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.

You said this:

We've shown how quantification can be handled without invoking abstract objects at all — it’s rule-based, normatively grounded, and socially coordinated. — Banno

Now apply that strategy to the empty set. You'll find that you can't. Set theory is fundamentally platonic. Eject platonism, and you've ejected set theory.

A no to what? Set your account out. Say something. Do the work. — Banno

I've just been observing the different stances people are taking. The only book on phil of math I've read is Mary Tiles' book. After reading it, I realized the ways that set theory is conceptually objectionable, which might not be surprising since Cantor was a mystic, and his mathematical views were directly related to mysticism. Tiles doesn't campaign against set theory by any means, but she does leave the reader with the thought that we may one day rethink the whole thing. It may be that Aristotle was right after all.

Is that a no?

This is platonism. The abstract object is independent from minds, but accessed by them. — Metaphysician Undercover

Yes. I know. You pretty much came up with Frege's argument all by yourself. That's pretty cool.

We've shown how quantification can be handled without invoking abstract objects at all — it’s rule-based, normatively grounded, and socially coordinated. — Banno

Ok. I don't object to that. I doubt you can do the same thing for ZFC, though. So are you now suspicious that ZFC might be bullshit?

What of quantification? — Banno

What about it?

Perhaps you misunderstood...? — Banno

Could be.

You could say that. The point though is that if a numeral refers to a number which is an object, and that object is said to be an idea in someone's mind, then it would be a different object in each mind. — Metaphysician Undercover

An object in your mind is called a mental object. An object in your hand is a physical object. An abstract object is something that isn't physical, but it's not simply mental either.

The only way to assume that the numeral refers to the same object for distinct individuals, is to assume that the object is independent. — Metaphysician Undercover

That is correct.

So you've just completely changed your mind here. You were quoting ZFC as if it were scripture a few pages back. Then you were a deflationary nominalist. Now.. I have no idea what you are. I think you might be constructing your view as you go along.

Dude. According to that survey, a small minority think the foundation of math is set theory. There aren't a lot of experts in phil of math, but they would all roll their eyes at that. :grin:

That's permitted, under the rules... — Banno

You have the minority view, so you must be following the minority rules. :razz:

Elements in a language game can be things - because we quantify over them... all these numbers are even, all those numbers are prime. — Banno

You're trying to have your cake and eat it too.

Despite my obvious addiction, I am still functional. But it's going to be 36℃ today, 42℃ tomorrow, so productivity occurs inside or in the early morning. — Banno

-15C here. :confused:

What I said, is that if a numeral is taken to refer to an object, a thing called a number, that object must be a platonic object — Metaphysician Undercover

So math is just language games, right?

Wow! Being productive. :up:

There was a lot of strenuous protesting in this thread to the effect that infinity is a thing. Turns out you actually agree with Meta. Numbers aren't things. They're just elements of language games.

Why should I care? — Banno

Because you're procrastinating from whatever it is you're supposed to be doing right now?