Counting to infinity pt2

Next he showed an example of what he called a non countable infinity. His example was the set of real numbers from 0 out to infinity, which includes all of the irrational numbers, things like fractions, and decimals. He asserted that this was a non countable infinity simply because there was an infinite possible amount of irrational numbers between each whole number. If you started at zero, no matter how long you counted for, you would never ever even make it to the number one.

Actually, I agreed with him about this one. This was an example of it being impossible to count to infinity. But, my original assertion was that it was not possible to count to infinity at all. And he never did anything to prove or disprove that. He totally ignored it and just said that the "normal" infinity had been redefined by mathematicians as countable.

As far as grammar and word usage actually goes, his first example basically defined countable infinity by saying it was simply infinity. He might as well have defined a chair by saying that a chair is a thing that you use for a chair. Then he went on, for his second example,  to say because this infinity has an infinite amount of infinities within it, it cannot be counted.

I pretty much told him so and at this point he began to get frustrated. He then proceeded to make several disparaging remarks about how I was not a mathematician and as such was more or less not equipped to understand. The sad fact is, I did understand. I just completely disagreed.

Regardless of whether or not one mathematician or a million tells me that there is an infinity that can be counted to, it does not change the fact that the very definition of the word infinity proves their assertion to be false. All infinities are limitless. None of them can ever be counted, whether there are an infinite amount of infinities nested within them or not.

The only difference between the first and the second example he provided to me is that on one of them you would be making progress in whole numbers and on the other you would never reach the next whole number. With both you would die thousands of years before even making a small dent in the work of reaching towards the far end of the endless stream of numbers. I did not disagree with him that they were different. I just disagreed that either one could be counted.

My primary beef with the conversation wasn't his fault at all. Well it sort of was but not really. The problem I had with what he was saying was the nomenclature being used. Now he did not come up with the jargon that he was using. But he did choose to use it around people that were not mathematicians. And even though the jargon chosen for this particular thing was actually completely ridiculous to the lay person, he did nothing to fight against it or to attempt to change it.

I can sort of understand him not wanting to argue semantics with the people teaching him, sort of. But when speaking to people that know nothing of math, using mathematical terms that directly disagree with common grammatical practices without precluding his statements with something to the effect that he realizes that the choice of jargon flies in the face of what the individual words actually mean was stupid. And it made him look like an idiot to every other person in the room. He isn't though. He is one of the smartest people I know.

This whole argument/debate could have been completely avoided. He could have said there is the normal infinity that everyone knows about including all the whole numbers from 0 to infinity. Next he could have talked about the infinity that includes both sides of the number line, positive and negative whole numbers from 0 to infinity. He could have described this as the integer infinity. He could have applied the adjective rational to both of these to show that they included only whole numbers. And finally he could have said that if either of them included fractions or decimals that the the adjective irrational would be applied instead of rational.

I am not a mathematician. I am a philosopher. Words are my tools and my weapons. There may be and probably are more infinities but simply mentioning these in this fashion would not have caused an argument. Mathematicians are very often brilliant people. Many of the things they have done have massively improved life for the rest of us. But when it comes to naming conventions for the new things that they discover, they are either idiots or so blinded be their current discovery that they just latch on to whatever seems appropriate at the time and stick with it as the "new" name for a thing and logic be damned.

He was arguing math. I was debating logic. Who was crazy? Who was right? Who is to say?