Let's just say we have an implied premise:
2.a Socrates is a philosopher (implied premise), but not explicit
Then is the following a formal fallacy?
- Socrates is a man.
- All men are mortal.
- Socrates is a mortal philosopher.
If it is, then you would have to say that the following is a fallacy too because some premises are implied and not express:
- John likes playing football
- John's friends also like playing football
- John plays football with his friends.
- John plays football because he like to.
- John's friends play football because they like to.
- John and his friends play football together.
Or to make it simpler, the following would also have to be a fallacy:
- My dog is happy when I look after him.
- I always look after my dog.
- Therefore my dog is happy.
2.a My dog is not happy when he injures himself (implied premise).
It seems to me that if implied premises don't count in the construction of a valid conclusion, then nearly every system of arguments is a fallacy because all information and premises are hardly ever given. So what about the Socrates example?
Edit: Sorry for making this long, but if implied premises can count, then there can't be fallacies:
- If P then Q
- Not P, therefore not Q.
1a. If M, then Q.