Law School Discussion

Chicago Countdown Thread

Brito

  • ****
  • 2413
    • AOL Instant Messenger - ViolaLovesMusic
    • View Profile
    • Email
Re: Chicago Countdown Thread
« Reply #20 on: January 13, 2007, 10:33:40 PM »

See, this thread is cool, because if the Chicago adcomms see it, they will realize how awesome we are and admit us all.  Please.


A pile of 10,000 grains is a heap.
For any number n>1, if a pile of n grains is a heap, then so is a pile of n - 1 grains.
So one grain is a heap.


A law school in the top 3 will provide great employment opportunities.
For any number n<100, if a law school in the top n will provide great employment opportunities, then so will a law school in the top n + 1.
All Tier 1 schools provide great employment opportunities.

EEtoJD

  • ****
  • 4136
  • Football!!!
    • View Profile
    • LSN
Re: Chicago Countdown Thread
« Reply #21 on: January 13, 2007, 10:36:03 PM »

But forgetting doesn't have to be a conscious decision, or a result of conscious habituation.  If you're setting your watch ahead because you're always short on time, say, in the mornings, then usually there's too much going on in too short an amount of time, which makes it easy to forget relatively minor details (such as "I set my clock forward at 9 PM last night). 

Aha! This is the real paradox. I was hoping it would get to this point quickly. So, this implies that the brain somehow has a built in "task manager" that brings important decisions to the fore and relegates less important ones to the rear (subconscious?). So, your brain remembers that you've made the decision, but your brain doesn't remind you, because you have more important things to worry about. You would "remember" if you saw a clock that had the correct, though, wouldn't you? You wouldn't think that this clock is wrong, because this stimuli would likely spur the memory of setting your watch ahead to come to the fore.

I'm no neuroscientist, but I feel (and think I've heard) that this compartmentalization and assigning importance to tasks (sort of like a priority queue that has smaller priority queues operating simultaneously within each queue) is what allows us to perceive the world without being overwhelmed by all the stimuli we're bombarded with. In fact, we don't really perceive the world as it is, but the brain helps us perceive it in a way that is easier for us to understand. For instance, some autistic savants have been shown to perceive the world without the tricks that our brain plays on us each day in order to keep our sanity.

EEtoJD

  • ****
  • 4136
  • Football!!!
    • View Profile
    • LSN
Re: Chicago Countdown Thread
« Reply #22 on: January 13, 2007, 10:46:09 PM »

I was going to say that the "degrees of truth" commits a logical fallacy (the slippery slope argument, of which the "heaps argument" is actually one variation).  The other thing is that in formal logic, the word "heap" doesn't necessarily have to mean what we, in everyday language, think of as a heap.  That's just our interpretation, and not a definition that the word is bound to.  Therefore, the cheap and easy way of resolving your heaps paradox is to say that you're committing another logical fallacy, that of equivocation.  <shrugs>

Your argument is true if we interpret "degrees of truth" in the realm of a system of logic. If, instead, we refrain from actually defining the "borderline" case, but state that the "borderline" (or the point where a person would begin to hesitate to call the thing a heap) varies from time to time and person to person (Oswald Hanfling's resolution), then a possible resolution shows itself. The whole problem is higher-order vagueness, but if we can eliminate the cause of the vagueness - namely, the vagueness of language - then we can resolve the paradox.

We're not actually committing equivocation, because equivocation implies a double meaning in formal logic, or taken more loosely (well, that's the whole problem , isn't it? Loose definitions...), language meant to mislead. We don't mean to mislead by saying that the word "heap" is not clearly defined. This is simply the way human language is set up. We're not computers, we need room to maneuver. That's how the law works. Remember the LSAT RC about using computers to solve legal problems. We'd have to get a program to resolve these vagaries, easier said than done.

Re: Chicago Countdown Thread
« Reply #23 on: January 13, 2007, 10:52:55 PM »

See, this thread is cool, because if the Chicago adcomms see it, they will realize how awesome we are and admit us all.  Please.

I have two books just about paradoxes. My favorite paradox of all time is called "The Heap". It goes like this (taken from Paradoxes from A to Z by Michael Clark):

A pile of 10,000 grains is a heap.
For any number n>1, if a pile of n grains is a heap, then so is a pile of n - 1 grains.
So one grain is a heap.

This form of argument (p->q; p; therefore, q) is known as modus ponens. It works fine with pure logic, but not with how we define a heap. The paradox lies in the definition of words. A "heap" is not a sharply defined word, so we don't have a specific point that we'd call the pile of grains a heap, or stop calling it a heap.

My favorite resolution of this argument comes about by using "degrees of truth". Let's say that we're at the borderline of a heap when we reach 70 grains, and consider the following:

If 71 grains makes a heap, then so do 70.

The "if" part of the statement (71 grains) is more true than the "then" part (70 grains). So, if one part of the if-then statement is more true than the other, then it's reasonable to say that the statement isn't strictly true. It may be only by a small degree, but if we keep making these inferences down the chain, the small errors propagate and make it impossible to say that only one grain is a heap.

There are other approaches (fuzzy logic, supervaluations), but they're not as interesting, I think.
You remind me of my philosophy classes. I had to write endless papers on topics like this. It was really fun though.

EEtoJD

  • ****
  • 4136
  • Football!!!
    • View Profile
    • LSN
Re: Chicago Countdown Thread
« Reply #24 on: January 13, 2007, 10:55:38 PM »
Interesting, I can see some of your CS background in your argument - it seems like you do believe in the computational theory of the mind/mechanist view of mind (not saying I don't, I'm just feeling contrary).  Your langauge, of having a "task manager" almost suggests the homunculi that Dennett formulated, which constitutes a mental hierarchy (more complicated homunculi at the top taking on complex tasks, but each homunculi is composd of simpler homunculi, etc. etc. until the most basic homunculi can be replaced with simple mechanisms and processes).

