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Logical Literacy

matt.might.net

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Re: Logical Literacy

#11

Post by Someone »

sid0 wrote: post #2

Good article overall, but I think I should make a comment: > Many understand implication intuitively, yet find its symbolic formulation puzzling. Yes, and for a reason: material implication (the kind of implication discussed in the article) cannot always explain our intuitive sense of implication. My favourite example, from Priest's Introduction to Non-Classical Logic : (A ⇒ B) ∧ (C ⇒ D) ⊦ (A ⇒ D) ∨ (C ⇒ B) is valid…

I also think it is unfortunate that his first theorem is incorrect (n=1 cannot be written as the product of two distinct integers)

That may cost the author some of the readers for whom this text is the most educational, i.e. the ones that have trouble grasping the logic.

Re: Logical Literacy

#12

Post by mattmight »

Someone wrote: post #11
sid0 wrote: post #2

Good article overall, but I think I should make a comment: > Many understand implication intuitively, yet find its symbolic formulation puzzling. Yes, and for a reason: material implication (the kind of implication discussed in the article) cannot always explain our intuitive sense of implication. My favourite example, from Priest's Introduction to Non-Classical Logic : (A ⇒ B) ∧ (C ⇒ D) ⊦ (A ⇒ D) ∨ (C ⇒ B) is valid…

I also think it is unfortunate that his first theorem is incorrect (n=1 cannot be written as the product of two distinct integers) That may cost the author some of the readers for whom this text is the most educational, i.e. the ones that have trouble grasping the logic.

Good catch!

Will fix. ;)

Re: Logical Literacy

#13

Post by nene »

Someone wrote: post #11
sid0 wrote: post #2

Good article overall, but I think I should make a comment: > Many understand implication intuitively, yet find its symbolic formulation puzzling. Yes, and for a reason: material implication (the kind of implication discussed in the article) cannot always explain our intuitive sense of implication. My favourite example, from Priest's Introduction to Non-Classical Logic : (A ⇒ B) ∧ (C ⇒ D) ⊦ (A ⇒ D) ∨ (C ⇒ B) is valid…

I also think it is unfortunate that his first theorem is incorrect (n=1 cannot be written as the product of two distinct integers) That may cost the author some of the readers for whom this text is the most educational, i.e. the ones that have trouble grasping the logic.

Even if it's not meant to be true, I find it even more disturbing that the symbolic and English formulations doesn't seem to quite match up. (IMHO the symbolic formulation doesn't state that n must be integer.)

It's like the source code and comments being out of sync - you don't know which one is wrong.

Re: Logical Literacy

#16

Post by yters »

gacba wrote: post #6

It's unfortunate that this kind of logic isn't emphasized more in mathematics or science in a pure form. I'm pretty sure in high school I had one semester of this kind of logic associated with geometry. That was it until I hit discrete structures in college. Failure to understand this logic might be part of the reason there's so much magical thinking about things relating to pseudoscience (e.g. paranormal activity, U…

Newton devoted much of his time to alchemy and theology.

Re: Logical Literacy

#17

Post by astrofinch »

sid0 wrote: post #2

Good article overall, but I think I should make a comment: > Many understand implication intuitively, yet find its symbolic formulation puzzling. Yes, and for a reason: material implication (the kind of implication discussed in the article) cannot always explain our intuitive sense of implication. My favourite example, from Priest's Introduction to Non-Classical Logic : (A ⇒ B) ∧ (C ⇒ D) ⊦ (A ⇒ D) ∨ (C ⇒ B) is valid…

It makes perfect intuitive sense if you're used to the way the word "if" is used in logic.

Re: Logical Literacy

#18

Post by astrofinch »

This is a great example of how awesome teaching yourself using the Internet can be. If you read and understood that in 30 minutes then you learned it in about one quarter of the time we spent covering this stuff in my discrete math class--and I'm supposedly going to a really good college.

Re: Logical Literacy

#19

Post by sid0 »

astrofinch wrote: post #17
sid0 wrote: post #2

Good article overall, but I think I should make a comment: > Many understand implication intuitively, yet find its symbolic formulation puzzling. Yes, and for a reason: material implication (the kind of implication discussed in the article) cannot always explain our intuitive sense of implication. My favourite example, from Priest's Introduction to Non-Classical Logic : (A ⇒ B) ∧ (C ⇒ D) ⊦ (A ⇒ D) ∨ (C ⇒ B) is valid…

It makes perfect intuitive sense if you're used to the way the word "if" is used in logic.

It makes perfect intuitive sense if you're used to the way the word "if" is used in classical logic. Remember that it's you who has bent your intuitive sense to fit how material implication works. Most people are not going to think it makes intuitive sense, and the fault doesn't lie with them -- it lies with the logic. Logic is like UI: it's Not the User's Fault he doesn't find implication intuitive.

Re: Logical Literacy

#20

Post by omaranto »

astrofinch wrote: post #18

This is a great example of how awesome teaching yourself using the Internet can be. If you read and understood that in 30 minutes then you learned it in about one quarter of the time we spent covering this stuff in my discrete math class--and I'm supposedly going to a really good college.

I don't see why you mention your college is good seemingly surprised it took longer than 30 minutes to cover this: wouldn't you expect a good college to have good teachers and wouldn't you expect a good teacher to go slowly enough that all or most students understand?
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