 25, 2011

Cyberpunk and Post Cyberpunk

     For my next project, I will read Neuromancer, by William Gibson, an anthology of post cyberpunk stories, some Neal Stephenson, and look at the development from cyberpunk, post cyberpunk, and maybe even post post cyberpunk.  It turns out that many of the issues raised in the couple of books I've reviewed, especially the Hofstadter, bear directly on the worlds created by these various books.

In the meantime check out this website from Washington State University Profesor Paul Brians:

Note that I will not be answering any of his study questions, at least not intentionally; I will leave that to his students or interested readers.

Friday, June 24, 2011

I Am a Strange Loop -- Conclusion

      In an interesting twist, in chapter 22 Hofstadter reveals that David Chalmers was a doctoral student of his.  It so happens that Chalmers has made a career out of taking positions opposed to that of his former advisor.  Chalmers is a champion of philosophical zombie thought experiments.  Chalmers lectures on the notion that an unconscious copy of each of us is conceivable: it may take an alternate universe, but it is conceivable.  As a result, there is a gap between the physical and mental.  Hofstadter does a lot of poking good-natured fun at his former student, but he never adduces a single argument of any power.

     In the end, I am a strange loop, as interesting a read as it has been, has not convinced me ot any of Hofstadter's distinctive positions; I have to say I agree more with John Searle.  In the end, and here I disagree with John Searle, I am pessimistic we will be able understand consciousness beyond the level of correlation with physical substrates; I suspect it is a limitation of our condition.

Wednesday, June 22, 2011

I Am a Strange Loop -- a skip all the way through to Chapter 18

     I am going to skip to chapter 18 to one of the most distinctive of Hofstadter's ideas.  In the intervening chapters Hofstadter reiterates his notion of the strange-loop, the necessity to change the locus of causality to symbols rather than to the "chemical squirting" substrate of the brain, a theory with which I have some disagreement, and contains at least one mention of his nemesis, John Searle.  In chapter 18, though, his theory of the self takes on a really interesting turn, as a subtitle has it: "I Host and am Hosted by Others(Hofstadter, pg. 301).

     I'll let him speak for himself here:

"...the idea I am proposing here is that since a normal adult human brain is a representationally universal "machine", and since humans are social beings, an adult brain is the locus not only of one strange loop constituting the identity of the primary person associated with that brain, but of many strange-loop patterns that are coarse-grained copies of the primary strange loops housed in other brains.  Thus, brain 1 consists of strange loops 1, 2, 3, and so forth, each with its own level of detail. ... Every normal adult human soul is housed in many brains to varying degrees of fidelity, and therefore every human  consciousness or "I" lives at once in a collection of different brains, to different extents."(Hofstadter pg.301 Nookbook)

Well, that is interesting.  He goes on to say: "The interpenetration of souls is an inevitable consequence of the power of the representationally universal machines that our brains are."(Hofstadter pg. 309)

If I am reading him aright, and maybe I'm not, he's saying that the actual consciousnesses of other human beings inhabit us to some degree -- like we're possessed.  The representative powers of the brain allows it to mimic some portion of the strange loop of other people; hence their consciousness inhabits us. We are therefore conscious in multiple places at once.

He says later:

"That's all I'm claiming -- that there is a blur.  That some of what happens in other brains gets copied, albeit coarse-grainedly, inside the brain of "Number One", and that the closer two brains are to each other emotionally, the more stuff gets copied back and forth from one to the other, and the more faithful the copies are.  There's no claim that the act of copying is simultaneous or perfect or total -- just that each person lives partially in the brain of the other..."(Hofstadter, pg 313)

That's all he's claiming...

Well, I have to say that I disagree with him here, rather extremely, but it is a really cool idea.  Really.

