Doc Rampage

The final issue of interest with null-A is the idea that genuinely logical people are moral people. This can be seen in "The Null-A Continuum" by references to evil acts as insane and various implications that the hero does the good thing because it is the sane or rational thing. But in reality logic and rationality cannot possibly produce morality. There are two reasons for this: the non-reducibility of moral propositions to non-moral propositions, and the requirement that to be morally good, one must intend to be morally good.

What I mean by the non-reducibility of moral propositions is that you cannot reason to a moral conclusion without moral premises. You cannot reason, for example

(1) Joe needs help.
(2) Ben has the ability to help Joe.
therefore
(3) Ben should help Joe.

The word "should" is the only word with moral force in the argument. The argument is not valid (as a matter of logic) as can be seen by another (clearly false) argument with the same form

(4) Joe needs heroine.
(5) Ben has the ability to give Joe heroine.
therefore
(6) Ben should give Joe heroine.

The meaning of "need" is arguably different in (4) than it is in (1), but I am just copying the form of the argument, not the meanings of the words. I could have picked words with entirely unrelated meanings, so a slight change in the meaning of one word does not matter.

You might have an intuition that the first argument is true, at least under some circumstances. Why? Well, presumably you think that if someone needs help and you have the ability to help, then you should do so. Let's call that idea GA1 for "Goodness Axiom 1" (we'll ignore all the complex qualifications that would need to be added for a really true goodness axiom). Now let's add GA1 to the original argument and see what we get:

(1) Joe needs help.
(2) Ben has the ability to help Joe.
(GA1) For all people X and Y, if X needs help and Y has the ability to help X then Y should help X.
therefore
(3) Ben should help Joe.

This is a valid argument but look at that little word "should" in GA1. That is a moral term. We have used logic to combine specific facts with a general moral judgment to get a specific moral judgment. But we did need the general moral judgment to begin with.

This is always the case. There is no way for logic to get from completely non-moral facts to moral facts --you have to start with moral facts of some sort.

But let's suppose that someone comes up with a logical theory GT that seem to have the same effect as morality. For example, suppose that the purely logical considerations of GT lead someone to GA1, and not only to GA1 but also to other goodness axioms like

(GA2) For all people X and all puppies Y, X should not kick Y.
(Ga3) For all people X and all kittens Y, X should not throw Y out the second-story window to see if Y lands feet first.

Suppose that GT actually seems to include all goodness axioms. Let's suppose that Ben wants to always be logical and so he always carefully reasons out his actions using logic and always ends up abiding by the goodness axioms because they are a part of the purely logical system, GT. Would this make Ben a good person? I'm not asking if it would Ben a good neighbor, or a nice guy to have around; I'm asking if Ben is morally good.

If someone sticks a knife in your throat, is that good? Well it depends on motivation. If the person who does it is performing a tracheotomy to save your life then it is good, but if the person does it to kill you then it is evil. And it is only the intention that counts. If a doctor slips and accidentally kills you while trying to save your life, his action in trying to save you was morally good. If someone tries to murder you and accidentally saves your life, his actions are still evil. In judging whether a person is good or not, you do not look at his actions or on their outcomes, but on his intentions.

So now you know what I'm going to say about the hyperlogical Ben. Ben is not motivated by the desire to be good; he is motivated by the desire to be logical. It does not matter what his actions are or what the consequences are. Ben only wants to be logical, so if it were logical to kidnap, kill, and eat babies then he would do that. The logical theory GT, no matter how close it is to real goodness is unlikely to be exact. At some point Ben will find a situation where logic leads one way and good leads another way, and because of his motivation, he will chose the evil act.

FOOTNOTE: By the way, "should" is not a true predicate and neither "should" nor other moral concepts can be handled by normal logic. You need a special kind of logic called deontic logic to deal with such subjects. But the issues are purely formal ones, and deontic logic is not a different form of reasoning from regular logic.

Cynthia Yockey is making a name for herself (with instalinks even) by going after David Letterman for his offensive jokes about Sarah Palin and her daughters. The jokes were pretty sleazy, even if the sex jokes had been aimed at an eighteen-year-old girl instead of a fourteen-year-old, but Letterman has apologized one and a half times now (the first was only half an apology).

