M: Being a Man

V: Being Valiant

F: Faith in a higher Power

1. If M is true, V is true
1.a If V is false, M is false
2.  F = V.

Combining 1 and 2
3. If M is true, F is true.
For Carlyle it is not just if you are a Man you are valiant, but if you are Valiant therefore you are a Man.

4. If V is True, M is true.
Combining 2 and 4, this means that If F is true, then V is true which means M is true, so F being true is a triggering condition for Manliness.

Conclusion: If one of these is true, all the others are true. Therefore only one needs to be true, and therefore any can act as the triggering condition for the others.

Rosen would dispute proposition 4 (and possibly proposition 1 and 2). Rosen believes that Manliness leads to Belief in Truth
i. M -> F     [If M is true, F may become true]

Rosen does not have any triggering conditions for Manliness, rather Manliness is the Triggering Condition for Valour.

If M is true, F may be true, which means that V is true. Therefore you can start with M being True, and arrive at F is true and V is true. However he doesn’t believe that V or F being true leads to M being true automatically.