Timeline for How is it correct for a lecturer to prove and "explain" a proof while explicitly knowing students are not familiar with logic itself?
Current License: CC BY-SA 4.0
12 events
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| Aug 7, 2022 at 9:54 | comment | added | ryang | @TurkhanBadalov "All cats are vertebrates. All mammals are vertebrates. So, all cats are mammals". The argument has a gap, even though every statement is correct. Without knowledge of logic, rarely a student can notice this gap. $\quad$ Recognising that the cats argument is a fallacy like "1=1, 2=2, thus 1=2" requires not knowledge of logic but concrete practice with reasoning, like those proofs that you refer to (during which logic can informally be taught). I like this Answer, which I think addresses your Question. | |
| Sep 13, 2018 at 21:45 | comment | added | Jasper | Then the question and its title is grossly misleading. | |
| Sep 13, 2018 at 20:52 | comment | added | Turkhan Badalov | @Jasper both of them. Mostly the first one | |
| Sep 13, 2018 at 20:43 | comment | added | Jasper | @TurkhanBadalov Are you concerned with the student's abilities to come up with own proofs or to follow the lecturer's presentation of proofs? | |
| Sep 13, 2018 at 20:39 | history | edited | Jasper | CC BY-SA 4.0 |
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| Sep 13, 2018 at 5:43 | comment | added | Turkhan Badalov | @Jasper you are demonstrating really clever and ideal students actually that can notice every mistake. Why do you think students make mistakes, leave gaps in their proofs? Let's put aside that concrete simple proof that I just gave as a simple example. | |
| Sep 13, 2018 at 5:37 | comment | added | Turkhan Badalov | Actually, factually correct (not sound) arguments are a good example of such proofs. Without prior knowledge of logic most of the students can be tricked to believe that proof while actually conclusion doesn't follow from the premises: "All cats are vertebrates. All mammals are vertebrates. So, all cats are mammals". You see every statement is correct having also a gap in the argument? What I am saying without knowledge of logic rarely a student can notice this gap and even properly explain to a professor his objection regarding the gap. | |
| Sep 13, 2018 at 5:27 | comment | added | Jasper | Of course there is a false statement because a/2=k. And studens should be able to point this out. | |
| Sep 13, 2018 at 5:22 | comment | added | Turkhan Badalov | The point is not whether students will understand it. The point is that adding "redundant" or even funny statements in between still will be accepted as something okay because "professor knows what he does". He could have said after second statement something sounding clever: "let's now divide $a = 2k$ by $2$ to explicitly see it is divisible. We get $a = k$, so it is divisible as we don't get fractions. $a^2=k^2$ but remember that reduced $2$? Putting it back again gives us $a^2=4k$", etc. Did he say false statenents? No. But they are useless while most of the students will just accept it | |
| Sep 12, 2018 at 21:48 | comment | added | Jasper | Exactly, and I tried to make a point that the knowledge about logic *to understand * a proof is rather limited and one can therefore use proofs before all students have taken a course in logic. | |
| Sep 12, 2018 at 21:22 | comment | added | Rusty Core | The question was not about coming up with a proof, it was about understanding what a proof is, and whether a certain assertion is a proof according to presently accepted logical rules. | |
| Sep 12, 2018 at 17:23 | history | answered | Jasper | CC BY-SA 4.0 |