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Some P are Q

Yesterday I had a very bad (VERY BAD!) experience while attending my “Critical Thinking” class at _______ University....

The professor offered a seemingly innocuous statement. He said, “The statement that ‘some P are Q’ implies that some P are not Q.” At first that sounded right, and everyone in the class nodded—except for me—and we started to move on to discuss something else. But I had to raise my hand and ask for a clarification, because I actually did not and do not agree with the statement as made. That’s because, as made, the statement is FALSE.

Of course, if we make a slight modification, so that the statement says, “Only some P are Q,” then of course it follows that “some P are not Q.” But the word “only” is critical. Without this additional word, there is NO inherent implication. Rather, by itself, the statement, “Some P are Q” merely BEGS THE QUESTION: “Gee, I wonder if ALL P are Q… or if perhaps only some P are Q…? Hmmm.”

This is empirically obvious. For example, “some fish swim in the sea” does NOT imply that “some fish DON’T swim in the sea.” And “some men are mortal” does NOT imply that “some men are not mortal.” Rather, again, “some P are Q” merely BEGS THE QUESTION, “Is the observed quality inherent to the class, or is it incidental?” And it does NOT imply an answer. (By definition, if it implies a real question, it does not imply an answer.)

However, not only did my professor and my classmates not see my point, they became exasperated with me. Several crowed… “CAN’T YOU SEE WHAT THE PROFESSOR IS SAYING?!!! Can’t you see that the statement some P are Q implies that some P are NOT Q?!!!” Of course, I also was exasperated with the situation and went up to the professor after class to try to explain what I see as the difference between “begging a question” and “implying an answer.”

Right. That didn’t work out so well. The professor spoke to me like I was a six-year-old--a slow one--and when I said, “I’m not stupid,” he said, “I’m not saying you’re stupid—you’re saying you’re stupid.” Then he said it even louder, “I’M NOT SAYING YOU’RE STUPID—YOU’RE SAYING YOU’RE STUPID!!!”

To make matters worse, he just handed out a take-home exam for the class. I imagine that would normally be a straightforward matter in a logic class, but the first question on his exam reads:

“I. Short answer [one paragraph]: Explain the relationship between the following terms: truth, logic, critical thinking, being, definition, genus, species.”

OMG—He is going to grade us as right or wrong on what we say in one paragraph about the relationship between truth, logic, and, among other things, BEING?!!! (By the way, he constantly misuses the word “being” in class as a synonym for “reality,” so I’m already in a hopeless mess trying to answer his question is some way that he won’t mark down.)

So I think I’m possibly going to have to drop this class in order to avoid having my GPA ruined, but that will cost me my scholarship.

Any suggestions? Thanks!!!


Washington, DC

Re: Some P are Q

Dear Disgruntled Student,

I read your story with the appropriate surprise and indignation.

Needless to say, if your account is accurate, you were 100% correct, and your so-called professor sounds like he does not know logic, and lacks ordinary intelligence and honesty.

'Some P are Q' does not imply 'some P are not Q', but is subcontrary to it, since the former is implied by the contradictory of the latter, namely 'all P are Q'. This is graphically stated in the 'square of oppositions'.

There is in Talmudic logic a reading of 'some P are Q' as implying 'some P are not Q' - but such reading of 'some' as definite is not used in common, Western logic - where 'some' is indefinite.

And indeed, 'some' must be indefinite for purposes of induction, as you well point out in your examples. If I observe some fishes swimming, I must be linguistically able to express this without committing myself to either of the outcomes some fishes do not swim or all fishes swim. The matter must remain open.

Indeed, normally, not knowing more than this, we would naturally generalize from some fishes swim to all fishes swim. After which, if we ever came across fishes that do not swim, we would have to particularize and admit that some fishes do not swim.

So your teacher is absurd in his teaching and unworthy in his closed-minded reaction to your correct objections. You can tell him I said so! But as for you, do not let this episode discourage you - you obviously have good potential as a 'critical thinker' who does not let himself be moved by authority or by peer group pressure!

Consider yourself as having passed through a live test and succeeded with flying colors. View this as an object lesson well learned. Don't feel bad towards your teacher or his other pupils, as human beings all have their limits in intellect and virtue. Accept the situation and move on.

As for the one paragraph test: "Explain the relationship between the following terms: truth, logic, critical thinking, being, definition, genus, species." - I wonder what inanity your teacher would himself briefly answer to that question. Of course, you're right 'being' and 'reality' are very different concepts, since being can also be illusory, i.e. unreal.

Look for another teacher of logic first chance you get. But don't give up on logic and philosophy.

Re: Some P are Q

Dr. Sion,

A Talmud scholar he is not.


p.s. Thanks for your encouragement. I am a 48-year-old who recently returned to school to complete a nascent degree begun over 30 years ago.

Re: Some P are Q

Hi Disgruntled.
Hang in there and finish the job!
If you want to reprove the professor and fellow students for their behavior you might want to read them our correspondence in class.
Alternatively, print it out and hand it out. At least to the professor. Maybe even to the faculty head.
Best, Avi.

P.S. By the way,the reason why the Talmud works that way is that it is essentially a conventional, rather deductive discourse. Probably your professor is so conventional minded that he actually thinks that way, i.e. with little inductive method. Hence his bad reaction to your intellectual independence.