But that's not enough for Yockey. After the real apology she writes

This [CBS's response] is why the campaign to get CBS to fire David Letterman must continue and expand with more and more people sending letters and e-mails of protest to CBS, Letterman’s sponsors and the sponsors of Letterman’s racing team to notify them that their products will be boycotted until Letterman is fired. It also will be important to send letters and e-mails of protest to anyone who appears on Letterman’s show to impress them that doing so will put a long-term stink on their careers.

CBS is still playing the “This will all blow over” card. No. It. Won’t.

Persistent, consistent effort on our part will persuade sponsors to drop Letterman’s show and CBS to fire David Letterman.

Elsewhere Yockey tells us that conservatives should be more like the Left. When someone on the other side makes a blunder, we should go after them relentlessly until we damage them in some dramatic way. Make an example of them so other people will be afraid to challenge us.

Yes, that's the Left all right, and that's one of the big reasons that the Left sucks. Stacy McCain quotes Yockey from a phone conversation:

Republicans are too willing to take that kind of abuse, Cynthia said, but she comes out of the gay-rights movement, and they don't roll that way.

No, they don't roll that way. Gay activists get people fired for contributing to the wrong proposition campaign. They maliciously set traps for young Christian beauty pageant contestants and attack them hatefully for weeks when they don't avoid the trap. Do you really want to be associated with that kind of attitude? I don't.

Is Yockey's idea good political strategy? It pretty clearly is. The Democrats have used the strategy with enormous success, to the point where people are afraid even to hint that they may have a difference on certain issues. A large part of why Democrats are able to force their caricatures of Republicans into the public consciousness is because entertainers go along. And a large part of why Republicans can't do this is because entertainers are afraid to go along with anything the Democrats don't like. If they were similarly afraid of Republicans, it would be politically very useful.

So, yes, politically powerful but wrong. One of the reasons that I identify as a conservative is because conservatives actually seem to care about right and wrong. The Left, of course, is famous for their holier-than-thou attitudes, but their morality changes with the political winds. They were the defenders of segregation until black people started voting. They were the defenders of recreational drugs and gun control until it became a political liability. They were the defenders of smoking until the tobacco companies started donating too much money to Republicans. They were the defenders of wars to defend the victims of dictators when Clinton did it but we all saw their change of view when it was Bush. They can take self-righteous moral positions on either side of an issue, depending on what's best for them politically.

By contrast, the conservatives base their morality on principles rather than on expediency. And my moral principle is that you shouldn't go after someone's livelihood to support your political goals.

Some people who seem to agree with me: Jim Treacher, datechguy, Sarah Palin. Not a lot of people on my side, but that last one is pretty significant...

yeah! The FCC has finally tracked down the assholes responsible for those "your auto warranty is about to expire" phone calls. I must have gotten thirty of those calls, and ATT was absolutely uninterested in helping me block them or even find out who it was.

Everyone involved is claiming innocence, but they were actually using software to spoof the caller-ID system. That action proves that they knew there could be negative consequences of their actions if they were identified. And it's not enough to go after the owners. The FCC needs to punish all of the operators also. Everyone of them must have been told thousands of times that what they were doing is against the law and they kept doing it.

Next question: why did it take the FCC so long to do anything?

I wonder if I can sue them myself...

citations: instapundit and slashdot

One of the premises of general semantics is that our thoughts are controlled by the meanings that we assign to words. I'll quote from John C. Wright's introduction to "The Null-A Continuum":

The theory of general semantics postulates that through a proper understanding of the relationship between words and the reality words allegedly represent a mind can be trained to avoid disorientation. On an emotional level, a lack of disorientation means the absence of neurotic and self-destructive behavior.

This is reminiscent of some philosophers of the early twentieth century who tried to reduce thought to symbol manipulation. Symbol manipulation is just computation, and I explained in the previous post why computation cannot expand reasoning power. In this post, I will concentrate on three points: it is implausible that our thoughts really are limited by the words (or other symbols) that we have available, symbols cannot represent without the presence of a mental act which comes before the symbol, and if our thoughts really are limited by symbols then we have no way to judge which symbols are good ones.

