Ok. Details? — Banno

Yea, you're wrong.

It's also an answer to this, I think. — Srap Tasmaner

How so?

The limit is not “almost” the value. — Banno

That's incorrect.

Tell me where I’m wrong if you can. — Banno

According to Zvi Rosen, the sum and the limit are not equal (according to Cauchy). They're just as close as we "want" them to be. This is Cauchy's definition of a limit:

When the values successively attributed to the same variable approach indefinitely a fixed value, eventually differing from it by as little as one could wish, that fixed value is called the limit of all the others. — Cauchy

So it's true that the idea of an infinitesimal was removed, but the idea of infinitely small remained, and we added the idea of "as small as we want."

We'll see what the other's said.

Wait, what? — AmadeusD

You don't have confidence that you can tell what's true and real?

That is to say, none of this discussion is responsive to the metaphysical question of what the fundamental constitution of reality is. As in, what is the apple in the noumena? — Hanover

That is correct. Both sides of this argument start with irrational confidence in our ability to discern what is true and real. Neither side proposes to build a bridge to that confidence. As you noted, there is no bridge to it. You just have it.

Starting with that confidence, we observe by way of anatomy and physiology that perception of the world appears to be constructed by the brain out of discreet electrical impulses. As you note, this is not a metaphysical argument, it's a scientific fact.

For a convergent series the sum is defined as the limit. There is no residual “infinitely small difference” between the sum and the limit. The sum is the limit. Partial sums are less than the limit, but their difference goes to zero in the standard real number system. — Banno

This is all from proofs by Cauchy that I don't understand. Do you understand it?

For a convergent series the sum is defined as the limit. There is no residual “infinitely small difference” between the sum and the limit — Banno

Ok.

I don't agree. I think the average scientist would say that it doesn't make sense to talk about infinitely short distances — Metaphysician Undercover

But an electron is conceived as a point. It doesn't have any length or height. Isn't that the same as the idea of an infinitesimal in math?

It is a difference between theory and practise. In theory, the sum approaches the limit. In practice the sum is the limit. The latter can be understood as "rounding off". Failure to recognize this is to misunderstand. — Metaphysician Undercover

It's not an ordinary sort of rounding off, though. The difference between the limit and the sum is an infinitely small number. We could say that this solves Zeno's paradox as along as space and time actually conform to the calculus framework. I think the average scientist would agree that they do conform, but there is still room to reject the calculus angle.

I'd say I directly perceive pain, colours, smells, tastes, etc. — Michael

The experience of pain is generated the same way the experience of seeing an apple is.

I didn't say that. — javi2541997

That's cool. So you know you aren't better anyone else. Anywhere. Ever.

I don't think there's any such thing as direct perception. The only perception there is is indirect.

We are not perfect, but at least we are not like you. — javi2541997

Simmer down there Franco, you aren't better than anyone else.

I mean lay out the methodology of this experiment, show me what we're measuring, and show me the results we have to arrive at to prove direct realism is true.

My point just being that the question is nonsense. It can't be proved in principle. It's unverifiable, just as is indirect realism is unfalsifiable. You would have to assume indirect realism to even perform an empirical analysis, considering empirical measurement relies upon perception.

For some reason this thread conflates "physical" with "metaphysical." Telling me we describe apples in the physical world as X doesn't tell me the fundamental nature of things. It can't. — Hanover

Some people wouldn't be able to accept what you're saying because it would mean they have to accept that the world may be a dream. We really don't know. It's emotion that makes them cling fiercely to a particular worldview, so they don't care if what they're saying is nonsense.

I think there's an incomprehensibility field around Wittgenstein's Tractatus. Even after a person understands it, they'll say yes, but.. the world is this or that. Emotion drags the mind around. The only way to free the mind is to admit: I don't know.

:grin:

What experiment would prove the validity of direct realism as you define direct realism? — Hanover

It would have to show that the world is actually a dream. You directly perceive the world because there's no interface. The world is created by you, from the contents of you. It would have to show that you're God.

BaShana, BaShana, BaShana

I think that this "Fort Sumter"- — ssu

A Fort Sumter moment would require that half the states had already seceded. :cool:

No, you described a long process, and the problem is with the use of "at some point". How does a process occur at a point? — Metaphysician Undercover

I think you just need some more of whatever mind altering substance you have available. Then you'll get it.

Since the Ukraine war started, Russia has engaged in "systematic dismantling of independent civil society, harsh suppression of anti-war dissent, and the persecution of minority groups."

