My take on modern Platonism is that abstract objects are considered the only real (fundamental) objects. Abstract objects can’t interact with concrete objects, because concrete objects don’t actually exist!
This isn’t modern Platonism.
Example of concrete mathematical objects: Software
A program is an abstract object. Particular copies of a program stored in your hard drive, are concrete.
Ok, then its Geddesian Platonism ;) The easiest solution is to do away with the concrete dynamic objects as anything fundamental and just regard reality as a timeless Platonia . I thought thats more or less what Julian Barbour suggests.
A program is an abstract object. Particular copies of a program stored in your hard drive, are concrete.
The actual timeless (abstract) math objects are the mathematical relations making up the algorithm in question. But the particular model or representation of a program stored on a computer can be regarded as a concrete math object. And an instantiated (running) program can be viewed as a concrete math object also ( a dynamical system with input, processing and output).
These analogies are exact:
Space is to physics as categories are to math
Time is to physics as dynamical systems (running programs) are to math
This isn’t modern Platonism.
A program is an abstract object. Particular copies of a program stored in your hard drive, are concrete.
Ok, then its Geddesian Platonism ;) The easiest solution is to do away with the concrete dynamic objects as anything fundamental and just regard reality as a timeless Platonia . I thought thats more or less what Julian Barbour suggests.
http://en.wikipedia.org/wiki/Platonia_(philosophy)
The actual timeless (abstract) math objects are the mathematical relations making up the algorithm in question. But the particular model or representation of a program stored on a computer can be regarded as a concrete math object. And an instantiated (running) program can be viewed as a concrete math object also ( a dynamical system with input, processing and output).
These analogies are exact:
Space is to physics as categories are to math
Time is to physics as dynamical systems (running programs) are to math
Matter is to physics as data models are to math