I sometimes think in sentences. This happens when I am formulating an argument or trying out in my head something that I may write or say. When it does happen I am fully aware of it. Other times I think in terms of diagrams or physical geometry. I do this when I am trying to solve a problem that is too complex for my bare intuition to handle; I (like most people) have a more effective grasp of spatial relationships than of abstract relationships. Again, when I am thinking this way, I am fully aware of it. Most of the time, whether I am working hard at solving a design problem or wandering idly down the beach enjoying the sound of the waves, I don't think in symbols.

Some philosophers and psychologists would say that I am thinking in symbols but am just not aware of it. This view was especially prevalent during the first half of the twentieth century. But how can I be thinking in symbols when I am not aware of the symbols? Symbols are objects of consciousness. A symbol is a symbol in virtue of what it means to someone. Awareness of meaning is a conscious mental state, and without awareness there is no meaning. Being aware of a symbol unconsciously is a contradiction in terms.

Is there a more plausible to understanding of this idea? Maybe the underlying idea is that I have mental states that are the cognitive equivalent of symbols in the sense that they are physical objects or states in my brain that represent or are about something else. But how could physical states in my brain represent something else? It can't be the normal form of representation because as I argued before, something cannot represent in the usual way without a conscious intention for it to represent. The only physical way for something to represent would be with physical properties. What physical properties and relationships go into the relationship of representing?

One proposal is that representation is the physical relationship of similarity. For example a portrait represents a face by being visually similar to the face. A map represents the terrain by having elements that are geometrically similar to the terrain. But this account fails for two reasons. First, the notion of similarity is completely arbitrary. Does a glass of water represent Lake Michigan by way of chemical similarity? Does a piece of granite represent the Hoover Damn by way of having similar hardness? Even if you restrict "similarity" to being a geometric similarity it is peculiar that the lines on a map, which are just discolored sections of the page become representation of actual physical objects on the terrain. And what if John has a portrait taken but then grows a beard so that the portrait no longer looks like him at all? Does the portrait then come to represent his twin brother James who is beardless?

Clearly similarity does not work. Even if it worked in those cases that I mentioned (maps and portraits) it would not work for arbitrary symbols such as the word "Obama". The word "Obama" is not at all similar to the person the word represents. Representation is not a physical property at all, it is a mental property. A symbol represents in virtue of a mind intending for it to represent. And if a mind intends for the symbol S to represent an object O, then the mind must be able to form the concept of O without already having the relationship of symbolizing or it would never have formed the intention to represent O. If the mind needs a symbol to entertain a concept, then there is no place to get started. It needs a symbol to have a concept, but it needs a concept to have a symbol.

Minds can grasp concepts and think about concepts without symbols. And that is a good thing because if we needed symbols to think about things then we would not be able to grasp novel situations.

But suppose, against all evidence, our thoughts actually are controlled by words and what we think that they represent. How then could we possibly judge that some semantics is better than another? After all, if you are going to tell me that this relationship is better than that one then I need to use another such relationship between words and reality to decided if you are correct. But how do I know that that prior relationship is correct?

It can turn boring lettuce and tomato into a fabulous BLT. It can top a boring casserole to turn it into a thing of wonder. Its grease can be used to fry some of the best eggs of all time. It can turn an ordinary cheese burger into a bacon cheeseburger. And now, it can be used for welding.

From Xrlq, wonder of wonders, NOW is actually criticizing someone for making sexually degrading remarks about a conservative woman and her daughter. Patterico and Allah also noted it. But I doubt that NOW has actually grown a spine as Xrlq suggests. I looked through their archives and there was nothing at all about the weeks of sexually degrading leftist hate visited upon on Carrie Prejean. That alone shows how politically biased this list is. They do criticize a few political personalities on the left for insensitivity on women's issues and they do criticize entertainers for sexually degrading remarks aimed at Governor Palin, but no political personality (I include commentators and reporters in that) on the left is criticized for making sexual attacks on women of the right. The two entertainers criticized for their attacks on Palin are David Letterman and Eminem. Frankly, David Letterman seems a lot less leftist than most in the New York entertainment business, and Eminem is grotesquely gynophobic, so I don't think you can give NOW too much credit on either of those.

