Common sense is something well known, logic in my opinion is basic reasoning which can be proven. You can have the false logic of "unicorns are real" but common sense tells you they are not real, and your eyes can see otherwise, though not everything you see is not 100% valid.
When you say common sense, what I think of is inductive reasoning. When you say "unicorns are not real", you are basing that off of numerous observations and experiences. You can't deductively prove that. Its just an observation.
In my opinion though, common sense can be deductive reasoning or inductive reasoning.
Prove that the sky is blue. People would see that as common sense and would have no idea how to prove that other than by numerous observations, but they are wrong. In order to deductively prove that, one would first have to understand what blue is, or understand the definition of blue. Then that person would look up to the sky. Finally that person would compare the color of the sky to his/her understanding of the meaning of blue. (I know that the sky isnt always blue, but you get the point)
All human observations and experiences have never involved a unicorn. There are numerous human observations and experiences. Therefore, unicorns don't exist.
---------- Post added at 03:02 PM ---------- Previous post was at 02:44 PM ----------
Back to my original post though. Why is a conditional proposition always true if the antecedent is false? To me, it seems like it is just a definition.
In my opinion, the conditional proposition shouldnt be true or false. How can one start with an illogical assumption and end with a logical argument and a logical conclusion. Propositions with false antecedents seem illogical and meaningless to me.
Can you prove to me the following: If two is odd, then two is even. Absolutely not!!! How can you say this is true if you dont even understand why it is true. The only way is by defining it to be true.
It is not common sense that a conditional proposition is always true if the antecedent is false. Common sense is something that the majority of the population knows and understands. Only logicians, philosophers, mathematicians, etc. know of this "illogical logic".