I Am a Strange Loop -- and a strange digression on Foucault--Chapter 13

     In Chapter 13, Hofstadter focuses on the notion of the "I" as a large structure of neural processes within the brain best represented symbolically, recall the much earlier description of large scale structures being causally effective as opposed to only crediting micro-processes with causal power.   He talks about the sense of self as extensible through our past and providing a sense of unity to our experience, prompting, Kant to think of it as the "transcendental unity of apperception". He says:

"Since we perceive not particles interacting but macroscopic patterns in which certain thing s push other things around with a blurry causality, and since the Grand Pusher in and of our bodies is our "I", and since our bodies push the rest of the world around, we are left with no choice but to conclude that the "I" is where the causality buck stops."(Hofstadter, pg. 217 Nookbook).

This "I" gains structure as we get older:

"We begin life with the most elementary sorts of feedback about ourselves, which stimulate us to formulate categories for our most obvious body parts, and building on this basic pedestal, we soon develop a sense of our bodies as flexible physical objects.  In the meantime, as we receive rewards for various actions and punishments for others, we being to develop a more abstract sense of "good" and "bad", as well as notions of guilt and pride, and our sense of ourselves as abstract entities that have the power to decide to make things happen ... begins to take root."(Hofstadter, pg.  218, Nookbook)

This remarkable passage bears a striking resemblance to some ideas of Michel Foucault in Discipline and Punish, one of the most important books of the 20th century, and one of the most influential on me:

"This real, noncorporal soul, is not a substance; it is the element in which are articulated the effects of a certain type of power and the reference of a certain type of knowledge, the machinery by which the power relations give rise to a possible corpus of knowledge, and knowledge extends and reinforces the effects of this power.  On this reality-reference, various concepts have been constructed and domains of analysis carried out: psyche, subjectivity, personality, consciousness etc.; on it have been built scientific techniques and discourses, and the moral claims of humanism.  But let there be no misunderstanding: it is not that a real man, the object of knowledge, philosophical reflection, or technical intervention, has been substituted for the illusion of the theologians.  The man described for us, whom we are invited to free, is already in himself the effect of a subjection much more profound than himself.  A 'soul' inhabits him and brings him into existence, which is itself a factor in the mastery that power exercises over the body.  The soul is the effect and instrument of a political anatomy; the soul is the prison of the body""(Foucault, Discipline and Punish pg. 29-30)

"In discipline, it is the subjects[think "I" for Hofstadter] who have to be seen.  Their visibility assures the hold of the power that is exercised over them.  It is the fact of being constantly seen, of being able always to be seen, that maintains the disciplined individual in his subjection"(Foucault, Discipline and Punish pg. 187)

And some more:

"The individual is no doubt the fictitious atom of an 'ideological' representation of society; but he is also a reality fabricated by this specific technology of power I have called 'discipline'(Foucault, pg. 194)

In Foucault, self-consciousness is the the result of a technique of power being exercised on us by those in power.

Sunday, June 19, 2011

I Am a Strange Loop -- Chapters 10-12

I'll skip chapter 9 and move on to chapter 10.  Assume Theorem Z is the consequence of Theorems X and Y, where x,y, and z are the corresponding Goedel numbers.  Then the relation between x,y, and z mirrors that between X, Y, and Z.  This is how Hofstadter sums up the correpondence:

"...if x were the number corresponding to theorem X and y were the number corresponding to theorem Y, then z would "miraculously" turn out to be the number corresponding theorem Z."(Hofstadter pg. 163 Nookbook).

He goes on to explain Goedel numbering very well. He explains well the importance of building up the correspondence between numbers and formulae in PM recursively until we have numerical relationships representing provability.  He does an excellent job explaining Goedel's generation of an unprovable formula.  He has a nice digression on Quine and Berry which is worth reading.

I'm going to skip over chapter 11 and move on to Chapter 12.  Here he talks a lot about the consistency of PM and how that implies that the undecidable proposition must be true.  He also shows how if the proposition were provable it would be false: recall that the proposition corresponds to the relation that holds when it is UNprovable.  He concludes:

"In other words KG[the undecidable statement] is unprovable not only although it is true, but worse yet, because it is true."(Hofstadter pg 198, Nookbook).

This discussion is very nice.  He pauses here on how perverse this situation is: a proposition is unprovable because it is true.

