The function can take an infinite number of values! This is the fundamental difference between a function and a FINITE set. The Abhidhamma explains reality not in the language of functions. The Abhidhamma explains reality through a finite set of types of dhammas. The number of possible combinations of a limited number of elements is finite, since the number of steps in combination is also finite. There is no eternal life. No endless text!Nicolas wrote: ↑Tue Mar 12, 2019 6:17 pm ally rephrase it if it's not a bother? Sorry/thanks.
My response based on my understanding of it:
I don't see why a deterministic event would have had to happen in the past. I've produced examples of deterministic things that happen in the future and haven't happened in the past. For example, function f(t)=t. If the present is t=0, the event "f(t)=10" is in the future, and has never happened in the past. It's not because there is an infinite amount of time elapsed in the past that there is no first time for certain events to have happened.
Theravada against mathematics
Re: The specificity of our example
The number of all possible consecutive combinations
http://mymathforum.com/advancedstatist ... inite.htmlDan74MkII wrote: ↑Tue Mar 12, 2019 8:02 amAs stated, it is of course infinite.Germann wrote: ↑Tue Mar 12, 2019 7:40 am Are you really going to argue that the number of all possible consecutive combinations (sequences with beginning and end, finite sequences) of a limited number of elements with a limited number of changes from one combination to another (in one sequence) is infinite???
 The number of all possible consecutive combinations (sequences with beginning and end, finite sequences) of a limited number of elements with a limited number of changes from one combination to another (in one sequence) is infinite?
 No. Why would it be?
Re: The specificity of our example
Ok, let's take another function. f(t)=0 if t<0 and f(t)=1 if t>=0.Germann wrote: ↑Tue Mar 12, 2019 6:40 pm The function can take an infinite number of values! This is the fundamental difference between a function and a FINITE set. The Abhidhamma explains reality not in the language of functions. The Abhidhamma explains reality through a finite set of types of dhammas. The number of possible combinations of a limited number of elements is finite, since the number of steps in combination is also finite. There is no eternal life. No endless text!
If t=10 is the present, the function only had 0 as a return value, even if 1 is a possible value in the future.
I get that Abhidhamma and mathematical functions aren't the same thing, but I'm using this as an example to show that the argument isn't conceptually valid in general.
Also, like I said, I know close to nothing of Abhidhamma, but the types of dhamma being finite doesn't mean that the dhammas themselves are finite in number; they all fit into finite categories, but each category could include an infinity of different dhammas? I'm asking, I don't know the answer to this.
And again, even if the dhammas are finite in number, it still doesn't mean that an infinite past means that all those dhammas must have happened. And this doesn't have anything to do with Theravada, all Buddhists would agree that we haven't attained Nibbana in the past, otherwise we wouldn't be here.

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Re: The specificity of our example
Having finite types of dhammas as you put it in no way constrains the persistence of dhammas. If there has been endless flinging fuel to a fire, it should not surprise anyone the fire is still burning.Germann wrote: ↑Tue Mar 12, 2019 6:40 pmThe function can take an infinite number of values! This is the fundamental difference between a function and a FINITE set. The Abhidhamma explains reality not in the language of functions. The Abhidhamma explains reality through a finite set of types of dhammas. The number of possible combinations of a limited number of elements is finite, since the number of steps in combination is also finite. There is no eternal life. No endless text!Nicolas wrote: ↑Tue Mar 12, 2019 6:17 pm ally rephrase it if it's not a bother? Sorry/thanks.
My response based on my understanding of it:
I don't see why a deterministic event would have had to happen in the past. I've produced examples of deterministic things that happen in the future and haven't happened in the past. For example, function f(t)=t. If the present is t=0, the event "f(t)=10" is in the future, and has never happened in the past. It's not because there is an infinite amount of time elapsed in the past that there is no first time for certain events to have happened.
Wish you all success in all your endeavours. Goodbye!
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Re: Theravada against mathematics
I posted this over at DWM as well:Germann wrote: ↑Tue Mar 12, 2019 6:31 pm Under the influence of the Mahayana, there is a departure from the traditional doctrine of the total nonexistence of satta. But on the periphery of Theravada, outside the influence of scholasticism, this kind of interpretation is possible  in boran kammatthana.
