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Hi Paul,
I will post my answer here as your last post includes a reference to the other one.
With all due respect, I think you are wrong. There is a clear answer to the question "one plus one what?", and the answer is "one plus one things". And I'm still within the domain of mathematics whether I tell you what the things are or not.
I think humans are a very confused bunch. We learn some basic things when we are very young, then as we grow up we forget how it is that we know those things, and as a result we tend to somehow mystify the nature of our knowledge. But think about it and tell me how it's possible that you know how much is "one plus one". As far as I can tell, there are only two possible ways: either you figured it out by yourself, or somebody told you. However, we can discard the second option right away, since in order for anyone to tell you they would first have had to figure it out by themselves. So there's actually only one possibility: people figure it out by themselves.
Now the question is, how do people do it? If you have no knowledge of math at all, how can you possibly learn what "one" and "plus" mean?
I contend that the failure to entertain that issue, which you clearly take for granted, is what is behind your assertion that math is not about reality.
As a final comment:
As soon as you ask "What?" you are casting about outside the domain of mathematics. As soon as you answer "What?" with something real, like an apple, you have established part of the isomorphism I talked about and you are no longer in the domain of mathematics. At this point, you are doing science.
What if instead of apples I answer the "what" question with "flying saucer", "angel", or "Loch Ness monster"? When I add one flying saucer and another flying saucer, do I still get two flying saucers, and am I now doing science?
Thanks for some thought-provoking posts.
Best regards...ML |
