I haven't denied the validity of any theorem  show me where. I denied the applicability.Germann wrote: ↑Sun Mar 10, 2019 7:26 amMy argument is mathematically correct. That you deny the validity of the theorem is another question (I understand that Theravada is really incompatible with it).Dan74MkII wrote: ↑Sat Mar 09, 2019 10:35 pmWhat you could do is acquire the requisite background before making assertions. Results rest upon assumptions. You appear neither aware nor concerned about these assumptions.
Theravada against mathematics
 Dan74MkII
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Re: Theravada against mathematics
Re: Theravada against mathematics
The printed text of the novel is a sequence of combinations of letters. The path to Nibbana is a sequence of combinations of dhammas. The set of printing monkeys is infinite, the set of past lives is infinite. The theorem is applicable.Dan74MkII wrote: ↑Sun Mar 10, 2019 7:50 amI haven't denied the validity of any theorem  show me where. I denied the applicability.Germann wrote: ↑Sun Mar 10, 2019 7:26 amMy argument is mathematically correct. That you deny the validity of the theorem is another question (I understand that Theravada is really incompatible with it).Dan74MkII wrote: ↑Sat Mar 09, 2019 10:35 pm
What you could do is acquire the requisite background before making assertions. Results rest upon assumptions. You appear neither aware nor concerned about these assumptions.

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Re: Theravada against mathematics
Sure, though I can't remember it being specifically ruled out either.
You are assuming that we are all infinite beings (have existed in a sense forever into the past) and that we have all lived for half of infinity already. There's a big difference between "no discernible beginning" and infinity.
Why does any kammic fruit need to be transferred? In my hypothesis, if some kammic chain is initiated in a very simple being/organism on the borderline between life and nonlife, then surely it would start with a fairly undifferentiated/clean kammic slate apart from basic ignorance/desire/survival impulse.If such budding is asserted, then kamma of one is capable of generating kammic effects from another  you can transfer your kammic fruit to another.
Or are you talking about branching flows (as in the manyworlds hypothesis)? Am not sure from your language. Even there, is it kamma transference? There was one being in one universe and then it splits into two beings in two universes (identical except for the particular quantum event/"choice"). Who gave the kamma and who received the kamma? Isn't it still just cause and effect (am not sure the Buddha ever considered the MW interpretation ).
 Dan74MkII
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Re: Theravada against mathematics
Please respond to my three points raised in the earlier post. Otherwise I see no.point in going further.Germann wrote: ↑Sun Mar 10, 2019 7:59 amThe printed text of the novel is a sequence of combinations of letters. The path to Nibbana is a sequence of combinations of dhammas. The set of printing monkeys is infinite, the set of past lives is infinite. The theorem is applicable.Dan74MkII wrote: ↑Sun Mar 10, 2019 7:50 amI haven't denied the validity of any theorem  show me where. I denied the applicability.
Re: Theravada against mathematics
The alphabet is a finite set. The number of dhammas from the Abhidhamma is a finite set. The theorem applies to dhammas in the same way as to buttons.Dan74MkII wrote: ↑Fri Mar 08, 2019 3:02 pm Infinity is a lot more subtle than it seems.
For instance if alphabet itself was infinite (say a letter for every whole number, A1, A2, A3,...), then a thousand monkeys even working very randomly on a thousand typewriters would not necessarily type up every book eventually.
Also, and perhaps more relevant, if one imagines a random walk on a line, meaning ever second one makes a step to the right or to the left at random, one is guaranteed to visit every stop (at 0, 1, +1, 2, +2, etc) ever more often and the same is true on a twodimensional grid, but in 3d, the situation changes and there will be heaps of unvisited locations (Polya's Random Walk Theorem).
In any case, all this has very little to do with the Dhamma...
Re: Theravada against mathematics
All combinations of dhammas from the Abhidhamma will be exhausted just like all combinations of buttons.Dan74MkII wrote: ↑Fri Mar 08, 2019 3:33 pm Well, it's obvious that we can cycle through the same finite states for ever without exhausting many possibilities at all.
The elements (dhammas) of the Abhidhamma are a finite set.Dan74MkII wrote: ↑Fri Mar 08, 2019 3:33 pmAnd what is to say that there aren't infinitely many possible states? Then one can have a timeline stretching back into infinite past with each configuration uniquely different and still not exhausting all.
