Cosmological argument, reformulated.

[beenherebeforeagain]

Your post is actually an extremely good example of the underlying issue because you read a statement and then apparently assumed that it had all kinds of implications which do not at all relate to the point that had been made. I was referring to the particular definition of God, you extended that without reason and assumed that I was saying all my definitions deductions were vague etc....

Not really. I was referring to my earlier post about your conclusions not following from your asserted "facts," on the one hand, and on the other that many other responders are offering very substantial challenges to either your "facts" or your conclusion, all of which are possible because your terms and reasoning path are not sufficiently well defined to make such objections unwarranted. Then, you just asserted that your definition of God is indeed vague. That you cannot clearly define what "God" is and is not prior to making your argument makes it impossible to come to a conclusion in logic. At least the way I have learned logic.

Over the years, philosophers and theologians and others have devoted considerable effort on formulating and refuting the cosmological argument, in much greater detail and with much greater precision than you have presented here, and than have the other respondents here. Neither side has yet won the debate, or perhaps more precisely, neither side has yet lost the debate. It may well be that the question cannot be finally resolved.

But your reformulation in this thread does nothing to advance the argument, because it is so imprecise and with a rather substantial gap between your assertions and your conclusion. In my opinion, at least.

 

[Enai de a lukal]

Over the years, philosophers and theologians and others have devoted considerable effort on formulating and refuting the cosmological argument... Neither side has yet won the debate, or perhaps more precisely, neither side has yet lost the debate. It may well be that the question cannot be finally resolved.

That's not very accurate; the cosmological argument has long been recognized as unsound and, outside of a handful of deluded idiots (like WLC) and devout Thomists (Gilson), is mainly of academic/historical interest only.

 

[Curious George]

Zeno thought he had some pretty good paradoxes as well.

 

[Enai de a lukal]

Zeno thought he had some pretty good paradoxes as well.

He did have some good paradoxes. Everyone assumes that either Aristotle or the calculus adequately resolved the stadium paradox- not exactly; even with the notion of a limit or convergent series, the paradox forces us to accept the conclusion that, when we travel a given distance, we traverse all the intervals therein, and do so successively, but never traverse any first or last interval, the traversal of which either sees us begin moving or reach our destination. A proper paradox? I dunno, but its a counter-intuitive result, and we're quite stuck with it.

 

[Curious George]

He did have some good paradoxes. Everyone assumes that either Aristotle or the calculus adequately resolved the stadium paradox- not exactly; even with the notion of a limit or convergent series, the paradox forces us to accept the conclusion that, when we travel a given distance, we traverse all the intervals therein, and do so successively, but never traverse any first or last interval, the traversal of which either sees us begin moving or reach our destination. A proper paradox? I dunno, but its a counter-intuitive result, and we're quite stuck with it.

I am in the.calculus camp.

My point was that the cause and effect argument here relies on a similar argument.

While intuition may not realize the infinite can rest in the finite that intuition is wrong. We can have an infinite chain of cause and effects in a finite time.

 

[cjschmidtz]

I have considered that Zeno’s paradox is easy to resolve. Yes mathematically you can make divisions indefinitely, however when we travel we are not traveling by halves we are traveling a set distance over a set amount of time. If the distance is a mile and you can travel a mile in an hour, you can get there in an hour. It is logical both mathematically and in our experience. The problem with Zeno’s paradox is simply an issue of associating a truth in a category to which it doesn’t apply.
This is completely different from the assertion that an infinite series of causes could exist in a finite period of time. The term infinite with regards to cause and effect is not helpful, you can never get to a number that is so great that adding another will make it an infinite; you would always merely have a larger number. I would use the term to describe a number that continues indefinitely not for a number that is meant to represent something particular.

 

[Enai de a lukal]

I am in the.calculus camp.

My point was that the cause and effect argument here relies on a similar argument.

While intuition may not realize the infinite can rest in the finite that intuition is wrong. We can have an infinite chain of cause and effects in a finite time.

I'm saying that there are constructions of the paradox such that the "paradox" is entirely different than usually assumed, and thus that none of this helps. The standard story is this- to traverse a given distance, you have to traverse an infinite number of intervals, each having some size; now, either the idea is that an infinite number of intervals each with some (positive) non-zero extension, the entire distance would be infinite, or the idea is that each interval takes some non-zero amount of time to traverse, so that traversing an infinite number of intervals takes an infinite amount of time. And I agree with you, so far as it goes, that this paradox has been solved, clearly.

But a different way to pose the paradox is by saying that, if we assume (as we generally do), that to traverse a given distance, we must traverse each of an infinite number of intervals (we don't skip any), and we traverse them successively (no herky-jerky, teleporting here and there type of motion), we have to conclude that we arrive at our destination despite never having traversed any first interval, the traversal of which sees us begin moving, or having traversed any last interval, the traversal of which sees us reach our destination. As I said, I don't know that this is as strong of a paradox, in the sense that it is as absurd/contradictory/etc. a result, but it is also alot harder to answer- most people just bite the bullet and concede the conclusion.

 

[LegionOnomaMoi]

not exactly; even with the notion of a limit or convergent series, the paradox forces us to accept the conclusion that, when we travel a given distance, we traverse all the intervals therein, and do so successively

We do not do so successively. Actually, Cantor proved that the kind of intervals possible with real numbers are incapable of being "successive" (they are uncountable or nondenumerable). It's more intuitive thanks to the formalization of infinitesimals by Abraham Robinson which render unnecessary the epsilon-delta definition of limits. Either way, however, the idea is that the summation of an infinite number of values (distances, increments of time, etc.) can sum to a finite values because traversal isn't successive, the summation is. And as the summation involves values that are "infinitesimally" small, one can formulate the summation of some succession and determine that the particular terms will infinitely extend as they become infinitely smaller. Simplistically, it's infinite summation of infinitely smaller values, such that as the cardinality of our set of terms approaches infinity, the added values approach 0.

I can express the same distance/increment/etc. in different ways because the actual traversal is not successive. A single step can be expressed in terms of the summation of ever increasingly small distances, but that does not mean the distance travelled is itself the successive traversal of these distances. More intuitively, I can express the number 1 as an infinite series or I can just use 1. The capacity to express some interval or increment as consisting of infinitely many terms, units, values, etc., does not mean that such infinite sets actually are the interval or increment. Were that so, then I would be confined to a specific expression of the summation of some infinite set/sequence for any and all specific representations of units (whether of time, distance, or whatever). I am not required to do this any more than I am required to denote the value "one" by 1/2 + 1/2. The unit can be expressed in various ways, but we arrive at the seemingly paradoxical traversal of an infinite number of increments only because we are expressing units differently. When I traverse one yard, I traverse 3 feet and 36 inches. I can continue to use smaller and smaller values but all I am doing is taking the distance traversed and expressing it in terms of some particular sequence of values that will sum to that increment's value.

 

[beenherebeforeagain]

That's not very accurate; the cosmological argument has long been recognized as unsound and, outside of a handful of deluded idiots (like WLC) and devout Thomists (Gilson), is mainly of academic/historical interest only.

Whether it's accurate to call people deluded idiots or not, the fact is that there are some who continue to try to advance the argument, and while I agree that these efforts generally fail on purely logical grounds, just because empiricist/materialists believe they have rejected the argument doesn't mean that it isn't considered valid by others.