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:
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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…
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— 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.
And if you missed the posts on If/then statements and contrapositives, or alternate forms of if/then statements, check those out now for more help with the unless challenge.
Happy studying! 🙂
-No B (some DIDN’T post comments)
-no A (because B did occur once)
-B (indicates B occured)
-no A (Travis didn’t refuse because comments were posted)
-A (Travis refused because B didn’t occur)
Nice work, Hans! One small clarification:
If I refuse to write another formal logic blog post, that means that NO ONE posted a comment. I think that’s what you meant when you said “some DIDN’T post comments,” but that’s slightly confusing wording. Remember, the opposite of “some/someone” is “none/no one.” It’ll make your life a lot easier on the exam if you get used to that wording.
Let me know if you have any other questions!
Travis
That was very useful
I’m following the drift. Some = one or more. So if none posted a comment then you won’t post a blog. Now that many have commented, we are sure to read another blog post from you. I hope I got the language correctly.
1) You refuse to write another formal logic blog post, in that case, we can be sure that none of us has posted a comment …
2) One person…You keep writing post
3) You write another….at least someone has posted a comment
4) 2 or more people…You keep writing post
5) None posts comment at all…You stop writing blog post
1) If you refuse to write another logic reasoning blog post, then no one left a comment explaining that the blog posts were helpful.
2) If one person posts a comment saying that the logical reasoning blog posts are useful, then you will continue to create blog posts.
3) If you write another blog post, then at least one person commented that they found the posts helpful.
4) If two or more people post a comment saying that the blog post is helpful, then you will continue to create blog posts.
5) If no one comments, then you will not continue to create blog posts.
Hey I’m actually confused about this one! I learned to turn “Unless” into “If Not.”
I refuse to keep writing formal logic blog posts unless some of you post comments telling me that you’re finding these helpful.
=
If some of you do not post comments, then I do not keep writing formal logic blog posts.
OR
If I do keep writing formal logic blog posts, then that means some of you posted comments.
— I refuse to write another formal logic blog post? – we can’t know that this means anything, because this is the result (not the trigger).
— one person posts a comment telling me he/she finds this post helpful? – we can’t know that this means anything, because this is the result (not the trigger).
— I write another formal logic blog post? – we know this means that some have posted comments.
— two or more people posts comments telling me they find these posts helpful? – we can’t know that this means anything, because this is the result (not the trigger).
— no one posts any comments at all? – we know you will not post.
Where am I goofing??
Hi Maria! Going off Travis’ comment above: remember that the opposite of “some/someone” is “none/no one.” So you might want to think of your first statement as, “If none of you post comments (saying the blog was helpful), then I do not keep writing formal logic blog posts.”