Why truth? And...

38Eliezer_Yudkowsky27 November 2006 01:49AM

Some of the comments in this blog have touched on the question of why we ought to seek truth.  (Thankfully not many have questioned what truth is.)  Our shaping motivation for configuring our thoughts to rationality, which determines whether a given configuration is "good" or "bad", comes from whyever we wanted to find truth in the first place.

It is written:  "The first virtue is curiosity."  Curiosity is one reason to seek truth, and it may not be the only one, but it has a special and admirable purity.  If your motive is curiosity, you will assign priority to questions according to how the questions, themselves, tickle your personal aesthetic sense.  A trickier challenge, with a greater probability of failure, may be worth more effort than a simpler one, just because it is more fun.

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Feeling Rational

51Eliezer_Yudkowsky26 April 2007 04:48AM

A popular belief about "rationality" is that rationality opposes all emotion—that all our sadness and all our joy are automatically anti-logical by virtue of being feelings.  Yet strangely enough, I can't find any theorem of probability theory which proves that I should appear ice-cold and expressionless.

So is rationality orthogonal to feeling?  No; our emotions arise from our models of reality.  If I believe that my dead brother has been discovered alive, I will be happy; if I wake up and realize it was a dream, I will be sad.  P. C. Hodgell said:  "That which can be destroyed by the truth should be."  My dreaming self's happiness was opposed by truth.  My sadness on waking is rational; there is no truth which destroys it.

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The Meditation on Curiosity

21Eliezer_Yudkowsky06 October 2007 12:26AM

"The first virtue is curiosity."
        —The Twelve Virtues of Rationality

As rationalists, we are obligated to criticize ourselves and question our beliefs... are we not?

Consider what happens to you, on a psychological level, if you begin by saying:  "It is my duty to criticize my own beliefs."  Roger Zelazny once distinguished between "wanting to be an author" versus "wanting to write".  Mark Twain said:  "A classic is something that everyone wants to have read and no one one wants to read."  Criticizing yourself from a sense of duty leaves you wanting to have investigated, so that you'll be able to say afterward that your faith is not blind.  This is not the same as wanting to investigate.

This can lead to motivated stopping of your investigation.  You consider an objection, then a counterargument to that objection, then you stop there.  You repeat this with several objections, until you feel that you have done your duty to investigate, and then you stop there. You have achieved your underlying psychological objective: to get rid of the cognitive dissonance that would result from thinking of yourself as a rationalist, and yet knowing that you had not tried to criticize your belief.  You might call it purchase of rationalist satisfaction—trying to create a "warm glow" of discharged duty.

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Guardians of the Truth

18Eliezer_Yudkowsky15 December 2007 06:44PM

Followup toTsuyoku Naritai, Reversed Stupidity is not Intelligence

The criticism is sometimes leveled against rationalists:  "The Inquisition thought they had the truth!  Clearly this 'truth' business is dangerous."

There are many obvious responses, such as "If you think that possessing the truth would license you to torture and kill, you're making a mistake that has nothing to do with epistemology."  Or, "So that historical statement you just made about the Inquisition—is it true?"

Reversed stupidity is not intelligence:  "If your current computer stops working, you can't conclude that everything about the current system is wrong and that you need a new system without an AMD processor, an ATI video card... even though your current system has all these things and it doesn't work.  Maybe you just need a new power cord."  To arrive at a poor conclusion requires only one wrong step, not every step wrong.  The Inquisitors believed that 2 + 2 = 4, but that wasn't the source of their madness.  Maybe epistemological realism wasn't the problem either?

It does seem plausible that if the Inquisition had been made up of relativists, professing that nothing was true and nothing mattered, they would have mustered less enthusiasm for their torture.  They would also have had been less enthusiastic if lobotomized.  I think that's a fair analogy.

And yet... I think the Inquisition's attitude toward truth played a role.  The Inquisition believed that there was such a thing as truth, and that it was important; well, likewise Richard Feynman.  But the Inquisitors were not Truth-Seekers.  They were Truth-Guardians.

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Fake Norms, or "Truth" vs. Truth

9Eliezer_Yudkowsky22 July 2008 10:23AM

Followup toApplause Lights

When you say the word "truth", people know that "truth" is a good thing, and that they're supposed to applaud.  So it might seem like there is a social norm in favor of "truth".  But when it comes to some particular truth, like whether God exists, or how likely their startup is to thrive, people will say:  "I just want to believe" or "you've got to be optimistic to succeed".