By contrast, three conservative commentators are criticized for taking shots at women of the left: G. Gordon Liddy, Glenn Beck, and Bill O'Reilly. The criticism of Liddy is a good one --he was acting like a pig-- but the criticisms of Beck and O'Reilly are partisan (I first wrote "embarrassingly partisan", but after NOW's reaction to Clinton and to O.J., they obviously cannot be embarrassed). Beck was criticized for criticizing Obama for his affirmative-action stance in picking Supreme Court nominees. O'Reilly was criticized twice, once for comparing a woman to the Wicked Witch of the West and once for doing a Michael-Moore ambush on a leftist woman blogger.

When O'Reilly (actually a female producer) did the ambush, they called it "stalking" to make it sound like sexually violent behavior but I didn't see any criticisms of Michael Moore himself. If they really think that camera ambushes are bad, this would have been a good time to criticize Micheal Moore, just like they took the criticism of David Letterman as a good opportunity to remind everyone how mean some conservatives were to Chelsea Clinton (if Rush really called a 13-year-old girl a dog on the air then he should be ashamed of himself, but I doubt that NOW is reporting his remarks accurately). As to O'Reilly's allusion to "The Wizard of Oz", it was not very nice, but the woman it was directed at, Helen Thomas can throw around insults with the best of them and I don't see how calling a woman the Wicked Witch of the West is sexist since men are often compared to unflattering male fictional characters.

So, although NOW should be congratulated for being able to suppress their partisanship long enough to criticize a relatively conservative entertainer for making a statutory-rape joke about a fourteen-year-old daughter of a Republican, let's not get too carried away congratulating them their new-found integrity until they show that it can actually apply in more politically-charged circumstances.

UPDATE: foxfire in the comments has unearthed a link that discusses the alleged case where Rush Limbaugh called Chelsea Clinton a dog. What actually happened: Rush (or his camera crew) showed a picture of a dog when Rush wanted a picture of Chelsea. Rush claimed immediately that it was an error and apologized immediately and then apologized again a few days later, again claiming that it was an error. Furthermore, if it was a joke, it's hard to see how it was aimed at Chelsea since they hadn't said her name yet. As a joke it would be the joke of referring to the Bush's dog as a child --it would be a joke aimed at the Bushes. Even better, Al Franken who started this story about Rush was a producer of Saturday Night Live at a time when they did a skit that very definitely make fun of Chelsea's looks in a very mean way --and Rush criticized them for it.

previous

Finally Matt's warning registered on the furious J.C. and he looked out the windshield. "Are you sure?"

On the radio, deputy Preason was shouting over the wind, "... again, Frank. Did you say that the tornado has reversed direction?"

"Yeah, it's coming right for you and that other SUV," the voice from the helicopter said, "I'd get my tail out of there if I were you."

J.C. put the Scout into reverse and hit the accelerator, bouncing everyone violently in their seats.

"Slow down, Julius." his wife said crossly, "It only goes ten miles an hour, remember?" She tried to resume typing but the vehicle was bouncing too much.

"Yeah, but it pulverizes stuff!" J.C. had to shout as the howling grew louder. His high-speed reverse had the Scout bouncing so hard that he was barely in control of the vehicle.

"Get off the track!" Matt yelled a few moments later, "It's gaining on us!"

"Snap out of it, Matt!" Katrina yelled back at him, barely holding onto her notebook in the bouncing seat. "You have been on the edge of panic all day! Storms do not follow any track!"

She slammed her notebook shut for emphasis, but it was lost on Matt who was busy watching through the windshield as the dust cloud overtook them and enveloped the vehicle. The two who were not madly driving raised their windows as the dust began pouring in and Matt used his passenger-side control to raise J.C.'s window.

The windows dampened the wailing winds enough for them to hear the helicopter pilot again. He was shouting also, "I think it's going a lot faster than twelve miles per hour. That civilian SUV looks like a goner."

"This isn't a normal storm," Matt told J.C. earnestly, trying to hold on to his bouncing seat with his hands. "It was traveling a straight path before and our only hope is if we guess right that it is traveling a straight path now. Get out of this rut."

J.C. was looking over his should, backing up a fast as he could. With a quick glance at Matt he steered hard and they were suddenly careening to the left nearly up on two wheels. The Scout was built for stability, but the rear wheel that was nearly off the ground hit a boulder at just the wrong height and just the wrong time. The Scout tumbled, crashed onto its right side and rolled upside down for half a turn, finally coming to rest on its left side.

The three of them sat in shock for a moment with J.C. and Matt staring up through the moon roof at the onrushing storm.

