Tuesday, November 13, 2007

Bigfoot Probably Doesn't Exist, or One Way of Creating a Defeater

This is a deductively valid form of argument:

It just so happens that this form of argument is useful for arguing that Bigfoot probably doesn't exist. This post used to be full of typos and mistakes, so I've cut most of it out and replaced it with this better-written and better-looking 'article'. Hooray for LaTeX!

Saturday, November 10, 2007

Why Not Adultery?

It occurs to me that each of the 10 commandments can be reformulated as rights, i.e.
  1. Thou shalt have no other gods before me.

  2. God has the right to the Israelites' primary allegiance and loyalties.

  3. Thou shalt not make unto thee any graven image, or any likeness of any thing that is in heaven above, or that is in the earth beneath, or that is in the water under the earth: Thou shalt not bow down thyself to them, nor serve them: for I the LORD thy God am a jealous God...

  4. God has the exclusive right to be worshipped by the Israelites.

  5. Thou shalt not take the name of the LORD thy God in vain; for the LORD will not hold him guiltless that taketh his name in vain.

  6. God has the right to be treated as sacred; God has the right to his good reputation.

  7. Remember the sabbath day, to keep it holy. Six days shalt thou labour, and do all thy work: But the seventh day is the sabbath of the LORD thy God: in it thou shalt not do any work, thou, nor thy son, nor thy daughter, thy manservant, nor thy maidservant, nor thy cattle, nor thy stranger that is within thy gates...

  8. Everyone has the right to a day off, even foreigners. Surprising? I think there's enough material in the rest of the Torah about how workers should be treated that I can fairly believe that this isn't just an odd religious observance done for no practical purpose.

  9. Honour thy father and thy mother: that thy days may be long upon the land which the LORD thy God giveth thee.

  10. Israelite parents have the right to be supported by their children in old age and respected by their children at any age.

  11. Thou shalt not kill.

  12. Israelites have the right to life.

  13. Thou shalt not commit adultery.

  14. Married Israelites have the right to a faithful spouse (or spouses, as the case may be).

  15. Thou shalt not steal.

  16. Israelites have the right to property.

  17. Thou shalt not bear false witness against thy neighbour.

  18. Israelites have the right to a fair trial.

  19. Thou shalt not covet thy neighbour's house, thou shalt not covet thy neighbour's wife, nor his manservant, nor his maidservant, nor his ox, nor his ass, nor any thing that is thy neighbour's.

  20. Once again, Israelites have the right to property, but this right isn't limited to keeping property; a person shouldn't be adversely treated in other ways for owning property. Maybe I'm stretching on this one.

It also occurs to me that we enjoy many of these rights in our own country, today (God enjoys none of his, but that's a natural consequence of freedom of religion). One right that is noticeably absent, at least to me, is the right to a faithful spouse. Adultery is not a crime in the US. Adultery is grounds for divorce, and therefore can be used to establish fault in a divorce, but this results in no penalties if the injured spouse doesn't want a divorce or was married in one of the 15 states where no-fault divorce is the only option. I suppose I can see the practical difficulties in punishing people for adultery, but still, it does give marriage, as a legal institution, a bit of a farcical quality. Think of it: two people get up in front of commonly dozens, if not hundreds of witnesses and swear before God to love each other for better or worse, richer or poorer, in sickness and in health, forsaking all others, and then a legal document is signed by several of the witnesses afterward to attest to this fact. Breaking an oath taken in a court of law will get you jail time. Breaking a cell phone contract can get you a couple hundred dollars in penalties. But breaking this vow, which was made much more ceremoniously, isn't necessarily such a big deal.

I like having a faithful spouse, and I'd like to have a right to her faithfulness. I'm perfectly willing to grant her the right to mine. I expect that most couples are the same way. Really, my wife and I both have a right to each others' faithfulness, just not a legal one. So why is there this particular gap between legal rights and social rights? Why can't a society's laws reflect a society's mores? Maybe they do. Maybe there are enough people out there who are in love with the idea of dressing up in white dresses and tuxedos and spouting romantic-sounding oaths solely as hyperbolic expressions of their warm feelings for each other that the laws really do reflect the mores of a significant portion of society. The question is: how did their mores come out on top?

