Buddhism and numbers incompatible?

[Loriciferan Universe]

There is a philosophical precept in Buddhism based on the “interrelationship of all things”, kinda like the idea of “the universe in a grain of sand and eternity in an hour”, although I am pretty sure this is a lower-level understanding of the principle. To me it seems like the point is that there IS no grain of sand, there is no eternity. Just like the way light and dark are two sides of a spectrum, not different unique bodies. Our consciousness likes to lump things into categories because we view the world through a very narrow spectrum. As Alan Watts put it (I’m paraphrasing here): looking through a crack in a fence you see a cat walk by very close to the fence. First you see the head, then the tail. This happens multiple times and you thus make a rule to describe the phenomenon: head causes tail. In truth the head and tail are both part of the same cat, but looking through your tiny crack (consciousness) you can only see the head and then the tail.

So if this is true than there are no discrete things, nothing stands alone and in truth nothing really stands at all. So with that said... what of numbers? If there is no single discrete thing in the universe, than you can’t say there is 1 of anything, or 2. The Buddhist philosophy makes sense, but so do numbers. Am I suffering from cognitive dissonance, holding two contradictory ideas as being equally true, or is there something I haven’t thought of that explains this. :confused:

[Kopji]

Hi and welcome to the forum.

It would seem that since you are reading these words, we are here and we exist. Perhaps for a Buddhist, numbers are 'here' in the same sense. Some things do seem to exist whether we believe in them or not.

Just my personal opinion and it may be too harsh, but when I read Alan Watts my attention really wanders. I put him up there with Deprek Copra in clarity and meaningfulness. (That is, 'not very').

[jimtron]

To me it seems like the point is that there IS no grain of sand, there is no eternity. So if you go to the beach, and pick up a grain of sand--what is that, an illusion? I'm not that familiar with Buddhism, but what you're describing is sounding to me like brain in a vat- (http://en.wikipedia.org/wiki/Brain_in_a_vat)-is that the idea? Solipsism? (http://en.wikipedia.org/wiki/Solipsism)

If there are no numbers, then there are zero numbers. Zero is a number! Do I win something?

[Z]

Zero is NOT a number; zero is a placeholder.

And if you get right down to it, a grain of sand really isn't, is it? That's just a convenient label we apply to a particular aggragate of atoms and sub-atomic structures at that particular location in spacetime...

[Loriciferan Universe]

So if you go to the beach, and pick up a grain of sand--what is that, an illusion? I'm not that familiar with Buddhism, but what you're describing is sounding to me like Brain in a vat-is that the idea? Solipsism?
If there are no numbers, then there are zero numbers. Zero is a number! Do I win something?

Prize: sand :)

No, I don’t think that’s what it means, I gave up on solipsism a long time ago. If I understand correctly it’s more like this: All of our senses are advanced versions of touch, that is, ways to detect mass/vibration. Seeing is based on light WAVES, sound on sound WAVES, touch on the vibration of molecules etc. We are making distinction based on wave patterns. We say, oh, that pattern is different than this one, so these things are fundamentally different But if you were looking at water in a vat, you might distinguish a ripple from a swell but you wouldn’t assume that the ripple is made of different stuff than the swell is.

I’m not good enough on the sand issue to clarify more than what I said above. Maybe to say it “doesn’t exist” is not correct. Rather, it is interconnected to everything else, and thus, is not a separate little thing alone and by itself. To call it a grain of sand ignores everything else that it is connected to.

[jimtron]

To call it a grain of sand ignores everything else that it is connected to.

How exactly is a grain of sand connected to everything else?


So if this is true than there are no discrete things, nothing stands alone and in truth nothing really stands at all.
What about a starving child? Is the child not discrete? Does the child not have an empty stomach? If the child is connected to food, why is she hungry?

I'm not asking these questions rhetorically, but to try to understand this concept. To me it seems interesting but abstract, and not necessarily useful.

[Kopji]

I still do not see the problem with Buddhists believing in numbers, except that perhaps they are a barrier like everything else.

We assign labels to the perceived patterns and packages of the universe for 'easier handling'. If there is a paradox, it seems it is this tendency to create labels. Our labels can become a barrier between understanding something as it really is, and as we labeled it. Numbers are just another kind of label.

[jimtron]

Yes, but a number is really just a concept, right? If you don't have a label for "2," you could still have the idea of it. Same with the grain of sand. Regardless of its label, or whether it has one or not, it still exists as a discrete object. Before there was language, grains of sand existed. Or am I missing something?

[l0rca]

It is true that Eastern philosophy has a mostly non-mathematical founding for itself, and expresses itself in a more physically-attached way. Ideas of quantity and number are much less relevant to Eastern philosophy, but this is more of a semantic propensity than an unrecoverable disposition. We would both readily agree that math is about getting as specific as possible. Where we may (depending on who; not culturally) disagree is any signifigance that numbers can truely lend to understanding reality.

An Eastern philosopher may claim that an intimate feeling towards the natural world, with a focus on a lucid account of unmeasurable change is most important; a Western philosopher, while recognizing this, might also make a charge of realism -- a superior understanding of the world through expressable models. I'd side more with the Easterner here, but I think more than he, I recognize the value in how understanding of a more specific model can give me insight into how I should feel about the world around me.

[jimtron]

Is Buddhism a philosophy, or religion? Or both? Neither?

[Kopji]

I guess my thought would be that the thing that '2' represents is only meaningful because we agree it is. "2" is a label.

[l0rca]

Is Buddhism a philosophy, or religion? Or both? Neither?

Both. It is in essence a philosophy, but religion, as a cultural phenomenon, transformed it (into many horrible forms, in my opinion). It is actually more respectable in the Western world; in the East, common people have surrounded it with lots of supernatural mumbo-jumbo. Just look at the Dali Llama.

[jimtron]

I guess my thought would be that the thing that '2' represents is only meaningful because we agree it is. "2" is a label.
Buddhism is a label as well, isn't it?

[l0rca]

Buddhism is a label as well, isn't it?

Mu!


(Hey look guys, I made a joke that didn't include Star Wars or Hitchikers'!)

[Loriciferan Universe]

It is true that Eastern philosophy has a mostly non-mathematical founding for itself, and expresses itself in a more physically-attached way. Ideas of quantity and number are much less relevant to Eastern philosophy, but this is more of a semantic propensity than an unrecoverable disposition. We would both readily agree that math is about getting as specific as possible. Where we may (depending on who; not culturally) disagree is any signifigance that numbers can truely lend to understanding reality.