So your issue with the Theravada, Abhidhamma in particular is the anatta doctrine and where you believe that this means beings don't exist? And you believe this issue doesn't exist in Mahayana? Mahayana is a very big school but the anatman doctrine is found in all of them, although perhaps to a lesser degree (i.e., not necessarily nonexistence) in some schools. And then some have argued that the nonexistence  extreme anatta is not found in all Theravada subtraditions, for example some (or most?) forest traditions.
 Dan74MkII
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Re: The number of all possible consecutive combinations
Just think of natural numbers. Each one is finite, made up of at most 10 different digits. Yet there are infinitely many of them.Germann wrote: ↑Tue Mar 12, 2019 6:47 pmhttp://mymathforum.com/advancedstatist ... inite.htmlDan74MkII wrote: ↑Tue Mar 12, 2019 8:02 amAs stated, it is of course infinite.Germann wrote: ↑Tue Mar 12, 2019 7:40 am Are you really going to argue that the number of all possible consecutive combinations (sequences with beginning and end, finite sequences) of a limited number of elements with a limited number of changes from one combination to another (in one sequence) is infinite???
 The number of all possible consecutive combinations (sequences with beginning and end, finite sequences) of a limited number of elements with a limited number of changes from one combination to another (in one sequence) is infinite?
 No. Why would it be?
Re: Theravada against mathematics
If you cannot agree that what is conditioned and what is unconditioned are mutually exclusive and therefore cannot exist within your argument at the same time, then it is not possible for me to agree with your argument since the fallacy of equivocation in your argument is not eliminated as far as I am concerned.Germann wrote: ↑Tue Mar 12, 2019 4:36 amNibbana can be anything (complete nonexistence, for example). It does not matter. The only important thing is that Nibbana manifests after a certain sequence of combinations of dhammas, which has a beginning and an end (after passing the entire Path).Sherab wrote: ↑Mon Mar 11, 2019 10:16 pmThen you don't understand the analogy of phase transition.
I did not want to use the usual analogy of a jewel covered in mud or the sun behind the cloud precisely because there is a tendency for your type of response which tended to have an underlying implication of eternalism.
I see the manifestation of Nibbana as a 'change' of regime for an individual from one where dhammas are conditioned to a regime where dhammas are 'unconditioned'. 'Change' is in quotes because it is not change as understood in the regime of conditioned dhammas, dhammas that are dependently arisen. 'Unconditioned' is in quotes because the meaning of 'unconditioned' is inextricably linked to the word 'condition' as understood in the regime of the conditioned whereas Nibbana is ineffable.
You on the other hand, sees Nibbana as an event no different from any other event in the regime of the conditioned or in the regime of the dependently arisen. I think this is the sticking point between us.
In Mahayana, the regime of the dependently arisen is nondeceptive when the point of view is within the regime but is deceptive when seen from the point of view of the ultimate truth. Hence the two truth: relative and ultimate where the relative is said to be deceptive and the ultimate is said to be nondeceptive. If you like, there is a change of state of cognition from one where the state of cognition results in deception to one where the state of cognition results in nondeception. The change is in the state and not the fundamental nature. Hence the analogy of phase transition (the sublimation of dry ice from a solid state to a gaseous state) that I provided earlier. Hence the statement that you will see in the Mahayana that there is no difference between the nature of samsara and nirvana.
Unless you can bring in a completely new perspective or argument, this discussion I think will proceed nowhere.
Re: Theravada against mathematics
Nibbana cannot be anything. It is 'something' very specific  a state of enlightenment. Sorry, I cannot agree with your argument even more. We are talking entirely about different things, first what dhammas really refer to in your argument and now Nibbana itself.Germann wrote: ↑Tue Mar 12, 2019 4:36 amNibbana can be anything (complete nonexistence, for example). It does not matter. The only important thing is that Nibbana manifests after a certain sequence of combinations of dhammas, which has a beginning and an end (after passing the entire Path).Sherab wrote: ↑Mon Mar 11, 2019 10:16 pmThen you don't understand the analogy of phase transition.
