Not exactly, but we can make a guess. In GoF, Harry scans the staff table 'more carefully' during the opening feast. He starts with Flitwick and goes on to mention Sprout, Sinistra and Snape sitting beside each other, followed by McGonagall's empty seat and ending with Dumbledore at the center. Since he was scanning carefully, we can assume that he started with Flitwick at one end.

We also know from the same chapter that three seats were empty before the sorting. One was McGonagall, which is said to be beside Dumbledore's, the other Hagrid's and finally Moody's. Later in the chapter we learn that Moody's seat is at Dumbledore's other side.

Now, we can either assume Hagrid's seat was either beside Flitwick or on the other side of the table from him. Either case would fit with the fact that Hagrid's seat is at one end of the table. To get the worst case estimate, let's assume it's beside Flitwick.

So we have one side of the table from Dumbledore with six seats. That, along with the fact that he is at the center can be used to estimate that the other side of the table contains roughly another six seats.

We also know that Trelawney doesn't come down to the staff table usually from HBP.

Based on these facts we can conclude that the staff table has roughly thirteen seats including Dumbledore but excluding Trelawney.

That brings the number of professors at Hogwarts to fourteen, assuming there aren't other professors who don't attend the opening feast.

 

I think you're missing the depth of the "unmentioned" point. The idea is that the narrator (Harry) is unreliable, in that he's incredibly focused on people directly relevant to his ongoing interests and adventures. Everyone else is treated like they don't exist, until they become relevant (hello, Cormac McClaggen). People who don't ever become relevant never get mentioned (the other two girls in Gryffindor, who share a dorm with Hermione, Lavender and Parvati).

Obviously without an unreliable narrator, the idea of large numbers of unmentioned students, and their attendant professors, becomes unworkable. It's simply too much of a stretch to think that the books would never mention other classes in Harry's year, other people sharing the same living space, etc. Unreliable narrator is the only way to go.

 

I think it's more that the extent to which I consider the narrator unreliable is much less than is needed to explain the large number of unmentioned professors.

That scene I mentioned in GoF has Harry looking specifically from one professor to the other and mentions that they are sitting next to each other. Is it reasonable to assume that the narrator is unreliable in specifically mentioning professors are sitting right next to each other, or that Dumbledore is at the center?

The sorting feast is one of the most important event of year, and I think it's reasonable to think that most professors would be expected to attend it.

That's why I used that scene to get a possible upper bound for the number of professors at the staff table during the sorting feast. It even has a space for 5 unmentioned professors.

Of course, there could be more unmentioned professors, but is it reasonable to assume that there would be a lot of professors who don't attend the sorting feast?

I'm perfectly fine with the idea of unmentioned students. I'm also fine with a few unmentioned professors. It's the scale of unmentioned professors required to have a reasonable student to faculty ratio is what I think is far-fetched. In fact, Hogwarts having a ridiculous ratio is likely a better explanation than the number of unmentioned professors. After all, it's wizards

 

While I can see perhaps three or four professors going unmentioned, it seems absurd to think Harry would have left out the 80-95% of the professors 1000 students would require.

If Harry is such an unreliable narrator as that, then you've ceased to have a window into the story. If even a "careful look" gives only 10% of the picture, you can't draw any meaningful conclusions whatsoever. You are left with only a pinhole.

 

There are plenty of ways to explain the GoF scene if you hold Harry as unreliable and want more teachers.

A second table of teachers behind the first, for example.

 

The only time the staff table is specified in plural is during the Yule ball.

That aside, by that logic Dumbledore might as well have been evil all along with the narrator being too unreliable to notice it. For all we know, shitfics actually have it right.

 

There's a difference, though, between an unreliable narrator and an intentionally misleading one. We're beginning to veer into the latter, here.

I think this may be a point where that which is logical and that which is described in canon are too different to reconcile. Either there are near 1000 students, or there are around 15 professors. Alternatives, such an absurd faculty-student ratio, don't seem to fit the text any better.

