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 Discussion on answer by Relaxed: Forc…

Imported from a comment discussion on travel.stackexchange.com...
DRF
Mar 8, 2023 05:13
@KateGregory I think the point is "it's a weeding dress" once you've worn it to a wedding you're not using it again. It's not a camera, it's not a watch. It's something that you're putting in the wardrobe to remember that one special day and it's not getting sold or used again. In other words, had she just left it in australia her usage of it would be pretty much the same. Paying 1000Euros for the privilege of showing your family a nice dress is pretty ridiculous.
 

 Discussion on question by Wrzlprmft: …

Imported from a comment discussion on academia.stackexchange.c...
DRF
Mar 2, 2023 11:46
At the same time the actual focus on understanding the subject matter as opposed to "regurgitation" typical for undergrad exams in the US, meant we didn't have to keep explaining how come the problems on the exam aren't exactly the same as what was on the homework.
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DRF
Mar 2, 2023 11:44
I wonder how much my experience is influenced by the two systems I've come in contact with: US written exams only vs. Czech oral exams only. I found the Czech system to be orders of magnitude more precise, allowing an examiner to actually figure out what the student knows and where they have gaps in understanding which also acted as much better feedback.
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DRF
Mar 2, 2023 11:41
While panic attacks are a problem that oral examinations may in some ways exacerbate, they are also something that in general you want to be treating anyway, since for most students the situations which trigger them do not go away because you stop going to school, they just morph into job interviews, one to one evaluations and many other real life scenarios.
DRF
Mar 2, 2023 11:37
@IanSudbery That's interesting. I'm strongly of the opinion that oral exams are many orders of magnitude better at judging a persons mastery of the subject than any possibly written exam could ever be. My experience is mostly in mathematics if that's important. So for me a ban on oral exam performance seems like it's extremely short sighted.
 

 Discussion on answer by Iñaki Viggers…

Imported from a comment discussion on law.stackexchange.com/qu...
DRF
Feb 24, 2023 21:43
@IñakiViggers There are a couple of exceptions to the first amendment but they have a very high bar. Obscenity in particular seems almost impossible to cross with anything "normal". I mean the penthouse example is pretty famous. Also I wouldn't say that black's law dictionary is as well known as you think. I would guess it's some English speaking jurisdiction but would have no clue which.
DRF
Feb 24, 2023 16:41
Also defamation, slander and libel are notoriously hard to prove in the US, while being scary easy to prove even against well meaning journalists in the EU.
DRF
Feb 24, 2023 16:38
Even in cases where the statement of opinion was "provably true". :) Someone called a government official an idiot based on an incorrectly assessed and repeatedly demanded fine and was fined for insulting him.
DRF
Feb 24, 2023 16:37
I wonder would it be useful to mention jurisdiction? From my (admittedly scant) knowledge your answer is pretty sure to be true in the US and probably UK, but these countries (US in particular) have really quite robust free speech laws which tend to trump copyright in many cases and definitely protect opinion. Even in other European countries this is definitely not necessarily the case. In my country (Czech Republic) you can for example be fined for insulting a government official.
 

 Discussion on answer by Dale M: Admit…

Imported from a comment discussion on law.stackexchange.com/qu...
DRF
Feb 24, 2023 20:36
@infinitezero you seem to think that trials are about finding the truth, that sadly is mostly not the case in an adversarial system. They are about who can convince the jury of their view. Truth doesn't necessarily come into it. We hope the prosecutors and judges act properly and that's one of the reasons they have very large discretion, but in the end the system is not really setup to find the truth.
 