Monday, October 01, 2007

The Problem of Who Lois Loves

The other day, I got to thinking about one of the discussion topics in from Intro to Philosophy class I took seven years ago. I don't know why. It's a philosophical problem that goes as follows: If two things are the same, then everything that is true of one of them is true of the other. Clark Kent and Superman are the same person, but Lois Lane loves Superman and Lois Lane doesn't love Clark Kent. What's up with that? This problem seems to belong in the same league as Socrates' House (or is it Plato's Boat?), the omnipotence of God and such, but unlike some of these other introductory-level philosophical problems, I think I actually have an answer to it. Here it is; sorry to bore you if you've already got it figured out.

The concepts of Superman and Clark Kent (especially Lois Lane's concepts) are different, but they both are attached to the same real-world entity. Thus, what is true of Lois Lane's concept of Superman is not always true of her concept of Superman (in fact, they are quite distinct), but they do have one thing in common: Lois connects both of them to the same thing in reality (though she does not know it).

This implies something interesting about love: The act of loving someone - or at least of loving someone in the romantic sense of the word "love" - requires having a particular concept of who that person is. If it didn't, Lois would feel the same way when thinking of Clark Kent as she would Superman.

Lois' love for Superman is ultimately directed at the same object as her indifference to Clark Kent, but since this sort of loving implies conceptualizing its object, and Lois' concepts of Clark Kent and Superman are distinct, it is possible for Lois not to love Clark Kent.

By the way, I found out that the creators of Superman first conceived of him as a human villain. Far out.

Sunday, August 26, 2007

A Little Knowledge is a Dangerous Thing

An Ig Nobel-winning study showed that, on average, people overestimate their ability, and the most incompetent people overestimate their ability the most, both in absolute terms and relative to their peers. I dabble a lot in subjects I don't know much about. I even read the aforementioned study and thought it was very well-presented, and its arguments in favor of the hypotheses were well-formed, even though I am not a psychologist and my knowledge of statistics is vague. Which makes me wonder just how competent I really am. According to the study results, if I believe I'm in the 3rd quartile of competence, I'm probably right, so maybe I'll say I think I am in the 3rd quartile just so people will have to assume I'm better than average.

Dabbling a lot in subjects I'm no expert in and reading lots of Wikipedia articles probably makes me broadly informed but rather fallible, which I don't like so much; I'd rather be narrow-minded but always acutally right. Even so, I'm too curious not to try to figure stuff out on my own. So discovering a website that displays the Greek New Testament with a pop-up window for every word which lists translations, a definition and (best of all!) the word's grammatical attributes, opens up a whole new world of trouble for me to get into. I don't know ancient Greek nor any accepted methods for translating Biblical texts, but I'm definitely going to have to fool with this a bit. I promise not to publish my own version of the Bible or propagate any heretical readings of The Gospel of John, if that makes things any better.

Tuesday, July 17, 2007

Distinguishing Working Class from Middle Class in America

I propose that we can determine whether an American is working-class or middle-class simply by their answer to the following question: Are public school teachers well-paid?

Sunday, May 27, 2007

The Number One, Part Two

My previous post could use some further explanation. The gigantic and unreadable definition for the number one which I posted is the result of giving the number one a precise, complete, logical definition without resorting to using any numbers except zero. Other numbers are avoided in the definition because they use the number one in their definitions; if we defined the number one using them, we would have a circular definition. In English, it's hard to define the word the word "is" without using the word "is". Similarly, it's difficult to define numbers without using numbers, but that's just what Russell, Whitehead, and later Quine, were trying to do. Hence the complexity.

