Different truths are not the same

[Tathagata]

This is false. This categorization of truth is not accurate.

The Buddha laid out the Two Truth Doctrine for us to have proper discernment.

"The Buddha's teaching of the Dharma is based on two truths: a truth of worldly convention and an ultimate truth. Those who do not understand the distinction drawn between these two truths do not understand the Buddha's profound truth. Without a foundation in the conventional truth the significance of the ultimate cannot be taught. Without understanding the significance of the ultimate, liberation is not achieved."

—Nagarjuna, Mulamadhyamakakarika 24:8-10



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[A-ManESL]

This isn't exactly accurate. Penrose here (p. 63) is dealing with the nominalism/realism debate, not subjectivity in mathematics. It's true that mathematicians do subjectively define some things. Order of operations in algebra. But that's just convention. Operations can be defined in different ways, but again this has less to do with subjectivity than with purpose. I can say subtraction is the addition of negative numbers, and then make addition the only operation in arithmetic is addition. I'll still get the same results. Our "body of maths" isn't subject to their opinions but is subject to the need for precise definitions.

Apparently my point is not getting across clearly. I very well understand that kind of subjectivity but that is not what I referring to. As my link said even in an established proof later errors may be pointed out. It is subject to mathematicians approval that we accept certain results, which may be proved wrong later. The upshot of this is that sometimes whatever people think is mathematically true, is subject to opinions of mathematicians.

Secondly if you want to get technical there is no mathematical guarantee that any result is true mathematically as its validity has been checked only by a finite number of people, each with a finite probability > 0 of being wrong. Hence mathematically speaking there is a mathematical positive probability of the proof being wrong. So no result can ever claim to be true mathematically 100%.

Furthermore, as Godel claims, there are mathematical results that may not be proved or disproved within a given sufficiently strong mathematical system.

 

[PolyHedral]

Secondly if you want to get technical there is no mathematical guarantee that any result is true mathematically as its validity has been checked only by a finite number of people, each with a finite probability > 0 of being wrong. Hence mathematically speaking there is a mathematical positive probability of the proof being wrong. So no result can ever claim to be true mathematically 100%.

Once you have refined and annotated a proof's steps with the exact rules that justify moving from one step to another, there is negligible possibility of you being wrong. Hardly any human-generated proofs do this, but hardly any have to, since the chances of the entire mathematics community making a mistake is phenomenally low.

Furthermore, as Godel claims, there are mathematical results that may not be proved or disproved within a given sufficiently strong mathematical system.

He does not, however, guarantee that any such truth is relevant to reality.

 

[Willamena]

He does not, however, guarantee that any such truth is relevant to reality.

Isn't there a relationship between truth and reality?

 

[LegionOnomaMoi]

It is subject to mathematicians approval that we accept certain results, which may be proved wrong later.

Sort of like a translation of a language you can't read is "subject to" the approval of the translator. If you can't read the language, be it ancient Greek or directed graphs, then your acceptance is based on the expertise of others.

Secondly if you want to get technical there is no mathematical guarantee that any result is true mathematically as its validity has been checked only by a finite number of people, each with a finite probability > 0 of being wrong.

That's simply a distortion of probability. "Mathematical guarantee" is absolutely "true mathematically." Certainly, mathematicians can be wrong. But this isn't a matter of simple probability. If you don't understand probability, you really can't use it as an argument.

Furthermore, as Godel claims, there are mathematical results that may not be proved or disproved within a given sufficiently strong mathematical system.

I've actually read Gödel's work in German. I don't think you understand his proofs.

 

[A-ManESL]

Once you have refined and annotated a proof's steps with the exact rules that justify moving from one step to another, there is negligible possibility of you being wrong. Hardly any human-generated proofs do this, but hardly any have to, since the chances of the entire mathematics community making a mistake is phenomenally low.

I know it is phenomenally low and am in no way against this finding proof exercise (in fact I love it), but my point is mathematically speaking there is such a positive probability. In other words it is mathematics which tells us that we can never be sure that what we have proved is true mathematically, and it is common sense which tells that we can be sure that what we have proved is true mathematically. As soon as "common sense" enters the picture, so does subjective opinion even though it is the subjective opinion of every person who ever lived. Purely mathematically speaking, any result is not true yet.