 Discussion between DRF and Lorenzo Po…

Imported from a comment discussion on math.stackexchange.com/q...
DRF
Feb 24, 2023 18:30
Also the whole importance of belief in ZF being true otherwise proofs go poof. Again you are right in essence, but ZF is incredibly powerful. ZFC in which we actually usually work even worse. You need really pretty small fragments of it to prove almost everything. There's quite a bit of work done on that. Showing how little you need to prove stuff.
DRF
Feb 24, 2023 18:27
Difference between proof and implication is mostly about meta theory. I will actually look into this again. I can't believe how much I've forgotten in just 10 years. I don't think your answer is wrong by the way. It's definitely trying to do the right thing, it's just that I think it stays to close to caring about the consistency of ZF.
DRF
Feb 24, 2023 18:19
Oh yeah that's a bloody tricky distinction. Let me see if I can remember it well enough to explain it.
DRF
Feb 24, 2023 18:18
His confusion seems to stem from getting to the point where he thinks: Hah and so I proved inconsistency of the whole set of axioms and decide it's in the new bit I proved, because I believe the old bit.
DRF
Feb 24, 2023 18:17
There's an extra slight issue. Not with anything being wrong but with what I think the OP is confused about.
DRF
Feb 24, 2023 18:14
I wonder if what I'm trying to say makes sense.
DRF
Feb 24, 2023 18:13
This is all the more true, because in most cases you aren't using anywhere near ZF. You can prove most of mathematics in some small extensions of PA.
DRF
Feb 24, 2023 18:12
I realize the difference is small, and you could (and in foundational studies sometimes do) get to the point where you say so either ZF is inconsistent or this thing holds, but it's not the way we think about it. Unless we're doing actual consistency proofs. I mean yes you do of course get stuff like "Con(ZF)\implies Con(ZF+CH)" but that's a completely different ball game and you are thinking of it that way for a reason. You don't want to drag consistency into it unless it's necessary.
DRF
Feb 24, 2023 18:10
Anyway the point I was trying to make is it's not that we think at the end hey, so either ZF is inconsistent or A holds. We aren't even getting to ZF\implies A. We are getting to ZF proves A *. Assuming classical logic.
DRF
Feb 24, 2023 18:08
Oh bugger this place doesn't parse mathjax.:(
DRF
Feb 24, 2023 18:08
But that's not the way I would ever think of it or teach it. In theory it's possible but I think it's really confusing. And I don't think that's the way we actually think of it. We think of it as $ZF\proves \neg A \implies A$ therefore $ZF\proves \neg(\neg A \wedge \neg A)$ therefore $ZF\proves \neg\neg A$ and by law of excluded middle (a little more work) $ZF\proves A$.
DRF
Feb 24, 2023 18:06
give me a sec I'm completely getting myself turned around in what I'm trying to write.:D Haven't done proper logic for ages.
DRF
Feb 24, 2023 17:54
Ahh ok I see where my confusion is. You say

I show that ZF and ¬A together imply A. Since it is simply false that both A and ¬A are true, it must be either ZF is false (and/or it has a contradiction inside), or ¬A is false (that is, A is true). This is equivalent to ¬A⟹¬ZF, that is, ZF⟹A
DRF
Feb 24, 2023 17:49
Ahh. Ok I think I see what you are saying. Let me reread the answer I might have completely misunderstood something.
DRF
Feb 24, 2023 17:48
There is no issue with consistency regarding law of excluded middle/proof by contradiction.
DRF
Feb 24, 2023 17:47
But there was no issue.
DRF
Feb 24, 2023 17:47
Just to try and explain a bit more, you're confusing your metatheory and theory. ZF is your set of axioms. Law of excluded middle is part of your metatheory/logic.
DRF
Feb 24, 2023 17:46
The point is consistency has nothing to do with the problem. Bringing it up just muddies the waters. The consistency of ZF is completely irrelevant to the proof by contradiction. In other words the consistency of math plays no special role in proof by contradiction. No more than it does in proving that 2+2 is 4. That's what I'm trying to explain.
DRF
Feb 24, 2023 17:46
Note that consistency works the other way. You have inconsistency if you know $A\wedge \neg A$ not $\neg (A\vee \neg A)$ this seems to be same thing because we are so used to law of excluded middle and $\neg \neg A \equiv A$.
DRF
Feb 24, 2023 17:46
I don't believe you actually need the consistency of math for proofs by contradiction any more than you need them for any other proofs. That is a bit of a red herring. You conclude $\neg A$ from $A\implies \neg A$ based on the Law of excluded middle not based on math being consistent. Without the law of excluded middle you could have math being consistent and $\neg (A\vee \neg A)$ holding.
 

