Most theories have counter examples if you look hard enough. Try going really fast and you will break most physics done earlier than Einstein. This is not to say that Newtonian mechanics is ‘wrong’ any more than relativistic mechanics is ‘right.’ Rather, Newtonian mechanics looses it’s usefulness for speeds close to that of light. It is no longer an appropriate abstraction. We always throw out information when we do science – or else we would just be concerned with tracking the state and behaviour of the most reduced aspects of the system we can find.

I suspect I know much less about the philosophers who concerned themselves with such things than you, but hopefully the following idea helps:

The real world is not a formal system. In a formal system we rigorously define truth values, and operations on those truth values. We operate by deductive logic, given a set of axioms. The real world is not amenable to such a treatment because the list of axioms that we take for granted is subjective. Whereas in a formal system, we can define axioms to be whatever we like and we get some interesting mathematical structure as a result; the axioms we choose for the real world have to do double duty – at once they need to spawn the things we want to believe about the world, and they have to be accurate in an endless number of ways with regard to the real world themselves. You can thus argue, subjectively, about what axioms are ‘right’ in the real world, whereas in a formal system you accept some things as right and observe the consequences – different axioms give rise to interesting and diferent logical structure.

Many apologies if this wandered. Maybe one should refrain from philosophy of science at 2 am?

I liked the article, not many want to communicate logic and science to the general audience. kudos.

Josh

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