So, the argument for the truth of the unobserved causal chain must be based on an analogy to some observed causal chain. The analogy will only work if the observed causal chain is isomorphic to the unobserved causal chain. Therefore, counterfactuals are claims about the isomorphism of an unobserved causal chain.
Exact isomorphism isn’t useful. The only things that’s exactly isomorphic to Viking colonisation of the US is
Viking colonisation of the US.
Usual disclaimer: there is no problem of counterfactuals in mainstream philosophy (only a problem of why rationalists see a problem). The following is a mainstream account not a novel theory:-
Any causal interaction can be understood as a token of a type. For instance, an apple falling from a tree is a token of the type “massive objects are subject to gravitational forces”. The type of a causal interaction defines a set of conditionals , and … this is the important part....not all of the conditionals can occur in a given token. The apple hits the ground first, or it hits Isaac Newton’s head first—it can’t do both. So a real counter factual is, very straightforwardly, a conditional outcome that didn’t occur in that particular token. But it’s still possible to make inferences about the non-actual conditionals , the counterfactuals of a causal token because they are inferred from the structure of the type.
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).
Exact isomorphism isn’t useful. The only things that’s exactly isomorphic to Viking colonisation of the US is Viking colonisation of the US.
Usual disclaimer: there is no problem of counterfactuals in mainstream philosophy (only a problem of why rationalists see a problem). The following is a mainstream account not a novel theory:-
Any causal interaction can be understood as a token of a type. For instance, an apple falling from a tree is a token of the type “massive objects are subject to gravitational forces”. The type of a causal interaction defines a set of conditionals , and … this is the important part....not all of the conditionals can occur in a given token. The apple hits the ground first, or it hits Isaac Newton’s head first—it can’t do both. So a real counter factual is, very straightforwardly, a conditional outcome that didn’t occur in that particular token. But it’s still possible to make inferences about the non-actual conditionals , the counterfactuals of a causal token because they are inferred from the structure of the type.
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).