Are types also tokens of types? And can we not and do we not have counterfactuals of types?
I’m not a type-theory expert, but I was under the impression that adopting it as explanation for counterfactuals precommits one to a variety of other notions in the philosophy of mathematics?
Maybe. But what implications does that have? What does it prove or disprove?
Edit:
We tend to think of things as evolving from a starting state, or “input”, according to a set of rules laws . Both need to be specified to determine the end state or output as much a it can be determined. When considering counterfactuals , we tend to imagine variations in the starting state, not the rules of evolution (physical laws). Since if you want to take it to a meta level, you could consider counterfactuals based on the laws being different.
But why?
I’m not a type-theory expert, but I was under the impression that adopting it as explanation for counterfactuals precommits one to a variety of other notions in the philosophy of mathematics?
I wasn’t referring to the type/token distinction in a specifically mathematical sense...it’s much broader than that.
Everyone’s commited to some sort of type/token distinction anyway. It’s not like you suddenly have to by into some weird occult idea that only a few people take seriously. In particular, it’s difficult to bring able to give an account of causal interaction s without physical laws …and it’s difficult to give an account of physical laws without a type/token distinction. (Nonetheless, rationalists don’t seem to have an account of physical laws).
Are types also tokens of types? And can we not and do we not have counterfactuals of types?
I’m not a type-theory expert, but I was under the impression that adopting it as explanation for counterfactuals precommits one to a variety of other notions in the philosophy of mathematics?
Maybe. But what implications does that have? What does it prove or disprove?
Edit:
We tend to think of things as evolving from a starting state, or “input”, according to a set of rules laws . Both need to be specified to determine the end state or output as much a it can be determined. When considering counterfactuals , we tend to imagine variations in the starting state, not the rules of evolution (physical laws). Since if you want to take it to a meta level, you could consider counterfactuals based on the laws being different.
But why?
I wasn’t referring to the type/token distinction in a specifically mathematical sense...it’s much broader than that.
Everyone’s commited to some sort of type/token distinction anyway. It’s not like you suddenly have to by into some weird occult idea that only a few people take seriously. In particular, it’s difficult to bring able to give an account of causal interaction s without physical laws …and it’s difficult to give an account of physical laws without a type/token distinction. (Nonetheless, rationalists don’t seem to have an account of physical laws).