Any one thinks abstract objects exist. AO is really at center stage in contemporary philosophy. If people do not think AO exist, then they are nominalist. There are arguments for nominalism. The standard example of AO are numbers:

1) 7 is greater than 3.

What is interesting about 1 is that it has the same form as:

2) Kate is taller than John.

The standard reason for why 2 is true is because there are two things in the world( Kate, John), and they have a certain "relation" to one another that "makes" 2 true. The people that believes in AO thinks that we can analyze 1 in the same way that we analyze 2. That there are Abstract objects( 7, 3), and they have the "relation" of "greater than":

1.a) Objects := { 7, 3} // abstract objects
1.b) relation := { N, M..} // relationship between AO


In 1.b, the relations are N-tuples. The notation is N( *, * ) where the place with * stands for Ob.

The "reason" 1 is true is because it corresponds to objects( 1.a), and their relations( N, M..). The objects and relations are also know as primtives.They are concepts left over in explanation, but are themselves unexplained. They are "basic" in the sense that they are part of reality.

Can anyone find ways to reject the existence of objects( AO) and relations by reinterpreting 1 and 2?

---------- Post added 07-07-2009 at 12:01 PM ----------

Another example are computer programming codes. Programmers always write codes about objects, and methods( see object orientated programming). Do these programming constructs really exist, or do we invent it when we program. At the end, these things has to work together in a working program.