I think you’re looking for errors in my understanding of very basic stuff, because you are trying to prove to me that my education has failed me. Am I correct?
Not exactly. I wasn’t looking for or expecting an error re the real number syllogism. I had a followup question in mind but didn’t get to it yet. (BTW your trig answer was problematic but I didn’t get to that yet either, and you didn’t volunteer information about mathematical induction or recursion so those are still pending to potentially follow up on.) And “failed [you]” is something like a value judgment, which wasn’t my point.
I was trying to help with identifying things that I thought you wanted to identify:
My broader purpose was to help discuss/clarify/explain the broad societal situation in which you’re making career choices, which could help you understand your options better, make more informed decisions, and have realistic expectations/plans/goals.
Okay, got it. Yes – I’m still interested in this conversation.
Regarding the syllogism thing, I think you interpreted it as more snarky than I actually meant it to be.
Basically, what happened is that the first change I thought of would make it valid but depended on some context (the context of knowing that 25 is an integer). Rather than asking for technical details about what you actually wanted me to do, I decided to make an edit such that it’s trivially true. I said Lol because I thought my edit was different from what you expected and therefore funny.
Your edit isn’t correct. From a contradiction, anything follows by a series of steps that you could do, but you didn’t include those steps, so it isn’t a valid syllogism.
Can you come up with a different one that works?
I know induction as well as I possibly could because I have used it a lot for math proofs.
I understand recursion because I’ve programmed with functional programming languages before. I actually started out wanting to do theoretical CS at the beginning of my career, and know (or did know) e.g. the stuff in CLRS.
Oh. Have you done SICP? (I have.)
I don’t know what the series of steps you are referring to is.
I come from a math background, and I interpreted the thing as being the proposition
(A and B) => C,
which is equivalent to
(not (A and B)) or C.
If A is false, the above expression evaluates to True.
I have not.
Can you think of any way this statement could be false?
If I’m a Boltzman brain and the memory is fake?
If by induction you meant transfinite induction?
edit:
I expect that someone who just did 100 induction practice problems involving arithmetic sequences could solve his 101st faster than I could, so maybe this is a sense in which I don’t know it “as well as I possibly could,” but does that really mean he understands mathematical induction better than I do? I think this is what you have in mind, but I generally wouldn’t describe this as someone knowing induction better than me, or a lack of knowledge about induction, etc.
Maybe you have an instrumentalist premise? Your sentence reads as absurd to me because conceptual understanding exists and is not maximized by using something a lot for calculations/proofs/problems (or any use).
Being able to do a skill and understanding a concept related to the skill are different things.
I edited my post like 30 seconds before you replied and I’m not completely sure if you saw.
By this
I mean something like: I think my conceptual understanding of induction is just as good as the guy who did 100 problems.
I did read the edit.
Oh I see, you mean this sentence:
Earlier you said I didn’t volunteer information about mathematical induction, and I remember thinking: What information could I volunteer that would show him I know induction?
Then I remember thinking: how could someone not know induction? What evidence could ET possibly want? Induction seems so incredibly simple to me that the only way someone could think they know it but not know it is if they learned it in a purely abstract way and have never actually used it. Since I have done a lot of math proofs with induction, that can’t apply to me.
That’s why I wrote what I wrote.
Yes, that is the one I quoted and discussed in Career, Physics and Goals (was: Artificial General Intelligence Speculations) - #109 by Elliot and which I thought (combined with your further replies) could indicate an instrumentalist premise. I’m unclear on what happened re some sort of confusion about which sentence I was talking about.
What information could I volunteer that would show him I know induction?
An explanation of what it is and how/why it works.
Induction seems so incredibly simple to me that the only way someone could think they know it but not know it is if they learned it in a purely abstract way and have never actually used it. Since I have done a lot of math proofs with induction, that can’t apply to me.
This helps explain your resistance to considering or analyzing arithmetic errors, since (I think we’ll agree) arithmetic is significantly simpler than mathematical induction.
Do you understand/agree how, in general, using a skill successfully doesn’t imply good conceptual understanding? Do you just think this (EDIT: this = induction) is a special case?
Here is an example of an explanation of mathematical induction. This is the kind of thing one might write to show that one understands induction. However, this particular explanation is bad. Despite it being bad, and convincing me that the author has a poor understanding of induction, I find it plausible (even likely) that he has done induction problems successfully. Do you find that implausible?
I thought you were referring to the sentence that I edited, because the original version stated an instrumentalist premise and made it look like I agree with the instrumentalist premise.
Definitely. I agree. I see people apply things all the time despite having poor conceptual understandings of the thing they are applying.
I will read the article you linked.
Good lord this article is atrocious. Not just the bullet points either. I was originally going to write down all the errors that I saw but it would be too much work b/c there were too many of them. I agree that this author has a poor understanding of induction.
I guess I find it plausible that the author has done some induction problems successfully, but I think he would have a high error rate.
When you hear that I make arithmetic mistakes, do you think that this indicates that some of my arithmetic knowledge is of a similar quality to this author’s induction knowledge?
I find that implausible. I’ll read your post about arithmetic mistakes and think about why.
No, I wasn’t suspecting something that bad! BTW that article was the top hit on my web search for mathematical induction 
Would you write a brief explanation of mathematical induction?
For each natural number n, let P(n) denote a proposition. If P(1) is true, and if it is true that P(k) implies P(k+1) for all natural numbers k, then P(n) holds for every natural number n.
That doesn’t say what it’s for or why it works. It’s more like saying how to do it or what the mathematical assertion is.