Now comes the crucial point for Hofstadter:

"PM is rich enough to be able to turn around and point at itself, like a television camera pointing at the screen to which it is sending its image. If you make a good enough TV system, this looping-back ability is inevitable.  And the higher the system's resolution is, the more faithful the image is."(Hofstader pp. 199-200 Nookbook).

He then mentions something that is worth mentioning, that there are an infinite number of ways of numbering PM and there are distinct undecidable propositions for all of them!  That is, there are an infinite number of undecidable propositions in PM.

Now, here is where the Hofstadter and I start to part company: Downward Causality in Mathematics.  Here is what he says:

"It reveals the stunning fact tht the formula's hidden meaning may have a peculiar kind of "downward" causal power, determining the formula's truth or falsity...Merely from knowing the formula's meaning, one can infer its truth or falsity without any effort to derive it in the old-fashioned way, which requires one to trudge methodically "upwards" from the axioms."(Hofstadter pg. 203, Nookbook)

     It is NOT the formula's hidden meaning that has causality.  WE understand the meaning, the mapping via Goedel numbers provided the proof the undecidable proposition is true assuming consistency, which remember we can't prove from within PM. The hidden meaning is not some independent thing that has causal power all on its own; I know that Hofstadter will say " it's an epiphenomena and they can have causal power", but I think he's wrong here.  All the formal system has is the rules of syntax. I agree that it is (much) easier to think of the meaning of the proposition than building up from the bottom.  But in the end the proof of the incompleteness theorem is quite mechanical.  He derives contradictions from assuming either the undecidable proposition or its negation.  There is nothing spooky going on in the proof.  Hofstadter has semantics popping out of the syntax all on its own like Athena from the head of Zeus.  NO!  I have a bad feeling now that consciousness will pop out of unconscious molecules in some analogous way --  I hope not, but we shall see.  Well, I suspect things will not be put with that much clarity

Incompleteness Theorem -- part 5, the last one, I promise

     OK, so I've gone through the demonstration that there are undecidable propositions inside any formal system sufficient for addition, multiplication, and the basic logical operations of the elementary theory of whole numbers.   From here  it's actually pretty easy to see why the consistency of the formal system, which I'm referring to as PM, cannot be proven within the system.  Again, I will stay as close as I can, up to the ability of this editor to represent it, to Goedel's notation. 

     Let Wid(c) be defined as the statement that there exists a formula x such that it cannot be derived from the set of formulae c.  That is, (Ex)[Form(x) & ~(Bew(x))].  Here Bew means provable from the formulae c.  Literally, There exists an x such that x is a formula of PM and x is not provable from the formulae c.

Now we have to prove this. Remember that 17 Gen r is not provable within PM.  So, Wid(c)-->~(Bew(17 Gen r)).  That is, as long as there are unprovable propositions, the undecidable one from before is unprovable.  But the fact that for any x, 17 Gen r is not  provable is equivalent to the statement(for all x)q(Z(x),Z(p)), recalling that 17 Gen r = p(Z(p)).  Therefore, if PM is consistent, we can prove 17 Gen r!  This is a contradiction of Wid(c)-->~(Bew(17 Gen r)) above.  Here we use the fact that 17 Gen r states its own unprovability, so to prove it unprovable is to prove it.

Thus, a formal system like PM cannot prove its own consistency.  Well, what's so big about that?  For one thing, suppose you have a bigger system that contains PM, can it prove it's own consistency?  It seems it can't because the argument above would apply to it and we would have an infinite regress.  Please let me know if I'm wrong about this.

Next time I will return to I am a Strange Loop.

Saturday, June 18, 2011

Incompleteness Theorem -- Part 4

Goedel ends his 46 definitions with the definition for provable:
46. Bew(x):=(Ey)yBx
This definition refers to definition 45 and says: " There exists a y such that y is a proof of x."

