Argument from Reason?

[Pyrrho]

I was experiencing this with the kalam argument and the actual vs potential infinite. One rebuttal I read was that actual infinites can exist in time and space, like by taking part  of some spatial object and dividing it infinitely. But then I wondered even  if you could divide it infinitely. Like wouldn't it have to stop after the sub atomic  level somewhere? Isn't there a place where you just can't divide  anymore? I don't know what to make of the premise then.

Conceptually, at least, there is no "smallest distance," so one may always divide any distance further, in feet or meters or whatever measure one uses (e.g., 0.00000000005 feet can be divided in half, for two measures of 0.000000000025 feet, which can be in turn divided in half, etc.).  So conceptually, length is infinitely divisible.  

What you can actually do, depends in part on what one means by that, and what measuring devices one has.  Certainly, you will run into a practically smallest length, beyond which you will not be able to measure.  If your measuring instrument is a ruler like schoolchildren typically use (or used to use), one will reach a practical limit before one would with whatever the finest measuring device is (assuming one knew how to use it).

I wish I could learn how to disect arguemnts. It would be so helpful.

If you live near a community college, you can enroll in a logic or critical thinking class.  The next term, you can also take an introduction to philosophy class, where people do analyze a variety of arguments.  Obviously, I cannot vouch for how good your classes will be, as it will be heavily dependent upon how good the teacher is, and that is quite variable.  Community College teachers can be great, terrible, or anything in between.

Now, if you want to study on your own, you can get a logic or critical thinking textbook.  Here is one that is good for a general reader (at least, earlier editions were good; I have not looked at the current edition at all):

http://smile.amazon.com/Logic-Contempora...0495804118

You do not need that edition; any of the earlier editions would be fine, and would probably be very cheap if you can find them, as they would not be used in a current class.

If you wanted to also include formal logic (which is unnecessary for your interests), the logic text Introduction to Logic by Irving M. Copi has been a standard for over half a century, and again, any edition would be fine.  If you were interested in formal logic, I would recommend Copi, as he properly explains material implication, unlike many other texts.  But I do not recommend trying to learn formal logic on your own, and recommend the book by Kahane instead for your purposes, if you cannot or will not go to a college to take a class.