In that case I'd say I'm in even less understanding of the difference between the "size" of infinite sets.

The way it was explained to me was the difference between the rationals and the reals -- my thought was to extend that to the rational sets "All Rational Numbers" and "All Rational Even numbers", and note how, intuitively at least, that the first seems to contain about twice as much as the second, even though both are infinite.

That's a paradox to me.

No. The measurement is true. Specifying the degree of error does not render the measurement untrue. The tank really does contain 25±1 litres. — Banno

Truth, so I'd put it, is a predicate which applies to sentences.

Measurements can be true, but it's not the same as "true" above.

I can be a true friend, and being a true friend is not the same as having a true sentence.

"The tank really does contain 25±1 liters" is true

Accuracy is the "25" and precision is the "±1 liters"

"The tank really does contain 25 liters", in this case, is true

"The tank contains '±1 liters' of what it reads" is also true

Does that confuse, or help, or do I need to say something else?

Physical measurements are not infinitely precise, nor is such precision needed. — Banno

Oh, definitely.

Or accurately? Precisely? :D

I think this lays out a good difference between truth and measurement -- we have to be able to say that the fuel gauge is precise, or accurate, in such and such a way in order to do the things we do. Thereby accuracy and precision get relegated to truth -- as the philosopher should want -- but then the truth of truth becomes wildly different from what the philosopher wanted.

It's due to the way that time exists, in conjunction with the limitations of our capacity to measure. We are limited in our ability to measure time by physical constraints. If we had a non-physical way to measure time we wouldn't be limited in that way. — Metaphysician Undercover

Heh.

Well, give it some time. Perhaps we'll figure out the non-physical way to measure time :D

I can't say I agree with your first statement because "the way that time exists" and "the limitations of our capacity to measure" are both things I think about with uncertainty all the time.

We're limited in terms of measuring -- but I want to say that Zeno's paradoxes are not problems of measurement at all. They are logical problems (which is why they evoke the difference between physics and logic and math, as the OP stated already)

I think it's a half-fib when I speak to people who really believe that what you measure is what you get.

You're right it's not a "fib" because measurement requires both, so as I understand it at least.

It's a half-fib because I know the person who thinks in terms of accuracy without precision will most likely not understand the difference. They'll understand that things can be uncertain, of course -- who doesn't? -- but probably doesn't understand that the reason this is uncertain is different from why the other things were uncertain.

There's that, and then there's the philosophically more interesting view expressed here:
Each measurement has a certain amount of uncertainty, or wiggle room. Basically, there’s an interval surrounding your measurement where the true value is expected to lie.
...the presumption that there is a true value; that given infinite precision we could set out the actual value as a real number. There is no reason to supose this to be true. — Banno

Yup.

The "accuracy" part of the distinction is what I consider to be a noble fib. Speaking to a person who believes that the gauge they've always used says exactly what's in there it's time to note a difference between accuracy and precision.

It's only a half-fib, because accuracy still ends up mattering. Using the fuel gauge example if you've used that fuel gauge so many times and know that when it says "a hair up from 1/4 tank" you can easily get from A to B and back to the Gas Station in time then it's accurate, if not precise. So accuracy is important -- it just has more to do with the reason things jump around. If a gauge jumps around over the usual precision limits you might have a problem with accuracy (i.e., the gauge is busted, most of the time -- or occasionally, from the history of science, you actually figure something new out)

Actual measurements fail beyond Planck's constants. These paradoxes are all hypothetical involving motions of dimensionless points along rational number scales. — jgill

Actual measurements fail far above Planck's constants :)

One of the concepts I've found hard to teach is the difference scientists attach to "accuracy" vs "precision"

Normally we'd interchange these words, which is the reason it's hard to differentiate. But they both deal with measurement, in reality, so are needed.