I did not want to use the usual analogy of a jewel covered in mud or the sun behind the cloud precisely because there is a tendency for your type of response which tended to have an underlying implication of eternalism.
If Nibbana is not something specific, this statement by the Buddha would not make sense:
"In any doctrine & discipline where the noble eightfold path is not found, no contemplative of the first... second... third... fourth order [streamwinner, oncereturner, nonreturner, or arahant] is found. But in any doctrine & discipline where the noble eightfold path is found, contemplatives of the first... second... third... fourth order are found. The noble eightfold path is found in this doctrine & discipline, and right here there are contemplatives of the first... second... third... fourth order. Other teachings are empty of knowledgeable contemplatives. And if the monks dwell rightly, this world will not be empty of arahants."
— DN 16
Re: Theravada against mathematics
One doesn't need Mahayana influence for that departure. It's enough that one simply doesn't appreciate being considered an automaton, a robot. It seems to be a given that people in general don't appreciate being considered an automaton, a robot.Germann wrote: ↑Tue Mar 12, 2019 6:31 pmUnder the influence of the Mahayana, there is a departure from the traditional doctrine of the total nonexistence of satta. But on the periphery of Theravada, outside the influence of scholasticism, this kind of interpretation is possible  in boran kammatthana.
Hic Rhodus, hic salta!
 Pseudobabble
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Re: Theravada against mathematics
Logic, and logical analysis, depend on abstraction and formalisation. Any logical term, be it an 'x', a 'y', or a dog, is only what it is in the scope of analysis as a result of the process of abstraction and formalisation. We say, a dog has four legs, a table has four legs, blah, blah. What is relevant in the scope of the analysis is the fact of four legs  this is what determines the progress and outcome of the analysis. But there is more to a dog than its number of legs.
Abstraction necessarily involves loss of information  information irrelevant to the scope of analysis, but information nonetheless.
Formalisation is the same, involving the generation of a ruleset within which the logical symbols (the information determined to be of relevance in the process of abstraction) and their relations are guaranteed to make sense. This results in loss of information because actual reality cannot be encompassed within any universal and coherent ruleset (Godel).
Proving these things is simple  there is no perfect circle to be found in the material world. Such things are purely abstract constructs, useful, but constructs all the same.
Mathematics is the ultimate application of these interpretive tools, and is wholly dependent on them.
As such, mathematics is not able to make statements about reality as it actually is, only about reality as modelled by the tools of abstraction and formalisation, which necessarily involve information loss, making any nontautological mathematical statements partial truths at best.
Abstraction necessarily involves loss of information  information irrelevant to the scope of analysis, but information nonetheless.
Formalisation is the same, involving the generation of a ruleset within which the logical symbols (the information determined to be of relevance in the process of abstraction) and their relations are guaranteed to make sense. This results in loss of information because actual reality cannot be encompassed within any universal and coherent ruleset (Godel).
Proving these things is simple  there is no perfect circle to be found in the material world. Such things are purely abstract constructs, useful, but constructs all the same.
Mathematics is the ultimate application of these interpretive tools, and is wholly dependent on them.
As such, mathematics is not able to make statements about reality as it actually is, only about reality as modelled by the tools of abstraction and formalisation, which necessarily involve information loss, making any nontautological mathematical statements partial truths at best.
"Does Master Gotama have any position at all?"
