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Fri 29 Aug, 2003 04:33 am
Hello people! Please help me out here, I am going insane wiht this stuff.
(also, I am new to these boards)
I just began working yesterday on essays regarding Nozick's "Philosophical Explanations", wrote about chapter 1, and earlier this afternoon I started writing about chapter 2, where I encountered a problem that I dont know how to deal with. (I have already about 20 pages, 10 on each chapter). My problem is in chp2, where he is talking about explainable groups (ill say what this is later), where there is eventually some ultimate parent truth which has no explanation. We have no way of fiuring out the truth value of this beast brute fact, and if it is false, then everything else beneath it must also be.
I tried to conjure up some solution, and I was pleased with myself untill my argument turned around to bite me in the ZAA (increment letters by 1).
He has two premesis:
P1: There is no x and y in T (T is the set of truths) such that xEy (x explains y) and yEx.
P2: If xEy and yEz, then xEz.
OK.
So I thought that P1 was no good, because it doesnt allow cyclic chains such as aEb, bEc, cEd ... zEa, which seem to occur in the natural world. Why does a cheetah have fast legs? So it can catch the wary gazelle. Why is the gazelle wary? Because the cheetah has fast legs. You guys get the idea.
Okay, so I thought that what was mucking Nozick up was P1. I said, forget P1, Im going for some eastern style philosophy, interconnectedness and all, and that way I will have a strong argum,ent. Here was the argument:
In Nozick's hierarchical E tree (what the set of truths will look like as structure by his E relation), there will be some ultimate unexplainable parent node ( I say node because it can be composed of groups of truths). The truth or falsehood of this node dicated the truth value of everything else. Trying to explain everything, it looks like he made a big achilles heel. His hierarchical tree is made up of one way implications, so anything being explainable is dependent *everything* above it being explainable, and ultimately, the truthvalue of the JesusLordChrist Node. Chance of total unexplainability seems pretty high here. note that the that the LordFather node being false does not imply not stuff below it also false. Descendent nodes can exist independently, so we cant use what we 'know' to prove the truthhood of the all father node.
Assuming that inter-relatedness would be okay, it feeling natrual, I said: in a C group one element implies the existence/explainability of every other element. Say the chance of any given node being false (hence not explaining other stuff) is f, where f is less than 1. There are infinitely many nodes. But since the truthhood of any given node, in this group, implies the truthhood/explainability of all other nodes, the chance of them all being unexplainable is f to the power of infinity, which has a limit of 0. So I say that it is probably sure that everything is explainable, and when somebody asks: "How can x be explained?" I can give them one of many different answers, as they are all interrelated, and if somebody says: why is your answer true?" I simply say probability. If they then question that, I give the a pretty red ball to play with.
but... It doesnt seem to work. Because instead of the links in these cyclical groups being implications, they are bijections (a <->b. if a then b. if not a then not b etc). if, say, n is false, then so must m be, because if m then n, and not n. etc etc. And my whole system is destroyed fire-cracker roasting chestnut style. The argument works both ways, as the probability of one node amoungst the countless being false is almost 1. So, using the same argument, I can say that the chance of everything being false in such a system is certain.
Maybe there is something that I am overlooking. Maybe I should just ditch teh argument.. wel, I am not going to do that. If it cannot be salvaged, then I am going to offer it as further proof that his P1 should hold, as opposed to my current stance as using it as a weapon against P1 and as a potential solution to the whole mess.
Okay, I will now go to sleep pondering this. Its my 3:22 am, and I just got back from festivities at the a neighborhood pub. Ah guinness.
Thanks board people!!! any help, alternative solutions, whatever, would be greatly appreciated.
Re: A Philosophical Problem, help!! Can Everything Be Explai
I'm not very familiar with Nozick, and I usually don't give homework advice on these kinds of boards, but I'll give it a shot here.
divineSynthesis wrote: He has two premesis:
P1: There is no x and y in T (T is the set of truths) such that xEy (x explains y) and yEx.
P2: If xEy and yEz, then xEz.
OK.
So I thought that P1 was no good, because it doesnt allow cyclic chains such as aEb, bEc, cEd ... zEa, which seem to occur in the natural world. Why does a cheetah have fast legs? So it can catch the wary gazelle. Why is the gazelle wary? Because the cheetah has fast legs. You guys get the idea.
No, that's not how I interpret P1. Nozick seems to be suggesting that tautologies are not self-explicable. If x is explicable by y, and y is explicable by x, then, in that closed set, it seems that x would equal y: in other words, it would be a tautology.
Your example of the cheetah and the gazelle is logically flawed. Why does the cheetah have fast legs?
So (i.e. in order that) it can catch the wary gazelle. Why is the gazelle wary?
Because the cheetah has fast legs. Your inconsistent use of "so" and "because" means there is no parallel here. The first describes a necessary relation, the second describes a causal relation.
divineSynthesis wrote:But since the truthhood of any given node, in this group, implies the truthhood/explainability of all other nodes, the chance of them all being unexplainable is f to the power of infinity, which has a limit of 0. So I say that it is probably sure that everything is explainable, and when somebody asks: "How can x be explained?" I can give them one of many different answers, as they are all interrelated, and if somebody says: why is your answer true?" I simply say probability. If they then question that, I give the a pretty red ball to play with.
