by Gord (Posted Mon Dec 02, 2013 6:02 am)
It's important to a philospher to define things in such a way as to support the importance of philosophy. But it has no effect on reality. In the reality where most of us live our everyday lives, the written number is the number itself. The number is a concept, and the writing confers that concept.
The written word "elephant" exists as certainly as an elephant exists. They both confer the concept of "elephant", and are interchangeable in that regard. As it exists in a physical form and conveys the concept of "elephant", it is the equivalent of being an elephant for many purposes. If I hold up a picture I drew of an elephant and said, "This is an elephant", it would be correct -- whatever confers the concept of "an elephant" is for that purpose an elephant.
The things you do in your mind are as physical as the things you write down on paper. They exist physically, just like writing exists physically.
Math as we know it exists because of our minds. This is demonstrable by the fact that different minds have created different forms of math. 2+2=4 is only true if someone is there to count forms they delineate from their surroundings. The universe itself does not perform the "edge detection" we do when we perceive one thing being separate from another thing. For example, if you take one big rock and split it in half, you have two rocks. To the universe, it doesn't matter; what existed before exists still, simply in a different arrangement.
In a universe with only three rocks, you can't take anything away. Matter cannot be created or destroyed. Neither can the rocks be counted, as there is no mind in the universe to count them. The matter in the universe can be rearranged so that an imaginary "outside mind" would consider there to be any given number of rocks, but to the universe itself, counting is an irrelevance which does not exist.
Mathematics is a language designed to describe the universe. That it does so should come as no surprise, since we've designed it that way.
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A Cup of Skepticism wrote:As far as the mathematical tangent, it's important to properly define what a number is.
It's important to a philospher to define things in such a way as to support the importance of philosophy. But it has no effect on reality. In the reality where most of us live our everyday lives, the written number is the number itself. The number is a concept, and the writing confers that concept.
The things we write down are not numbers themselves but mere representations of numbers. Like the word "elephant" represents that big gray mammal with tusks. Notice that the word and the animal are qualitatively two very different things. To say what we write down are the numbers themselves is to say that the word "elephant" is an actual elephant. This is a mistake, in my view.
The written word "elephant" exists as certainly as an elephant exists. They both confer the concept of "elephant", and are interchangeable in that regard. As it exists in a physical form and conveys the concept of "elephant", it is the equivalent of being an elephant for many purposes. If I hold up a picture I drew of an elephant and said, "This is an elephant", it would be correct -- whatever confers the concept of "an elephant" is for that purpose an elephant.
Rather a number is a non-physical entity with which we can do mathematical operations. It's non-physical because we (or at least I) can do basic mathematical operations entirely in my mind, without writing it down. Indeed in a world without writing, mathematical operations still work perfectly fine, so numbers must be non-physical.
The things you do in your mind are as physical as the things you write down on paper. They exist physically, just like writing exists physically.
Moreover, I think these mathematical operations are not invented, or created by the mind, they are discovered. This is because if math were created by the mind, then different minds would create different math. And just like subjective creations can be changed, mathematical operations and values would be mutable. But math can't be changed. 2+2=4 is true, even if there are no minds in the universe, or there are minds but none of them agree that 2+2=4.
Math as we know it exists because of our minds. This is demonstrable by the fact that different minds have created different forms of math. 2+2=4 is only true if someone is there to count forms they delineate from their surroundings. The universe itself does not perform the "edge detection" we do when we perceive one thing being separate from another thing. For example, if you take one big rock and split it in half, you have two rocks. To the universe, it doesn't matter; what existed before exists still, simply in a different arrangement.
For these reasons, I think mathematical objects are non-physical and independent of minds. In a possible world where only three rocks existed, take away one rock and only two rocks would remain, whether or not there was a mind in that universe to do the math.
In a universe with only three rocks, you can't take anything away. Matter cannot be created or destroyed. Neither can the rocks be counted, as there is no mind in the universe to count them. The matter in the universe can be rearranged so that an imaginary "outside mind" would consider there to be any given number of rocks, but to the universe itself, counting is an irrelevance which does not exist.
Mathematics is a language designed to describe the universe. That it does so should come as no surprise, since we've designed it that way.
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