Katrina screamed, "I told you to stay in the path..."

The radio was screaming as well, "... SUV has rolled and the storm is quickly overtaking it..."

J.C. was retracting the hydraulic suspension with one hand and opening the moon roof with the other. "We have to get out and rock it back up!" He shouted. They all felt a sudden pain in their ears from pressure change. Matt stared at him for a moment, thinking that they had nowhere near enough time for such an operation, but when J.C started unlatching his seat belt, Matt did also. "Come on!" J.C. shouted, retracting the steering wheel to give him room as Matt tried to squeeze out the small opening without falling down onto J.C. Then they felt the Scout begin to spin slowly on the ground and J.C. paused, beginning to realize how short their time was. When the vehicle started to scrape across the torn clay, both men gave up on the idea and started trying to buckle themselves back in.

"This is a heavy vehicle," J.C. gasped, tugging at his seatbelt. They skidded ever faster along the ground. "Now that we are on the ground we may be ..."

He stopped as the Scout hit something and flipped. Both men clicked their belts just before they would have been thrown from their seats. The Scout tumbled a couple of more times and they all felt a sinking feeling as it became airborne. There was a confusing set of sense impressions: the howling of the wind, the banging and pinging from objects hitting metal, the cracking sound of rocks hitting glass, the cloud of choking dust filling the interior, the gravel and rocks pelting them through the open moon roof. Then they were spinning violently, but only for a short time. And then they were falling, and that seemed to go on forever.

Null-A stands for non-Aristotlean logic. It was, along with General Semantics, introduced by A. E. Van Vogt in a science fiction story in the 1940s. As I threatened earlier I am now beginning a series on the plausibility of null-A. This post will concentrate on one aspect of null-A --the fact that it is not restricted to two truth values. In fact, that seems to be primarily what is meant by "non-Aristotlean". I presume that it is intended to be analogous to non-Euclidean geometry.

So, just how plausible is it that adding more truth values to logic would increase our reasoning powers significantly (or at all)? I'll get to that after an introduction to logic and then some examples of real logics that have more than two truth values.

Logic 101a: the Syllogism
Logic is the study of forms of argument. It looks at how an argument is structured rather than at the content of the argument. For example the following two arguments are structured in the same way

Argument 1:

All men are mortal.
No mortal is perfect.
Therefore no man is perfect.

Argument 2:

All trees are blue.
Nothing blue is wet.
Therefore no tree is wet.

Now a person reading these arguments may notice that the first one seems reasonable and the second one seems silly, but that is because you are looking at the content. If you look at the form, you will see that they both follow the pattern

every X is a Y
no Y is a Z
therefore no X is a Z

This argument form is valid. What that means is that if the first two sentences (the premises) are true, then the last sentence (the conclusion) must be true also. But this is logic, so it doesn't say anything about whether the premises are true in the first place. Other argument forms similar to those above are not valid. For example

All men are mortal.
Some mortals are fools.
therefore some men are fools

regardless of what you may think of the conclusion, the conclusion does not follow from the premises. Often the non-validity of a form is shown by way of a counter example which can be easily seen to be false. For example the following argument has the same form as the one above:

All squares have corners.
Some things with corners are triangles.
Therefore, some squares are triangles.

The examples above are all syllogisms. The logic of Aristotle dealt entirely with syllogisms and their various patterns.

The logic of syllogism is a sort of class theory (except that it is not extensional like most class theories are). The descriptive terms of the sentences are viewed as classes and the rest of the sentence expresses some relationship of the classes. The relationships can all be expressed with the following relations:

A is contained in B
A is not contained in B
A overlaps with B
A does not overlap with B

The logic of syllogisms is essentially a list of the mathematical properties of these four relations on classes.

Logic 101b: the Proposition
Modern logic does not deal with syllogisms as such (although the sentences of syllogisms are included in propositions). Instead modern logic deals with abstract propositions in various combinations. You can think of a proposition as a declarative sentence. Each of the sentences in the examples above is a proposition, but so are

John went to the store.
John is married to Mary.
John and Mary went to the store.

None of these sentences could be part of a classical syllogism, but to modern logic they are just fine. Propositional logic has rules about combining propositions. For example, let P, Q, and R be propositions. The propositional logic has rules like

if "P or Q" is true, and "P" is false, then "Q" is true.
if "P" is false, then "P and Q" is false.