Yeah. I’ve heard people speculate that part of the reason many eastern peoples progressed little in the area of science is because of a belief system that did not allow for “fragmentation” of phenomenon, although I’m not so sure the former statement is all that true. So sure, “2" might just be another agreed upon symbol, but the problem is that it is not consciously seen as such by most ppl. Math, physics, all these things do an amazing job explaining the universe, right up to a certain point (moments after the big bang, the really tiny and really big things, making the really tiny things fit with the really big things). Could the break-down in math/physics at key points be a result of our silly, yet efficient little “name game”? And if we recognize the fault is ours, now what?

I personally vote we all head off to a Buddhist monastery and mediate our lives away, but I’m intervened and bitter, so I may be biased.

[FireGarden]

As Alan Watts put it (I’m paraphrasing here): looking through a crack in a fence you see a cat walk by very close to the fence. First you see the head, then the tail. This happens multiple times and you thus make a rule to describe the phenomenon: head causes tail. In truth the head and tail are both part of the same cat, but looking through your tiny crack (consciousness) you can only see the head and then the tail.

But the crack in the fence is real, and limits our view.
It would be nice to be able to see everything all at once. But we cannot. And we must form our concept of the world on what we experience of it.

“the universe in a grain of sand and eternity in an hour”

I would connect this to the other bit by saying,
It would be nice if I could look at a grain of sand and learn everything I needed to know about the universe. But I can't. Or, at least, I don't know how.

Ditto for an hour and the history of the universe.

So if this is true than there are no discrete things, nothing stands alone and in truth nothing really stands at all. So with that said... what of numbers? If there is no single discrete thing in the universe, than you can’t say there is 1 of anything, or 2. The Buddhist philosophy makes sense, but so do numbers. Am I suffering from cognitive dissonance, holding two contradictory ideas as being equally true, or is there something I haven’t thought of that explains this. :confused:

Again, I would make the connection thus:
Can I learn everything about numbers by considering the number one?

Maths kind of unpacks itself from a small number of axioms. I got a U on geography O-level (So bad, they couldn't grade it!) But an A in maths and physics.

The former subject requires a lot of data memorisation. The latter I found easier because what I forgot I could work out from what I remembered. I did both without any revision. Hence the results.

I think the maths example, though falling short, comes closer to fitting the requirements of learning the whole from a study of a part. So far from knocking your faith in the earlier ideas, it should have bolstered it.

Did you like maths at school? Or did you feel that maths was rote memorisation, and geography was more natural?

[Ryokan]

Is Buddhism a philosophy, or religion? Or both? Neither?

Yes.

[Dancing David]

There is a philosophical precept in Buddhism based on the “interrelationship of all things”, kinda like the idea of “the universe in a grain of sand and eternity in an hour”, although I am pretty sure this is a lower-level understanding of the principle. To me it seems like the point is that there IS no grain of sand, there is no eternity. Just like the way light and dark are two sides of a spectrum, not different unique bodies. Our consciousness likes to lump things into categories because we view the world through a very narrow spectrum. As Alan Watts put it (I’m paraphrasing here): looking through a crack in a fence you see a cat walk by very close to the fence. First you see the head, then the tail. This happens multiple times and you thus make a rule to describe the phenomenon: head causes tail. In truth the head and tail are both part of the same cat, but looking through your tiny crack (consciousness) you can only see the head and then the tail.

So if this is true than there are no discrete things, nothing stands alone and in truth nothing really stands at all. So with that said... what of numbers? If there is no single discrete thing in the universe, than you can’t say there is 1 of anything, or 2. The Buddhist philosophy makes sense, but so do numbers. Am I suffering from cognitive dissonance, holding two contradictory ideas as being equally true, or is there something I haven’t thought of that explains this. :confused:

Well there are number of interpretations of what interdependant nature means, there are the twelve nidanas of being, then each person and object has a contingent history, so one has a hard time viewing things in isolation. that man went nuts and killed someone, may not be an accurate description of the event.

Numbers only exist in the judgement passed by humans.

[jimtron]

Math, physics, all these things do an amazing job explaining the universe, right up to a certain point (moments after the big bang, the really tiny and really big things, making the really tiny things fit with the really big things). Could the break-down in math/physics at key points be a result of our silly, yet efficient little “name game”? And if we recognize the fault is ours, now what?

We haven't figured everything out (yet anyway) with science--certainly it has limits. But what system is better? As Carl Sagan in "Demon Haunted World" said, (paraphrasing from memory) "if something better/more effective than science comes along, I'm all for it". Can Buddhism explain what happened moments after the big bang, or really tiny/big things, etc?

Is there evidence that all things are interconnected? Is there evidence that Buddhism can accurately explain the universe? Other religions make this claim, but I'm skeptical. It's not enough to have an explanation--evidence is required. But this is why I asked if Buddhism is a religion, philosophy, or something else. If it's a religion, it doesn't require evidence. Religions make claims and a leap of faith is required to believe them, unlike with science.

[Dancing David]

How exactly is a grain of sand connected to everything else?


What about a starving child? Is the child not discrete? Does the child not have an empty stomach? If the child is connected to food, why is she hungry?

I'm not asking these questions rhetorically, but to try to understand this concept. To me it seems interesting but abstract, and not necessarily useful.

here we get to some of the interesting myths of buddhism.

"the world is illusion"

that is not what the buddha taught, the buddha did not argue about the ontology or existance of the world, he made an argument that there is no place for the self to reside (jason believes differently), all in the world is transitory and changing. there is no place for a self to reside, there is a body, there are sensation, there are thoughts, there are feelings, there are habits but the idea of 'me' outside of this aggregate of body, sensations, thought, emotions and habits does not exist. so too numbers do not exist they are human constructs.

[Dancing David]

Is Buddhism a philosophy, or religion? Or both? Neither?

the sunrise

[jimtron]

If we can't define Buddhism, I'm not sure we can determine if it's compatible or not with numbers.

