Definition 1: A number is composite if it is a product of two numbers other than 1 and itself.
Definition 2: A number is prime if it is not composite.
Thus prime numbers are defined in terms of negation. Philosophically, I can attribute a negation to something negative. Thus primes are negatively defined. They are in the 'background' of composites. Can primes be positively defined ? It turns out that primes can also be positively defined. And it appeals to our logic that anything that can be negatively defined can also be positively defined.
As another example consider the following Figure 1.
Definition 2: A number is prime if it is not composite.
Thus prime numbers are defined in terms of negation. Philosophically, I can attribute a negation to something negative. Thus primes are negatively defined. They are in the 'background' of composites. Can primes be positively defined ? It turns out that primes can also be positively defined. And it appeals to our logic that anything that can be negatively defined can also be positively defined.
As another example consider the following Figure 1.
Figure 1
There is moon and the background space. When I look at the moon, I say it is positively defined (as it looks like moon is the major theme of Figure 1) and the background space gets characterized. But one can reverse the roles and say the space is positively defined (by looking at the space) and the moon gets negatively characterized. It perfectly appeals to our logic that we can look the picture either way. So, it seems logic (hence mathematics) and arts are 'natural systems' in which one can define things in one way and the 'background' gets characterized. But, life is not that simple. Even within the realm of logic not all the 'background' things gets characterized if we positively define something. In other words, there are things that can be positively defined but the negative space cannot be characterized in anyway. An analogy in arts is given by this picture.
Figure 2
Can you distinguish the background in the above figure?
I could appreciate much more beauty in this. I am sure the second pic will appeal special to almost all the people as the reason being 'foreground and the background are the same'. In other words, it appeals special to us because it is both positively and negatively defined 'equally'. While our logic naturally proposes that something that can be positively defined can also be negatively defined, this picture should not have something 'special' in it. Or to put it in a different way, if the special appeal comes because of our natural logical perception, Figure 1 should be even 'more special' because it defies our logic. So take your stand, which is more 'special' - Figure 1 or Figure 2 ? ! Doesn't this draw a line between thought and reason ?
Figure 2
Can you distinguish the background in the above figure?
I could appreciate much more beauty in this. I am sure the second pic will appeal special to almost all the people as the reason being 'foreground and the background are the same'. In other words, it appeals special to us because it is both positively and negatively defined 'equally'. While our logic naturally proposes that something that can be positively defined can also be negatively defined, this picture should not have something 'special' in it. Or to put it in a different way, if the special appeal comes because of our natural logical perception, Figure 1 should be even 'more special' because it defies our logic. So take your stand, which is more 'special' - Figure 1 or Figure 2 ? ! Doesn't this draw a line between thought and reason ?
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