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From the OP at least I made the connection. That's what really intrigues me. Especially when you look at how famous and still puzzling these proofs ar...

Thank you, @"fishfry" It seems that from you I get extremely good answers. Yes, Lawvere's fixed point theorem was exactly the kind of result that I wa...

Thanks for the educative response. But it seems that you went back to my earlier post. So just to make things clear, I'll ask again: Now why I'm ranti...

Wrong. Aren't you forgetting the oldest monotheistic religion, the one of the oldest Empires and Rome's old nemesis, the Fire worshipping Persians? Zo...

The study of religion is bit different from the attempt to prove God's existence. The questioning doesn't even start from the obvious question: Is the...

If the US walks away from Europe, then naturally Continental Europe would love to have the support from the UK. Two aircraft carriers are always welco...

If it would only be possible that there could be a dog, but there wouldn't be that next dog, then obviously the number of dogs on the beach would be f...

Well, if it's so, then the counterarguments of the actual Zeno of Elea gave us are quite relevant. And if you think that is nonsense, how about then t...

During Trump's office, the British Parliament understood quite clearly that if Trump really walks out of NATO, they have to take more role in Continen...

Notice that he wasn't an atheist and he did believe in God.

Really? Acting righteously, being good to other people all those things...you do because only because of God? And without God it would be pointless?

First of all, Biden has been already for a long time a demented politician holding for power and totally incapable of seeing that he himself is not up...

Plato doesn't accept the existence of Zeno's dogs. Or in reality, Aristotle and many in the following Centuries believe that there is only a potential...

Exactly. So I'm puzzled by those who want to give a proof of God, because they usually are religious people. Why not simply follow the given manuals a...

Yes, But if you start from that there is no bijection, and then prove it by: If there is a bijection then there is a surjection There is no surjection...

OK, so let me try get your viewpoint here: having the list g and constructing the real that is not on the list isn't itself using reductio ad absurdum...

:grin:

And what is his follower assumed to do? To reason God's existence? Or perhaps to do something else?

That's why the task was for the philosophers "to tell a way to feed all the dogs on the beach without any dog being left out hungry and Themis would m...

Ok, I think I now understood you. By g you referred to the list, while I thought you meant the constructed real that isn't on g.

Math is confusing. It's far more closer to philosophy than mathematicians and logicians want to admit. For example, I've followed Chaitin's story and ...

And I thought in my ignorance, that there's at least this obvious limit in Physics! Of course, what is Physics else than the study of change and movem...

Err, isn't there actually an absolute lowest temperature, - 273,15 Celsius? We cannot talk then about a temperature of - 2 000 000 Celsius or lower te...

Please, I value everybody's contribution as I cannot overstate here just how difficult and open ended question this is. Yet it's very simple and you c...

Well, in my example (which is common), I was referring to reals between 0 an 1, not ALL reals. I think that we aren't understanding each other here: I...

Thanks for answering my ramblings, @"TonesInDeepFreeze", As an non-mathematician/logician, I'm not familiar with the terminology. So it is sentence - ...

To show one way how an at least 2400 year old (but likely older) difficulty in mathematics emerges, which hasn't gone away. You should read the answer...

I can't fathom it would be for anybody else. I think so. As I said: if you double the amount of food to every dog, it doesn't matter as they can be on...

I'm not so sure that mathematics starts from exactly one thing. :smile: Well, think in the story about how much all dogs eat, then remember the rules.

On the other hand, with Plato's dog, we can do something as important as count and measure. The first thing that mathematics evolved from, and somethi...

Any proof will contain at most a finite number of characters. At least for us finite entities. That's actually not Cantor's theorem (the power set of ...

Ok, If you start from Plato's dog as the measure for all dogs, let's call it dog 1, you get dog 2 (that eats twice the amount), dog 3 (eating triple a...

Hopefully I didn't. All the dogs eat exactly a defined amount of food different from any other dog, not less, not more. (BTW, if someone is puzzled wh...

Absolutely fantastic! :grin: And yes, #2 gives us the opportunity to do this. Not by reason of counting as obviously both of Zeno's dogs are literally...

Nope, this is basically Plato's argument in the story: increasing the food or decreasing the food size you always get a new dog's meal. So he reasons ...

Yes, absolutely! All the various philosophical schools of thought have contributed each their way. Even if I criticize reductionism and favour the ide...

Well, the reasoning of the Eleatic school isn't this, but do notice that Zeno's paradoxes are handled by limits ...or infinitesimals. So it begs the q...

I would agree with @"Tarskian", especially a mix of both can be harmful, because one can come to be so dogmatic that one starts to think that model or...

Did he? Or did he try to make an counterargument to Plato? During the time, you tried to make questions that the one answering you would make the argu...

Your second statement goes with the lines of Plato then. Poor of Zeno's dogs. And with the transfinite, Cantors set of theory of ever larger and large...

If you refer to "an universal statement that ought to apply to everything", I would agree (assuming I understood your point). Provability, if I have u...

Especially to my statements, yes! But that's why you are here, to correct if there's something wrong or is mistaken. :wink:

Fear not, the dogs too are imaginary. And yes, it's a story I invented. And for Zeno's two dogs, later people (now mathematicians) have put them on a ...

I agree Gödel didn't make it easy. In my opinion Cantor's diagonalization is an easier model. Or basically just use negative self reference with avoid...

The basic problem is that people simply have these ideas what mathematics should be like and don't notice that their own premises, which they hold as ...

That is the obvious standard line, been for thousands of years. But it's a limitation, when you start from Plato's dog. Yet doesn't the dog that eats ...

Perhaps some can see this as chaotic, but math itself is quite logical and hence quite orderly. Unprovability or uncomputability doesn't mean chaotic....

Coercion usually means forcing someone to do something he or she doesn't want to do. That kind of idea of determinism does away with lot of things. An...

Then I have to remind about the problem that LD had in predicting the future. I don't think LD has any problem in predicting billiard balls as they fo...

Yes, but in order to be "free to act on the desires and decisions of that machine", which is yourself, you have to have the awareness that you are mak...