[Dancing David]

Buddhism is a large inclusive set that includes the people who call themselves buddhists

[jimtron]

Is Buddhism an effective system for understanding the nature of the universe, like science? Or more like religion, having unsubstantiated ideas about the world? I ask in response to LU: Math, physics, all these things do an amazing job explaining the universe, right up to a certain point (moments after the big bang, the really tiny and really big things, making the really tiny things fit with the really big things). Could the break-down in math/physics at key points be a result of our silly, yet efficient little “name game”? And if we recognize the fault is ours, now what?

that is not what the buddha taught, the buddha did not argue about the ontology or existance of the world, he made an argument that there is no place for the self to reside (jason believes differently), all in the world is transitory and changing. there is no place for a self to reside, there is a body, there are sensation, there are thoughts, there are feelings, there are habits but the idea of 'me' outside of this aggregate of body, sensations, thought, emotions and habits does not exist. so too numbers do not exist they are human constructs.

So how might a Buddhist apply this to her life?

[jimtron]

I'm guessing the vast majority of modern day Buddhists use numbers in their everyday life? Maybe the point is not that numbers are incompatible or nonexistent to Buddhists, but that they are more interested in loftier, more ambiguous, cosmic thoughts? And less interested in spending time on material objects and petty, inconsequential things? Or am I getting this wrong?

[FireGarden]

Is there evidence that all things are interconnected?

Connected in the sense that if I move a bit here, something over there moves? Or connected in the sense that if I understand this bit here, then I can understand that bit there? Science itself assumes we can do the latter.

"Seeing the universe in a grain of sand" is like that line from Superman I. Lex Luthor is orating to his henchpeople, and says: "Some people can read the recipe on a chewing gum wrapper and unlock the secrets of the universe." And henchman 1 reads said wrapper, looking very thoughtful.

Still, to give Lex his due...
I never would have guessed Kryptonite would be lethal to a Kryptonian.

That's probably because I cannot see the universe in a grain of sand.

[FireGarden]

If we can't define Buddhism, I'm not sure we can determine if it's compatible or not with numbers.

But we could try and determine if the particular facet of Buddhism in the OP is compatible with numbers.

I think maths is where it is easiest to see the (nature of the) whole within a part.

[jimtron]

Which nature of the universe? (or its components)
Chemistry, biology, physics, psychology, sociology....?
Any of these.

Connected in the sense that if I move a bit here, something over there moves? Or connected in the sense that if I understand this bit here, then I can understand that bit there? Science itself assumes we can do the latter.

Is there evidence that everything is interconnected according to Buddhist ideas.

But we could try and determine if the particular facet of Buddhism in the OP is compatible with numbers.

OK, let's begin. Maybe LU could define his/her idea of what Buddhism is.

If we can't define Buddhism, I don't see how we can figure out the thread title question.

[Loriciferan Universe]

FireGarden: Did you like maths at school? Or did you feel that maths was rote memorization, and geography was more natural? Physics and history were about on par. Math was fun but too mechanistic (I hear it gets better higher up, but I could only squeeze Calc II in), I prefer stories although algorithms are fine.

jimtron: Can Buddhism explain what happened moments after the big bang, or really tiny/big things, etc?
I bet a Buddhist could care less about the big bang. The idea is to be in the here and now. For this thread I am taking what appears to be a sound idea in Buddhism- interconnectedness and change, and trying to figure out if this is truly as well supported of an idea as it appears, or whether it is faith and numbers win out. If the former is true, what happens to numbers?
Is there evidence that all things are interconnected? From a Buddhist perspective? In Old Path White Clouds an example was given of a leaf on a tree. This leaf receives energy from the sun (which is quite remarkable given the sun is ~150 million kilometer away). So starting at the leaf you look at all the things on which the leaf depends, the sun, the soil and its nutrients, the air, water etc. Then look at the things the leaf is connected to and examine what they require in order to be: soil requires weathering and erosion, nutrients require decomposition, the sun, in order to have formed required a collection of interstellar gasses etc. Then look at all the things that in turn depend of the leaf, deer, rabbits, bugs, etc. which may in turn be decomposed later for the leaf, or though some other process influence the leaf once again. And on and on. From a scientific perspective: I think this question is now being explored in the field of marcoecology. I don’t know enough about the field to feel comfortable saying anything about it.
Is Buddhism an effective system for understanding the nature of the universe, like science? Or more like religion, having unsubstantiated ideas about the world? Unsubstantiated? Not necessarily. The facet I am focusing on is more of a philosophy, there is a great deal of logic involved, and certainly observation, but I don’t think it provides the same “factual” understanding of the universe that science does. The issue I’m having is that it seems to propose a good argument against the idea that we can truly have a “factual” understanding of the universe. Which is a mind trip and freak out for me because I have spent more years than I care to remember in school getting all the little facts.
I'm guessing the vast majority of modern day Buddhists use numbers in their everyday life? Probably. I can’t speak for the Buddhist of the world, but I would imagine you are correct. Again, I don’t think (although I could be wrong???) that this is an issue of organized religion. My problem is that there is this great idea which appears to be relatively well supported that asserts that fractionation of the universe into parts will ultimately result in a false (although false to what degree???) picture of the universe.
FireGarden:
Connected in the sense that if I move a bit here, something over there moves? Or connected in the sense that if I understand this bit here, then I can understand that bit there?Both. But I’m guessing more the former.

[jimtron]

So starting at the leaf you look at all the things on which the leaf depends, the sun, the soil and its nutrients, the air, water etc. Then look at the things the leaf is connected to and examine what they require in order to be: soil requires weathering and erosion, nutrients require decomposition, the sun, in order to have formed required a collection of interstellar gasses etc. Then look at all the things that in turn depend of the leaf, deer, rabbits, bugs, etc. which may in turn be decomposed later for the leaf, or though some other process influence the leaf once again.

I don't think anyone would disagree with the above--scientist, atheist, Jew, Muslim, or Christian. But Buddhism gets more cosmic or religious, no?

Is Buddhism an effective system for understanding the nature of the universe, like science? Or more like religion, having unsubstantiated ideas about the world? Unsubstantiated? Not necessarily.
If some of it is backed up with evidence, could you please elaborate? Which uniquely Buddhist ideas have been objectively verified with evidence?

The issue I’m having is that it seems to propose a good argument against the idea that we can truly have a “factual” understanding of the universe.
What's stopping us from understanding at least some aspects of the universe factually? Of course there are many unanswered questions, but on the other hand using the scientific method we have learned a great deal about the universe. What, if anything, does Buddhism teach us about the universe that facts and/or science cannot? Or are you saying the universe is unknowable?

