Philosophy and Literature Blog

     "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 de...

     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 ...

     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.  ...

     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: http://public.wsu.edu/~brians/science_fiction/neuromancer.html 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.

      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 consciou...

     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...

     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: ...

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 ...

     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)--...

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...

See the great wikipedia page on the proof of Goedel's incompleteness theorem: http://en.wikipedia.org/wiki/Proof_sketch_for_G%C3%B6del%27s_first_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 pow...

    See the following by Torkel Franzen for insight into the incompleteness theorems: http://www.hashref.com/summaries/GodelsTheorem.pdf      Important for Hofstadter is the notion of recursion.  This notion also plays a central role in the Goedel's proof.  Goedel gives the following definition: phi(x1,x2,...,xn) is said to be recursively defined in terms of psi(x1,x2,,...,x(n-1)) and mu(x1,x2,...,x(n+1)) if phi(0,x2,...,xn)=psi(x2,...,xn) and phi(k+1,x2,...,xn)=mu(k,phi(k,x2,...,xn),x2,...,xn). So, phi is initialized by psi, and increasing values of x1 are given in terms of mu where he have substituted the previous k's phi value in for the value before x2 in mu.  Of course we could iterated back from k+1 to zero by back substituting.  Oddly, the mu is a function of more variables than phi itself and yet phi is written recursively in terms of it.  Well, I guess I don't understand that too well.  But then Goed...

"The most comprehensive formal systems that have been set up hitherto are the system of Principia Mathematica(PM ) on the one hand and the Zermelo-Fraenkel axiom system of set theory (further developed by J. von Neumann) on the other.  These two systems are so comprehensive that in them all methods of proof today used in mathematics are formalized, that is, reduced to a few axioms and rules of inference.  One might therefore conjecture that these axioms and rules of inference are sufficient to decide any  mathematical question that can at all be formally expressed in these systems.  It will be shown below that this is not the case ...This situation is not in any way due to the special nature of the systems that have been set up but holds for a wide class of formal systems..." On Formally Undecidable Propositions of Principia Mathematica and Related Systems I -- Kurt Goedel It was with these words that Goedel announced what he was going to demonstrate....

     Chapter 8 is where get the definition of the strange loop , the "I" being itself one of these.  Hofstadter defines a strange loop as "not a physical circuit but an abstract loop in which, in the series of stages that constitute the cycling-around, there is a shift from one level of abstraction (or structure) to another, which feels like an upwards movement in a hierarchy, and yet somehow the successive "upwards" shifts turn out to give rise to a closed cycle."       He gives the example of Escher's Drawing Hands, a picture of a left hand and right hand drawing each other:  "Here, the abstract shift in level would be the upward leap from drawn to drawer"; believe it or not there is a wikipedia page on Drawing Hands --( http ://en.wikipedia.org/wiki/Drawing_Hands ) -- check it out!      As noted before, the self, despite its epiphenomenal status, is a prime mover, a real causal agent in the wor...

   In Chapter 7, Hofstadter embarks on some of his central notions, most central of all is the concept of the "I".  The "I" is a concept that has obsessed philosophers for centuries, especially it seems, the idealists, who  believed that fundamental to reality were conscious perceptions, the physical world being merely a supposition of the self.  The "I" is a transcendental point, a center of perception that itself is not part of empirical world.  The analytic philosopher, Wittgenstein, has a famous drawing of the self not being in the field of perception in his Tractatus Logico Philosophicus -- you should check this book out if you haven't read it.  The "I", even for idealists is not empirically real, but rather is part of a transcendental reality.      For Hofstadter, the self is an epiphenomena, by that he means a phenomena which is the result of many things occuring at more micro levels, having no reality itself.  He rela...

     In chapter 5 Hofstadter relates his experience on what we could refer to as a "holiday with video feedback."   He points a camera at a screen and makes images of images of images etc... and investigates the patterns that can emerge from this exercise.  Some patterns "emerge" out of the systems, and persist, in a way that seems mysterious.      The infinitely rich video feedback he describes really represents a chaotic dynamical system. The dynamics is thought of as the light bouncing back and forth on patterns formed by previous bounces. In dynamical systems, the state of the system at time t+1 is dependent on its state at time t.  Similarly, when you point a camera at a screen to get a video loop, whether a structure is present in the iteration of the loop at time t+1 is dependent on its placement at time t.  Structures in the intersection of all iterations of the loop survive all iter...

"But science, spurred by its powerful illusion, speeds irresistably toward its limits where its optimism, concealed in the essence of logic, suffers shipwreck.  For the periphery of the circle of science has an infinite number of points; and while there is no telling how this circle can ever be portrayed completely, noble and gifted men nevertheless reach, e'er half their time and inevitably, such boundary points on the periphery from which one gazes into what defies illumination.  When they see to their horror how logic coils up at these boundaries and finally bites its own tail  -- suddenly the new form of insight breaks through, tragic insight which, merely to be endured, needs art as a protection and remedy." -- Friedrich Nietzsche The Birth of Tragedy      When I was 12 I got a pair of flippers and goggles.  One day I got into the water of this dock where I could stand.  I decided to do the backstroke out about 50 feet.  I...

     In Chapter 2, Hofstadter begins his assault on pure reductionism, and also on John Searle(I also recommend the wikipedia page on John Searle).  Hofstadter emphasizes that reductionism as he defines it, reducing all explanation to the microphysical, is not the best way to go about understanding consciousness.  He believes that consciousness is the result of many, many, neurons firing in just the right way. He gives a lot of examples of how it is better in some contexts to explain things in terms of collections rather than in terms of the individual particles that make up a system.      While discussing the explanatory superiority of collectives over individuals, he states further that abstractions, like "dog"(i.e.,concepts within consciousness), are the proper objects of study for really understanding the brain, which he describes as a thinking organ.  But I think sometimes he gets collections and conscious idea...

     I've been thinking about experience and qualia and I can't see a way around the conclusion that our current science does not bridge the gap Levine talks about in the essay I gave a reference to a couple of posts ago.  One doesn't need to follow the entire gobbledy-gook of his argument to see that there is something about subjective experience that, from an explanatory point of view, is missing from physical explanations.  Even though I believe that mental phenomena are ultimately dependent on the physical(I am prone to optical migranes, have been on a variety of medications that have affected my mental state, am affected reliably by caffeine, etc.. and have concluded that if the physical substrates of my body are changed, so is the mental, with the inference also that when I die my mental experience will cease) it seems clear to me that there is an explanatory gap when it comes to reducing my experience of the color red to some combination of...

"A Mote it is to trouble the mind's eye" -- Hamlet Here's another one: "Thoughts beyond the reaches of our souls" -- Hamlet      One of my favorite parts of "Men In Black" is when the alien is talking about human beings and he calls us "barely conscious pond scum".   The alien clearly believes he has no reason to respect life forms that possess comparatively impoverished levels of consciousness.  Ironically, this alien is actually a bug, a form of life humans think of as barely conscious -- unless you're in a Kafka story. Later, Tommy Lee Jones says that human thought is considered a form of disease by the rest of the galaxy.      In Chapter 1 of I am a Strange Loop , the most controversial, and to some troubling,  thing Hofstadter does is arrange sentient beings on a scale of consciousness, what's more, he ranks normal adults higher than retarded people, children, people with Alzheimer's dis...

I followed-up and found some really cool websites. For Philosophical Zombies see http://www.consc.net/zombies.html For more on Qualia see: http://cognet.mit.edu/posters/TUCSON3/Levine.html and for Daniel Dennett see http://ase.tufts.edu/cogstud/papers/quinqual.htm