What you read on your fuel gauge on your car is a measure of how much fuel you have in your tank. The accuracy and precision of that gauge can be described as such -- suppose you have a particularly imprecise but mostly accurate fuel gauge, as I suspect most of them are. Then when it reads "1/2 tank" you know it's about, in terms of 16'ths, about 6/16's to 10/16's. Precision is saying "looks, you don't know between these numbers what it actually is" and accuracy is saying "it's definitely within this range that the precision says, and the "real" number is there but this is what you get"

****

What I'm asking is more about Heisenberg's Uncertainty Principle, which as he interpreted it meant that reality itself doesn't allow for a precision of both, but rather demands aprecision, or position,* of any one particle. But due to cuz that's how nature works, not cuz how we measure it.

*Blah. Speaking from memory makes me say wrong things. The precision of position and momentum are proportional to eachother such that a greater precision of position results in a lesser precision of momentum. Einstein interpreted this in mechanical terms, but the quantum scientists, at least of the time, interpreted this in real terms -- it wasn't the apparatus measuring but rather the behavior of the quantum particles which differed from the old billiard ball model.

More or less in the case of Zeno. Mathematics is often said to resolve the paradox in terms of the topological continuity of the continuum, by treating the open sets of the real line as solid lines and by forgetting the fact that continuum has points, meaning that the paradox resurfaces when the continuum is deconstructed in terms of points. — sime

The paradox between discrete and continuous seems a good example, to me on the outside, as something to treat Zeno's paradoxes as genuine paradoxes.

The way I put it to make it make sense to me: I can say there are "more" rational numbers than there are even numbers. Both sets are infinite, but it seems to me that the Rational Numbers > the Even Rational Numbers, as I understand the notions.

But that there can be "larger" infinites is a paradox to my mind.

In my view, Zeno's arguments pointed towards position and motion being incompatible properties, but the continuum which presumes both to coexist doesn't permit this semantic interpretation.

Is this in any way motivated by the uncertainty principle?

Mostly, though, I want people who are interested in the idea to participate; insofar that the "rules" enhance participation then thems the rules we should adopt.

In terms of choosing a topic: I think the format of "ask a question, answer a question" is good.

In terms of topics -- well, I already said I think it's a good idea to throw out topics. So say what topics you want! :D

"What is thinking worth in our political era?", "Why are we tempted to say that mathematics are universal?", "What are the reasons, if there are any, for our belief that Shakespeare is good?"

But we can still brainstorm topics here

It's not yet June ;)

And 500 words is a small ask. So treat this exercise as a small topic.

As having difficulty choosing a topic, I do wonder if having a theme (or several) would have made the activity seem less daunting. At one point, I remember that I'magination' was suggested but I think it was dismissed. Anyone could choose to use it as a prompt although it may be seen as unimaginive to do so. — Jack Cummins

I'm good with spinning out some possible topics for help here in this thread insofar that we all are thinking together.

Kant wanted to disprove metaphysics as a science with Newtonian materialism. What do you think? — Gregory

Not quite.

@Jamal robbed me of this notion once upon a time -- it's not Newtonian mechanics as much as the basis of natural science which contrasts with the philosophical history of metaphysics.

To break it down it's more like: Hey, you notice how we know shit about the world? And can predict it? And that the history of metaphysics, in comparison, is nothing but verbal disagreements?

Must be that the metaphysicians don't know as much as the scientists -- at least they can agree upon things I can't disbelieve, unlike the metaphysicians.

Hah! :D

And, also, I may be lost in the noise.

I’d be surprised if you were not with the familiar 1783 passage regarding “dogmatic slumbers”. THAT….is the root of Kantian dualism, the unity of rational vs empirical doctrines prevalent in his time. The two-world or two-aspect-of-one world confabulation was the illegitimate, red-headed stepchild of a veritable PLETHORA of successors, except Schopenhauer, methinks to be the foremost immediate peer that actually understood wtf the noise was all about.

Noise. Including, but not limited to….whether or not that which can be treated as a science, actually is one. — Mww

Heh, fair. I'm familiar, but undecided on the right way to read.

