A heap is more than one, but it's not exact. — ssu
Meaning that they do have a size, but the size is obviously unmeasurable — ssu
So, could it be then there would be Absolute Infinity? — ssu
But isn't an infinite set bigger than any finite set? Doesn't that imply size, even if obviously you cannot measure it like a finite set? — ssu
Yeah, you cannot just say that set theory is wrong. You would actually need to give a proof of it in mathematics. — ssu
God's existence wouldn't make life "objectively significant" because significance is always subjective — Relativist
The only fact in evidence is: there is life in the universe. But this fact is consistent with both alternatives, so it doesn't make your preferred alternative any more likely. — Relativist
Well.. I don't like it too, but nobody has shown that is inconsistent yet, and it's used since a very long time. So, I would guess that it's not inconsistent! — Mephist
Sorry, I don't know transfinite aritmetics.. :sad: But if you have some good links to documents that explain what is it I would be interested! — Mephist
Naught and c; whether c equals 1 is an open question. And nothing else? That's just plain wrong. — tim wood
Well, the problem is to give a definition of "size" for sets that you cannot count — Mephist
Saying "it is only natural" does not constitute objective evidence. Consider that in a fair lottery, some random person will win - and yet (per your admission) every winner will suspect the lottery was rigged for him, but he will be wrong — Relativist
To be honest, I think you've hit on the source of the fallacious thinking: it's based on the unsupported belief that there "must be a reason" for all subjectively significant events. — Relativist
On the number line between zero and one: are there more rational than real numbers? Or the other way round? To know, you have to have a way of quantifying both. How do you go about these? — tim wood
That's correct, but my point is that the mere fact that the dwarf won does not serve as evidence that the organiser wanted the dwarf to win. It's POSSIBLE that he did, but there's no basis for considering it probable — Relativist
God really wanted some intelligent life to entertain him so he created some (14 billion years into the whole project, for some reason), stuck it one one tiny planet in the middle of empty space, populated the rest of the entire universe with lifeless rocks and then buggered off (minus one brief showing to set fire to a bush and hand down some instructions about neighbour's oxen). — Isaac
This isn't news to mathematicians. When the concept of infinity was invented, there was a (perceived) need for it to be integrated into mathematics. (The alternative was to leave infinity standing alone and lonely, and this (apparently) was unacceptable.) The mess you observe is the result of that 'integration'. — Pattern-chaser
You have avoided responding to my analogy of a one-eyed, hemophiliac dwarf (I'll abbreviate as OEHD) winning a lottery — Relativist
Regarding your case for a creator - Try again. You didn't show that the creator would be likely to desire life to exist. — Relativist
And then you have to be careful, which you neither are nor appreciate the need to be, with the concepts applied to transfinite sets. That is, basic arithmetic functions don't work quite the same way. And so on. — tim wood
Regarding the epistemic probability of God: bear in mind that you're referring to specifically to a God that would choose to create life. What evidence is there for such a God? Cosmological arguments only point to a first cause; contingency arguments only point to there being a creative force that exists out of metaphysical necessity. What objective basis do you propose for assigning a probability to a God that wants to create life? — Relativist
Clearly you know how many even numbers there are and you know how many natural numbers there are. And since you argue the set of natural number is the larger, then in consequence it must be possible to count the even numbers. Please do so and tell us how many even numbers there are. — tim wood
Back to my analogy, a one-eyed hemophiliac dwarf winning is consistent with a lottery that is rigged for one-eyed hemophiliac dwarves, and also consistent with an honest lottery in which everyone has an equal chance. You're treating the mere fact that such a person won as evidence of a dishonest lottery. — Relativist
If you do not treat life as a design objective, there is no relevant coincidence. — Relativist
"the set B is bigger than the set A if there isn't any function that for every element of A gives an element of B and covers all B" ( i.e. each element of B corresponds to some element of A ) — Mephist
This is what it means "an infinite hierarchy of of infinite sets each one bigger than the other". — Mephist
In the standard contemporary mathematics based on set theory you can't speak of the "set of all sets" because it's not a set itself — Mephist
What I wanted to say is that Russel's paradox invalidates the use of "naive set theory", that is the kind of set theory used on Principia Mathematica — Mephist
There is not a 'probability' of the existence of God. You have misunderstood how probability works and you have already had this repeatedly explained to you. — Isaac
It doesn't 'happen to be' it is the only number it could ever possibly have been because had it been any other number we wouldn't be here. We are here, so it is completely unsurprising that it is that number. — Isaac
BUT IT HAPPENS. — Frank Apisa
We are here to wonder about it so it is not in the least bit surprising that the universe is supportive of life. In fact, it's an absolute pre-requisite for us being able to ask the question. — Isaac
You are assuming the fundamental constants could have been different, so each combination of constants participates in the lottery. — Relativist
You seem to be blind to the fact that you are treating life as a design objective. If you do not treat life as special, your argument falls apart. If you do treat life as special, your argument is circular. — Relativist
You're overlooking that every one of the billion possibilities had an equal chance of being drawn (1 in a billion), and therefore it's not remarkable that the winner was a 1 in a billion shot. — Relativist