'm guessing the vast majority of modern day Buddhists use numbers in their everyday life? Probably. I can’t speak for the Buddhist of the world, but I would imagine you are correct. So if the vast majority of Buddhists use numbers in their every day life (which is only a guess by me), then it would be fair to say that Buddhism and numbers are compatible, right? I would think it would be hard to live in today's world without using numbers.

My problem is that there is this great idea which appears to be relatively well supported that asserts that fractionation of the universe into parts will ultimately result in a false (although false to what degree???) picture of the universe.

Could you please explain how this is well supported? How do you know that "fractionation of the universe into parts will... result in a false picture of the universe"? Would Buddhism offer a more accurate, less "false" picture of the universe?

Sorry for all the questions, but I'm curious to hear your views on this.

[jimtron]

The Official Dalai Lama Web site (http://www.dalailama.com/) says, on the home page, "His Holiness the 14th Dalai Lama of Tibet." Apparently Buddhism and numbers are not incompatible according to him. And this page (http://www.dalailama.com/page.2.htm) seems to rely on numbers. And this exerpt from a prayer by DL #14: "Words of Truth:" Buddha's full teachings dispel the pain of worldly
existence and self-oriented peace;
May they flourish, spreading prosperity and happiness through-
out this spacious world.

O holders of the Dharma: scholars
and realized practitioners;
May your ten fold virtuous practice prevail.
(bold added)


Also, the Dalai Lama does have use for science; he is interested in (http://www.mindhacks.com/blog/2005/07/dalai_lama_to_lectur.html) the neuroscience of meditation. And wants Tibetans to get a modern education (http://www.dalailama.com/page.8.htm), including science.

[nosho]

I'm guessing the vast majority of modern day Buddhists use numbers in their everyday life? Maybe the point is not that numbers are incompatible or nonexistent to Buddhists, but that they are more interested in loftier, more ambiguous, cosmic thoughts? And less interested in spending time on material objects and petty, inconsequential things? Or am I getting this wrong?

In my personal opinion, Buddhist practice can be just the opposite, helping one to cut through ambiguous thoughts and come into more immediate contact with reality right here and now -- reality that we might otherwise regard as petty or inconsequential.

One problem in trying to discuss the OP is that there are many different kinds of "Buddhism," lots of different traditions and variations. I don't think it's practical to try to define "Buddhism" for the purposes of the OP unless we're zeroing in on a particular tradition.

I think that in many traditions, however, people would agree that numbers very much are compatible with practice. The eightfold path is about living in this world and working with reality as we experience it right now. For example, you have right livelihood. For most of us, our jobs involve numbers at least some of the time. If we are going to practice right livelihood in our jobs, then we have to work with numbers. Practice starts right where you are.

The whole philosophical discussion about whether interconnectedness somehow negates the validity of numeric reference points seems to me like a distraction from what the Buddhist path is all about.

That said, there is something poetic about the notion that numbers might be meaningless in Buddhism, which teaches the four noble truths, the eightfold path, the triple gem, the five aggregates, the twelve nidanas, and on and on.

[Dancing David]

Is Buddhism an effective system for understanding the nature of the universe, like science? Or more like religion, having unsubstantiated ideas about the world? I ask in response to LU:



So how might a Buddhist apply this to her life?

Um, by recognising the effect that being attached to the pleasurable and avoiding the unpleasant has on one's life. By realizing there are a lot of things to worry about that are just not really imporatant. taking care of the body is important, if the body is not healthy there is ill health. taking care of the thoughts is important, if the thoughts are not healthy there is ill health. taking care of the emotions is important, if the emotions are unhealthy there is ill health. taking care of the habits is important, if the habits are unhealthy there is ill health.

by persuing the dragons tail of pleasure and running from the ogre's fist of the unpleasant one can waste considerable time on things that don't exist.

enjoy pleasure, accept the unpleasant, change what one can.

[Dancing David]

I'm guessing the vast majority of modern day Buddhists use numbers in their everyday life? Maybe the point is not that numbers are incompatible or nonexistent to Buddhists, but that they are more interested in loftier, more ambiguous, cosmic thoughts? And less interested in spending time on material objects and petty, inconsequential things? Or am I getting this wrong?


Weeeel, the eightfold path is rather concrete in that it addresses only behaviors. yet as the dao de ching says 'the path is straight and broad but people are easily distracted'.

[Dancing David]

BTW, 90% of what passes as buddhism is something to be sceptical of, maybe 93% or 87%.

[FireGarden]

Physics and history were about on par. Math was fun but too mechanistic (I hear it gets better higher up, but I could only squeeze Calc II in), I prefer stories although algorithms are fine.

The way maths is taught can be mechanistic. But, even early on, there are alternatives to rote memorisation.

FireGarden:
Connected in the sense that if I move a bit here, something over there moves? Or connected in the sense that if I understand this bit here, then I can understand that bit there?Both. But I’m guessing more the former.

Your leaf example is the former. But I can't see even a hint of the former in the phrase "Seeing the universe in a grain of sand". However, checking you OP, I note that you didn't use any verbs at all in your quote.

“the universe in a grain of sand and eternity in an hour”

Maybe the quote I'm thinking of isn't directly Buddhist.

To see a world in a grain of sand
and a heaven in a wild flower,
hold infinity in the palm of your hand
and eternity in an hour.
-William Blake

I didn't know how much Buddhism Blake was exposed to. So I did a bit of googling. You might enjoy this:
http://ccbs.ntu.edu.tw/FULLTEXT/JR-JOCP/ferrar1.htm


In Songs of Expenrience (1794) it is a common fly that Blake identifies with:

Am not I
a fly like thee?
Or art not thou
A man like me?


In Ch'an Buddhism this identification plays a key role in
shaping the philosophy of the Bodhisattva, and even develops
into the Mahayana doctrine of "mind only'' which is advocated
by the Lankavatara Sutra. This sutra states that "When there
takes place a revulsion at the seat of discrimination by
realizing that external objects are appearances or
manifestations of of one's own mind, then there is
deliverance, which is not annihilation."

I'm not sure yet, but solipsism doesn't seem far off.

Of course, poets can't force us to interpret their work the way they intended. I still take it to mean understanding the whole through experience of a part. Hyperbole, of course. Because a world is more complex than a grain of sand. But a great verse.

I wonder if it's representative of the rest of the poem.
;)

[JetLeg]

deleted by user

[Loriciferan Universe]

BTW, 90% of what passes as buddhism is something to be sceptical of, maybe 93% or 87%.