My preference is actually for the one-world interpretation, though it may only be a prejudice extending from my way of reading Pluhar's translation.

I think it gets along with the anti-metaphysics Kant espouses -- if there were two worlds then we could say there is a noumenal and phenomenal world, which looks a lot like a knowledge claim to me. Rather than two-worlds I think the two-aspect view gets along with the notion that we cannot know the noumenal -- it could be a second world, but it could also just be the things we can't know about the world we are in. Only God knows.

In that case, I am not sure if Hegel was understanding Kant properly. Because from my view, it is not clear that Kant's world view was dualism. What Kant said was that our knowledge can only give us understanding to the point of our experience, and that is the limit our reason. — Corvus

And @Mww

I don't believe that Hegel cared to understand Kant in the "proper" sense --i.e. in the sense that he'd count as a Kantian -- he only riffs on Kantian ideas to do his own thing.

But whether or not Kant was a dualist I think is still a matter up for debate because it sounds like the question of whether or not Kant was a one-world or two-world theorist. (Theorist isn't the right word -- these are two competing interpretations in the literature): https://plato.stanford.edu/entries/kant/#TwoAspInt

I own a copy of Science of Logic by Hegel, but it's huge. It's the A. V. Miller translation.

I'm wondering what the ISBN of that book is in your picture? I want to look it up and see what the difference is.

Far too few of us, I'm afraid.

Ahhh OK. Makes sense.

...

Now I might be contradicting myself, but then it seems like philosophy might be useful at something after all ;)

I should preface by saying that I've never been all too enamoured with morality as a field of study quite frankly. Using obtuse thought experiments to parse what is good and bad simply always seemed like a rather pointless endeavour, and I personally feel it's more fruitful to investigate morality in specific terms rather than universal terms and evaluate morality more so from a personal and societal perspective than from a seemingly objective view-point. — Dorrian

I cannot claim to say I always felt this way, but I do now.

But the question I wish to ask is, in some sense, aren't all universal moral systems inevitably going to be flawed in some way and therefore rendered futile? — Dorrian

I believe that all moral systems are flawed.

I do not believe that they are futile.

I can understand the feeling between the two. But upon examination it seems to not hold up.

A moral system can be flawed in this or that circumstance, and I have even less control over what circumstance I'm in than I have with respect to my believed moral system.

I'd point this out as at least an analogy for living: When I first started building wood structures I was terrible, now I'm OK. It takes time to become better, and on top of that there is more than one acceptable moral system to follow depending on what you're doing.

Continuing the craftsman analogy: You need to call a plumber, an electrician, a building maintenance manager, an automated engineering technology specialist, etc., to fix the job.

Why not treat morality as specifically as we treat the various industries where we make specifications?

In some ways I feel like it's the first social morality -- as I was influenced to pursue what I wanted as a child, so goes the moral systems.

They're not futile systems as much as incomplete, but necessary (in spite of their incompleteness!) ways of thinking. Or suggestions.

Heidegger ends Being and Time on Hegel's analysis of time. — Gregory

I think it's important to see that Heidegger never ended Being and Time by his own design.

I think he got lost in his own hermeneutic, or perhaps just ended in aporia from his initial ambitions.

The important thing to note is that he never finished his thoughts -- so they are interesting, but he didn't do what Camus did, for instance, in posing a question and then answering it.

You're making me want to become persnickity in the use of terms :D

"Intuition" has a special meaning in Kant, for instance -- it's the form in which the given is given. He doesn't insist upon intuition, though, but argues for it in the Transcendental Aesthetic.

I'd say that Kant's formulation of the categories of cause are the response to Hume.

But, I agree that these considerations are often...

a luxury not available to all. — Paine

For Hegel contradiction is the essential element in the changes and progress of the world. — Corvus

Yeahrp.