 

Maybe the professors are using time-turners to get to the extra classes which would be required for about 1000 students. After all if Hermione got one just to take extra classes it wouldn't be unreasonable to think that the professors had access to them. And if I remember correctly there isn't mentioned any limitations as to how far back you can go and how many times.

 

There is.

Maybe teachers use some sort of apprentice system, so that older students would teach younger ones.

 

This is an overly restrictive view of language, regardless of the narrator's reliability. "The" is often used to refer to the most important/relevant entity in a group, in such a way as to make it sound like they are the only one.

E.g. if you're in a government department, you might say "The Minister" to refer to the Secretary of State for your department, even though there will be a number of Ministers working in the department (as junior ministers). If you took the language literally, you'd think there was only one Minister in the department, but context makes it clear that you're referring to the most important Minister.

Similarly, Harry can be sitting in the Great Hall and say "Look at the staff table" and this is not inconsistent with there being more than one table. Context makes it clear which table he is talking about: the one with the teachers most relevant to their conversation, the one with Dumbledore on, the most visually prominent one, etc.

The narrator being unreliable about all things does not logically follow from the narrator being unreliable about one narrow topic (i.e. ignoring numbers of people where they're not directly involved in his life).

The reason why it's feasible to suggest Harry as an unreliable narrator with respect to numbers is that we have evidence to point in that direction: contradictory facts relating to numbers that can only be completely resolved by calling Harry unreliable.

There's no corresponding evidence to suggest to us that evil Dumbledore is something we should seriously consider.

 

Your idea of context requires familiarity with the system. The idea that Harry's unreliability causes him to miss multiple tables when he sees them for the first time defies imagination. Do note that it will have to be multiple tables and not just two, to accommodate the large gap of unmentioned professors.


There is also ample evidence that points to the fact that the multiple tables theory can't be true:

1. When the Goblet was revealed, two chairs were added to each side of the table. There wasn't any need to do this. Some teachers could have been sent to one of the other tables to make way for the judges.

2. Since we're discussing prominence of possible multiple tables, Hagrid being at the main table itself is highly inconsistent, especially when he was only the gamekeeper. This further ties into my first point. The same goes for Quirrel, who was not seen in high regard.

3. It is also extremely hard to believe that every one of the professors that Harry had any familiarity with would have been at the main table, especially so in case of Lupin in PoA, as it is very inconsistent with his character. (Lupin was on the same table as Snape)

 

There are so many obvious ways around all of those points.

For a start, this assumes teachers would be completely happy to move.

It also assumes that there's space at the other tables for teachers to move to.

It also assumes that putting out extra chairs is so much more onerous than asking teachers to move.

Honestly, using the setting out of extra chairs to try to justify anything is a real stretch lol.

Assumes table placement has to do with position.

Assumes table placement has to do with regard.

Assumes Hagrid isn't held in high regard by the faculty.

Assumes the teachers don't vary their seating placement at different meals.

Assumes no logical connection between their seating placement and them being Harry's teachers (if, for example, they are seated at the primary table because they're the "heads of department", then it's not surprising that Harry Potter's classes are all with the heads).

To recap, evidence for a larger Hogwarts in general:

- The 200 Slytherins passage in PoA.

- JKR statement as to the school having ~1000 students.

- Hints at a larger wizarding population in general (Quidditch world cup crowd, size of Ministry) combined with Hogwarts being the only school they can go to (JKR statement, Pottermore, DH order that all children attend).

- JKR statement that there were other girls in Hermione's dorm, other than Lavender and Parvati, which indicates a high level of "ignore everyone not relevant" in the narration, even if Hogwarts doesn't have 1000 students.

- Snape being said to be Hogwarts' Potion's Master. In traditional British boarding schools, "Master" refers to the head of a department (e.g. History). This would be rather strange if it were a department of one.