Propositional logic has logical operators. The three most common are "and", "or" and "not". The rules that go with the operators can be expressed in a truth table like this:

P	Q	P and Q	P or Q	not P
T	T	T	T	F
T	F	F	T	F
F	T	F	T	T
F	F	F	F	T

Notice that "P or Q" is true if "P" is true or if "Q" is true, or if both are true.

This is just a taste of how different modern logic is from Aristotle's logic. So the word non-Aristotlean logic to describe the special logic of null-A is a little misleading.

Logic 201: Multi-valued Logic
What Van Vogt says disginguished null-A from Aristotlean logic is that it is a logic that recognizes more than true and false. Today, such logics are called multi-valued logics and there are several of them that are studied.

So how can there be something more than true and false? Well, sometimes you just don't know the answer. Suppose someone tells you the two sentences

B. John is at the store
and
C. Mary is at home.

Suppose you don't know where John is, so you cannot assign a truth value to B. But you were just over at Mary's house so you know that she is not at home. You can reliably say that the combination "B and C" is false. How do you know that? Well, by looking at the truth table above, you know that for the combination "P and Q", if "Q" is F, then it doesn't matter what "P" is, the combination is always false.

We can formalize this reasoning process by adding a third value to logic, let us call it "N" for Null (the name doesn't come from null-A, but from the programming language SQL).

The typical truth table for a three-valued logic is like this:

P	Q	P and Q	P or Q	not P
T	T	T	T	F
T	F	F	T	F
T	N	N	T	N
F	T	F	T	T
F	F	F	F	T
F	N	F	N	N
N	T	N	T	N
N	F	F	N	N
N	N	N	N	N

You might find it interesting to see if you can justify the rules as an extension of the rules for two-valued logic.

Now let's consider B and C again. Suppose you know that there is a 50% chance that B is true and a 100% that C is true. What can you say about the truth of "B and C"? Questions like this are answered by probability. Most mathematicians and other people who work with probability think of it as a sort of measure on "outcomes". But you can just as well think of it as a multi-valued logic where true is replaced by a probability of 1, false is replaced by a probability of 0, and the values in between are intermediate values of certainty or uncertainty. Then you can make a logic based on probability. Obviously you can't make truth tables for an infinite number of truth values, but you can write formulas such as

p(P and Q) = p(P) * p(Q) (P and Q independent)
p(P or Q) = p(P) + p(Q) - p(P and Q)
p(P) = 1 - p(not P)

But there are other ways to have infinite logical values. Some propositions don't really have exact truth values, but the fuziness is not from uncertainty but from inexactness of language. Are roses actually red? Well, kind of. Let's say roses are 90% red. Are violets actually blue? Well, not really. Let's say violets are 30% blue. Then what can we say about the proposition

roses are red and violets are blue

? Well since the claim of the sentence is that both propositions are true this can't be any more true than the least true part of it, or 30%. On the other hand, the sentence

roses are red or violets are blue

is as true as the most true part of it, or 90%.

Such issues are the topic of fuzzy logic. Like probability, fuzzy logic has an infinite number of truth values from 0 to 1, with 0 corresponding to false and 1 corresponding to true. But in between those two extremes, the answers are a little fuzzy. Some of the formulas for fuzzy logic are

f(P and Q) = min(f(P), f(Q))
f(P or Q) = max(f(P), f(Q))
f(not P) = 1 - f(P)

Logic 401: Theory of Computation
Well, all of these multi-valued logics and more have have been around for quite a while and they don't seem to have generated any great advances in human understanding such as are postulated in "The World of Null-A". Why not? It should be pretty clear that while multi-valued logics may be convenient formalisms, and may be interesting in their own right, none of them are revolutionary advances in human thought. In fact, they don't add any additional reasoning power at all to the original two-valued logic. The most obvious way to see this is to notice that probability is almost always used as a mathematical theory rather than a logic, and that when people use probability theory they usually do so within a two-valued logic framework, saying things like

p(A or B) = p(A)+p(B)-p(AB)

which uses the old-fashioned true-or-false relation of equality. So probability can be viewed as a multi-valued logic, but you can do the same reasoning by putting a theory over two-valued logic. The same is true of 3-value logic and of fuzzy logic. Any reasoning that you can do with those systems, you can also do with normal two-valued logic and a bit of extra machinery.