Quine actually defines one and zero as:

where the funny symbols represent things commonly used in set theory (Quine uses the word "class" rather than "set") and symbolic logic, which aren't numbers or arithmetical operations. To translate into plain English, the Lamba means the null or empty set, which is the class with no members; the mathematical version of an empty plastic bag with all the air sucked out of it. Iota followed by some object means the class containing only that object; a plastic bag with one thing in it and all the air sucked out of it. So zero, according to the logicians, is a plastic bag containing another plastic bag that is empty. It's weird, but it works.

Furthermore, the "x" with the carat ("^") followed by a statement means the class of all objects x for which the statement (which usually mentions x) happens to be true. The backwards "E" followed by "y" means that there is something in existence called y and the statement following the "E" and the "y" (which usually describes y in some useful way) is true. The square dot means about the same as the word "and". y-epsilon-x means that y is a member of class x. The arc turned downward combines two classes into a single class made up of everything found in both of those classes (which might be nothing at all - the empty set). Finally, iota-y with the line over the top of it means "everything except y".

Most of these symbols can be defined in terms of even more basic symbols, many of which can be defined in terms of even more basic symbols, just as one is defined in terms of zero, and zero is defined in terms of the empty set and a set with just the empty set in it. The definition given in my previous post is an attempt at unraveling these definitions in such a way that one is defined in terms of the most basic logical and set theoretical concepts.

I couldn't translate the huge definition of one into plain English, but I can try to translate the definition given above. Here it goes... the number one is every class, collection or set we can define which has an object in it, and nothing other than that particular object in it. Interestingly, one, by this definition, is not just one thing, but the aggregate of everything that has the property of oneness e.g. God is one, I am one, the set of all wives which belong to me is one, etc.

Saturday, May 19, 2007

What It Means To Be Number One

I just finished reading W.V.O. Quine's textbook, Mathematical Logic. It only took me about 3 years to finish it (literally), and it was by far the most difficult book I have ever read, but it was worth it. The book defines predicate logic, basic set operations, natural, rational, and real numbers, arithmetic, and some other things all in terms of set membership, universal quantification, and joint denial. Then it proves and explains a version of Godel's Incompleteness Theorem. It is fascinating stuff. I hope I'll understand it all someday.

To celebrate, I wrote in truly nerdy fashion a Perl script to generate the natural number one expressed in terms of class membership, class abstraction, universal quantification, and joint denial, according to Quine's definitions. Here it is.

Thursday, April 26, 2007

Some Interesting Biblical Cross-Referencing

From the sixth hour until the ninth hour darkness came over all the land. About the ninth hour Jesus cried out in a loud voice, "Eloi, Eloi, lama sabachthani?"—which means, "My God, my God, why have you forsaken me?"
--Matthew 27:45-46

1 My God, my God, why have you forsaken me?
Why are you so far from saving me,
so far from the words of my groaning?

2 O my God, I cry out by day, but you do not answer,
by night, and am not silent.

3 Yet you are enthroned as the Holy One;
you are the praise of Israel.

4 In you our fathers put their trust;
they trusted and you delivered them.

5 They cried to you and were saved;
in you they trusted and were not disappointed.

6 But I am a worm and not a man,
scorned by men and despised by the people.

7 All who see me mock me;
they hurl insults, shaking their heads:

8 "He trusts in the LORD;
let the LORD rescue him.
Let him deliver him,
since he delights in him."

9 Yet you brought me out of the womb;
you made me trust in you
even at my mother's breast.

10 From birth I was cast upon you;
from my mother's womb you have been my God.

11 Do not be far from me,
for trouble is near
and there is no one to help.

12 Many bulls surround me;
strong bulls of Bashan encircle me.

13 Roaring lions tearing their prey
open their mouths wide against me.

14 I am poured out like water,
and all my bones are out of joint.
My heart has turned to wax;
it has melted away within me.

15 My strength is dried up like a potsherd,
and my tongue sticks to the roof of my mouth;
you lay me in the dust of death.