Okay, how about the non-sketchy Buddhists? All I'm really wondering about here in a precept in Buddhism, not the whole thing. I am sure Buddhist use numbers, just like good Catholic boys use condoms, it's matter of modern necessity. What I am wondering is if numbers are just a made up little thing that make life easier, or something that is actually a property of the universe. As far as I can tell a Buddhist would say its just a made up thing. And that appears to be the general consensus here as well. But then there is an issue. If they are made up, how can we be sure we are actually using them in a way that tells us something about the universe?

And yes, there are a myriad of examples that support numbers, suggesting there is some "truth" in organizing the world this way. But there are also many examples where they don't work. Now science has a long way to go and maybe one day someone will get EVERYTHING to work out. But until then it is interesting to ponder whether they CAN work...

[jimtron]

I am sure Buddhist use numbers, just like good Catholic boys use condoms, it's matter of modern necessity. The Pope (if I'm not mistaken) says it's wrong for Catholics to use condoms. There are no Buddhist leaders suggesting that Buddhists shouldn't use numbers, as far as I know. The Dalai Lama uses numbers. I still haven't seen evidence that numbers and Buddhism are incompatible--we don't know that to be true, do we?

As far as I can tell a Buddhist would say its just a made up thing.As is Buddhism--a made up thing. What's wrong with numbers? On the official Dalai Lama Web site, numbers are used often. Numbers help us communicate, and help with science, etc.

If they are made up, how can we be sure we are actually using them in a way that tells us something about the universe? Numbers and math helped us put men on the Moon, and robots on Mars. Numbers and Math help us eliminate diseases. If Buddhism is made up, how can we be sure Buddhists are actually using it in a way that tells us something about the universe?

Again, what's wrong with numbers? To me it seems they're quite beneficial in many ways. Where's the downside? And are they more of a construct than Buddhism? Or language?

And yes, there are a myriad of examples that support numbers, suggesting there is some "truth" in organizing the world this way. But there are also many examples where they don't work. Now science has a long way to go and maybe one day someone will get EVERYTHING to work out. But until then it is interesting to ponder whether they CAN work...I'm not sure what you mean by this--could you provide an example of when numbers don't work (I'm not saying you're wrong, I just want to understand your point). Has science or Buddhism taught us more about the universe?

[Loriciferan Universe]

I'm not sure what you mean by this--could you provide an example of when numbers don't work (I'm not saying you're wrong, I just want to understand your point). Has science or Buddhism taught us more about the universe?

Okay okay. Let’s forget Buddhism on the whole, bad title to the tread. Sorry. Rather, I’m just focusing on the issue of compete interconnectedness, the idea stands without Buddhism backing it up, or at least as far as I can tell (that’s why I’m here). As for where numbers might not work? Well, I’m not formally trained in math. Biology. Not math. But from what I’ve heard there is an issue with expressing the universe in mathematical terms right near the beginning of the Big Bang. Another place might be a unified Theory of Everything (putting the big big and the small small stuff together).
I’m not concerned about what Buddhists tell us is true. I stopped listening with blind faith when my mom told me Santa wasn’t real. My issue is that we label things as discrete things and then create models and concepts based on this idea. But is there anything to suggests that the idea of a discrete thing if founded on anything other than assumption (something Buddhism suggests)? I would be interested on your opinion on this.

[jimtron]

Rather, I’m just focusing on the issue of compete interconnectedness*, the idea stands without Buddhism backing it up, or at least as far as I can tell (that’s why I’m here). As for where numbers might not work? Well, I’m not formally trained in math. Biology. Not math. But from what I’ve heard there is an issue with expressing the universe in mathematical terms right near the beginning of the Big Bang. Another place might be a unified Theory of Everything (putting the big big and the small small stuff together).When you say interconnectedness, do you mean that in a scientific way? Religious? Other? As far as I know math and science are the best ways we have so far to understand the natural world (but of course they are limited), including the universe. Do you agree? If not, what's a better method?

eta: * It would help if you could be specific in defining what you mean by interconnectedness. I'm not sure if you mean this in a religious, "cosmic," arguably vague way, or if you mean it in more natural, scientific terms.

[Loriciferan Universe]

When you say interconnectedness, do you mean that in a scientific way? Religious? Other? As far as I know math and science are the best ways we have so far to understand the natural world (but of course they are limited), including the universe. Do you agree? If not, what's a better method?

eta: * It would help if you could be specific in defining what you mean by interconnectedness. I'm not sure if you mean this in a religious, "cosmic," arguably vague way, or if you mean it in more natural, scientific terms.

Interconnectedness: The interrelationship of one thing to all other things. I am trying to approach it from a philosophical perspective. Example would be that of the leaf, which I discussed earlier. Or the ripples on water example. The way I see it, things are either discrete and interacting with one another, or not.
I would agree to an extent that math and science are the best ways to know the natural world. If one is interested in understanding the world, I mean, really digging it, than I don’t think they are necessarily the best ways. You grok? ;)

[JetLeg]

Interconnectedness: The interrelationship of one thing to all other things. I am trying to approach it from a philosophical perspective. Example would be that of the leaf, which I discussed earlier. Or the ripples on water example. The way I see it, things are either discrete and interacting with one another, or not.
I would agree to an extent that math and science are the best ways to know the natural world. If one is interested in understanding the world, I mean, really digging it, than I don’t think they are necessarily the best ways. You grok? ;)

I think that interrlelationship (when you think of it) implies that things are discrete. How can connectedness exist other than between things that are different and discreet???

[Loriciferan Universe]

I think that interrlelationship (when you think of it) implies that things are discrete. How can connectedness exist other than between things that are different and discreet???

Touche. Although I think the issue here is more linguistic than actual. I don’t think there is a word for distinguishing a facet while still acknowledging the whole. In our language we don’t say, “that tree-and-the-whole-of-the-universe-that-it-is-a-part-of-and-for-which-it-is-an-essential-component”. We just say “tree” and forget the rest. Maybe it’s assumed that the rest is redundant? Interesting point though. Hmmm....

[Dancing David]

Okay, how about the non-sketchy Buddhists? All I'm really wondering about here in a precept in Buddhism, not the whole thing. I am sure Buddhist use numbers, just like good Catholic boys use condoms, it's matter of modern necessity. What I am wondering is if numbers are just a made up little thing that make life easier, or something that is actually a property of the universe. As far as I can tell a Buddhist would say its just a made up thing. And that appears to be the general consensus here as well. But then there is an issue. If they are made up, how can we be sure we are actually using them in a way that tells us something about the universe?

