frank

Frege and Godel both believed something similar to this: Quine Putman Indispensability Argument

Right. It's a strawman that indirect realists deny that we know truths about the world. That's what you mean, right?

This is what we call trying to have our cake and eat it too.

catfish

I'm actually Socrates. I forgot to tell you.

Baloney.

Ok. I'm going fishing.

Don't bait me into giving my sociological report on this thread. :cool:

I agree with Hanover that if the question is supposed to be metaphysics, it isn't resolvable. I agree with Banno, that indirect realists do claim to k...

It kind of looks like your alternative involves people walking into a fictional world and pretending it's all real, drawing conclusions based on it's ...

How would you characterize the view of your opponent?

It's a rejection of set theory. We wouldn't even talk about the extension of the real numbers. There is no extension.

If you keep reading, the SEP explains that the arguments that he wasn't a finitist are weak. He would say there's no fact of the matter regarding who ...

According to the SEP he was a finitist. You're imagining that there is some finitist approach to set theory. There isn't. Look it up. :brow:

This thread is a war of definitions.

Wittgenstein would agree with this view, and it's why he rejected set theory. I posted a couple of quotes above that show that.

That is correct.

It sounds like you're saying that zero times infinity equals 12. :lol:

Sure. Prior to the 19th Century, a convergent series would have been treated as if it reaches the limit, though it would have been ok to say it's actu...

@"Metaphysician Undercover" I think you would approve of Wittgenstein's view. He was a finitist, and a math anti-realist. He didn't believe in set the...

Indeed. Neither has it been shown that something goes wrong in practice if we treat a convergent series as unequal to the limit by an infinitesimal am...

I notice numerous posters have the same attitude: that math is somehow immune from philosophical inquiry, and that if it's all built on nonsense, that...

I understand. In my approach to any topic, I need a skeleton, and then I put flesh on it. As it grows, my comprehension grows. So with any philosophic...

What? I thought you were telling me to drop it. :lol:

I wasn't being critical. Defending an idea without understanding it is a sign of a conservative spirit. Nothing wrong with that. Ok. We can drop it.

Point-wise convergence is considered to be a weak explanation for how a series converges in a way that allows us to say the limit is the sum. Uniform ...

Actually, I was trying to understand it myself. It's tough finding an explanation in plain english.

Oh dear. It seems you can't.

No. Can you explain the difference between point-wise and uniform convergence?

I read about it, yes. Cauchy's original solution was eventually rejected in favor of Weierstrass's solution. As has been mentioned, this is history th...

No.

Absolutely. Never to come up again. :grin: My first calculus teacher was awesome. He told us this story about when he was young and he dropped some me...

Cauchy, Weierstrass, and Riemann saved calculus from mounting criticism that it doesn't make sense. So, that did become the topic. We've finished talk...

Yes. I don't think either of us is interested in arguing about what that actually means. Let's leave it.

I actually took a deep dive on this at one point. The electron is, in fact, conceived by scientists as a point. It's startling, but true.

You're right that per Cauchy, the sum of the series is the limit. However, the devil is in the details. The sum and the limit are never equal. see her...

It is. An electron is a point particle.

Yea, you're wrong. How so?

That's incorrect.

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 def...

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

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 t...

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

Ok.

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'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 ...

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

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.

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