What's the purpose in introducing a probabilistic analysis here? You're confusing two very different methods of "proof": deduction (which Nozick apparently is attempting) and induction (basing truth or proof on a probabilistic basis). Analyzing a deductive proof by means of an inductive test is, practically speaking, meaningless.
divineSynthesis wrote:but... It doesnt seem to work. Because instead of the links in these cyclical groups being implications, they are bijections (a <->b. if a then b. if not a then not b etc). if, say, n is false, then so must m be, because if m then n, and not n. etc etc. And my whole system is destroyed fire-cracker roasting chestnut style.
And well it should be.
divine, Philosophy was my minor, but I can't help you with this problem. All I can do is WELCOME YOU to A2K. Sorry, c.i.
joefromchicago wrote:
No, that's not how I interpret P1. Nozick seems to be suggesting that tautologies are not self-explicable. If x is explicable by y, and y is explicable by x, then, in that closed set, it seems that x would equal y: in other words, it would be a tautology.
In its strictest sense, all P1 says is that no tautologies, but in in conjunction with P2 it says that C groups are impossible. If we construct a cyclyical group of truths connected via E, say for example (a_1, a_2, .. a_n) where (a_i)E(a_i+1), and most importantly (a_n) E (a_1), if we apply P2 a whole bunch of times then it turns out that any element in this set explains every other element in it, breaking P1. all these statements would be true,
for (i = 0; a<n; i++) {
for (j=0; j<n; j++) {
a_i E a_j; }}
joefromchicago wrote:
Your example of the cheetah and the gazelle is logically flawed. Why does the cheetah have fast legs? So (i.e. in order that) it can catch the wary gazelle. Why is the gazelle wary? Because the cheetah has fast legs. Your inconsistent use of "so" and "because" means there is no parallel here. The first describes a necessary relation, the second describes a causal relation.
Hrm. Neccessary relation? Im not sure. Sorry, I just woke up, and I'll think about that one further. This is an example of the sort of thing I think
which should ally cyclical explanations, intuitively, it seems unlikely that if you take all chains of truths, sturctured by E, that some truth at some arbitarary point down the line will not stand in E to something earlier. Then again, I cant think of any examples. For the moment, I think I am going to have to assume that its possible, untill I see otherwise.
joefromchicago wrote:
What's the purpose in introducing a probabilistic analysis here? You're confusing two very different methods of "proof": deduction (which Nozick apparently is attempting) and induction (basing truth or proof on a probabilistic basis). Analyzing a deductive proof by means of an inductive test is, practically speaking, meaningless.
Hrm. Ill have to think about this. For the moment I still dont see a problem with that particular aspect of how I set up the problem, but maybe you are right. I think that more likely the problem lies with my using inifinity, which is a messy pseudonumber. If there is a probability of something being false, then one is false. But there is also a probability of one being true, so one is true, then I have a paradox. That is if I consider the individual probability of any given node. Since in this case if one is true, then all is true, and if one is false then the rest fallow, it was incorrect to consider their individual probabilities. Maybe instead to construct some sort of mean. I dont know.
Well, thank you guys for your input, any further input will be welcomed. btw, this is exactly for a homework assignment. My philo prof gave me Nozick's book to read for extra-curricular purposes. None of the stuff I write will be submitted for a grade.
again, thanks all!
divineSynthesis
Some observations.
1. Binary logic is a limited subsystem of general semantics and seems to lie "below" the level required to analyse the different nuances of the word "explanation". It therefore seems inappropriate to attempt to employ it to investigate "explanatory chains".
2. I thought Godel had already shown that all systems have at least one axiom whose "truth value" cannot be ascertained. All further analysis seems to be redundant.
3. From the point of view of the "social construction of reality" truth values are never objective and are subject to the degree of consensus between participants in the interaction. Thus what constitutes "facts" and the "explanation" of such facts are a matter of negotiation in specific contexts.
divineSynthesis, probably I can give a answer that thrusts into the very weakness of your self-subversive argument.
It is a misunderstanding of Nozcik's epistemological argument that makes you introduce probability to reveal in it a paradox. In other words, from the very beginning your argument based on this probability modeling is doomed. The hierarchical E tree of a linear way of one node explaining the other presupposes that the probability of a node being explained by another is just 1 - where you made it less than 1 - or put differently, there must exist a node explaining the other. The problem is not whether a node can be explained but how we can find out that explanatory node.
The paradox previously in the Nozick's argument, however, appears to be transfered to another question that can be put as: the chance of we finding out explanations for everying is ultimately nill; so is that of we being unable to find out. But the paradoxical statement does not escape the fate of having in it an implicit philosophical dogma - which is that the world and human history are subject to the whims of the unknow power - as agaisnt another philosophical belief that takes a more determinist approach to understanding of the reality. Applying probability techniques to explain the vageries of world is itself not completely tenable, and awaits more clarification.