In the elements (dhammas) of the Abhidhamma there is not one that is inaccessible, never manifest. Nibbana appears when a previously known sequence of button combinations is pressed. This sequence corresponds to the "novel", which prints the "monkey" from the theorem.Dan74MkII wrote: ↑Fri Mar 08, 2019 3:33 pmAnd then, finally, Nibbana is said to be unconditioned, uncaused, so it appears to be outside such framework anyway.
Re: Theravada against mathematics
There are only two options  either there is no first life, or there is first life. If there is a first life, then there are the first impermanent dhammas that arose without kammic reasons.suaimhneas wrote: ↑Sun Mar 10, 2019 8:43 am There's a big difference between "no discernible beginning" and infinity.
Can Theravada admit that nonpermanent dhammas may not have kammic reasons? No. Therefore, there is no first life  therefore, the number of past lives is infinite.
Re: Theravada against mathematics
I disagree. Your argument can only hold for dhammas that are conditioned. Even if you redefined your argument to cover events, the events that are being covered are still valid only for conditioned dhammas. If you include Nibbana event into your events, you will have committed the fallacy of equivocation.
Re: Theravada against mathematics
No dhamma combination ends with the manifestation of Nibbana? Is there no Ways to Nibbana? Can you go all the way from beginning to end, but not reach Nibbana? My argument has not changed:Sherab wrote: ↑Sun Mar 10, 2019 10:04 amI disagree. Your argument can only hold for dhammas that are conditioned. Even if you redefined your argument to cover events, the events that are being covered are still valid only for conditioned dhammas. If you include Nibbana event into your events, you will have committed the fallacy of equivocation.
A "text" is a sequence of combinations of dhammas, culminating in the realization of Nibbana.
 Dan74MkII
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Re: Theravada against mathematics
Asserting it doesn't make it so. The dhammas are causally connected. We know that we keep repeating yhe same mistakes, history repeats itself. There is a lot of cycling, a complex causally linked dependent dynamic  very far from a random sequence that your socalled theorems consider. Hence they don't apply.Germann wrote: ↑Sun Mar 10, 2019 9:50 amAll combinations of dhammas from the Abhidhamma will be exhausted just like all combinations of buttons.Dan74MkII wrote: ↑Fri Mar 08, 2019 3:33 pm Well, it's obvious that we can cycle through the same finite states for ever without exhausting many possibilities at all.
A reference would be nice, but still I wonder..The elements (dhammas) of the Abhidhamma are a finite set.Dan74MkII wrote: ↑Fri Mar 08, 2019 3:33 pmAnd what is to say that there aren't infinitely many possible states? Then one can have a timeline stretching back into infinite past with each configuration uniquely different and still not exhausting all.
Again, it is not at all clear to me that nibbana is a combination of dhammas. Why? Uncaused, unconditioned, it is called.In the elements (dhammas) of the Abhidhamma there is not one that is inaccessible, never manifest. Nibbana appears when a previously known sequence of button combinations is pressed. This sequence corresponds to the "novel", which prints the "monkey" from the theorem.Dan74MkII wrote: ↑Fri Mar 08, 2019 3:33 pmAnd then, finally, Nibbana is said to be unconditioned, uncaused, so it appears to be outside such framework anyway.
Your 'case' falls apart on a number of grounds..

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Re: Theravada against mathematics
Kamma is always to do with life in the suttas (dependent origination applies to beings). There is cause and effect outside of that but it isn't kamma. Impermanent stuff can arise in the universe not due to kamma. I'm not neccesarily arguing from a Theravadian viewpoint (more from the perspective of the suttas). There is cause and effect but not total kammic determinism in the suttas. The approach seems to be somewhere in the middle between thinking everything is determined by past kamma and everything is random and without cause. Misfortune can happen just due to chance also, e.g. see SN36.21. So there seems to be a certain room for nonkammic chance and happenstance in the universe as pictured by the suttas. Maybe DO chains can spontaneously arise from this borderline between kammic and nonkammic causes (or from some background condition of ignorance; Bhikkhu Bodhi speculated something along those lines might be the case)?Germann wrote: ↑Sun Mar 10, 2019 9:53 am There are only two options  either there is no first life, or there is first life. If there is a first life, then there are the first impermanent dhammas that arose without kammic reasons.
