Quote:
Originally Posted by lastcardcharlie
In other words, what is the realist position on the ontology of units of measurement?
The distance between any 2 points is infinitely divisible. However you choose to divide that distance there will be counting/numbers involved. Numbers are universals.
The distance between two particulars (e.g., two separate trees 1000's of km's away) relates them together and can apply to any two particulars, and as such, can also be considered a universal (Kant disagrees here and considers distance/space and the existence of space as entirely dependent on mind).
If it helps let's look at an example discussed in The History of Western Philosophy.
2+2 = 4
In this mathematical example, both 2's are universals. The addition (+) is also a universal but not of the same type. The addition is a
relation that relates one universal (2) with another (2). 4 is the sum of the relation between one universal and another. The sum between these two universals will always be 4. The sum is considered 'new knowledge' created from a "
relation between universals".
This 'new knowledge' created out of the relation between universals is a special type of knowledge: a priori knowledge.
If we were to instead say that Sue and Sally...added to Bob and Joe makes Sue, Sally, Bob and Joe the 'new knowledge' is the sum: Sue, Sally, Bob and Joe. However, this is new knowledge is empirical knowledge, since it includes particulars (particular people that exist in the world with those names).
Bertrand Russell, amongst many, believes that mathematical knowledge, like all a priori knowledge, is knowledge solely derived by the
relations between universals. Empirical knowledge, on the other hand, always requires a particular.
Universals
have being independently of the mind, and independently of the physical world/space-time. Particulars exist in the world, in the sense that a tree or a colour or a person exists. As such, universals are said to have
being instead, since they do not exist in the same sense as particulars. Since they do not exist in space-time, nor in the mind, they must have being somewhere...? No one knows where.
What we do know about
the being of universals is that it is unchanging/eternal. For example: we may not know empirical knowledge about the future, but we can know a priori knowledge about it. We may not know how many people will live in your suburb or city 100 years from now, but we can know that if there are any 2 people who are added to any other 2, that will make 4 people. How we can know this about the future is a question that's puzzled many philosophers, especially Kant. Universals provide the answer.
Last edited by VeeDDzz`; 07-07-2017 at 10:58 PM.