"A 'position,' Vaccha, is something that a Tathagata has done away with. What a Tathagata sees is this: 'Such is form, such its origination, such its disappearance; such is feeling, such its origination, such its disappearance; such is perception...such are fabrications...such is consciousness, such its origination, such its disappearance.'"  AggiVacchagotta Sutta
'Dust thou art, and unto dust thou shalt return.'  Genesis 3:19
'Some fart freely, some try to hide and silence it. Which one is correct?'  Saegnapha
"A 'position,' Vaccha, is something that a Tathagata has done away with. What a Tathagata sees is this: 'Such is form, such its origination, such its disappearance; such is feeling, such its origination, such its disappearance; such is perception...such are fabrications...such is consciousness, such its origination, such its disappearance.'"  AggiVacchagotta Sutta
'Dust thou art, and unto dust thou shalt return.'  Genesis 3:19
'Some fart freely, some try to hide and silence it. Which one is correct?'  Saegnapha
Re: Theravada against mathematics
Pseudobabble wrote: ↑Wed Mar 13, 2019 12:38 pm Logic, and logical analysis, depend on abstraction and formalisation. Any logical term, be it an 'x', a 'y', or a dog, is only what it is in the scope of analysis as a result of the process of abstraction and formalisation. We say, a dog has four legs, a table has four legs, blah, blah. What is relevant in the scope of the analysis is the fact of four legs  this is what determines the progress and outcome of the analysis. But there is more to a dog than its number of legs.
Abstraction necessarily involves loss of information  information irrelevant to the scope of analysis, but information nonetheless.
Formalisation is the same, involving the generation of a ruleset within which the logical symbols (the information determined to be of relevance in the process of abstraction) and their relations are guaranteed to make sense. This results in loss of information because actual reality cannot be encompassed within any universal and coherent ruleset (Godel).
Proving these things is simple  there is no perfect circle to be found in the material world. Such things are purely abstract constructs, useful, but constructs all the same.
Mathematics is the ultimate application of these interpretive tools, and is wholly dependent on them.
As such, mathematics is not able to make statements about reality as it actually is, only about reality as modelled by the tools of abstraction and formalisation, which necessarily involve information loss, making any nontautological mathematical statements partial truths at best.
And the Blessed One addressed the bhikkhus, saying: "Behold now, bhikkhus, I exhort you: All compounded things are subject to vanish. Strive with earnestness!"
This was the last word of the Tathagata.
This was the last word of the Tathagata.
 dhammacoustic
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Re: Theravada against mathematics
you beat me to it.Pseudobabble wrote: ↑Wed Mar 13, 2019 12:38 pm Logic, and logical analysis, depend on abstraction and formalisation. Any logical term, be it an 'x', a 'y', or a dog, is only what it is in the scope of analysis as a result of the process of abstraction and formalisation. We say, a dog has four legs, a table has four legs, blah, blah. What is relevant in the scope of the analysis is the fact of four legs  this is what determines the progress and outcome of the analysis. But there is more to a dog than its number of legs.
Abstraction necessarily involves loss of information  information irrelevant to the scope of analysis, but information nonetheless.
Formalisation is the same, involving the generation of a ruleset within which the logical symbols (the information determined to be of relevance in the process of abstraction) and their relations are guaranteed to make sense. This results in loss of information because actual reality cannot be encompassed within any universal and coherent ruleset (Godel).
Proving these things is simple  there is no perfect circle to be found in the material world. Such things are purely abstract constructs, useful, but constructs all the same.
Mathematics is the ultimate application of these interpretive tools, and is wholly dependent on them.
As such, mathematics is not able to make statements about reality as it actually is, only about reality as modelled by the tools of abstraction and formalisation, which necessarily involve information loss, making any nontautological mathematical statements partial truths at best.
the very concept of "information" owes its emergence to "lack"..... for that matter, no amount of mathematics will suffice to encompass the potential of mathematics, as each approach would be "named" by its very own finitude, which means that "a finitude" as an actualization is already a quality of infinity.
@germann, you're mistaking mathematics for what's ontologically real...
Re: Theravada against mathematics
And if i may add to your good points, what is ontologically real is what has an independent existence (or what we call objectivemind independent reality). Mathematical models, which are based on negating the infinite, are able to prove themselves by comparing the abstracted results of the mathematical model with an abstracted vision of the world (the senses) which takes control and human intervention to be proven, and because they match (depending on negating the infinite), mathematical models are considered as real/reliable.dhammacoustic wrote: ↑Wed Mar 13, 2019 1:00 pm @germann, you're mistaking mathematics for what's ontologically real...
And the Blessed One addressed the bhikkhus, saying: "Behold now, bhikkhus, I exhort you: All compounded things are subject to vanish. Strive with earnestness!"