 Discussion between DRF and Frank

Imported from a comment discussion on philosophy.stackexchange...
DRF
Feb 24, 2023 16:13
I assume you're happy with empty sets as long as their untyped? It's the group of unicorns that annoys you not just empty group, right? Or do you prefer to say that there is no set on the desk? Even an empty one? That would have the annoying side effect that you could never even have an empty set and that is an issue I think.
DRF
Feb 24, 2023 16:11
I think our argument is really about where you want to draw lines. You don't like empty typed sets. I do.
DRF
Feb 24, 2023 16:10
*been stripped
DRF
Feb 24, 2023 16:10
And I still claim that a definition of nothing as all "container objects" have 0 elements is just fine. In reality as I've pointed out, what we normally agree on as nothing is usually "the things we expect to be there". When I say that house empty, I rarely mean all the furnishings have stripped and air pumped out. I mean there are no people living there.
DRF
Feb 24, 2023 16:07
When I get my computer shipped to me from the dealer and someone asks me what's in it I say computer. If they say oh I thought there was packing material in there I'm not gonna disagree. If they actually recycle packing material, for them that might be what they see the box containing. They don't care about the computer.
DRF
Feb 24, 2023 16:06
Those aren't contradictory statements. I can absolutely have both a group of unicorns and a heap of sand in the same place while it's empty. Same as I can have a empty box that holds ~10^23rd atoms of nitrogen.
DRF
Feb 24, 2023 15:16
Actually even nothing there is very tricky. What about the huge heap of air.
DRF
Feb 24, 2023 15:15
I don't lose the meaning of nothing there. Nothing there is all heaps in that space are size 0
DRF
Feb 24, 2023 15:15
Everywhere I look I see a heap of size 0 of every thing that you can dream up. That's fine. It's what you learn the beginning of mathematical abstraction. I look at 5 chairs and I see a 5 element abelian group if it takes my fancy.
DRF
Feb 24, 2023 15:13
Yes. Agreed.
DRF
Feb 24, 2023 15:05
To get back to the original claim I was trying to make though. If we try and talk about a heap for which the only measure is amount of items, I think going all the way to 0 makes the best sense if you want a bright dividing line that doesn't lend itself to a paradox. Arguably I'm influenced by a background in mathematical logic, set theory and CS.
DRF
Feb 24, 2023 15:03
Back to the heap though, I think there might actually be a physical definition regarding shape and shape holding. For example 30000 thousand grains of sand poured in a cone shape are a heap, the same 30000 thousand grains spread equally over 2 square kilometers are not.
DRF
Feb 24, 2023 15:01
To answer some of the computer science stuff you posted:
The first is not about whether the array is empty but where it starts being indexed.

The second is again not about it being empty but about memory allocation. I want to be able to have an empty heap, for programming purposes. The fact the compiler preallocates memory is completely beside the point. The question is if I'm doing heap sort, can I have a heap with no elements? If I'm pulling stuff out of a stack can I end up with an empty stack? etc. There the answer is (pretty much universally) yes I want to be able to have empty string…
DRF
Feb 24, 2023 14:58
I addressed that. "In real life you gain logical consistency without having to learn a strange new type of logic."
I personally would go with a heap is something that's reasonably shaped like a heap and I'll "know it if I see it". But if you press me for a more specific definition I will argue for 0 size heaps because they make sense.
DRF
Feb 24, 2023 14:55
That's a different issue. That's numbering not size.
DRF
Feb 24, 2023 14:54
Only philosophers think about when is the ship of Theseus still THE ship of Theseus. It's fun and you can bring math or comp sci or physics to bear on the question and you get different answers depending on how you've set up your axioms and what's more useful.
DRF
Feb 24, 2023 14:52
So what people in real life do, is say nerts to the philosophers I don't need to know exactly when a heap turns into not a heap. It's a useless distinction without a difference and there is no paradox to worry about. If it looks like a heap I'll call it a heap and if doesn't I'll call it a handful. And if I disagree with someone about it I will either not care or shout at them loudly.
DRF
Feb 24, 2023 14:50
By which I mean people in real life. We just don't care enough because what we use heap for is to describe something to other people. And the distinctive line between heap and not a heap anymore is not important enough to bother with.
DRF
Feb 24, 2023 14:49
I don't think normal people actually do that though.
DRF
Feb 24, 2023 14:49
In real life you gain logical consistency without having to learn a strange new type of logic.