We could assign points to a piece of knowledge based on how many other pieces of knowledge depend on it, which is the same as how many facts would lose their factual status if that piece were either disproved or forgotten.

The trouble with that is, knowing you live on planet Earth would have more knowledge points than knowing that there are 12 stars with planets in the Pegasus constellation, even though the latter contributes to knowledge much more than the former, which is trivial and obvious.

Does it even make sense to quantify knowledge? — Moliere

No less sense than it makes to quantify ignorance.

so long as time passes, there is knowledge of it to be had: ever moment, ever temporal event has new knowledge as it evolves from whence it came - the past.

That's interesting though because it shows how there should also be some qualitative dimension if we're going to say something like "A knows more than B", but the quality is a relationship to other bits of knowledge. So we have trivial knowledge, like "I live on planet Earth" and non-trivial knowledge, which seems to take some kind of either work, or evaluation.

I agree! These things sit together. And why it's almost a real question -- because we often do make this comparison between persons. We trust a mechanic to be able, to know, how to fix a car, and a dentist how to diagnose health problems of teeth -- but also we will often dismiss persons who demonstrate ignorance.

So there is a comparative notion which seems to indicate that one can have more or less knowledge. But what is the unit, then? That's the part that seems nonsensical, but if something is more usually we'd say it is a larger quantity, rather than a larger quality.

True! Let's say for any given time-frame, given that knowledge is in flux.

Some would say knowledge is identical to actions (or inaction as the case may be.)

Everything either acts or doesn't, so basically the size of Knowledge is the size of the universe. But the universe is probably infinite.

In comparison to the set of real numbers is it a bigger or smaller infinite?

EDIT: A bit of a nonsense question in follow up to a nonsense question -- but it'd at least give a basis of comparison.

It could be that knowledge is innumerable, which I suspect, but then how do we get to comparing people who have more or less?

In comparison to the set of real numbers is it a bigger or smaller infinite? — Moliere

I think it would just resist quantization. The universe has no size.

It could be that knowledge is innumerable, which I suspect, but then how do we get to comparing people who have more or less? — Moliere

We can probably only guage the extent of a person's knowledge about a certain topic. The plumber knows more about pipes. The homeless junkie knows more about how to find a place to sleep.

Sounds right to me. And I'm fine with waiting until after we see a particular person do something or any other criteria we might imagine. So a plumber knows more about pipes than me. I want to resist the homeless junkie bit, but I agree that homeless persons know more about surviving without a job or home than those who have a job and home.

You see how strange it is that knowledge is innumerable and that there are people who know more?

Does it even make sense to quantify knowledge?
— Moliere
No less sense than it makes to quantify ignorance. — 180 Proof

:lol: :ok:

Does it even make sense to quantify knowledge? — Moliere

No, not if it is the case it is impossible for an otherwise rationally competent subject to have no knowledge.

To quantify knowledge of, or knowledge that, is readily admissible, but that’s not the same as quantifying knowledge in and of itself.

How much knowledge is there? Only as much as there are subjects to which it belongs.

Owie-powie -- I feel I missed the joke at my expense.

Not that I mind it. I put this in the lounge for a reason.

No, it's not at your expense. It's just a playful juxtaposition. :pray:

Heh. Cool.

I suppose, in spite of my Epicurean aspirations, I am a sensitive whatever. I appreciate the clarification :)

You see how strange it is that knowledge is innumerable and that there are people who know more? — Moliere

Yes. And then there's Meno's paradox:

If you know what you're looking for, inquiry is unnecessary. If you don't know what you're looking for, inquiry is impossible

I think there might be something like latent knowledge, maybe part of the structure of mental processing, that develops with socialization. It occurred to me as a child that I can't teach someone what blue is. They just have to experience it for themselves. A lot of math is like that too. You can't drill a hole in someone's head and pour it in, they have to discover it for themselves, again, as if they already knew it and the math teacher is just pointing to the knowledge to help them gain consciousness of it.

If that's true, that we all have the same (or similar?) latent knowledge, then what's left is the novel and the unique. But think about how you would tell someone about something that is truly unique. If it's completely outside their experience, I don't think you'll be able to convey it. You'd have to try to compare it to something they do know about.