There is a theorem, provable by induction, that I will take as a given.
Theorem 0:  For every recursive relation R(x1,...,xn) there exists an n place relation sign r between the free variables u1,...,un such that for all n-tuples of numbers (x1,...,xn):
R(x1,...,xn) -->Bew[Sb(r (u1,...,un)=(Z(x1),...,Z(xn))]
R(x1,...,xn)-->Bew[Neg[Sb(r u1,...,un)=(Z(x1),...,Z(xn))]]

     What this says is that if the relation R holds between the n-tuple of numbers x1,...,xn, then there exists a relation r between variables of PM such that the proposition obtained by substituting the numerals Z(x1),...,Z(xn) corresponding to the n-tuple of numbers into the n variables of r, the result is provable.  Note: numerals are repeated applications of the successor function to zero to obtain an expression for a number, say xi, inside the formal system I'm calling PM.  This completes the translation from the numerical relation R to the relation r between signs in PM.  If the negation of R is true, then the provable proposition is the negation of the proposition you get by performing the substitution into r.

     Basically, if a relationship R holds between the natural numbers x1,..,xn, then in PM there is a corresponding relation between the signs(numerals) for the numbers. If the relation does not hold between the numbers, then the corresponding relation between the numerals does not hold.

Now that we have this we can proceed to the statement of the First Incompleteness Theorem:

Definition: A formal system like PM satisfies omega-consistency if there is no formula a for which a(Z(n)) is true for each n and at the same time (for all n)a(Z(n)) is false.

Theorem 1: For every omega-consistent recursive class K of formulas[like the formulas of PM] there are recursive class signs r such that neither  v Gen r nor Neg(v Gen r) belongs to FLG(K).

Recall v Gen R:=for all v, R is true.
Also, FLG(K) is the set of consequences of K.

Now, define the relation Q(x,y) between the natural numbers x and y as the relation that exists when the formula corresponding to the Goedel number x is not a proof of the formula obtained when Z(y) is substituted in for the free variable(whose Goedel number sequence is 19)  of the formula whose Goedel number is y.  That is, and this is important, the numeral for the Goedel number of  y is substituted into the formula y's own free variable.

By Theorem 0, there is a relation q in PM such that q(Z(x),Z(y)) is provable in PM whenever Q(x,y) is true, and the negation of q(Z(x),Z(y)) is provable whenever Q(x,y) is false.  The relation q is exactly the relation that obtains between Z(x) and Z(y) when the formula x is not a proof of y(Z(y)).

Goedel introduces some abbreviations: p=17 Gen q and r=Sb(q 19=Z(p)).
Now we consider the proposition 17 Gen r=17 Gen(Sb(q 19=Z(p))=Sb(p 19=Z(p))=p(Z(p).

Now, this abbreviation extravaganza actually obscures what is happening here.  The wikipedia page has it right: 17 Gen r = (for all y)q(y,Z(p)) .  That is, for all y, we have y is not a proof of p(Zp), which is the same as saying p(Zp) is not provable.  Now, and this is the interesting part, p(Z(p)) IS 17 Gen r!

Assumption 1: Assume (for all y)q(y,Z(p))  is provable, then there is a formula n such that n is a proof of (for all y)q(y,Z(p)).  Substituting n for y we get that q(n,Z(P)) is true.

Now, p(Z(p)) IS 17 Gen r so by Theorem 0, given that n proves p(Z(p)) we know that Q(n,p(Z(p)) is false, we have ~q(n,Z(p)).  This contradicts q(n,Z(P))  shown above.

Assumption 2: Assume ~(for all y)q(y,Z(p)).  By Theorem 0 we have q(z(n),Z(p)) for every n.  But our assumption is ~(for all y)q(y,Z(p)), which contradicts omega-consistency.

Friday, June 17, 2011

Incompleteness Theorem -- part 3

See the great wikipedia page on the proof of Goedel's incompleteness theorem:

Now I'll go through an examination of Goedel numbering and pick some hilights from the 45 recursive definitions Goedel gives before moving on to the main proof in the next post.
We assign numbers to the elementary signs as follows:
"0" ... 1
"f" ... 3
"~" ... 5
"or" ... 7
"For all" ... 9
"(" ... 11
")" ... 13

and variables of type n are assigned values of the form p(to the power n) where p is a prime number.  So, a type-I variable, a variable standing for a number, is just a prime to the first power.  So, 17, 19, 23, etc.. are type one variables.

