Tuesday, May 02, 2006

Maybe we are on the wrong track assuming that definitions should have anything to do with physical characteristics.

Can we not define things that do not have physical manifestations? We can define a thought, or a concept, I could give a definition of an "argument" which certainly has definite properties (reaches a conclusion, presents a point of view, should be valid...) but has no molecules or anything like that


Blogger Joel K said...

When dealing with definitions you I feel have to include both the concrete and abstract. Some things are going to be defined with physical traits and others are goingd to be defined by thoughts, or ideas. For some both can be done.
But we can just look at everything abstractly.

8:21 PM  
Blogger linford86 said...

I would argue that to define form, this is exactly what you have to do. That is, form is an abstract characteristic of an object.

However, in the philosophy of mathematics, there is an idea known as physicalism, which holds that in order for a mathematical statement to refer to anything, it must refer to something physical. So, for instance, (according to physicalism) the only reason that it is the case that "1+1=2" is because when you have a collection of physical objects, and you have one object, and then another object, you end up with a collection that contains two objects. Such a philosophy would also hold that there is no such thing as the abstract - or that at the very least any abstractions at all that can be allowed to exist must refer to physical objects. However, such a philosophy leads to statements such as: spheres don't exist because nothing is "perfectly" round; irrational or imaginary numbers do not exist; and so forth. No mathematician in his or her right mind would be comfortable with those statements. In fact, most mathematicians hold the view that mathematical statements are almost exclusively made about things which do not appear in physical reality. The most trivial example is the existence of numbers: no matter where you look in the universe, you will never find a number. You will find numbers of objects - it's possible to have 2 apples for example - but its not possible to find numbers, themselves - try showing me what "2" looks like (you can't - the best that you can do is write the symbol that we use to represent "2"; but that only tells me how it is that we refer to it, not what it actually looks like.) As Einstein once said, "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." That is, we can never be certain that our mathematical descriptions of reality are accurate, and whenever we are sure about something in mathematics, it is a statement about abstract entities.

1:03 PM  

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