In my humble opinion people spend little time concerning themselves with the question of the meanings of words. Somehow everyone seems to believe that words themselves have meaning; that the meanings they personally attribute to these words are identical to the meanings others attribute to these self same words. If that were the case, languages would be static and unchanging. When one gets as old as I am the change in meanings of many words becomes quite obvious. In many cases, the younger generation has utterly no idea of the meanings of words held by their elders and vice versa.
It may seem that this harangue has little to do with the discussion postulated by this thread but it actually has a lot to do with the issue. Before one can even begin to discuss the question, “Did we discover or create it?”, one needs to first define mathematics. Now I have no idea as to what the posters intend to mean by the word because they have made no effort to tell me. I only know what I mean by the word. Long long ago, I defined mathematics (in my mind) to be the invention and study of internally self consistent systems. Self consistent systems are epistemological constructs which lack any contradiction.
Do self consistent systems exist before we invent or discover them? Well of course they do; we don't invent self consistent systems; what we invent are the representations as, without a way of representing them, we certainly cannot study them. So the answer to the question becomes quite clear, we discover or create representations of self consistent systems so that we can study them.
This brings up another issue often brought up by professional scientists. Why does the universe seem to be bound by so many “mathematical” relationships? The answer should be clear to any thinking person. If mathematics is the invention and study of internally self consistent systems then any usable explanation of anything is indeed a mathematical expression (if the mental model underlying that explanation is not internally self consistent, it fails as an explanation: i.e., it yields inconsistent answers).
What is commonly referred to as “mathematics” are those constructs sufficiently complex to be held as “not obvious” and yet strongly established as “internally self consistent”. A number of years ago I posted a thread pointing out the difference between two very important mechanisms of thought which I called “logical thought” and “squirrel thought” which seemed to fall on deaf ears.
Logical thought has the advantage that the conclusions are absolutely as valid as the axioms (being logical, it is internally consistent); however, it has the problem that, sans mathematics, it is inherently limited to but a few steps.
Squirrel thought (and you need to understand my definition of “squirrel thought”) has the advantage that it is a holistic approach bringing to bear a lifetime of experience thus providing us with quick solutions to problems far to complex to even begin to analyze analytically; however, it has it's own flaw: it cannot be checked and thus must always be taken with a grain of salt as all squirrel decisions can be erroneous.
If you are interested in thinking, you might peruse the thread.
Quote:
Originally Posted by Doctordick
This is, in fact, the single biggest problem in trying to understand the universe. Most everyone believes the ideas they have arrived at via their personal squirrel decisions are the only possible conclusions which can be reached. The reader should understand that "belief" of anything is a squirrel decision. The ability to communicate (language itself) was acquired through squirrel thought. Accept your squirrel decisions as your best bet when it comes to any serious question, but don't ever think that those squirrel decisions are infallible. You don't have to believe they are infallible before you can follow them; when it comes to life, "you pays your money and you takes your chances".
On the other hand, if you want to do science, you should remember that even your most cherished squirrel decisions could be wrong. Even you guys who are not "crackpots" should remember that. A lot of science is done in the total absence of logical thought and that has to be so; but scientists should not forget that fact. If they do, science folds over to religion. It may work great, but that does not mean it is valid. Think about that next time you see a "poor squirrel decision".
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Have fun -- Dick