He does not, however, guarantee that any such truth is relevant to reality.

Yes of course. I dont think Godel's theorem has any relevance here at all. It was a mistake to talk about it.

 

[A-ManESL]

That's simply a distortion of probability. "Mathematical guarantee" is absolutely "true mathematically." Certainly, mathematicians can be wrong. But this isn't a matter of simple probability. If you don't understand probability, you really can't use it as an argument.

I am not saying that mathematical guarantee is not absolutely true mathematically. I am saying that Theorem X may be wrong but people may think it is true. This is because mathematicians think it is true because people may have not found an error yet.

I think I understand probability but here I was using probability in the colloquial sense and not in the probability measure sense. Also I think I understand the point you are trying to make. I am not sure that you understand mine. What is the worth in your opinion of a body of knowledge which contains truths but no fool-proof mechanism to find truths?

I've actually read Gödel's work in German. I don't think you understand his proofs.

I have not read the proofs but only his claims.

 

[LegionOnomaMoi]

What is the worth in your opinion of a body of knowledge which contains truths but no fool-proof mechanism to find truths?

Complex. But mathematics DOES have "fool-proof mechanisms." They are limited in their ability to go beyond their enclosed systems, but the point remains.

 

[A-ManESL]

Do you mean that within a set of axioms and logic rules predefined it is possible to find mathematical truths. In that case, my reply is that it is indeed so, but there is no way one can be certain that it is a truth. As my link showed, there are many examples of proofs accepted for many years until flaws were found in them. The absoluteness of the truth of the statement is thus in question for ever. Personally we may all use common sense and get on with our lives if a proof has stood the test of time, but that is not the point I am harping on.

 

[filthy tugboat]

The rules of deductive reasoning used in mathematics are not formed by an external scale but within the gambit of mathematics itself. These laws are therefore not independent of the current reasoning techniques in vogue. What guarantee is there that what we regard as proved today (eg Fermat's last theorem) may turn out to be disproved tomorrow because our deductive reasoning process had a fundamental flaw which has not been understood today? See this for a list of widely accepted mathematical results which were later rejected. The value of such a truth which changes and measures its robustness by its own scale cannot be called a truth in my opinion and should be called as a theorem instead.

They are called theorem's i.e Mathematical theorem. You don't have to regard them as truth for them to be acknowledged and demonstrably true. It is true according to it's own scale. What else this scale applies to is what makes it applicably true to reality.

Secondly I understand that Euclidean geometry is neither true/false in the absolute sense (to which I was referring to in my OP) and subject to its axioms can be established. But you can judge the subjectiveness adopted by mathematicians in accepting it by the fact that Gauss hid his work on non-Euclidean geometry for a long time for fear of an outcry. Mathematicians display a certain subjectiveness in accepting what is mathematically true or not (hence people call negative numbers as "negative", and imaginary numbers as "imaginary"; although all numbers are after all imagined by us) and this filters down, because practically speaking it is mathematicians who decide whether a certain result is valid or not. Hence subject to their opinion, we get our body of maths.

Not really, an equation in mathematics is either true or false and the conclusion is demonstrable. mathematicians do not decide this, it is decided upon by the mathematical model being used and the equation itself.

You probably dont think this is a thing because you don't know.

Or because you can't know. To me, spirituality seems to be essentially a faith based thing and sometimes it is outright confused with emotional and mental states. Spirituality itself is poorly defined and encompasses many ideas, some of which contradict other notions of spirituality. No authority exists on the matter, there is no demonstrable truth in spirituality, there are a lot of fraud's that take advantage of people who actually believe in it. I've seen no reason to believe anything to do with spirituality is reasonable or holds any truth and all in all, both the terms "spirit" and "spirituality" are poorly defined and subsequently open for interpretation.

If you want to know I could recommend a few books for you.

I doubt that these books have any more credible information than I have on the subject already.

 

[A-ManESL]

I don't think you understood clearly my point. Your statement "an equation in mathematics is either true or false and the conclusion is demonstrable." is wrong on two counts:

1. Firstly there are many statements which within a given mathematical system are neither true or false and cannot be demonstrated either way. Such as the continuum hypothesis cannot be established within ZFC set theory.