There are some pretty general results about this sort of thing. Two distinct symbols is sufficient to represent anything that can be represented in any symbols, even an infinite (countable) number of symbols. Above a certain level, all systems of computation (or formal reasoning) are equivalent in power. Any system that is powerful enough to do general arithmetic is incomplete in the sense that there are true things that the system can say but cannot prove.

All of the above are results about computation, not about reasoning. They do not rule out the possibility that there may be ways of reasoning that get around the limitations. But whatever form of reasoning this is, it will not be a logic. Logic is about the form of reasoning; it is essentially computational and therefore subject to the limits of computation.

On a more general level, the purpose of logic is not to create insights or to produce knowledge; the purpose of logic is to check your reasoning. Logic cannot guide you to new thoughts except in the most mechanical sense; it can only tell you if your thought processes are well-founded after the fact, and then only within a fairly limited domain.

I've added John C. Wright's Journal to my sidebar. More significantly, I've finally removed Soxblog. Soxblog was the blog of Dean Barnett who died last year of complications arising from cystic fibrosis. He was one of people who made the internet worthwhile. I kept the link around for sentimental reasons, but I suppose it has by now gone from sentimental to maudlin. I do miss his wise and humorous writing, though.

In the 1940's A E. Van Vogt published a story called "The World of Null-A". There are characters in this story who practice a science/mental discipline called General Semantics which involves non-Aristotlean logic or null-A logic. There were some sequels to the story, and now another sequel by another author, John C. Wright called "The Null-A Continuum". I've just finished the "The Null-A Continuum".

I think I first looked up John C. Wright in a bookstore after reading a blog entry of his, and I think I probably reached the blog entry from Head Noises, but the details are now lost in the mists of time.

The first book of his that I read was "Orphans of Chaos". The book is a fantasy story that uses an ingenious device to meld various mythological traditions to each other and to the modern world. I enjoyed the book so much that I finished it, went back to the book store the next day for the next two, and would have finished the whole trilogy in a weekend if I could have found the second book. As it was, I bought the third book and then under great temptation managed to avoid reading it for several weeks until I found the second one. And I did read the last two books in one weekend.

The cosmology and magic system of those books is fascinating. It has some philosophical underpinnings and I suspect that Wright was consciously founding his magic on the idealist philosophy of Berkeley or Kant. I was actually planning to write a couple of posts analyzing the ideas in the Chaos trilogy, but then I moved and I'm afraid the books ended up in storage so I had no way to check my memory.

"The Null-A Continuum" is also very good if you like the A. E. Van Vogt style. I confess that although I liked A. E. Van Vogt, his null-A books are a bit disorienting. There is a Deus ex machina on every other page in the form of a previously unknown character with special powers, a previously unknown power that one of the characters has, someone who was dead and comes back, or something similar. The new null-A book by Wright follows this style with enthusiasm. Although I enjoyed it, I did find it a bit exhausting trying to keep up with all of the actors and their powers.

As an interesting aside, I suspect that "The World of Null-A" was part of the inspiration for Mr. Spock of Star Trek. The hero of "The World of Null-A" was not emotionless like Spock, but he did have special control over his emotions compared to normal people due to mastery of null-A, a form of logic. Null-A also gave him greater physical powers, greater powers of observation, and apparently miraculous insights. Null-A was also responsible for the ethics of its practitioners. The idea is that fully "sane" behavior is ethical behavior. Compare to Spock bringing up logic in defense of his own ethics, most famously in "it is logical that the one should sacrifice for the many".

Well, this is all just fiction, but is there any possibility that something like it could exist? Might there be some special way of reasoning that would give one almost magical powers of prediction and control over the natural world? The answer is an unqualified "yes" --it's called mathematics. But more to the point, is there such a system that could lead to the sorts of powers that null-A practitioners have in the book?

And more interestingly, is it actually possible that ethical behavior is more rational than non-ethical behavior? Could we come up with a reasoning system that would make us smarter, better people?

Here are three posts on three different aspects of null-A:
mult-valued logic
words and thought
morality

UPDATE: after reading Wright's journal for a few days, it is clear that he is familiar with Kant. No mention of Berkely yet...