fishfry

Banach-Tarski means nothing about actual space. It's a valid technical result that applies to mathematical Euclidean space. There's no reason to belie...

I remember my logic professor telling us about the Scheffer stroke, which can be used to define all the other logical operations. It's equivalent to N...

Sadly I must agree with you. Trump's been captured by the neocon warmongers. He got rid of Bolton but Bolton is still running US foreign policy. Trump...

There's no war, everyone needs to chill out. As Trump said, he killed the Iranian general to avoid a war, not to start one. Trump is the only person i...

I think I realized that a little later but didn't go back and update my post. Ok so there is no complement of the empty set, but the negation of T is ...

Gun rights aren't a core issue for me. I don't actually know any gun rights sites or spend any time thinking about the issue. I do read some right win...

Part 2 A lot here to work with. Let me break it down a little at a time. I've already made many of these points in other threads lately so I'll try to...

@Meta, I've read through much if not most of your writings in this thread. I think I understand where you're coming from. I found two remarks I can ge...

Look at the national orgy of bloodlust when the US kills some Iranian general whose name you never heard of yesterday. Bloodlust is popular these days...

The context is that "this" is the discovery by the Pythagoreans that for any pair of integers, the ratio of their squares can not be 2. @Meta as I men...

Buzz. Wrong. There's no universal set. Russell's paradox. You can't take the complement of the empt set except with respect to some given enclosing se...

The opposite argument is that it's bad pedagogy to expect high school students to understand the sophisticated constructions of higher math. It's true...

Difficult to take abstract at grad level without undergrad. Abstract algebra shows up everywhere. Physics is a lot of group theory these days.

You know Penrose's idea? He thinks consciousness originates in quantum interactions in the microtubules of the brain. https://en.wikipedia.org/wiki/Qu...

Yup. New math, new new math, Common Core. One educrat failure after another. I have no idea what the answer is.

I don't know enough. I know that it's categorical in flavor ... but then again so is differential geometry. I'll dispatch a clone to study up on SIA a...

Yes, that was an attempt to teach set theory in grade school. Needless to say the teachers were confused and the students were confused. Big fail. Now...

So just as I call modern constructivism Brouwers revenge, I can call SIA Peirce's revenge. This is very interesting. Do you happen to know how SIA rel...

Construct in this context means build a thingie within set theory that behaves exactly like we want our thingie to do. For this purpose, the construct...

We're in deep and complete agreement on this. The mathematical definition of the real numbers is far beyond high school students; in analogy with the ...

https://en.wikipedia.org/wiki/Hyperreal_number The hyperreals are a model of the first-order axioms of the real numbers that contain infinitesimals. T...

Perhaps you could state them succinctly. I prefer not to wade into this. You have an ax to grind and I've only succeeded in upsetting you. If you'll l...

I'm not an expert in these matters. Perhaps someone else can jump in.

Your eyes tell you there is a continuous gradation of light. Physics proves otherwise. For that matter your senses tell you the world is flat. Science...

It's worth noting that the pedagogy retraces the history. Newton developed calculus to study the motions of the heavens. He was not able to drill down...

I do not believe that could be true according to the known laws of physics. A sufficiently high frequency would eventually require back-and-forth move...

What?? First, the technical construction(s) of the reals are taught only to math majors in a class called Real Analysis. Nobody who's not either a mat...

I admit to not understanding the distinction between real and actual as you tried to explain it in this post. But consider Internet security. Are cryp...

Yes I do. That's why I can't so easily sign on to the proposition that math isn't true. Some parts of math are obviously true, or actual. It's easy en...

Question: Do you think that "5 is prime" is true? Or merely logically possible? Or a complete fiction made up by evil set theorists? I think "5 is pri...

I quite agree. The Internet was going to change the world for the better but in many very serious ways made it worse. Just look at China's social cred...

But enough about Obama, who ran a brilliant social media campaign. https://www.theatlantic.com/technology/archive/2017/01/did-america-need-a-social-me...

A server. They run the Internet. This website runs on a server in some datacenter. There's no display connected to it. When the IT folks need to acces...

Sure, everyone who disagrees with Searle about the Chinese room argument. Just Google Chinese room and half the links will be on one side and half on ...

There are two distinct ideas that are often conflated in the literature. * The video game argument. In the 70's we had Pong and now we have realtime n...

I don't think that helps any. You're starting out with bad notation and that's leading to incorrect conclusions. By collection do you mean a proper cl...

Then we have nothing to talk about. I still owe you my thoughts on the bijection thread, where you made a couple of remarks that I can use as a starti...

Good, I thought it was just me. In fact after I posted I looked up his name and found that when he submitted his 2005 papers (so fifteen years ago) on...

Inaccurate notation, since by the axiom of extensionality, the set {b,b,b,b,b,...} is the exact same set as {b}. Perhaps if you notate it \{b_1, b_2, ...

Ah. But I'd call that a strawman. The "widespread misconception." There isn't ANYBODY out there beating the drum for the proposition that the mathemat...

Wow that nutball Peter Lynds is still around? I heard of him about ten years ago ... maybe fifteen or twenty, now that I think about it. It was on Use...

Naming conventions are a matter of historical accident. Banach-Tarski is a theorem. It's not actually a paradox. It is however a veridical paradox, wh...

Oops thanks I left out the exponent of the -1. Fixed it. Not sure I followed the rest of your remark. My post is intended to clarify the thinking of a...

I happened on this remark which you made a while ago. I wanted to note a correction. Consider the rational numbers. They have what's called a dense li...

Quibble-wise this is not true. Originally, a cardinal was the class of all sets with that cardinality. The trouble is that those classes are proper cl...

I have not followed all these posts for a while so I don't know if this is still a point of confusion. I just want to assure you that I never could ha...

Depends on what you mean by mark. Every point on the real line "marks" that point. All the irrationals and even the noncomputable reals. Every real nu...

Rock and roll Brother Tim. Thanks for the kind words. It's all good. I haven't read the intervening posts so perhaps some of these points have been co...

No, this is not true. But it's such a common misunderstanding that a bit of exposition is in order. One of the first things to know about the philosop...

Ok then what's wrong with, "Can you please explain yourself," versus, "My drill sergeant says you should suck it up, buttercup." What is the point? I ...