See the first few chapters of Godel, Escher, Bach for a good primer on formal systems. The upshot is that a formal system is a set of symbols and some rules describing what combinations of symbols are in the formal system (theorems) and which are not. Formal systems may map onto predictions about reality (for instance the Natural numbers 0 .. infinity are composed of the symbols for those numbers and the rules of multiplication, division and subtraction with the caveats that certain divisions and subtractions are undefined (like 7/5 or 5 -7), it so happens that this system corresponds to counting things like desks and so we can use it to make predictions about desk-counting that work out).
To reason is to form a formal system and apply it to reality and to discard it or change the way it fits with reality when it fails to reflect the behavior of some phenomenon in the world.
This kind of reasoning won't get us far but I am afraid it is all there is. If we really want to talk about it, I can review formal systems more carefully over 3-4 posts. I could use the review
Wikipedia: Formal System
No comments:
Post a Comment