Applications of Russell's Paradox

[chriscase]

Well this has been a refreshing moment of lucidity. I have the notion, however, that it's coming to an end. I don't understand why you'd say that "to God, nothing is morally neutral", but then you can imagine that any sentence that starts with "to God" and then makes some assertion about what God thinks just sounds like nonsense to me. But even in your example, if medical knowledge can be used for good or evil purposes, this means the knowledge itself is neutral. I'd go so far as to say that the concept of God is itself morally neutral - it's been enlisted in causes for good and evil. My position - as stated above - is that making good decisions about what to do with knowledge is contingent on having acquired the knowledge in the first place. Until that's happened we really are just fumbling around and creating unintended consequences.

[basics]

Well this has been a refreshing moment of lucidity. I have the notion, however, that it's coming to an end. I don't understand why you'd say that "to God, nothing is morally neutral", but then you can imagine that any sentence that starts with "to God" and then makes some assertion about what God thinks just sounds like nonsense to me. But even in your example, if medical knowledge can be used for good or evil purposes, this means the knowledge itself is neutral. I'd go so far as to say that the concept of God is itself morally neutral - it's been enlisted in causes for good and evil. My position - as stated above - is that making good decisions about what to do with knowledge is contingent on having acquired the knowledge in the first place. Until that's happened we really are just fumbling around and creating unintended consequences.

chriscase,

Well, if we take it seriously enough we can start at no-one being neutral in God's eyes. One is for Him or against Him. There is no middle ground. While it is true that knowledge is good, it usually comes from the experience of knowing bad or experieincing bad at sometime to begin to understand what really is good. There are no bounderies that restrict either. Whilst yes it may be true that people have used the name of God to do evil that does not make God neutral about it.

[chriscase]

I don't see what this has to do with logic or knowledge.

[basics]

I don't see what this has to do with logic or knowledge.

chriscase,

Knowledge is a great thing so it is logical that we as a species gather as much as possible. Sometimes it is good and sometimes it is bad and so logic plays a great part in our decisions. Morality however is based on what the society we live in makes it. Are we more moral today than say fifty years ago? One would logically expect, not just think, that life would be better but is that so? Is the world a better place? Were all the supposed great revolutions a success and I speak of all aspects of knowledge here when people still die in the numbers they do for the reasons they do?

[chriscase]

The reason that study of logic and sound reasoning is important is because without it, we make avoidable mistakes in our thinking. Now once some level of knowledge is attained, one must be concerned with the moral use of that knowledge. But this is an after-the-fact consideration that presupposes the acquisition of solid knowledge in the first place, and it's the reliability of the reasoning process that underpins that acquisition we are concerned with when considering logic. That's the thumbnail answer to your original questioning of whether this is all too arcane for regular folks like us to worry about.

[basics]

chriscase,

The problem with your argument which sounds right enough is that it is not consistent with events. For example Marx thought he had a solid case for revolution based on the facts that were evident then. Was he morally right? At the time probably. Today we see communism as a failed enterprize that has taken the lives of millions in its course as happened to all of the countries that adopted it. Now with the exception of a few still going through the despair all the others are into free market concepts yet havs not solved the difference between rich and poor as we who never adopted communism still can't seem to solve the same problem. Today we live with technology so advanced that instead of morally closing the rich/poor divide it appears to be getting greater. Is there a family anywhere in the world that does not see those facts and yet appear to be able to do little about them? Regular folks are not entirely stupid.

[chriscase]

A better analogy would be to ask if we ought to have an understanding of economic theory or statistics. Regardless of whether we agree about one application or another, if you just misunderstand the basics ( ) there's no point worrying about whether a particular application is good.

[basics]

chriscase,

Must admit the funny face does look a bit like me. As far as economic theory and statistics are concerned I think the average Joe Bloggs knows when he is being done over simply because he is incapable of doing anything to change matters no matter who controls the economy and the statistics. My point is however that if one finds themselves in an impossible situation like losing their home, their job, that is not a great situation to be in both physically or mentally. In most cases it affects the whole family putting more pressure on the head of the house which in some cases has had devastating consequences. Life shouldn't be like that.

[chriscase]

OK, and we also agree that when a young woman dies along with her infant in childbirth, life shouldn't be like that either. So we start with the desire to make things better. But how? That's where genuine understanding, study, and knowledge are important - and we don't get there without sound reasoning.

