Damnit, I can't fix my spelling error in the title of the thread.

Our main question is: “Does an object (a table in this case) have an infinite length?”

Ok, so I’ve been thinking about this whole infinite thing. The best I can come up with is that there are basically three different logical arguments we could be looking at. All of these arguments seem to be false to me. I’ll go over those arguments and why they seem false. The first argument is this:

1. All distances can be measured infinitely. The length of this table is a distance. The length of this table can be measured infinitely.

Ok, let’s talk about this argument first. This argument is perfectly logical but is it true? It is true (as far as we know) that distance can be measured infinitely using that half, then half again thing. Is the length of the table a distance? As far as we know it is. The conclusion is drawn from the prerequisites without logical error. Since the two prerequisites are true (as far as we know) then the conclusion is also true. This is all well and good except that it doesn’t account for the main question. Saying that the table can be measured infinitely is not the same as saying that the length of the table is infinite. If we wanted to say that we need a different argument based on what we know; which brings us to the next argument.

2. All distances can be measured infinitely. The length of this table is a distance. The length of this table is infinite.

This, as far as I can figure, is the argument being used to describe the “infinite” length of the table. Here we have the same two prerequisites as the first argument. The difference lies in the conclusion we are drawing from those prerequisites. Now our argument directly relates to the main question. We have concluded in this argument that the length of the table is, in fact, infinite. However, is our logic flawed? Yes, indeed it is. The conclusion we have drawn makes a jump from the prerequisites. Based on those prerequisites we cannot logically come to the conclusion we have. Nowhere in the prerequisites does it talk about distance being infinite, only the measure of distance is infinite. The measurement of distance and distance itself are two different things. Like our first argument, this one also does not answer our main question.

3. All distances can be measured infinitely. If a distance can be measured infinitely then the distance is infinite. The length of this table is a distance. The length of this table is infinite.

This argument now accounts for our question in the most complete way. It has two of the same prerequisites as our first two arguments. Now we have a third prerequisite added in to account for the correlation between measurement and distance. The problem with this argument is: does the fact that we can measure a distance infinitely truly mean that the distance is infinite? Perhaps it does. If it did then this would then become an argument about philosophy and the physical properties of our world and our universe. As it is; we, as a people, generally believe that physical things are finite. Thus the statement “If a distance can be measured infinitely then the distance is infinite” is a fallacy. This is only a fallacy under the physical laws we have come to use to help us understand our world. Were we to accept different truths about the physical properties of our world then perhaps we could find a different answer to our main question.

*Fixed a spelling error