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I saw an explanation that said A -> B and A-some-> C = can conclude C -some-> B. Why is that and where can I find lessons on these types of conditionals?
1
I saw an explanation that said A -> B and A-some-> C = can conclude C -some-> B. Why is that and where can I find lessons on these types of conditionals?
1 comments
It's in the "Foundations" section of the core curriculum, in the lesson "Logic of Intersecting Sets". An example of this valid form would be "Some pets are mammals. All mammals are animals. Therefore, some pets are animals."
Be careful with this one because the "some" relationship has to come "before" in the conditional chain to be valid. A not valid argument form would be: (A -> B <-s-> C, therefore A <-s-> C). An example of this dubious argument would be "All dinosaurs are reptiles. Some reptiles are pets. Therefore, some dinosaurs are pets."
The intuition is that unless specified, dinosaurs are just one of many sufficient conditions that could "arrive at" reptiles and so you don't know if the "some" reptiles that are pets, are the same "some" reptiles that are dinosaurs. If you replaced "dinosaurs" with "iguanas", the premises and conclusion might all be true, but the key is that the structure of the argument does not have to be true. Valid argument forms are all forms that guarantee that a true conclusion follows from the premises.