So Robin and I were talking about this, and Robin asked me how it is that people prevent themselves from noticing the conflict.

I replied that I don't think active prevention is required.  First, as I quoted Michael Vassar:

"It seems to me that much of the frustration in my life prior to a few years ago has been due to thinking that all other human minds necessarily and consistently implement modus ponens."

But more importantly, I don't think there does exist any social norm in favor of truth.  There's a social norm in favor of "truth".  There's a difference.

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The two meanings of mathematical terms

-3JamesCole15 June 2009 02:30PM

[edit: sorry, the formatting of links and italics in this is all screwy.  I've tried editing both the rich-text and the HTML and either way it looks ok while i'm editing it but the formatted terms either come out with no surrounding spaces or two surrounding spaces]

In the latest Rationality Quotes thread, CronoDAS  quoted  Paul Graham: 

It would not be a bad definition of math to call it the study of terms that have precise meanings.

Sort of. I started writing a this as a reply to that comment, but it grew into a post.
We've all heard of the story of  epicycles  and how before Copernicus came along the movement of the stars and planets were explained by the idea of them being attached to rotating epicycles, some of which were embedded within other larger, rotating epicycles (I'm simplifying the terminology a little here).
As we now know, the Epicycles theory was completely wrong.  The stars and planets were not at the distances from earth posited by the theory, or of the size presumed by it, nor were they moving about on some giant clockwork structure of rings.  
In the theory of Epicycles the terms had precise mathematical meanings.  The problem was that what the terms were meant to represent in reality were wrong.  The theory involved applied mathematical statements, and in any such statements the terms don’t just have their mathematical meaning -- what the equations say about them -- they also have an ‘external’ meaning concerning what they’re supposed to represent in or about reality.
Lets consider these two types of meanings.  The mathematical, or  ‘internal’, meaning of a statement like ‘1 + 1 = 2’ is very precise.  ‘1 + 1’ is  defined as ‘2’, so ‘1 + 1 = 2’ is pretty much  the pre-eminent fact or truth.  This is why mathematical truth is usually given such an exhaulted place.  So far so good with saying that mathematics is the study of terms with precise meanings. 
But what if ‘1 + 1 = 2’ happens to be used to describe something in reality?  Each of the terms will then take on a  second meaning -- concerning what they are meant to be representing in reality.  This meaning lies outside the mathematical theory, and there is no guarantee that it is accurate.
The problem with saying that mathematics is the study of terms with precise meanings is that it’s all to easy to take this as trivially true, because the terms obviously have a precise mathematical sense.  It’s easy to overlook the other type of meaning, to think there is just  the meaning of the term, and that there is justthequestion of the precision of their meanings.   This is why we get people saying "numbers don’t lie".  
‘Precise’ is a synonym for "accurate" and "exact" and it is characterized by "perfect conformity to fact or truth" (according to WordNet).  So when someone says that mathematics is the study of terms with precise meanings, we have a tendancy to take it as meaning it’s the study of things that are accurate and true.  The problem with that is, mathematical precision clearly doesnotguarantee the precision -- the accuracy or truth -- of applied mathematical statements, which need to conform with reality.
There are quite subtle ways of falling into this trap of confusing the two meanings.  A believer in epicycles would likely have thought that it must have been correct because it gave mathematically correct answers.  And  it actually did .  Epicycles actually did precisely calculate the positions of the stars and planets (not absolutely perfectly, but in principle the theory could have been adjusted to give perfectly precise results).  If the mathematics was right, how could it be wrong?  
But what the theory was actually calcualting was not the movement of galactic clockwork machinery and stars and planets embedded within it, but the movement of points of light (corresponding to the real stars and planets) as those points of light moved across the sky.  Those positions were right but they had it conceptualised all wrong.  
Which begs the question of whether it really matters if the conceptualisation is wrong, as long as the numbers are right?  Isn’t instrumental correctness all that really matters?  We might think so, but this is not true.  How would Pluto’s existence been predicted  under an epicycles conceptualisation?  How would we have thought about space travel under such a conceptualisation?
The moral is, when we're looking at mathematical statements, numbers are representations, and representations can lie.



If you're interested in knowing more about epicycles and how that theory was overthrown by the Copernican one, Thomas Kuhn's quite readable  The Copernican Revolution  is an excellent resource.  

 

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