And yes, there are a myriad of examples that support numbers, suggesting there is some "truth" in organizing the world this way. But there are also many examples where they don't work. Now science has a long way to go and maybe one day someone will get EVERYTHING to work out. But until then it is interesting to ponder whether they CAN work...


Yup, numbers are made up things, that may represent there own world and are interfacing with the reality. (The number world is not a separate place, it is the set of self referenced expression of the expression of numeric values)

The fact that numbers behave rationally is no surprise and not evidence of anything other than the expression of the interaction of numeric sets.

[Dancing David]

I am not sure what you mean by discrete thing, contingent history is part of science.

The issue seems to be that the nature of human expression is what it is, it is a self referencing set of symbols used in reference to the objective reality (assumed or axiomatic). Therefore- Things In And Of Themselves (TIAOT) are an idea based upon the sensations, perceptions thoughts and emotions. The ontology of the world is not important. Axiomatically our senses interact with TIAOT, we form perceptions in our brains, we learn to speak with other humans and we learn an associative set of rules about language and the behavior of TIAOT through experience , contingent history and social transmission through language and the symbol set of numbers.

So we have a point of contact with TIAOT, the senses, we have our learned associative interaction with TIAOT, we have the assumed set of expectation of the behavior of TIAOT, we have the cultural, social and person transmission of information regarding TIAOT.

Which is why I like to annoy people by making the statement, all human thoughts are equally true and equally false. Some just have a higher validity in the approximation of the external reality than others. Science is the method by which we may determine which thoughts are just idiosyncratic association and which have validity for making predictions based upon the observed behavior of TIAOT.

As far as interconnectedness, it exists in many real and metaphorical senses.

[Dancing David]

Interconnectedness: The interrelationship of one thing to all other things.

each objects has a contingent listory. Some interconnections are real in the sense of the connections of forces and fields. Soem are a product of contingent history.

I am trying to approach it from a philosophical perspective. Example would be that of the leaf, which I discussed earlier. Or the ripples on water example. The way I see it, things are either discrete and interacting with one another, or not.

That is a dichotomy of thought, reality will behave the way it does regardless of what we think.

I would agree to an extent that math and science are the best ways to know the natural world. If one is interested in understanding the world, I mean, really digging it, than I don’t think they are necessarily the best ways. You grok? ;)

We are the world...

[drkitten]

So if this is true than there are no discrete things, nothing stands alone and in truth nothing really stands at all. So with that said... what of numbers?

I think you're being way too literal here (and, frankly, rather silly).

I took a vacation last year. Me, my partner, my partner's parents, my sister-in-law and her husband, and their daughter (my niece).

Were we one family on vacation, or three? Or were we seven individual people? I suggest that the correct answer to that question is "yes," especially from a Buddhist perspective.

The vacation was to an island in the Caribbean Sea. Is that a separate body of water from the Arctic Ocean or not? Just how many oceans are there -- and how come I can sail from one to the other?

Just because you can apply the label "two" to something doesn't mean that the two things are entirely separate and separable. Just because you can apply the label "one" to something doesn't mean that it's uniformly and homogenously the same. Every individual snowflake is different, but I'm throwing one snowball at you. Every drop of water is different, but I'm diving in a single ocean.

If there is no single discrete thing in the universe, than you can’t say there is 1 of anything, or 2.

Sure I can. I have one cup of coffee on my deak -- I just said it. Of course, it all came out of the same departmental urn, so in that sense everyone in the department is drinking "the same" coffee. In fact, it all came as part of a single shipment of beans, so we've really been drinking "the same coffee" for the better part of a month. But nevertheless, the cup that I'm drinking now is different from the one my department chair had last Thursday.

Heck, I have "my grandfather's" eyes. I inherited them from him (they have a very distinct color). I also have my grandfather's watch, which I also inherited from him. It seems obvious that I got both from my grandfather, but in entirely different way. Does it make sense to talk about "my grandfather's eyes" as being separate from my own?

The Buddhist perspective is simply that to ignore the connections and see only the separations is a limited (and false) vision.

[Ryokan]

You can't step into the same river twice.

[Darth Rotor]

A nice post, ending in . . .

The Buddhist perspective is simply that to ignore the connections and see only the separations is a limited (and false) vision.
Nice post. :)

To address a couple of things mentioned earlier.

1. The remark about "Buddhists believing in numbers" seems a non sequitur, as a number is a tool, or a symbol, rather than a matter of belief.

2. Numbers, names and labels are aids to understanding, but should not be confused with TIAOT. (Thanks for the acronym, Dancing David. :) )

I am not sure if what I just wrote is an original thought, (the sentence ending in TIAOT) but it came to me as I read the thread. If someone else has already taken the same idea and put it into an identical arrangement of words, was my thought original if I had not yet heard it quite that way? Was it independently formed? Or, was it a predictable outcome of the various inputs in this thread, my brain's synthesis of same, and the probability dice inside my brain housing group caming up with the right die roll to spit out that observation?

(My brain uses d20, by the way. ;) )

DR

[drkitten]

You can't step into the same river twice.

Sure I can. There's a river right by where my father works that I've stepped into thousands of times.

[jimtron]

Sure I can. There's a river right by where my father works that I've stepped into thousands of times.

I'm guessing this is supposed to mean you can't step in the same river twice because it changes from moment to moment?

[Darth Rotor]

I'm guessing this is supposed to mean you can't step in the same river twice because it changes from moment to moment?

That depends on what your definition of "same" is. ;)

DR

[Dancing David]

Sure I can. There's a river right by where my father works that I've stepped into thousands of times.
According to Herodetus it isn't. The water changes, the banks change, your presense changes the river, etc..


I think it even made it into Pocahantas by Disney

[JoeTheJuggler]

I think you're talking about the Doctrine of Dependent Origination. There are in different Buddhist sects very different understandings of the concept.

One is simply that all things arise due to causes and conditions. That is, everything is interconnected.

An example is what we call a "rainbow". The phenomenon that we put a label on is really an interaction of light, water vapor, our eyes and our minds. (Can there be such a thing as "consciousness" or "mind" without there being something to be conscious of?) Teachers will frequently say, is that sound we all hear outside the window or inside the mind?

As to the numbers issue: I think most Buddhist recognize a difference between the essential nature of things, and conventional usage. (By convention I mean how we use words and concepts by agreement, which, as with language, can be arbitrary to a greater or lesser extent.)