:up:

Reason itself is a faculty which analyses and finds truths, but if it is to employ transcendental logic for its operation, then does it not duplicate itself with another faculty of truth telling system? Does it imply that reason says true on X, but the logic says false on X at the same time? If both of them says true, then why does reason need the logic, and why logic needs reason?

Are they not rather actually the same faculty expressed in different terms? — Corvus

No.

There's a lot of lingo there that can be interpreted in various ways. But "No", I think, is the true answer to all of your questions above.

"Faculty" is a fun word from the early modern period. It doesn't specify much other than thought-furniture/functions in the imaginations of the early moderns.

Reason, in Kant, is a generalizations of the various powers of judgment which ultimately want truth.

I'd compare "Faculty" to "Category" in Kant, though -- not so much that reason itself is a faculty but faculties (categories) are a part of Reason.

Can it be that it it is the concept of "beyond our grasp" that is beyond our grasp?
(My old friend Ludvic suggested this to me.) — unenlightened

I think that's about right. To continue the metaphor, though, I'd say that we're grasping for something we sense but do not know where it's at -- such as when we feel a vibration through water of a liferaft being thrown to us. It's just out of grasp and yet we have a sense of where that's at without having a grasp of it.

:chin: I've no idea what you're talking about. Any links for the ignorant?

What is Kant's one great idea? — Gregory

According to Bertrand Russell it was the transcendental aesthetic, in the CPR.

I'd say it's his introduction to the CPR, though. A and B editions make different arguments, but the distinctions he's exploring in each just by way of formulating his question is amazing and great.

He had more than one, however ;)

In relation to Hegel I'd say his distinction between "Logic as such" (formal logic) and "Transcendental Logic" is similar in height to Hegels historical dialectic.

****

But really I think the two thinkers are different -- as a historicist might say :)

I, and others, do understand what it is to follow plus and quus and to choose which to enact. — Banno

Can confirm.

I would encourage people to participate, especially if they enjoy philosophy. — Sam26

I encourage you to participate on that basis, else fall into performative contradiction ;)

But, yes -- my thinking is that it ought be a celebration of the philosophical creative mind, and not necessarily the "greatest" paper ever or whatever that might mean. I promise to give constructive feedback to any entrant, as in I'll try to improve the essay from the perspective of the writer writing it, as the "hook".

But I say that because I look forward to reading lots of brave and original philosophy essays from our people.

except I rather think contradiction is certainly a necessary part of logic. Or, maybe, if not a necessary part, then at least the fundamental ground for the validity of logical constructs. — Mww

Good point.

"contradiction" is part of the logic, but in Kantian terms I'd say he'd deny that contradiction is ever true in the transcendental logic.

Heh, if Kant was anything he was not an absurdist, in my view. More the opposite -- that everything which can be understood can be understood in logical form. "One side", again, is a Hegelian philosophical concept. Kant does not subscribe to Hegel's notion of concepts having sides at all. "sides" would be, were I to take a guess, part of the categories in some fashion. Cartesian coordinates come to mind as a conjunct of the qualitative and quantitative super-categories. And the Ideas, in Kant, are things like God, Freedom, and Immortality -- there is no anti-God which defines God, or anti-Freedom which defines freedom (or whatever the contrary we'd decide to pick for the concepts).

The big difference between Kant and Hegel is that Kant set out to create a static philosophy that could be referenced in the future in resolving problems, much like Copernicus' science. His question is the possibility of treating philosophy, especially metaphysics, in terms of the sciences like Newton and Leibniz, but with a reflection to the problems of empiricism due to Hume. And Hegel incorporated the notion of history which moves rather than a static logic.

Hegel's notion of "one-sided" is basically his critique of Kant -- to be able to name an antinomy you have to be able to stand on both sides of it.

I disagree with Hegel's argument, for what it's worth -- I can point to a mountain without climbing over it, for instance.

j

was contradiction a necessary part of logic and/or reality in the worldview of Kant? — Gregory

No.

If we can only see two sides of an idea, how do we know they unite at a highet level?