Not exactly. I think it is more intertwined than this. The priority queues I've formulated, or the homunculi that you've formulated (homunculi scare me), actually mesh and communicate with each other. These complex interactions can't be broken down to constituent parts, because there are none - they're always changing, reforming themselves to deal with new stimuli. That's how the brain works, at least for a while - forming new connections, new neural pathways to deal with the new information we learn. This is why growing old sucks... we do this at incredible speeds when we're young, but then it levels off (saturation) and then starts to decline in old age, so we forget things. Of course, this is just generally speaking, and it doesn't happen to everyone. But it happens to most of us.

I think that a lot of these interactions start to break down as we age, so that we "forget" how to prioritize and compartmentalize, until it's more important to us to get our peaches n' cream than to pay our bills so we don't get kicked out of our houses. We haven't learned to prioritize yet when we're young, either, because these interactions aren't in place yet.

Quote
I always had a problem with this view though, because of the whole consciousness issue - it seems like mechanism edges out the possibility that there's something []more[/i] to consciousness.  For instance, if you take mental processes and perception as purely physical processes, then where's the connection between brain synapses and consciousness?

Ignore my philosophical ramblings if you guys want!

I will not ignore any philosophical rambling, I'll just try to disprove it. ;) Too bad this is nearly impossible.

I agree with what you're saying, hence my "meshing" argument above. This is no simple mechanistic process, at least not one that we've discovered yet. I do have full confidence that, one day, given enough time, we will discover exactly how the brain works. Then we'll make some new brains in jars, couple them with technology, and they'll take over the world. No more humans!  ;D

Re: Chicago Countdown Thread
« Reply #25 on: January 13, 2007, 10:57:13 PM »

Your argument is true if we interpret "degrees of truth" in the realm of a system of logic. If, instead, we refrain from actually defining the "borderline" case, but state that the "borderline" (or the point where a person would begin to hesitate to call the thing a heap) varies from time to time and person to person (Oswald Hanfling's resolution), then a possible resolution shows itself. The whole problem is higher-order vagueness, but if we can eliminate the cause of the vagueness - namely, the vagueness of language - then we can resolve the paradox.



Yes, but to say that the "borderline" varies from time to time and person to person means you risk making any resolutions you draw relativistic.  Eliminating the vagueness of language is also not always possible - just take translation from English language to formal logic symbols.  Most sentences are capable of being expressed in symbols, but some you aren't going to be able to, maybe because of vagueness in how the sentence is expressed or even vagueness in the scope of a given quantifier.  So at best, eliminating vagueness and/or having personalized "borderlines" for each person is an incomplete resolution of the paradox.  

Quote

We're not actually committing equivocation, because equivocation implies a double meaning in formal logic, or taken more loosely (well, that's the whole problem , isn't it? Loose definitions...), language meant to mislead. We don't mean to mislead by saying that the word "heap" is not clearly defined. This is simply the way human language is set up. We're not computers, we need room to maneuver. That's how the law works. Remember the LSAT RC about using computers to solve legal problems. We'd have to get a program to resolve these vagaries, easier said than done.

Also, the other part about the "if" part being more true than the "then" part doesn't hold either - if you try to use the formal definition of conditionals (which I assume you are, since you're bringing in modus ponens), then you can't say that the antecedent is more true than the consequent.  It doesn't work that way.  Granted, if the "if" is true, then the "then" has to be true, or the entire conditional itself is false.  You don't say that the "if" is more true than the "then" - it's either True or False.  
You're assuming that things can't be both true and false. For instance, take the previous sentence- i can claim that it's both true and false. You can respond by saying "no that's false" and i'll come back with "yea, i know, but it is also true".  

Brito

  • ****
  • 2413
    • AOL Instant Messenger - ViolaLovesMusic
    • View Profile
    • Email
Re: Chicago Countdown Thread
« Reply #26 on: January 13, 2007, 10:57:38 PM »
I don't really have anything to contribute here, but this is the best thread ever.  I love you people!

Hank Rearden

  • *****
  • 8241
  • Zurich is stained
    • View Profile
Re: Chicago Countdown Thread
« Reply #27 on: January 13, 2007, 10:58:23 PM »
Possibly the nerdiest thread ever.  Congratulations--you all belong at Chicago.

(secretly I am one of you!)

Brito

  • ****
  • 2413
    • AOL Instant Messenger - ViolaLovesMusic
    • View Profile
    • Email
Re: Chicago Countdown Thread
« Reply #28 on: January 13, 2007, 10:59:06 PM »
Possibly the nerdiest thread ever.  Congratulations--you all belong at Chicago.

(secretly I am one of you!)

I will be upfront about the fact that I want to be one of you!

Brito

  • ****
  • 2413
    • AOL Instant Messenger - ViolaLovesMusic
    • View Profile
    • Email
Re: Chicago Countdown Thread
« Reply #29 on: January 13, 2007, 11:04:30 PM »
I don't really have anything to contribute here, but this is the best thread ever.  I love you people!

Brito, we love you for starting this craziness!

Please jump in!

Nah, my philosophy background is too shallow to contribute anything substantive to this discussion.  I'm just enjoying reading all this.  :)  On the one hand, I hope you get into Harvard.  But secretly, I hope we both end up at Chicago...