16 Dogs have surrounded me;
a band of evil men has encircled me,
they have pierced my hands and my feet.

17 I can count all my bones;
people stare and gloat over me.

18 They divide my garments among them
and cast lots for my clothing.

19 But you, O LORD, be not far off;
O my Strength, come quickly to help me.

20 Deliver my life from the sword,
my precious life from the power of the dogs.

21 Rescue me from the mouth of the lions;
save me from the horns of the wild oxen.

22 I will declare your name to my brothers;
in the congregation I will praise you.

23 You who fear the LORD, praise him!
All you descendants of Jacob, honor him!
Revere him, all you descendants of Israel!

24 For he has not despised or disdained
the suffering of the afflicted one;
he has not hidden his face from him
but has listened to his cry for help.

25 From you comes the theme of my praise in the great assembly;
before those who fear you will I fulfill my vows.

26 The poor will eat and be satisfied;
they who seek the LORD will praise him—
may your hearts live forever!

27 All the ends of the earth
will remember and turn to the LORD,
and all the families of the nations
will bow down before him,

28 for dominion belongs to the LORD
and he rules over the nations.

29 All the rich of the earth will feast and worship;
all who go down to the dust will kneel before him—
those who cannot keep themselves alive.

30 Posterity will serve him;
future generations will be told about the Lord.

31 They will proclaim his righteousness
to a people yet unborn—
for he has done it.

--Psalm 22

Later, knowing that all was now completed, and so that the Scripture would be fulfilled, Jesus said, "I am thirsty." A jar of wine vinegar was there, so they soaked a sponge in it, put the sponge on a stalk of the hyssop plant, and lifted it to Jesus' lips. When he had received the drink, Jesus said, "It is finished." With that, he bowed his head and gave up his spirit.

John 19:28-30

Saturday, April 14, 2007

Created Meaning

Suppose I woke up one afternoon in a Macy's department store and I had no idea how I got there. After rubbing my face, visiting the restroom, and checking men's slacks just in case they actually have anything in my size, I'm sure I'd begin to ask questions like "Why am I here?", "How did I get here?", and "Did someone put me here, and, if so, then for what purpose?". I was having a hard time answering these questions on my own, but an elderly sales associate told me that I was placed there by Macy himself so that I might begin a lifelong career in retail. Of source, I rejected the associate's explanation; for all I knew, it might have been a self-serving lie on her part, and I had no direct evidence that such a person as Macy existed, much less that this putative Macy cared anything about my career. I was not wearing clothes suitable for an interview, and I woke up at the opposite end of the store from the service desk where the job applications were kept. If I was meant to get a job there, I had no special indication this was so.

My appearance in the department store may have a meaning: Perhaps Macy did indeed bring me there (kidnapper!) to get a job. Perhaps it is a prank my friends are playing on me. Perhaps it is a sign from God that I should not get wasted then go wandering around town, passing out in random locations.

My appearance in the department store may not have a meaning: Perhaps I merely suffered from simultaneous attacks of narcolepsy and somnambulism. Perhaps I got wasted and went wandering around town, but God wasn't trying to show me anything from it. Perhaps, because of some unanticipated consequence of quantum physics, I teleported into that Macy's store while taking an afternoon nap.

What if, I tried to create a meaning for the situation I was in? I don't know why I would want to do this, since I'd much rather know the actual meaning of my appearance in Macy's, if there is one; but suppose I did. If we take the phrase "create a meaning" literally, then it is simply absurd. I cannot create a meaning for my appearance in Macy's. I may discover it, I may imagine it or pretend it, but I can't create meaning after the fact, simply because I cannot change the past nor intentionally cause something that I did not intentionally cause. Is this what existentialists mean when they talk of creating meaning?

