Before I start chattering, let me pose four logic examples. I got them from Dodd & White, “Cognition”, ISBN 0205069304, 1980. (They, in turn, are reporting some results of a test done by Johnson-Laird and Steedman.)
All four are syllogisms.
some A are B
no B are C
no B are A
some C are B
no A are B
some B are C
some B are A
no C are B
So: what valid conclusion or conclusions, if any, may we draw from each syllogism?
I had fully intended to put the answers — and much fuller discussion — at the end of this post… but when I actually started looking at them as syllogisms — as having mood and figure — I came to a screeching halt.
I would invite you to try them in your head first. Then, having done that, you could try at least three other things.
- One, you could draw some Venn diagrams. (No, I haven’t shown you any, anywhere.)
- Two, you could convert them to symbolic logic, using the post about “all” and “some”.
Three, you could go look for them among the 15 valid syllogisms in this post. (I think that only this path poses interesting challenges.)
Now to chatter. It sure seems to me that I didn’t get a whole lot done last weekend.
And yet, I actually did a good job on the blog: last week’s “happenings” post took four hours to write, but I think it was worth it; last week’s logic post took most of a day. Let me give myself credit for both those posts.
I need to say that because I tend to focus on that I didn’t have any real breakthroughs in mathematics: no sudden flash of insight, no beautiful example to work out and post.
Well, it just can’t happen all the time.
The fact is, I made a little progress on trajectories, logic, and color. I’ll have to be content.
Now, those four syllogisms.
… Well, I’ve just had a surprise — those four syllogisms are not as simple to analyze as I expected them to be! At the very least, it looks like somebody has messed up subject and predicate for two of them. Not a crime, because we can fix it — but their summary seems flawed.
So, I’ve just come up with an interesting example — and I reckon I’ll be writing a post about these four syllogisms. Now I’ll just go back to the beginning of this post, and correct it to say that the answers will be forthcoming.