The problem against a larger Hogwarts:

- DADA curse being on one teacher/year.

That issue is a real stumbling block, and is probably enough to derail the issue, as I recognised on the previous page. But I think the objections raised on this page are all somewhat trivial.

 

First of all, I'm only referring to the sorting feast arrangements, or other important events like revealing of the Goblet and not everyday arrangements.

In the scenes that I have referred to, the focus has been on the table where Dumbledore is on, and therefore the most prominent one.

This assumes that the judges would be Happy to share the space at the prominent table, especially the judges from the Ministry. Doesn't even remotely sound like them.

It also assumes that the extra chairs couldn't be added to a table of lower prominence.

Assumes the placement doesn't have to do with position, especially when the table is where Dumbledore sits, which is again a far-fetched assumption. Note: McGonagall, Umbridge, Moody, the prominent teachers sit next to Dumbledore. Hagrid sits at the end of Dumbledore's table.

Hagrid is noted to have a fixed place on that table, which basically means that he is in that position not just at the feasts but on any day.

Assumes Hagrid IS held in high regard by the faculty, especially when we have scenes with McGonagall contradicting this.

Assumes they do vary their seating placements. Hagrid has a fixed place at one end of the table that Dumbledore sits on, which is mentioned in OotP. If Hagrid doesn't move, what are the chances that others do?

Assumes that those seating at Dumbledore's table are 'heads of departments'. Note: Hagrid was a gamekeeper in Harry's first year, certainly not the head of a department.

All of this is true, but the evidence exists only for the larger number of students, and it is still inconsistent with the number of professors.

There is absolutely no evidence that even hints at the possibility of a large number of missing professors as it does with the students.

The only way I can see a large number of students existing in Hogwarts is that Hogwarts has a ridiculous student to faculty ratio, which while it sounds ridiculous might be one of those wizarding world things that sound crazy in the Muggle world.

 

:facepalm

I didn't assume anything, because I didn't propose anything. I was merely pointing out numerous ways in which your objections failed to logically compel people to agree.

You're trying to say that it's impossible that there are more teachers than depicted in canon. To disprove this, I merely need to show a single possibility. If there is a single possible explanation, then this means it's not impossible.

If your arguments fail to logically exclude all possibilities, then a possible explanation remains. As your argument relied upon contentious assumptions to which there are many alternatives, I successfully demonstrated that you had not excluded all possibilities.

TL;DR: by trying to say something is impossible, you've given yourself a much higher burden of proof.

Though, as I say, the DADA argument is a strong one for impossibility.

 

Actually, you did propose something. To be specific:

I even agree with this partly, just not when the number of professors would be as proportionally large as the number of students, which I assume it would have to be. The idea that there are about 1000 students very likely requires more than five or possibly ten times the number of professors we see in canon. Such a large number of teachers existing without a shred of evidence is just not reasonably believable.


Also, what I'm trying to say is that the posibility that there exist significantly more teachers than depicted in canon, is highly improbable, to the extent that it could be considered impossible.


What I'm also doing here is trying to demonstrate that there exists no evidence to make us even think of the possibility of the existence of such a large number of teachers. It is very similar to your argument of why the idea of even considering an evil Dumbledore is not reasonable because there exists absolutely no evidence even hinting at it.

 

I was proposing a possibility, not an actuality i.e. it is possible that there are more teachers. I'm not saying that in canon there are more teachers, only that it's a possible interpretation of canon (i.e. it does not directly contradict canon).

Improbability does not disprove a possibility. Indeed, improbability by its nature actively admits the existence of possibilities other than the one which is most probable.

I consider there evidence enough in canon, listed above, for the existence of more students and a numerically-unreliable narrator to be an arguable possibility. (Again, not saying this is the case, just that it's a valid interpretation).

