To get a similar result, it'd be as if "Colorless green ideas sleep furiously" turned out to accurately describe ideas, without modifying the terms.
i.e., if it turns out ideas and "green" operate in the same locations in the brain, and if you exhibit anger + sleep patterns of thought while brainstorming.
Hm, it's not productive to argue over analogies. They're just used to illustrate a point. I was saying math was explicitly designed to work & to be general. Likewise words were designed for communication (not just for describing the real world), & I'd say that sentence communicates your meaning very well.
eg later he says:
>"Is it not remarkable that 6 sheep plus 7 sheep make 13 sheep; that 6 stones plus 7 stones make 13 stones? Is it not a miracle that the universe is so constructed that such a simple abstraction as a number is possible? To me this is one of the strongest examples of the unreasonable effectiveness of mathematics. Indeed, l find it both strange and unexplainable. "
That makes absolutely no sense. You might as well wonder why the word "wheel" describes wheels. Or wonder why wheels exist. These are empirical facts.
It's right there on the top: "It is evident from the title that this is a philosophical discussion". In case you aren't interested in philosophy, I don't see why bother reading the article and commenting on it -- unless perhaps you want to say something against doing any philosophy in the first place.
But if you are interested in philosophy, then you should know that the philosopher often starts by wondering about something that most sane people take for granted. Case in point, some people do wonder why the word "wheel" describes wheels. There are tons of papers and books about philosophy of language.
Others ask why wheels exist, what is a wheel, or whether do they really exist at all. You can only be sure that the existence of wheels is an "empirical fact" after you have examined these questions. After all, "empirical fact" is a philosophical term.
Incidentally, "6 sheep + 7 sheep = 13 sheep" is not an empirical fact.
Prefacing an article with "this is a philosophical discussion" is not an excuse to stumble through nonsense like a drunken sailor staggering home. Similarly if I preface this post with "I don't mean to be rude" only to continue to slander and defame, I've not excused my actions.
Counting is defined by objects, and 13 is the sum of 6 and 7. Indeed it is an empirical fact in as much as it has a physical interpretation.
> Is it not remarkable that 6 sheep plus 7 sheep make 13 sheep; that 6 stones plus 7 stones make 13 stones?
Personally, I find it rather remarkable that a pattern observed from pebbles, sheep or apples (i.e., 6 + 7 = 13) should hold for any set of discrete objects anywhere in the universe. It could well have been that, say, 1 apple + 1 apple = 2.5 apples, but 1 kitten + 1 kitten = 1.5 kittens.
It doesn't hold for loads of things. 1 heap + 1 heap = 1 heap. 1 bunny + 1 bunny = 12 bunnies, depending on how fast you are with your observing. 1 dl of ethanol + 10 dl of water < 11 dl of diluted alcohol.
Mathematicians still are split into formalists, realists, intuitionists and logicists, debating around the nature of mathematical truth; i. e. does mathematical truth pre-exists (and is just "discovered") or is it a human invention? Good luck sorting this one out!
Interesting. So are you so down-to-earth that you consider philosophical speculation on the nature of mathematics (or anything else, I suppose) to be nonsensical?
Don't make this about me. Read the history of math & tell me what conclusion you come to when you see people making algorithms, essentially, for dealing with natural processes.
Of course, as long as you stay in the realm of measurable things. However, we still need to explain how and why the perfect abstract mathematical objects are of any use in the real world (as opposed to other abstract objects such as patonician ideas, or more commonly gods).
>(as opposed to other abstract objects such as patonician ideas, or more commonly gods)
Well neither of those two deal with counting... We already know (historically, empirically) that counting & manipulating 'stuff' is what works for making applicable theories. Mathematical abstraction preserves those "traits", & makes the object more general - ie more flexible. Chess for example is about counting, but it's not explicitly written in a form that allows you to drop it in a theory.
I think the important thing is the traits aren't arbitrary. They were forced on people, eg you need to learn counting if you want to keep track of your goats.
i.e., if it turns out ideas and "green" operate in the same locations in the brain, and if you exhibit anger + sleep patterns of thought while brainstorming.