This was the last word of the Tathagata.
This was the last word of the Tathagata.
 Pseudobabble
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Re: Theravada against mathematics
Bundokji wrote: ↑Wed Mar 13, 2019 1:23 pmAnd if i may add to your good points, what is ontologically real is what has an independent existence (or what we call objectivemind independent reality). Mathematical models, which are based on negating the infinite, are able to prove themselves by comparing the abstracted results of the mathematical model with an abstracted vision of the world (the senses) which takes control and human intervention to be proven, and because they match (depending on negating the infinite), mathematical models are considered as real/reliable.dhammacoustic wrote: ↑Wed Mar 13, 2019 1:00 pm @germann, you're mistaking mathematics for what's ontologically real...
Exactly. That's the part I didn't get to.
"Does Master Gotama have any position at all?"
"A 'position,' Vaccha, is something that a Tathagata has done away with. What a Tathagata sees is this: 'Such is form, such its origination, such its disappearance; such is feeling, such its origination, such its disappearance; such is perception...such are fabrications...such is consciousness, such its origination, such its disappearance.'"  AggiVacchagotta Sutta
'Dust thou art, and unto dust thou shalt return.'  Genesis 3:19
'Some fart freely, some try to hide and silence it. Which one is correct?'  Saegnapha
"A 'position,' Vaccha, is something that a Tathagata has done away with. What a Tathagata sees is this: 'Such is form, such its origination, such its disappearance; such is feeling, such its origination, such its disappearance; such is perception...such are fabrications...such is consciousness, such its origination, such its disappearance.'"  AggiVacchagotta Sutta
'Dust thou art, and unto dust thou shalt return.'  Genesis 3:19
'Some fart freely, some try to hide and silence it. Which one is correct?'  Saegnapha
Re: Theravada against mathematics
I have not yet read all the 20 pages of this topic, but has anyone explained this correctly already? Buddha answered like that because of the "almost surely paradox": https://en.wikipedia.org/wiki/Almost_surely
Buddha was once asked: Since beings will get reborn here to infinity and all sorts of conditions will arise, surely at one point there will arise the proper conditions for a being to get enlightened. Therefore, all beings will get enlightened.
Buddha answered that nope, a being can get reborn to infinity and never get enlightened. This confused even Bhikkhu Bodhi in an interview with B. Sujato. B.Bodhi did not know how to answer and why Buddha said that.
In order to understand the almost surely paradox, imagine you are throwing a dart at a flat TV screen. Let's say you split the TV screen in half by drawing a line straight in the middle. Wherever the dart will land, it can only be in either one of these 2 parts. But the dart can also land straight in the middle, on that line. Now let's say you make that line smaller. Well, it still can land right on it. No matter how much you try, there will always be that small possibility of the dart not landing in any of the 2 squares. Therefore, all that can be said is that "almost surely that the dar will land in either of those squares".
https://en.wikipedia.org/wiki/Almost_surely
If the Buddha said anything other than almost surely, then you would have a huge problem for buddhism, not the other way around.
Buddha was once asked: Since beings will get reborn here to infinity and all sorts of conditions will arise, surely at one point there will arise the proper conditions for a being to get enlightened. Therefore, all beings will get enlightened.
Buddha answered that nope, a being can get reborn to infinity and never get enlightened. This confused even Bhikkhu Bodhi in an interview with B. Sujato. B.Bodhi did not know how to answer and why Buddha said that.
In order to understand the almost surely paradox, imagine you are throwing a dart at a flat TV screen. Let's say you split the TV screen in half by drawing a line straight in the middle. Wherever the dart will land, it can only be in either one of these 2 parts. But the dart can also land straight in the middle, on that line. Now let's say you make that line smaller. Well, it still can land right on it. No matter how much you try, there will always be that small possibility of the dart not landing in any of the 2 squares. Therefore, all that can be said is that "almost surely that the dar will land in either of those squares".
https://en.wikipedia.org/wiki/Almost_surely
If the Buddha said anything other than almost surely, then you would have a huge problem for buddhism, not the other way around.