In our continuing exploration of the wonderful world of formal logic, I bring you: unless.
But this time, you have to work it out for yourself via this real world example:
I refuse to keep writing formal logic blog posts unless some of you post comments telling me that you’re finding these helpful. 😉
A Quick Challenge
Your challenge is to figure out how to translate the statement above into a standard if/then form. Here are some questions to ponder as you work through this one:
What can you be absolutely sure of if…
— I refuse to write another formal logic blog post?
— one person posts a comment telling me he/she finds this post helpful?
— I write another formal logic blog post?
— two or more people posts comments telling me they find these posts helpful?
— no one posts any comments at all?
The truth of one term is sufficient to deduce the truth of the other term. The truth of that other term is necessary, but not sufficient, to deduce the truth of the former. But can you tell which is which?
Think through the answer to each of these questions. Then, on your own, try to determine whether the statement, “A unless B” is logically equivalent to “if A→ B”. If so, that’s conveniently simple. If not, then how do you translate “A unless B” into a standard if/then form? And what is its contrapositive?
Lastly, which term is the trigger in the statement “A unless B”? And what is the trigger in the contrapositive?
When You’re Done
Once you’ve spent some time working on this one, post a comment with your answer or check back soon for an explanation.
Happy studying! 🙂