[basics]

chriscase,

One could begin with understanding why man is in the situation he is in. If one considers that he is the prime race on the planet one has to ask why is it in sheer chaos at the moment? Seven billion plus and rising yet the only uniformity among us is to disagree in just about anywhere an argument can be made. Everyone knows right from wrong yet collectively it is as far distant that these bring us together, rather separate more, so understanding, study and knowledge are not working, why? What is it in our makeup that causes two brothers, two sisters, to disagree and yet expect billions of others to agree?

[chriscase]

I'm not sure I agree with your assessment as to the extent of disagreement among the entire species.

Yet the fact remains that, as we agreed earlier, it's easy to misinterpret a situation even with accurate information in hand. Add to this the all too human predilection to imagine what we wish for rather than what a sober assessment would judge to be likely, and we've got a recipe for error. It's these very flaws that rules of inference and the study of fallacious reasoning are meant to address. Once we know that fallacies like ad populum and ad hominem are invalid forms of argument, we can spot and be wary of inferences that rely on them.

[fkizz]

The real boss of Set theory was Georg Cantor. He studied mathematics of infinity with much sacrifice, including his sanity. Infinity has a that sooner or later brings to mind to God, but sadly the brain of the Mathematician eventually got too exausted and he fell in madness.

[Iskar]

Cantor's definition was inadequate, though, as it was a) naive (in the non-judging sense) and b) somewhat circular, in that he defined a set to be a collection of objects of our "Anschauung" (roughly, objects of consideration, both mentally and materially) - where the notion of "collection" already encapsulates an intuitive idea of a set without further clarifying or explaining it. In fact if you combine Cantor's definition of a set with formal logics you arrive exactly at Russel's paradox, as it allows you to consider sets as objects of consideration and as such allows for sets of sets, and the set of all sets that do not contain themselves in particular.

Russel's paradox is easily avoided when paying attention to terminology and accepting a certain hierarchy of sets, type-0 sets being primary elements, type-1 sets what we naively call a set, type-2 sets collections of type-1 (or lower) sets etc. with the rule that any type-n set can only contain sets of type lower than n.

To be frank, though, most mathematicians rarely refer to this explicitly and only some logicians actively do type-theory. It is rather that everyone is aware of the problems arising from naive set-notions and uses an implicit, makeshift type theory: Mathematicians avoid sets of sets (of sets of sets of sets...) simply by changing words (rather than clearly defined notions or notation) and talk about families of sets, collections of families, etc. whenever unstructured sets need to be nested. The problem vanishes in most applications, though, simply by the fact that interesting sets have more defining characteristics and then receive special names anyway: A group is a set with an algebraic structure, a vector space one with a scaling structure, a manifold one with a locally Euclidian structure, etc. and nesting these (groups of groups, etc.) is subject to such heavy restrictions that you end up with the empty set before Russel's paradox can kick in.
I personally like to think of it as an instructive thought experiment teaching us to be careful with our notions and exemplifying that just because we can say words that does not make them carry meaning (a lesson many self-styled "philosophers" still need to learn).

[chriscase]

I wonder if I can enlist your caution against careless thought in the context of my original critique of the transcendent God.

[Iskar]

I think what your critique shows can be read in two equally enlightening ways:

1) Faith in a transcendent, omnipotent god must necessarily involve a translogical element. I am not saying "illogical" as that would imply it is still subject to logics but simply fails to comply with it, while "translogical" implies that at the very least parts of it cannot even be approached by logics. (Hej, Søren!)
As a corollary, if an omnipotent god exists (whatever that word may mean in a translogical context) no purely logical approach can hope to grasp it.

2) The concept of a transcendent omnipotent god can never claim cogent or full relevance to the world of experience in a rational discourse, as it would have to subject to the rules of logics, which is impossible as you showed. Making it relevant to one's life must be an unforced decision of the individual.

As a general consequence, which for my taste is way too rarely stated, philosophy and religion are sharply distinct. While the former is the strictly logical science exploring the structure of necessary thought, the latter always has a translogical element and can never fully subject to logical arguments.

(Nota Bene, That does not exclude partial usage of logics to approach some aspects of the omnipotent object of faith, as is beautifully shown by St. Augustin, the scholastics, Benedict XVI, and many more. Spelling out faith in an omnipotent creator of us humans - with our both rational and irrational ways of conduct - in a way that includes both logical and translogical elements would even be logically consistent (hah!).)

[basics]

Yep, the proof of the pudding is always in the eating thereof.