2. My original point is that since whether the demonstration itself is a valid demonstration is decided by human beings (who check it as per set-rules) who may make mistake hence there is no 100% guarantee that the demonstration is valid and the result indeed true. There are many results which were thought to be proved for many many years until the demonstration was found wrong by someone. Hence there is no guarantee that whatever has thought to be demonstrated today may not be shown to be false tomorrow. See the link for examples.

And regarding spirituality etc, since you seem to know about it, suit yourself. I just wanted to say that those who also claim to know about it in the books I was referring to (which you have a conclusion of) essentially claim the opposite of what you say. At any rate, it is a moot point.

 

[filthy tugboat]

I don't think you understood clearly my point. Your statement "an equation in mathematics is either true or false and the conclusion is demonstrable." is wrong on two counts:

1. Firstly there are many statements which within a given mathematical system are neither true or false and cannot be demonstrated either way. Such as the continuum hypothesis cannot be established within ZFC set theory.

I didn't say statements thought did I? I said equations.

2. My original point is that since whether the demonstration itself is a valid demonstration is decided by human beings (who check it as per set-rules) who may make mistake hence there is no 100% guarantee that the demonstration is valid and the result indeed true.

In order for anything to be considered true or false, it has to be judged by humans. On this basis you are saying no truth truly exists or at least no truth can ever be found by humans because they must subjectively view it and determine whether it is true or false. This is not a fault of maths in any part, it is a fault in humans.

There are many results which were thought to be proved for many many years until the demonstration was found wrong by someone.

Like what? Are we discussing math equations or the application of mathematical models? Can you show any mathematical equations within the original mathematical model intended to present their truth are now false? Why were they originally considered true? What changed to determine their falsehood?

Hence there is no guarantee that whatever has thought to be demonstrated today may not be shown to be false tomorrow.

I don't think this is true of maths, until examples are given, we will have to see.

See the link for examples.

What link?

And regarding spirituality etc, since you seem to know about it, suit yourself.

I know very little about it, if anything at all, I am aware of much speculation however.

I just wanted to say that those who also claim to know about it in the books I was referring to (which you have a conclusion of) essentially claim the opposite of what you say. At any rate, it is a moot point.

I am aware many people view spirituality very differently to myself. My point was that the whole "field" of spirituality is vague, undefined and speculative. There is no authority, there is no clear definition, nobody is right and nobody is wrong about it. It is guesswork and no claims made of it can be(or at least have been) confirmed.

What is a method that can be employed within the field of "spirituality" that can determine truth? Logic would be advisable but there are some that think spirituality is "above and beyond" logic. Is it? Who knows?

 

[A-ManESL]

What you call an equation may be represented by a mathematical statement about equality of two sets, and with proper meaning given to equality and other "symbols", mathematical statements may be represented as equations. In that sense any distinction between them is meaningless. At any rate every equation is a statement.

This is the link that I posted previously, about mathematical results which were thought to be proved earlier (some of them for centuries) and later flaws were found in the proof.

On this basis you are saying no truth truly exists or at least no truth can ever be found by humans because they must subjectively view it and determine whether it is true or false.

This is my point regarding maths. Regarding spirituality it is said (I don't know whether it is right or wrong) that the knowledge transcends this subjectivity by ascending from man to Godliness, but I wont talk much about all that because for one I dont know enough about it myself, and secondly I am not sure whether you do either.

What is a method that can be employed within the field of "spirituality" that can determine truth? Logic would be advisable but there are some that think spirituality is "above and beyond" logic. Is it? Who knows?

Perhaps some books could have been helpful. Hence I suggested that you may be interested in some of the books which I found a little insightful but you didn't seem interested.

 

[gnostic]

Isn't there a relationship between truth and reality?

With religious or spiritual truth, they are miles apart.

 

[Twilight Hue]

Isn't there a relationship between truth and reality?

I think so. The direction by which it takes a person however, can take on a life of it's own.

 

[filthy tugboat]

What you call an equation may be represented by a mathematical statement about equality of two sets, and with proper meaning given to equality and other "symbols", mathematical statements may be represented as equations. In that sense any distinction between them is meaningless. At any rate every equation is a statement.

Every equation is a statement but not every statement is an equation, the statement you presented in your previous post was not an equation.

