Judgments and Judgment

I often read Scott Adams blog. A lot of his ideas are just crazy, but every once in a while he makes an observation I totally agree with. In a recent post he mentions that kids decide what they want to be when they grow up based on the few careers they are aware of, without any knowledge of the thousands of occupations that are out there. It's so true, but it's so rarely mentioned by anyone. But I do take issue with Adams saying that a person must believe another person's judgment is inferior if they do not believe in the same religion. I would have posted a comment on his blog, but it already had over 200 comments by the time I read the post, so what's the point?

When Adams' uses the word "judgment", he isn't talking about a particular instance of a person making a judgment, rather a person's general ability to discern truth and falsehood. It might be called intelligence, reason or rationality as well. His concept of judgment is missing something important: the fact that rational judgments are made on the basis of the information a person has available to them. It may be rational for me to think that Christianity is true after reading the likes of C.S. Lewis and N.T. Wright. I can't avoid the conclusion that Christian morality works in practice, after seeing it practiced consistently by much of my friends and family. But I wouldn't expect a person whose only knowledge of Christianity comes from watching snippets of televangelists' preaching, and who has never seen anyone practice what Jesus or Paul taught, to believe Christianity any more than any other ideology they know practically nothing about.

Many of our judgments of fact are based on probability, inductive reasoning, memory, and testimony; none of which are infallible. So, in principle, any of these judgments may be nullified on the basis of new information. Only perfect deductive reasoning from absolutely sure premises avoids this possibility. By way of example, let's consider a person named Jay who is at work and ask ourselves whether a rational person should think Jay ate cereal for breakfast this morning. If all the rational person knows about Jay is that Jay is a live person who eats food, the rational person won't believe anything regarding Jay's current status a person who has eaten cereal for breakfast today. If the rational person knows that Jay is an American, and 49% of Americans eat cereal for breakfast on any given day, they will believe that Jay, as likely as not, ate cereal for breakfast. If the rational person learns from a reliable source that Jay eats cereal every morning for breakfast, they will believe Jay almost certainly ate cereal for breakfast this morning. But if they then find out that Jay is extremely allergic to wheat and the only cereal that Jay encountered this morning was bran flakes, they will believe he did not eat cereal for breakfast this morning, as evidenced by the fact that Jay is at work and not in the ER. Each step of the way, the rational opinion is superseded because of new information.

Good judgments are a function of both "how good [a person is] at determining truth from nonsense" and the information the person has. If it were otherwise, I would have to conclude that Isaac Newton was a crappy scientist for not believing in the Theory of General Relativity. If a politician, or anyone, disagrees with me on religious matters, I can't be obliged to think they are stupid, unless I know their reasoning is flawed. That's my judgment on the matter.

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.

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


2. 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...

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


3. 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.

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


4. 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...

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.


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

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


6. Thou shalt not kill.

Israelites have the right to life.


7. Thou shalt not commit adultery.

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


8. Thou shalt not steal.

Israelites have the right to property.


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

Israelites have the right to a fair trial.


10. 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.

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?

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.

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.

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?

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.

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.