In the US, we're about to explode because 2 people were murdered by ICE. That's actually a good sign about the health of rule of law.

would say the opposite is the case, what you say sounds bizarre. You are representing driving through British Columbia, as being in British Columbia at some point. What does "at some point" even mean in this context? You use it because it's an acceptable figure of speech, but taken literally, it doesn't fit. So what does it really mean? — Metaphysician Undercover

Being in British Columbia usually entails waking up in your car with a Canadian citizen tapping on your window to see if you're ok. You roll your window down and try to do a Canadian accent so they don't know you're American, at which point they just stare at you. Does that explain it?

Yes and this is, as you probably know, one of Nietzsches main issues with a purely utilitarian view on morality. We need some adversity to be able to grow. The quest to reduce all suffering would ultimately also reduce what we can be as human beings. — ChatteringMonkey

:up:

This is the real natu — Metaphysician Undercover

Ok. All I know is that it's common sense that if you're driving from Washington DC to Alaska, you will, at some point, be in British Columbia. Those who claim this view is wrong should at least acknowledge that what they're saying sounds bizarre.

I read you as basically saying there's a higher truth missed by Zeno. Per tradition, his point was exactly that: that the way we picture the world, the way we commonly think, is missing something.

If you go back and look at one of the paradoxes, they're pretty simple. Looking at in terms of truth it starts here:

Isn't it true that in order to get from point A to point B, you have to travel half the distance between them?

Who would say no to that? How could you get from A to B without arriving at a point that's halfway between? If you say no to that, you've already ejected yourself from common sense. If you say yes to it, you're on your way to being ejected from common sense because there's a convergent series of points between. Either way: common sense has a problem.

There are two kinds of people: ones who can tolerate a threat to common sense, and those who can't. I think the first category is usually non-linear thinkers.

A Euglena is a one celled thing that has both mitochondria and chlorophyll. It's hard to kill because if it has light, it gets energy that way. If there's no light, it can eat.

Plants and animals both went through all sorts of evolution trying to survive, and in the process, became complex, but they're still precarious compared to the Euglena (algae).

Which just goes to show: we humans exist because of adversity. If we had utopia, we would just sit there.

Supertask. It's the reason Zeno's paradox stands.

:up:

I don't think anyone in this thread had forgotten, or that anyone was confused. — Srap Tasmaner

I think I could find cases of it in this thread. I'm not going to mine it to find them though

Some people reject talking about infinite collections — Srap Tasmaner

And since you bring that up, let's look at the difference between a collection, an extensional definition, and a set. Just because I think we need to stuff that difference down this thread's throat. :blush:

The extension of an idea need not be thought of as an abstract object. A set has to be thought of that way. There's no choice. The people who invented set theory knew that.

Which some authors prefer, but it means what other authors mean by "countable". So long as we know what we mean, "The natural numbers are violet" would do just fine. — Srap Tasmaner

Absolutely. Let's keep in mind that it does not mean the same thing as countable as the word is commonly understood.

And yet they are countable. Look it up. — Banno

Denumerable, yes. Let's not mistake that for countable in the common sense of the term. I think that's where some of the confusion in this thread is coming from.

The natural numbers are also a proper subset of the rationals, but they're the same size. — Srap Tasmaner

You mean they have the same cardinality. Neither one really has a size.

The natural numbers are countable. — Banno

You couldn't finish counting them.

Still, forcing the unwieldy mass of rational numbers to line up single file to be counted was a master stroke. — Srap Tasmaner

It's just that the extension of the idea of the real numbers seems to be somehow bigger than the extension of the idea of the natural numbers. We could express that by saying it appears the set of natural numbers is a subset of the set of reals.

Neither set is countable, but that sense that one is bigger than the other was expressed in terms of cardinality.

Chickadees are dinosaurs, but they are a far tweet from T-Rex — BC

They're doing the best they can. There was an asteroid issue.

I like to emphasize that we are part of a continuum of life which has been created over a long period of time. Our evolutionary history is why "we are what we are" and every other species is what it is as well. — BC

About 99% of species that have existed on earth are now extinct. Do you have thoughts about the end of our species? I always thought it was kind of un-face-able, but do you feel like the possibility can be faced, and accepted? If we really are part of a continuum, maybe it's ok, because something else will take our place.

Being an object is a role in a language game, not an ontological status. — Banno

So the same thing will work for "abstract" and "platonism.". They're parts of a language game. You can't reject them without special pleading.

Godel said we perceive abstract objects. He would know.

L. Ron Hubbard didn't win a Hugo. In my collection, Asimov talks about the convention where his followers showed up demanding that he win. There was this weird tone in Asimov's writing when he talked about it.

It's a Hugo winner. It's in a collection of winners I have, edited by Asimov.

Why not? I have nothing in my pocket, therefore I have nothing. — Banno

It doesn't sound like you know what a set is.