Of course, existentialists are smarter than that. But then, what does it mean to create meaning? I suppose if I appeared in Macy's without intending to be there, I could let the visit serve some purpose. I couldn't properly say "I'm here because I need to buy a new belt", but I could say "Since I'm here, I might as well buy a new belt." This makes perfect sense. The thing is, it seems to me that none of the existentialists are as bland as that. Nietzche could have saved a lot of paper if he merely said "Life is meaningless, but, since we're here, we might as well do what we like and not let any old customs or religious dogmas get in our way", but he didn't. Maybe I've just answered my own question. If life is meaningless and we might as well do as we like, then thinking people might as well do the absurd and create meaning, just because they like doing it.

Sunday, January 14, 2007

Past Events and Probability

I once read an article that tried to invalidate a favorite premise of people who argue in favor of Intelligent Design, specifically the extreme improbability of life spontaneously arising from non-life. The article started with the assertion that the probability of any past event is necessarily 1, therefore Intelligent Design partisans were committing a dark and dangerous fallacy by insisting that of life existence of life was highly improbable if it arose through purely natural means. I won't deny that Intelligent Design partisans can and do commit dark and dangerous fallacies, but I don't think that believing the stated premise is one of them. Instead, I doubt the validity of the notion that we should always consider the probability of a known past event to be 1 when reasoning about past events. I do so because such an assumption to deduce some apparently false conclusions. Since we should not be able to deduce false conclusions from any true premise, we should not make it a rule that the probability of any known past event is 1, modus tollens.

Here goes my argument. Let's call the assertion under dispute "Proposition 1" and state it as follows:
  1. If an event occurred in the past, then the probability that the event occurred is 1.
At first glance, this seems reasonable, even intuitively true. It seems internally consistent, and can I think of a way to derive a contradiction from it (not that I've thought that much about it). But that's not what I'm arguing.

Now for Propositions 2 and 3:
  1. 1 is greater than 1/2
  2. If an event has a probability of 1, then the probability that the event occurred is greater than 1/2.
Proposition 2 should be axiomatic enough for anyone, and Proposition 3 is just an instance of Proposition 2. Sorry to bore you with such triviality, but I need Proposition 3 so I can use it in a Hypothetical Syllogism with Proposition 1 to infer Proposition 4:
  1. If an event occurred in the past, then the probability that the event occurred is greater than 1/2.
To state it more simply, if it happened, then it probably happened. This does not seem to pose a problem; if George Washington crossed the Delaware, then we wouldn't be amiss to say that George Washington probably crossed the Delaware, right?

Things only become interesting when we consider a particular case of the contrapositive of Proposition 4:
  1. If the probability of a past event occurring is less than or equal to 1/2, then the event did not occur.
  2. If the probability of a past event occurring is less than 1/2, then the event did not occur.
(Proposition 6 is just Proposition 5 limited to the particular case where the probability of the event is not equal to 1/2). Proposition 6 is my basis for rejecting Proposition 1. To state it simply, if something probably didn't happen, then it didn't happen, or, in other words, improbable events never occur. In a sense, this is believable. If something happened, then it can't not have happened, right? Maybe so. I can't disprove the law of cause and effect. But I can say that trouble ensues when we try to apply Proposition 6 to a situation where something "probably would have" or "probably shouldn't have" happened.

Take an example: Let's say I find out that my brother the college student failed an exam. I know he's a smart guy, and the class he failed it for wasn't anything difficult like thermodynamics, and most of the professors at the college he goes to are competent teachers and test writers. Therefore, he probably didn't study for the test. If I accept Proposition 6, then I must conclude that he simply did not study for the test.

Here is the problem: I should not be able to draw this conclusion based on the information I have. It is still possible that he did study, but he got a bad professor or he just wasn't understanding the material or perhaps something else. However, Proposition 6 follows necessarily from Proposition 1, Proposition 1 makes this conclusion not only possible, but logically necessary!

Therefore, it would be an obvious fallacy to apply Proposition 1 to reasoning about the probabilities of past events. I am not saying that I've reduced Proposition 1 to absurdity. I'm just saying that it is not a valid rule to be used for reasoning about the probability of past events, which is exactly what was attempted in the aforementioned article regarding intelligent design.