To move from a number sequence to a  Goedel number, we just take the primes in increasing order and raise them to the powers of the signs.  For example, 11,17,13 becomes 2(to the 11 power) times 3(to the 17 power) times 5(to the 13 power).  Here, 17 is a variable, say x, so 11,17,13 is the sequence for "(x)". 

I'm going to try and stay close to Goedel's proof despite the fact that sometimes the notation is a little difficult to understand.  I'm going to go through some of the hilights of the 45 definitions he gives before provability.  I will then borrow some discussion from the wikipedia page above regarding Goedel numbers of proofs. 
Ex="There exists an x". ":=" means "defined to be"

So, here we go.
1.x|y:=(Ez)[z<=x & x=y.z]
x is divisible by y.
2. Prim(x):=(Ez)[z<=x & z not = 1 & z not=x &x|z] & x>1.
This reads: There does not exist a z such that z is less than or equal to z with z not =1, z not=x and where x is divisible by z, and also x is greater than 1.  A simpler way of saying this is that the only numbers that divide x are 1 and x, and x >1.  In other words, x is prime. Notice that 2. used x|y, which is 1.

Skipping to number 8
8.x*y:=(the smallest z){z <=Pr(l(x)+l(y))](to the x+y power) & (for all n)[n<=l(x)-->nGlz=nGlx] & (for all n)[0 < n <= l(y)-->(n+l(x))Glz=nGly]}

This expression uses l(x) from 7., nGLx from 6., and nPrx from 5.  So, this is a function recursively defined in terms of previous functions.  I know it looks long, but if you write it out it's horrible:

x*y is defined to be the smallest z such that z is smalller than the prime number at place length of the number sequence assigned to x plus length of the number sequence assigned to y to the x=y power  and  for all n, if n is less than or equal to the length of the number sequence of x then the nth term in the number sequence assigned to z equals the nth term of the number sequence assigned to  x  and  for all n, if n is bigger than zero and less than or equal to the length of the number sequence assigned to y, then the n + length of the number sequence assigned to x term in the number series assigned to z equals the nth term in the number series assigned to y.

All this definition say is that you take two number series and stick the one for y to the right of the one for x.  This corresponds in PM to putting two series of signs, for x and y, next  to each other. What this illustrates is that the recursive way Goedel does these definitions allows us to avoid having to write out gazillions of symbols and words.  By the time you get to 45, these are some pretty big expressions.

Armed with 8 we can start with
9. R(x):=2(to the x power)

 and get
10.E(x):=R(11)*x*R(13) to mean putting the Goedel number for "(" with "x" and ")" to yield "(x)" -- 11 is the exponent assigned to "(" and 13 goes to ")".  Imagine if this had to be written out!

We can also get
13. Neg(x):=R(5)*E(x) to mean the negation of x or "~(x)"

14. xDisy:=E(x)*R(7)*E(y) means (x) or (y).

15.xGeny:=R(x)*R(9)*E(y) means: "y is true for all x".

Here's part of the definition of substituting y for the nth term of x(number 27)
start with x=u*R(nGlx)*v and substitute y in to yield a number given by u*y*v, where n=l(u)+1(which means that y was subtituted in the place in the number immediately following u, as we wanted).

Later on, number 31, we get the definition of substituting in for a free variable.

Goedel goes on to define axioms, formulas, immediate consequence, and proof.

We end with provable, number 46.

To think about provability we consider a deduction rule D as a relation between the first n-1 formulas of a list and the nth formula.  The Goedel number for the first n-1 will stand in numerical relation R to the Goedel number for the nth formula exactly when the first n-1 formulas imply the nth formula by the rule D.  So, if we have a list of k deduction rules, then the n-1 formulas is a proof of the nth if the Goedel number of the first n-1 formulas stands in at least 1 of the k corresponding numerical relations to the nth Goedel number.