From: David (firstname.lastname@example.org)
Date: Fri Aug 13 2004 - 08:56:33 MDT
The time spent in reply to my post by Paul Fidika was much appreciated, however I do take exception to a few points.
[mathematical statements are entities in and of themselves which exist in a "Platonic realm" in the sense that they are either as objectively true or false as anything in our universe can be objective]
Non physical things can exist without existing in the same sense the universe, planets, people etc exist. A set of instructions has no physical existence but to say that they don't exist would be wrong. The word exist can mean things that physically exist or not but to mix the two, or say that there is an equivalence is obviously wrong. How do you compare an apple to an orange? The idea of existence is not just a label in our mind. If it was then physical things would exist exactly like non physical things. (and in the same sense) However, there is an existence that is physical and fundamentally not the same as non physical entities. Existence is not just a label created in our minds.
[When the people on this list (as far as I can determine) say that "All is number", they mean that a piece of Mathematics exists, in the strongest sense of the word "exists", regardless of whether or not someone has discovered it. To me, this is simply an "obvious" truth]
Even if "exists" in this context doesn't mean physically existing, to assert that "All is number" is obviously un-provable. How can you test infinite entities (most of which you don't know) and determine that they are all "number"? To suggest that "a piece of Mathematics exists" seems to be a huge leap of faith, unless you just define Mathematics to be everything. If I define all colors to be black, then only one color would exist. I have programmed as a profession since 1976 and I have used almost no Mathematics. I have a minor in Math from University and have rarely used anything more than grade 12 algebra in my career. The essence of programming is to determine patterns so you can use the looping mechanism of the computer to do more than what you can code in a line. If a computer program doesn't loop, then it would be over almost immediately and would produce very little work. I am not saying that patterns are not used in Mathematics but in my experience looping is not part of Mathematics. (If it is used in some small way, it was probably borrowed from Computer Science.) All my adult life, I have seen Mathematicians look down their noses at the Computer Science people when it comes to designing systems. I had a partner for 8 years who was a senior full professor at a University with 20,000 students. He has written a number of Mathematical books and at least 15 years ago, was the most quoted professor in Lattice Theory in the world. I have entertained first class Hungarian Mathematicians in my home but I definitely don't call myself one. All of these people (even though they don't know it) have absolutely no clue what it takes to make a good programming system. They are absolutely 2 different fields requiring very different skill sets. To call Computer Science just another branch of Mathematics is a slap in the face to all those like myself who profess to quite a lot about Computer Science and not so much about Math.
If you still just define Mathematics to be everything, I guess we have to agree to disagree.
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