Within that possible interpretation, if there are more students, there must be more professors. It's a school, they have to be getting taught by someone. The time turner explanation is not a serious contender, given their rarity and limitations, and the fact that we know they were all destroyed after OotP and Hogwarts didn't collapse.

Now, if it could be shown that more professors is completely impossible, this would disprove their existence (and along with it, the existence of the additional students, by modus tollens, thus showing that the possibility of more students is in fact impossible).

I do not think you have managed to do this (show impossibility). In particular, raising possible interpretations of your own in which there aren't more students does nothing to contradict the "more students" possible interpretation. Any successful argument on your part has to apply across all possible interpretations of canon i.e. it has to show direct contradiction of canon from which there is no ability to escape via canon-compatible "what-ifs".

 

Agreed

'Must': This is what I don't agree with. Just because we don't have other explanations, doesn't mean they can't possibly exist. It seems like a logical conclusion, but there is no evidence to suggest the case.

Agreed

I haven't managed to prove the impossibility, yet what I'm saying is that there isn't enough evidence to even consider the need for proving such a thing.

I find the problem in your conclusion that because there are more students there must be more professors. There is absolutely no evidence pointing to it, which is why I don't believe I need to prove the impossibility of it.

EDIT: What's worse is that the possibility of the existence of more students itself is not a proven fact. It is a possibility, one that has contradictions of it's own. In such a case, the need for proving the impossibility of a conclusion claimed (without evidence) from a probable but not definite statement doesn't even arise.

 

This is a methodological maxim, not a logical principle. It saves you time and enhances efficiency of investigation, but all it does is allow you to evade issues that you consider unimportant. It doesn't allow you to say you're correct on those issues, because all you've done is ignore them.

If someone does push the issue, the maxim of "we don't need to address it" no longer applies, because it's already being addressed. Once it's on the table, it has to be considered on its logical merits.

You can say that you don't think the issue is important enough to merit discussion and walk away, but that's not the same thing as demonstrating the proposal to be false.

 

No, not really. What I'm doing is that saying there are two possibilities, and you stated both in your earlier post, the possibility and the actuality:

1) The Possibility: If there are more students, there MIGHT be more professors

While this case is possible, there isn't any evidence in canon to consider it. In fact, canon facts that I have stated in my previous posts suggest against considering this possibility. While it's not a definite proof, combined with the fact that there isn't any canon fact pointing towards it means that it doesn't really merit investigation.

Basically, while there are facts in canon that reasonably merit the investigation into proving or disproving whether there are a large number of unmentioned students at Hogwarts, the same cannot be said for the case where there are a large number of unmentioned professors.

This case also means that there could be other explanations of how the disproportionate number of students are taught, and since the larger number of unmentioned professors doesn't seem to merit investigation, it might make more sense to look into other possibilities.

2) The Actuality: If there are more students, there MUST be more professors.

Even within the framework of the existence of a large number of unmentioned students, this is a logical consequence, not an implication, which means that you need to back it up with proof. While you stated this in your earlier post too, you provided no evidence to back it up. In this case, the burden of proof is on you.

 

That issue (the truth of the "must be more professors" issue) is not connected to your assertion that there is insufficient evidence to make the entire issue of more professors worth addressing.

But nonetheless, I shall indulge you on the rather trivial issue:

Axioms:

1. All students at Hogwarts are taught magic in classes.
2. Teaching magic is performed by teachers.
3. Each class is taught by one teacher.

Argument:

1. There are 1000 students.

2. There is a maximum of 40 students per class (this is generous, it's probably much lower)

3. At any one time there are 25 classes.

4. Some 6th and 7th year students have free periods. Even if all of them have free periods at once, there are still at least 17 classes at once.

4. There is one teacher per subject (12).

5. 12 teachers cannot be in 17 classes simultaneously.

6. Either are are not 12 teachers, or there are not 1000 students.

7. If there are 1000 students, there are more than 12 teachers.


The only way to say that there are 1000 students without more teachers is to hold that there are 83 students per class.