Question: Do you put the same constraint on Cinderella's coach? Why or why not? Want to understand your answer. Regarding the rest of it, I'm lamped o...
Thank you. If you're interested in this stuff, do you know the nLab Cafe? It's a category theory wiki. Here's their page on the theorem It's all very ...
Use of language. When a mathematician says, "X can be done," that's just as good as doing it. There are many jokes around that idea. There's a formali...
Not link, quote. Either quote a fragment of my post, as I just did to yours; or else just mention me as @"fishfry", where you have to type "" around t...
Yes. Quite the epiphany. I've actually just found several web pages and articles explaining all this. One even mentioned that the converse of extensio...
@"TonesInDeepFreeze" I didn't get to your most recent yet. But I did have a bit of an epiphany and it's possible you may be steering me to enlightenme...
Ok I'll check again. I'm reading the SEP article on identity, and it's interesting reading. Puts some of what you've been saying in context. They did ...
Ok thank you for that specific reference. You should know that I generally respond to my mentions and don't always monitor the threads. Please give me...
Oh thanks. I dropped by the site and saw I had 6 mentions and that they were all from you so I was snapping back pretty quickly without actually readi...
wut? axiom of infinity. what's wrong with you tonight? you just blasted out six mentions of me, one more mindless than the next. (edit) Some of them w...
Spare me. I just looked through Enderton's logic book, The word indiscernible does not appear in the index. I looked up identity and did not find any ...
Was referring to all of us, not anyone in particular. https://en.wikipedia.org/wiki/Mostowski_collapse_lemma So I see now that I recommended Enderton'...
Here's the general theorem in the setting of category theory. It's called Lawvere's fixed point theorem. Not necessary to understand it, just handy to...
Ok wrong question. I asked why are you concerned, and you wrote that para. What I should have asked is, why do you think I care? What is this to me? I...
I'm afraid that in the absence of a bottom-up approach, I have no idea what are fractions or reals. Perhaps your entire approach is pre-axiomatic, in ...
Which is why I endlessly challenge @"Michael" to make his version explicit once and for all. And why he won't. What justifies such an assumption with ...
You're agreeing with me. Play the lamp game twice. Sometimes the terminal state is on, other times it's off, other times the lamp turns into a plate o...
Not so. What lamp? Describe the full setup. Not possible, else Benacerraf's objections to Thomson's formulation would apply. My charity ran out long a...
Good point there. The DNC screwed Bernie in 2016 and 2020. (edit) The least democratic institution in the country is the Democratic national committee...
So not necessarily for me. Ok good to know. Maybe this site should have a @"Whoever" generalized user so that people can direct their rantings to the ...
Yes, another one of @"Micheal"'s conceptual confusions. That's why I mention Cinderella's coach. The lamp is a fairy tale, and it's a fallacy to try t...
Ok, thanks. Rather not say. It did me in, sadly. Of course it is. It's an axiom. It says what is true about all the things we call sets. Therefore we ...
I'm curious to know what that notation 1/1 means. In abstract algebra class I learned how to construct the rational numbers as the field of quotients ...
Really? I thought you made a pretty good point. You got me to understand what epsilon is. Ahhhhhhhh ... now I understand your point of view. You use c...
The terminal state of the lamp is not defined, so it may be on or off. What on earth is wrong about that? If you flip a coin it might be heads or tail...
Yes fair. Though I am not entirely sure I ever understood the distinction you're making. Of course I do understand the difference between an algorithm...
Right. Only mentioning it because when I asked for references you mentioned it. I might look at his logic book. I confess, as you insightfully noted, ...
You know, that's a very interesting point. One difference is that rationals get arbitrarily close to 0. But I'm not sure it's all that different. Mayb...
Good question. Nothing, really. Can we work on getting these posts shorter? Physical collections have inherent order. Sets don't. That's all I'm sayin...
Didn't follow that. The claim was that multiple possible outcomes of a process is inconsistent. Not so. Each outcome is consistent with the rules of t...
Mercifully short. Thank you muchly. Logic isn't constrained to computability. "However, I would argue that these truths are contingent on a computer c...
Same way I see it. The sequence 0, 1, 0, 1, ... has no limit, so one terminal state is as good as any other. This is regarding the puff of smoke or th...
That is far from "established." That's why I keep asking you to write out a complete description of the problem, as if I've never heard of it before. ...
Perhaps the Democrats should have thought of this last fall, when there was a chance to have a robust series of primary contests. Biden's age-related ...
I repeat: Please post a complete description of the problem. In P1 I have no idea what "the lamp" is. It's perfectly clear that you are adding hidden ...
You're the one who gave me Enderton's set theory book as a reference. Ok whatever. Nevermind that. I will agree with you that identity is implicitly i...
I'm only trying to figure out what you're talking about. There are many theories of identity. Wiki actually has a disambiguation page on the subject. ...
I found a pdf of that here: https://docs.ufpr.br/~hoefel/ensino/CM304_CompleMat_PE3/livros/Enderton_Elements%20of%20set%20theory_%281977%29.pdf I look...
Foundations are a bit of a backwater. My grad school had an excellent math faculty but no interest in foundations. They had one professor who was an e...
At Biden's last physical, a cognitive test was not given. The doctors gave him a clean bill of health. It seems to me that the doctors didn't look for...
I'll stipulate that maybe you have a point to make. You have not communicated it to me. I didn't have the heart to tackle this long post tonight. (edi...
You know, I studied math and I never heard that said, anywhere. I don't think it's true. I'd be glad for a mathematical reference. Pick up a text book...
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