Kant's use of the antinomies was to demonstrate that we do not know such things -- we can rationally argue for both the assertion and the negation, and both will appeal to reason, and they can be put side-by-side and end up in contradiction. For Kant this shows a limitation on reason's ability to answer some questions.

Ideas having a two-sidedness is very much a Hegel move and not a Kant move.

I agree, but feel like I shouldn't... — Banno

Welcome, brother! :D

To my circle of thinking that ends in . .. circles... of thinking......

Well he seems to think differently, though in my view if irony is based on expectation then nothing is ironic if you have no expectations.

That's why I'm thinking he's meaning relative or subjective, not ironic. — Darkneos

Does anyone have no expectations? Is that a good basis for understanding irony at all?

I can't say what David Moore means.

I don't take Quora seriously, to be honest. I participated a for a small time there in answering labor questions and saw how it's basically a social media game.

I don't think that irony is relativism, though. I'd go back to Plato to define Irony ostensively.

https://www.gutenberg.org/files/1635/1635-h/1635-h.htm

Ion is a great dialogue for defining irony; it ends in an aporia that makes Ion the butt of the joke, and it doesn't explain that throughout. You have to "get it"

I don't think irony is based on a lack of expectations, though if you're a dullard without any expectations I could see how irony is lost on a person.

heh ,no.

The thought that came to mind was how if the thread was posited this or the other way @Banno would say his bit, and I was thinking how it'd be right to say it -- whether it be against big knowledge claims or for small knowledge claims, it'd be right to point out those difficulties in relation to a philosophical question.

And you would have been right, just as you are right now. :D

To keep my annoying persona, I must say both-and :D

I didn't mean that up front though. And find:

My joke is rimshot cheese shit eating grin opportunity strikes... yours and Banno's joke is different and I definitely didn't think about it at all, until being pinged by Banno. — DifferentiatingEgg

A refreshing change of pace.

Well, here we are, talking about π - so, no, it is not beyond our grasp...

At least for some of us.

And what that AI describes as "the philosophy of Pi", isn't - any more than are the outbreaks of verse that sometimes litter these fora. Fluffy nonsense, like knowing the millionth digit of Pi — Banno

I'll take as the original joke. Not beyond our grasp, though there are some of us... -- it's a rimshot joke.

Though if forced I'd say that the litter of outbreaks in verse on these fora are closer to philosophy than the nonsense of the AI bots.

Well, you responding in this manner makes me wonder if I understand the joke?

I'm guessing we all pretty much get the joke?

We shall overcome, though. Unless we throw spanners in.

Stop which - the calculation, or the thread? — Banno

Well, it must be the calculation since the thread will never satisfy -- given how often we go past the point of explanation here :D

Well, here we are, talking about π - so, no, it is not beyond our grasp... — Banno

That's what I first thought -- and not just talking about pi, but knowing what we're talking about in saying pi.

Pi = the ratio of a circle's circumference to its diameter. — ucarr

What else could "grasping" consist in such that we don't grasp pi in the manner @ucarr says above?

There could be something deep in there --

What do we do with numbers like pi that go on forever? — frank

I'd suggest we stop at the point we are satisfied, while knowing that the procedure can carry on.

I think dude in Quora is expressing a point that makes enough sense, but I wouldn't put it in the terms of "everything is ironic" on a philosophy board.

Plato, I think, expresses an ironic attitude towards life; given the nature of the dialogues we can't say it was his intent or whatever, but Plato almost invented the notion of irony with his dialogues.

But he did so on the background of a universal desire for truth, at least. Even his allegories can be read ironically, as poetic testaments to a feeling of communing with the forms.

But, and this is what is so delicious about Plato, this interpretation will remain ironic in the technical sense -- that it's unexpected, a step removed, and itself will have contenders that bring about a deeper meaning without settling the question of irony or the question of the essay.

Everything isn't irony because most things don't end in aporia or comedy.