You see how strange it is that knowledge is innumerable and that there are people who know more? — Moliere

I come from a sociology background; this sounds rather... mundane? Quantifying innumerable things is what sociologists have always done. But they don't usually do it for the sake of it; there's a research question that drives how to quantify things.

I've once been asked, on the street, to test new recipees for orange juice. They'd ask questions about how much I liked the taste, colour, etc., and they provided me with a ordinal scale from 1 to 10. Oh goody. The ordinal scale made sense. I mean, the minimal ordinal scale would be: (1) don't like, (2) like. It's an ordinal scale, because we value (2) more (I won't buy juice I don't like). What's not there is a stable distance between (1) and (2). It's just an order.

The minimal ordinal scale isn't very thorough, though, and judging can become kind of arbitrary for so-so cases, which might fall in either slot, depending on mood. So maybe something like this (1) yuk, (2) meh, (3) yum.

Or maybe (1) get this away from me, (2) if it's all there is, (3) maybe sometimes, if I'm in the mood, (4) yeah, that's good, (5) MUST HAVE!

Go higher than (5) and the accuracy of the scale falls apart, because it's really hard to even figure out what the bullet points mean. (Rating behaviours are interesting: you create a five star rating system and people give out half-stars, if they can't decide between two ratings, but you make a 10 star rating system, and for a significant portion of people who rate, five stars will be bad rather than avarage, and around 7 will be avarage. Quantifying ordinal scales with no clear numerical substratus is common, but it has its quirks.)

Knowledge is easier to quantify if you have a topic in mind. For example, reading on this boards its clear to me that I know more about philosophy than some, but less about it than most on here. There are questions about the quality of the knowledge, too: what I know about philosophy I mostly know from secondary literature - I usually haven't read more than excerpts from the philosophers themselves. And what I have read is more spread out than focussed. Also, because of the Dunning-Kruger effect, asking people how much they know is tricky as a form of collecting the data: If you don't know anything about a subject, you also don't know what areas you're particularly ignorant about, so it feels like you know a higher ratio than you do. The more you learn, the more your ignorance becomes apparent, and then you feel you know less than you do (knowing what you don't know is relevant knowledge, too, and it also presents the opportunity to learn).

So, yeah, knowledge is probably best described as an ordinal scale. It doesn't meet the requirements for an interval scale. And how you quantify it depends on what you want to know, and how you can fruitfully measure it.

I come from a sociology background; this sounds rather... mundane? — Dawnstorm

I think that likely. :)

Quantifying innumerable things is what sociologists have always done. But they don't usually do it for the sake of it; there's a research question that drives how to quantify things.

I've once been asked, on the street, to test new recipees for orange juice. They'd ask questions about how much I liked the taste, colour, etc., and they provided me with a ordinal scale from 1 to 10. Oh goody. The ordinal scale made sense. I mean, the minimal ordinal scale would be: (1) don't like, (2) like. It's an ordinal scale, because we value (2) more (I won't buy juice I don't like). What's not there is a stable distance between (1) and (2). It's just an order.

The minimal ordinal scale isn't very thorough, though, and judging can become kind of arbitrary for so-so cases, which might fall in either slot, depending on mood. So maybe something like this (1) yuk, (2) meh, (3) yum.

Or maybe (1) get this away from me, (2) if it's all there is, (3) maybe sometimes, if I'm in the mood, (4) yeah, that's good, (5) MUST HAVE!

Go higher than (5) and the accuracy of the scale falls apart, because it's really hard to even figure out what the bullet points mean. — Dawnstorm

So one of the things that's different here is that with sociology you're interested in the opinions of others, at least in this form of numeration. So with the orange juice research they were probably interested in which orange juice formula would sell more, and hoping that if they test it out in small batches with opinion surveys they can find which formulation might sell better.

There's no such question with respect to numerating knowledge. At least, if I were to come up with a scale for knowledge then I wouldn't ask people's opinions about it. Knowledge isn't opinion-relative, unlike the example of using numbers to give an order to how much someone likes something or doesn't like something.

