--- K-S-Taber <kst24@...> wrote:
>>
> Of course, neo-Piagetians would warn of the limited structrues for
> understanding logic available to younger learners - and from first
hand
> experience I would suggest many 16-19 year olds may surprise in how
limited
> their use of rigorous logic is!

Let me suggest a test. One is told to take for granted that Q is a
corollary of P, where P and Q are some propositions. Then one is
offered the following propositions:

1. P is a necessary condition for Q.

2. P is a sufficient condition for Q.

3. Q is a necessary condition for P.

4. Q is a sufficient condition for P.

5. If P then Q.

6. If Q then P.

7. If and only if P then Q.

8. If and only if Q then P.

9. If P is false then Q is false.

10. If Q is false then P is false.

Which among the propositions 1-10 are true? The test is difficult,
although the forms of the propositions are commonly used. Things are
much more difficult in a deductive science (thermodynamics). In my
view, even general chemistry should be preceded by a suitable course
of logic.

Pentcho