You can talk about waves in the ocean as things--and therefore things that can be numbered, even though we know that they're really composed of water, and the water isn't really moving along with the wave. (The water is mostly moving up and down, yet the wave moves across.)

FWIW, I don't consider myself a Buddhist or even a Buddhist apologist. I don't see a necessary incompatibility between a concept of numbers and the Doctrine of Dependent Origination.

[drkitten]

According to Herodetus it isn't.

And according to the Tooth Fairy, Herodetus is wrong. (Isn't argument from authority fun?) To say that the river is never the same is exactly as wrong as saying it's always the same.

[JoeTheJuggler]

Yeah. I’ve heard people speculate that part of the reason many eastern peoples progressed little in the area of science is because of a belief system that did not allow for “fragmentation” of phenomenon, although I’m not so sure the former statement is all that true.

I agree with your suspicion of this speculaiton. It sounds like an explanation in need of something to be explained. First, they'd need to prove that eastern peoples have progressed little in the area of science. Second they'd need to prove that said lack of progress is somehow connected to their religious beliefs.

I suppose Europe's prodigious mathematical progress came from belief in a triune deity? :)

[Loriciferan Universe]

And according to the Tooth Fairy, Herodetus is wrong. (Isn't argument from authority fun?) To say that the river is never the same is exactly as wrong as saying it's always the same.

Hmmm... Well damned if you do, damned if you don’t. That’s a safe, but ultimately a dead-end view. It may be the most correct, but it certainly doesn’t leave much to say... Perhaps you’re right in that I’m just being silly drKitten, hence the anonymous forum ;) Regardless of how “silly” it may be, debate over the nature of numbers and mathematics has been a fiery subject form the time of the Greek and continues to rage (in fact, Santa’s opinion on the issue is quite enlightening ;)).

Below are just a sampling of philosophical school that focus on the nature of mathematics. So while this conversation may seem laughable there are some people out there who get paid to ponder on this stuff, and thus it is at least as good as porter potty cleaning, if not better.

From the Wiki page on Philosophy of Mathematics:

Mathematical realism, like realism in general, holds that mathematical entities exist independently of the human mind.

Platonism is the form of realism that suggests that mathematical entities are abstract, have no spatiotemporal or causal properties, and are eternal and unchanging. This is often claimed to be the naive view most people have of numbers.

Logicism is the thesis that mathematics is reducible to logic, and hence nothing but a part of logic (Carnap 1931/1883, 41). Logicists hold that mathematics can be known a priori, but suggest that our knowledge of mathematics is just part of our knowledge of logic in general, and is thus analytic, not requiring any special faculty of mathematical intuition.

Empiricism is a form of realism that denies that mathematics can be known a priori at all. It says that we discovered mathematical facts by empirical research, just like facts in any of the other sciences

Formalism holds that mathematical statements may be thought of as statements about the consequences of certain string manipulation rules. For example, in the "game" of Euclidean geometry (which is seen as consisting of some strings called "axioms", and some "rules of inference" to generate new strings from given ones), one can prove that the Pythagorean theorem holds (that is, you can generate the string corresponding to the Pythagorean theorem). Mathematical truths are not about numbers and sets and triangles and the like — in fact, they aren't "about" anything at all!

Mathematical intuitionism: In mathematics, intuitionism is a program of methodological reform whose motto is that "there are no non-experienced mathematical truths" (L.E.J. Brouwer).

Constructivism: Like intuitionism, constructivism involves the regulative principle that only mathematical entities which can be explicitly constructed in a certain sense should be admitted to mathematical discourse. In this view, mathematics is an exercise of the human intuition, not a game played with meaningless symbols. Instead, it is about entities that we can create directly through mental activity. In addition, some adherents of these schools reject non-constructive proofs, such as a proof by contradiction.

Fictionalism was introduced in 1980 when Hartry Field published Science Without Numbers, which rejected and in fact reversed Quine's indispensability argument. Where Quine suggested that mathematics was indispensable for our best scientific theories, and therefore should be accepted as a body of truths talking about independently existing entities, Field suggested that mathematics was dispensable, and therefore should be considered as a body of falsehoods not talking about anything real.

***Embodied mind theories hold that mathematical thought is a natural outgrowth of the human cognitive apparatus which finds itself in our physical universe. For example, the abstract concept of number springs from the experience of counting discrete objects. It is held that mathematics is not universal and does not exist in any real sense, other than in human brains. Humans construct, but do not discover, mathematics.
*** this is the one I gather most people here ascribe to.

Social constructivism or social realism theories see mathematics primarily as a social construct, as a product of culture, subject to correction and change.


There were also “non-traditional schools listed but I though it best to keep this post in the category of “obnoxiously long” as opposed to “not worth the effort”.

[FireGarden]

The Buddhist perspective is simply that to ignore the connections and see only the separations is a limited (and false) vision.

I can agree with that.
And I liked the examples in the rest of the post.

[Dancing David]

And according to the Tooth Fairy, Herodetus is wrong. (Isn't argument from authority fun?) To say that the river is never the same is exactly as wrong as saying it's always the same.

I don't believe that I put Herodetus in the role of authority, it was more an attribution of the quote.

So the water is really the same? ;)

:)

[Dancing David]

Hmmm... Well damned if you do, damned if you don’t. That’s a safe, but ultimately a dead-end view. It may be the most correct, but it certainly doesn’t leave much to say... Perhaps you’re right in that I’m just being silly drKitten, hence the anonymous forum ;) Regardless of how “silly” it may be, debate over the nature of numbers and mathematics has been a fiery subject form the time of the Greek and continues to rage (in fact, Santa’s opinion on the issue is quite enlightening ;)).

Below are just a sampling of philosophical school that focus on the nature of mathematics. So while this conversation may seem laughable there are some people out there who get paid to ponder on this stuff, and thus it is at least as good as porter potty cleaning, if not better.

From the Wiki page on Philosophy of Mathematics:

Mathematical realism, like realism in general, holds that mathematical entities exist independently of the human mind.

Platonism is the form of realism that suggests that mathematical entities are abstract, have no spatiotemporal or causal properties, and are eternal and unchanging. This is often claimed to be the naive view most people have of numbers.

Logicism is the thesis that mathematics is reducible to logic, and hence nothing but a part of logic (Carnap 1931/1883, 41). Logicists hold that mathematics can be known a priori, but suggest that our knowledge of mathematics is just part of our knowledge of logic in general, and is thus analytic, not requiring any special faculty of mathematical intuition.