At least with the orange juice example you can say what 1 and 2 and 3 mean -- Good, meh, and bad. In a way it's more of a counting exercise where there are three sets of persons and you're asking people to classify themselves into one of the sets as the operation of counting.

But what possible operation of counting would there be for quantifying knowledge that actually somewhat tracks with what we intend when we make a judgment that a person has more or less knowledge than something else?

(also, is knowledge the sort of thing that can only be judged by comparison? I.e., it is more or less, but not numerated, even in an ordered sense)

So, yeah, knowledge is probably best described as an ordinal scale. It doesn't meet the requirements for an interval scale. And how you quantify it depends on what you want to know, and how you can fruitfully measure it. — Dawnstorm

So let's just take the example problem of comparison, since we're on the same page there -- we agree that we can make a comparison between persons and have a vague but still true idea that someone is more or less knowledgeable within a particular discipline in comparison to another person within that same discipline.

So would the operation of counting be relative to some kind of expert who knows more? Such that the comparative judgment is also relative to a third person, a judge or expert?

So would the operation of counting be relative to some kind of expert who knows more? Such that the comparative judgment is also relative to a third person, a judge or expert? — Moliere

Well, we could look at school grades as an ordinal scale to measure knowledge retained until test time. We have the institution of grading, the syllabus, the judgement of the teacher, the studen't mindset during test situations... To what degrees to school grades represent knoweldge? An A definitely represents more knowledge than an F, but what you're counting is success. How does success at tests relate to the student's knowledge? Why is society interested in grades (and what about alternative teaching models not relying on grades)? And so on.

I'd say an A does not definitely represent more knowledge than an F -- for instance, if one grades on a standard curve such that there will always be a person who gets an F and always be a person who gets an A the grading system forces people into a grade rather than measures knowledge because the teacher believes it fairest. Grades are awarded on a basis of merit, which in turn requires a standard -- but the standard is never the same between classes, or even between teachers.

What's more, in a comparison between persons I wouldn't ask what someone's grade was or their respective GPA's -- these things are very much a feature of our social world wanting hierarchies associated with merit and less to do with what people know. In a workplace no one cares what grades someone got, they only care that the person is competent.

In a way -- in order for us to posit a grade scale we already have to be able to make this judgment about how knowledgeable someone is.

I'd say an A does not definitely represent more knowledge than an F -- for instance, if one grades on a standard curve such that there will always be a person who gets an F and always be a person who gets an A the grading system forces people into a grade rather than measures knowledge because the teacher believes it fairest. Grades are awarded on a basis of merit, which in turn requires a standard -- but the standard is never the same between classes, or even between teachers. — Moliere

Yeah, I agree. I was being sloppy here. (I've discarded a much longer post, where I went into more detail, both before and after I mentioned grades.) Beyond it being hard to compare grades, there's also the fact that failure on tests can be non-knowledge related: nerves, motivation, distraction, illness, and so on. I personally once decided to skip a course at University, but I still took the test, for the heck of it. I didn't bother to think through questions that didn't interest me, so not even I know how well I'd have done had I been motivated.

It is, however, something you can count; and you'll need to think through why you're thinking of counting just this, and what the weak points are here in your assumptions, and if/how you can make up for those.

In a workplace no one cares what grades someone got, they only care that the person is competent. — Moliere

Yes. Which is why I asked why the question is important. Depending on the motivation for asking that question, what counts as knowledge might even change. (I mean, if what you're counting were directly related to knowledge, you'd probably have an interval scale - and a limited operational definition of what knowledge is in that context. For example, for someone to take a test, that person needs to know what a test is, but that particular piece of knowledge isn't tested for, and thus outside of the scope this particular counting operation.)

And the word "competent" is interesting, too. What's its relation to knowledge? Know how. Know that. Know why...

(I'm not being at my most systematic here, I'm afraid, but luckily this *is* the lounge.)

(I'm not being at my most systematic here, I'm afraid, but luckily this *is* the lounge.) — Dawnstorm

:) no worries. I put it here for that reason -- there's something-ish there, but I am also not being systematic. More floating and grasping.

A joke version of the question: how are a priori synthetic judgments of a priori synthetic knowledge possible?