Can Theravada admit that nonpermanent dhammas may not have kammic reasons? No. Therefore, there is no first life  therefore, the number of past lives is infinite.
Anyway, even if not, you never addressed my Hilbert Hotel point, which does assume an infinite past.
You say in your OP:
But isn't the "mathematically impossible" scenario you describe in your OP just a dressedup form of Hilbert's Hotel? If every day half of the people in Hilbert's infinite hotel can check out (like perhaps a fixed percentage of people might achieve nibbana in an eon) and if this process goes on day after day for infinity, then the hotel will still always remain completely full. Isn't your statement, therefore, the mathematically dubious one?Nibbana should be already realized for the infinity of the past by all "people" without exception.
Re: Theravada against mathematics
No dhamma combination ends with the manifestation of Nibbana? Yes no combination of conditioned dhammas can end with the manisfestation of Nibbana. This is because what is conditioned and what is unconditioned are mutually exclusive.Germann wrote: ↑Sun Mar 10, 2019 11:36 amNo dhamma combination ends with the manifestation of Nibbana? Is there no Ways to Nibbana? Can you go all the way from beginning to end, but not reach Nibbana? My argument has not changed:Sherab wrote: ↑Sun Mar 10, 2019 10:04 amI disagree. Your argument can only hold for dhammas that are conditioned. Even if you redefined your argument to cover events, the events that are being covered are still valid only for conditioned dhammas. If you include Nibbana event into your events, you will have committed the fallacy of equivocation.
A "text" is a sequence of combinations of dhammas, culminating in the realization of Nibbana.
Is there no Ways to Nibbana? Yes there is no ways within the dependently arisen regime to Nibbana, because Nibbana is the cessation of all that are dependently arisen, and that have to include any dependently arisen ways within the dependently arisen regime.
Can you go all the way from beginning to end, but not reach Nibbana? You cannot make something conditioned become unconditioned since what is conditioned and what is unconditioned are mutually exclusive. When you are in the dependently arisen regime, there is no beginning and there is no end. The only end is the ending of the dependently arisen regime as a whole where it all ceases for you.
Re: Theravada against mathematics
Nibbana is the extinguishment of life although No Self is being annihilated . Life (of five aggregates) is dependently arising .
You always gain by giving
Re: Theravada against mathematics
First, you cut a sophism by giving a finite set (the list of dhammas in the Abhidhamma is finite) for an infinite. Then they eliminated deterministic processes from the subject of probability theory — although they also have probability. Then they ignored the doctrinal fact that behind a specific sequence of combinations of dhammas (after a specific sequence of keystrokes)  after passing the Path  Nibbana manifests itself.Dan74MkII wrote: ↑Sun Mar 10, 2019 11:56 amAsserting it doesn't make it so. The dhammas are causally connected. We know that we keep repeating yhe same mistakes, history repeats itself. There is a lot of cycling, a complex causally linked dependent dynamic  very far from a random sequence that your socalled theorems consider. Hence they don't apply.Germann wrote: ↑Sun Mar 10, 2019 9:50 amAll combinations of dhammas from the Abhidhamma will be exhausted just like all combinations of buttons.Dan74MkII wrote: ↑Fri Mar 08, 2019 3:33 pm Well, it's obvious that we can cycle through the same finite states for ever without exhausting many possibilities at all.
A reference would be nice, but still I wonder..The elements (dhammas) of the Abhidhamma are a finite set.Dan74MkII wrote: ↑Fri Mar 08, 2019 3:33 pmAnd what is to say that there aren't infinitely many possible states? Then one can have a timeline stretching back into infinite past with each configuration uniquely different and still not exhausting all.
Again, it is not at all clear to me that nibbana is a combination of dhammas. Why? Uncaused, unconditioned, it is called.In the elements (dhammas) of the Abhidhamma there is not one that is inaccessible, never manifest. Nibbana appears when a previously known sequence of button combinations is pressed. This sequence corresponds to the "novel", which prints the "monkey" from the theorem.Dan74MkII wrote: ↑Fri Mar 08, 2019 3:33 pmAnd then, finally, Nibbana is said to be unconditioned, uncaused, so it appears to be outside such framework anyway.
Your 'case' falls apart on a number of grounds..
This is not an argument.
Re: Theravada against mathematics
This means that the complete passage of the Path, from beginning to end, does not lead to Nibbana. Such a Path is not a Path.