Empiricism is a form of realism that denies that mathematics can be known a priori at all. It says that we discovered mathematical facts by empirical research, just like facts in any of the other sciences

Formalism holds that mathematical statements may be thought of as statements about the consequences of certain string manipulation rules. For example, in the "game" of Euclidean geometry (which is seen as consisting of some strings called "axioms", and some "rules of inference" to generate new strings from given ones), one can prove that the Pythagorean theorem holds (that is, you can generate the string corresponding to the Pythagorean theorem). Mathematical truths are not about numbers and sets and triangles and the like — in fact, they aren't "about" anything at all!

Mathematical intuitionism: In mathematics, intuitionism is a program of methodological reform whose motto is that "there are no non-experienced mathematical truths" (L.E.J. Brouwer).

Constructivism: Like intuitionism, constructivism involves the regulative principle that only mathematical entities which can be explicitly constructed in a certain sense should be admitted to mathematical discourse. In this view, mathematics is an exercise of the human intuition, not a game played with meaningless symbols. Instead, it is about entities that we can create directly through mental activity. In addition, some adherents of these schools reject non-constructive proofs, such as a proof by contradiction.

Fictionalism was introduced in 1980 when Hartry Field published Science Without Numbers, which rejected and in fact reversed Quine's indispensability argument. Where Quine suggested that mathematics was indispensable for our best scientific theories, and therefore should be accepted as a body of truths talking about independently existing entities, Field suggested that mathematics was dispensable, and therefore should be considered as a body of falsehoods not talking about anything real.

***Embodied mind theories hold that mathematical thought is a natural outgrowth of the human cognitive apparatus which finds itself in our physical universe. For example, the abstract concept of number springs from the experience of counting discrete objects. It is held that mathematics is not universal and does not exist in any real sense, other than in human brains. Humans construct, but do not discover, mathematics.
*** this is the one I gather most people here ascribe to.

Social constructivism or social realism theories see mathematics primarily as a social construct, as a product of culture, subject to correction and change.


There were also “non-traditional schools listed but I though it best to keep this post in the category of “obnoxiously long” as opposed to “not worth the effort”.


Wow, Santa and the Tooth Fairy sure have a lot of time on their hands!

That was very enlightening, thank you.

[Loriciferan Universe]

Wow, Santa and the Tooth Fairy sure have a lot of time on their hands!

That was very enlightening, thank you.

Glad I could bring you something new :).

drKitten (or anyone else), I have a question. The examples you listed were interesting, but they stemmed from several different sources so for now I’m going to pick just one point you made and go from there. You stated:

“Just because you can apply the label "two" to something doesn't mean that the two things are entirely separate and separable. Just because you can apply the label "one" to something doesn't mean that it's uniformly and homogenously the same.”

But isn’t it a mathematical axiom that if I am working an equation with x and y, that they are related so far as the equation shows, but no more so. In other words, x and y are completely different things and you are describing a relationship between them. Now, isn’t this kind of mathematics used to describe physical properties of the universe. And if you are correct that “Just because you can apply the label "two" to something doesn't mean that the two things are entirely separate and separable” doesn’t that present a problem for using math as a way to understand the universe?

[Dancing David]

The key word being describe, which means to write about. Do not mistake the map for the road?

[cyborg]

1) The metaphysical is not the physical.
2) Metaphysical concepts can be represented physically.

[drkitten]

“Just because you can apply the label "two" to something doesn't mean that the two things are entirely separate and separable. Just because you can apply the label "one" to something doesn't mean that it's uniformly and homogenously the same.”

But isn’t it a mathematical axiom that if I am working an equation with x and y, that they are related so far as the equation shows, but no more so.

Not at all; in fact, much of mathematical reasearch consists of showing that if two things are related in one way, then they must also be related in a second way. For example, if you have a set of objects that are related in such a way that they form a planar graph, then they must also be related in such a way that their chromatic number is four or less (this is the famous "Four-color theorem"). If you know that x and y are related by being relatively prime, then you also know that they are both related to the number xy in that xy is their least common multiple. If you know that three points are related in the form of an equilateral triangle, then they are also related in that their internal angles are each sixty degrees. And so forth.

Now, of course, if all you know is that x and y are related in one way, you can't assume without justification that they are related in another way as well -- I share a last name with a guy I've never met from Kansas, but I can't assume on that basis that we are genetically related as well. This applies to mathematics as well as to "raal life"; you don't get to make unfounded assumptions.

{QUOTE] And if you are correct that “Just because you can apply the label "two" to something doesn't mean that the two things are entirely separate and separable” doesn’t that present a problem for using math as a way to understand the universe?[/QUOTE]

Not at all. I assume (because I know it) that this guy in Kansas shares my name. But I also assume (with equal validity) that he's a different person from me. Can I assume that he's a relative? Not with any confidence. Now, it might be that he is. He might be part of my extended family and I will eventually inherit millions from him -- but that's not an assumption that I should make. My understanding of the universe is limited by what I know about it.

But because I know he's a different person than I, I also know that if we took a trip together, we would probably need to rent two hotel rooms. Two people = two rooms. Even if we're relatives, that doesn't mean that we should share a room. Even if he were my long-lost brother, that doesn't mean that we should share a room. One family (perhaps) -- but still two hotel rooms.

[blobru]

According to Herodetus it isn't. The water changes, the banks change, your presense changes the river, etc...


The Pre-Socratic philosopher Heraclitus is the source of the quote, "you can't step into the same river twice", though it may have been recorded in Herodotus' Histories.
His disciple Cratylus took it a step :rolleyes: further and declared, "you can't step in the same river once!"
In opposition to the "change is all there is" school, Parmenides and Zeno (he of the paradoxes) argued change is impossible.
Of course Plato reconciles the two by saying universal Ideas don't change whereas particular objects do.

[Dancing David]

The Pre-Socratic philosopher Heraclitus is the source of the quote, "you can't step into the same river twice", though it may have been recorded in Herodotus' Histories.
His disciple Cratylus took it a step :rolleyes: further and declared, "you can't step in the same river once!"
In opposition to the "change is all there is" school, Parmenides and Zeno (he of the paradoxes) argued change is impossible.
Of course Plato reconciles the two by saying universal Ideas don't change whereas particular objects do.


Ooops, it is Heraclites isn't it. Old brain.