Probably the paradox can be explained away by tracing to some underlying philosophical beliefs of both probability technique, which you applied, and the argument by Nozick. As I said in the last post, probability technique carries with it a connotation of the belief that chance determines everything. If it is plausible to trace the Nozick's argument to some determinist philosophy or other principles that contrast the belief of chance, the paradox can then be resolved, because the underlying principles of Nozick's argument and probability technique are not at all compatible so that mixing the two is definitely prone to culminating in some paraxical arguments.
Alas, I am thinking terribly hard but so little progress, so far,in tracing Nozick's argument to its underlying principle.
acepoly,
Thank you for your posts. As of yet your obeservations have been on the ball. As you said, , "the underlying principles of Nozick's argument and probability technique are not at all compatable so mixing the two is definitely prone to culminating in some paradoxical arguments." Or is it? Im not entirely sure.
For the moment, I just returned from an evening of rampant drinking and debauchery. If you have not guessed it yet, I am a college student, and we are prone to such activities. In any case, I will try to post something now to provide thinking fuel.
I realized that the probabalistic argument I attempted has no way of being salvaged. It just doesnt work, so I have perhaps another argument which might prove to be a little stronger. Here it is:
Recall that Nozick's premisis:
P1: for all x and y in Truths, exists no x such that xEy and yEx.
P2: if xEy and yEz, then xEz.
From these, if we are asked the question: Is every thing explainable? The answer is no. If everything is explainable then there exists at least one x and y pair such that xEy and yEx. These we can group as one truth, which then constitutes some brute fact. It has no explanation. So there is no explanation for everything.
My probabalistic argument was an attempt to remove arbitrariness from this brute fact. If we actually look at the nature of this C group (I in fact turned the whole set of truths into a C group in my failed argument) then we see that as a whole, it constitutes a brute fact. I attempted to remove the arbitrariness of it (at least some) through the use of probability. Okay, it doesnt works. Which led me to an alternative theory, one which uses 'weightings' on truth nodes.
In one of Nozick's hierarchic E trees, the explainability of any given node is totally dependent on all of its parent nodes being true. But, since this E tree is hiearchic, the E links are not bijective. In other words, Not the ultimate parent node does not imply not its children nodes. It just means that this given path of explanation is wrong.
So in my 'weighted' theory, I give the following: the weight of a given node is the number of nodes dependent/beneath it. So in an one of Nozicks hierarchic E trees, the ultimate parent node would have a weight of n, where n is the total number of truths in the group. Any other node j would have a weight of k, where k is the number of nodes in the subtree which has that node j as its parent. Note that the reason why I give sub-nodes weights is that they could be true even if their parent nodes are not. We are not dealing with "iff' relationships here.
So if we had the tree: a[5,10]; 5[2,6], 2[1], 10[9,13], 9[8,]13[14]
a
/ \
5 10
/ \ / \
2 6 9 13
/ / \
1 8 14
Then (a) would have weight 10. Nodes 1, 8 and 14 would have wieght 0. 5 would have weight 3, 10 would have 4, etc etc. This is a type of measure of the amount of truths which is dependent on some given truth. For our purposes, the lower the number, the better. in this particular case, the total combined weight of all nodes is something like 20. I may have counted wrong. If thats the case, sorry. If not 20 then its real close.
If, however, these nodes were in a c group:
a <-> 5 <-> 2 <-> 6 <-> 1 <-> 10 <-> 9 <-> 8 <-> 13 <-> 14 <-> a (its cyclic)
Then the weight of any given node would be something like this (suggested methods would vary, but whatever they might offer, teh weight of the total structure would never be less than k, where k is the total number of nodes in the set) The weight of any given node would be 1/k. All other nodes are dependent on all other nodes, so for any node x, it is dependent on some other node y by 1/k. If we add up all these weights we get 1, and 1 is less than 20 (by a long shot). As we increase the number of nodes in our set, the weight difference between hierarchic E groups and cyclic E groups will also increase proportionally. So C groups are good.
What do you think?
Now I must sleep and hopefully by tomorrow be in my right mind. College is fun like that.
thanks,
Quote:a <-> 5 <-> 2 <-> 6 <-> 1 <-> 10 <-> 9 <-> 8 <-> 13 <-> 14 <-> a (its cyclic)
DvineSynthesis, I am confused on this conclusion. Would you clarify your premises once again, after you've got in your right mind?
(I suppose there isn't a hangover)
What exactly is it that needs to be clarified? Is it what you quoted me about? Thats just an example of one of a cylcic group, as structured by E. The order of elements is arbitrary in such a group, since they are interrelated.
Well, I was writing an essay about all of this stuff (for fun) and I have just finished it. If you would like a copy, send me your email address (if there is some private way to do that. Im not sure, I am new to this particular service). Its in appleworks, with imbedded images. If you dont have appleworks, I can send it as html. Ill send the essay to anybody else who is interested.
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