1) The map/territory tool can be used more extensively. Let us take the territory as fairly ‘unknowable’ except that using our map, we can make predictions. If our predictions are wrong then we assume that is a failing in our map and we try to repair the map. Math is a tautological system that has not failed us yet and we use it as part of the map. If it did fail us, we would change it or abandon it from the map. We think the chances of this are vanishingly small.
2) We can construct enlargements to Math tautologically. I think of this as invention but discovery is OK if it pleases. They are enlargements of the map and not objects in the territory. There is a danger in treating Math objects as part of the territory—an infinite regression of maps of maps of maps.....of territory.
3) The reason we invented Math originally and the reason it maps the territory so well are both because its roots are in the structure of the brain and the brain has evolved to do a good (passable) predictive model of reality (or map of the territory).
Please carry on with your investigation of the subject and post on it again.
This was a great post.
Some observations:
1) The map/territory tool can be used more extensively. Let us take the territory as fairly ‘unknowable’ except that using our map, we can make predictions. If our predictions are wrong then we assume that is a failing in our map and we try to repair the map. Math is a tautological system that has not failed us yet and we use it as part of the map. If it did fail us, we would change it or abandon it from the map. We think the chances of this are vanishingly small.
2) We can construct enlargements to Math tautologically. I think of this as invention but discovery is OK if it pleases. They are enlargements of the map and not objects in the territory. There is a danger in treating Math objects as part of the territory—an infinite regression of maps of maps of maps.....of territory.
3) The reason we invented Math originally and the reason it maps the territory so well are both because its roots are in the structure of the brain and the brain has evolved to do a good (passable) predictive model of reality (or map of the territory).
Please carry on with your investigation of the subject and post on it again.