Logic

[Tellos Athenaios]

Can someone please help me with this problem :P

Hempel's Criteria: Jus(E, H), evidence E justifies (Jus) hypothesis H.
1. Implication-condition: if E → H , then Jus(E, H) .
2. Consistency-condition : if Jus(E, H) and Jus(E, F), then H and F are consistent.
3. Special consequence-condition : if Jus(E, H) and H → F , then Jus(E, F).
4. Reversed Consequence-condition: if Jus(E, H) and F → H , then Jus(E, F).

As it stands here, for (3) and (4) to be true at the same time it must follow that H and F are logically equivalent. (H -> F && F -> H). Except that from F ->H we may not derive H -> F, and from H -> F we may not derive F ->H.

I.e.:

E
Jus(E,H)
F -> H
--------
E -> H
E
F -> H
--------
H
F -> H
--------

How do you get from there to “H -> F” ?