URL="http://mathoverflow.net/questions/35468/widely-accepted-mathematical-results-that-were-later-shown-wrong"]This is the link[/URL] that I posted previously, about mathematical results which were thought to be proved earlier (some of them for centuries) and later flaws were found in the proof.

Perhaps you would like to post some individual ones here you think represent your point. I try to avoid debating links.

This is my point regarding maths.

That was what I was referring to and if that is truly what you are trying to say then you have effectively invalidated the term "truth" by suggesting it can never truly exist. It is an unobtainable thing, a standard no "proof" could ever meet.

Regarding spirituality it is said (I don't know whether it is right or wrong) that the knowledge transcends this subjectivity by ascending from man to Godliness,

Why should I consider this statement as authoritative? Why should I take it seriously? Some people that use the term spirituality don't think it has anything to do with a God. Are you suggesting that the religious(people that believe in God) have some sort of monopoly on the term "spirit" and "spirituality"?

but I wont talk much about all that because for one I dont know enough about it myself, and secondly I am not sure whether you do either.

Does anyone? I know people think they do and tell others that they do but can they show that what they are saying is true? I don't even necessarily mean empirically true, can they show it's true in any meaningful way?

Perhaps some books could have been helpful. Hence I suggested that you may be interested in some of the books which I found a little insightful but you didn't seem interested.

I'm not particularly interested, I've read a lot on the subject from a wide variety of sources and I have never seen a good reason to take "spirituality" seriously or give any credence to those claiming to know what it is and/or relate to it.

 

[A-ManESL]

I don't understand why you can't just click on the link and read the examples :S.

The Euler Characteristic V-E+F has an interesting history. It was initially stated that, for all polyhedra, V(ertices)−E(dges)+F(aces)=2 and its proof was widely accepted, until people found counter-examples.

Why should I consider this statement as authoritative? Why should I take it seriously? Some people that use the term spirituality don't think it has anything to do with a God. Are you suggesting that the religious(people that believe in God) have some sort of monopoly on the term "spirit" and "spirituality"?

No I am not. You are welcome not to consider this statement authoritative. Even I said clearly I do not know whether it is true or not.

I'm not particularly interested, I've read a lot on the subject from a wide variety of sources and I have never seen a good reason to take "spirituality" seriously or give any credence to those claiming to know what it is and/or relate to it.

If you haven't found a good reason yet, and believe you won't find a good reason if you keep reading it is your personal choice. In that case I don't think there is anything we may gain from talking about spirituality.

 

[filthy tugboat]

I don't understand why you can't just click on the link and read the examples :S.

Because I do not debate links, there was a whole lot of information in that link and if I were to cite and respond to every bit of it, it would make a massive bloody post and you might (for all i know) disagree with a lot of what I cited. I want you to specifically state your views, express what you are arguing rather than me assume you agree with absolutely everything you linked from a site.

The Euler Characteristic V-E+F has an interesting history. It was initially stated that, for all polyhedra, V(ertices)−E(dges)+F(aces)=2 and its proof was widely accepted, until people found counter-examples.

Was it widely accepted? From my understanding it was actually changed by the person who discovered the theorem and it was changed shortly after introducing it. The reason this is a poor example to give is that it doesn't support your argument at all. It was never mathematically true. You haven't taken a mathematically true statement or equation and proven it was false, you've taken the failings of a man and suggested that mathematical truths cannot be considered "true". The Euler Characteristic is true, it is still considered true today, as far as I'm aware, it works for all polyhedrons. The original assertion provided by the author was untrue but after an in depth analysis, the theorem was amended. this is not a mathematical proof that was true at one time and false at another, it was believed true by a man or perhaps a few men and when it was shown to be false, it then became known that it was false the whole time subsequently it was amended in a way that corrected it's failures.

No I am not.

Oh good, it just looked that way because you posted this quote; "Regarding spirituality it is said (I don't know whether it is right or wrong) that the knowledge transcends this subjectivity by ascending from man to Godliness." From this I kind of assumed that you agreed with the notion that spirituality had something to do with Godliness.

You are welcome not to consider this statement authoritative. Even I said clearly I do not know whether it is true or not.

OK then, I won't.

If you haven't found a good reason yet, and believe you won't find a good reason if you keep reading it is your personal choice.

My choice was to not read suggested material because I doubt any suggestion you give will put me closer to finding any truth within all potential fields of "spirituality". I will continue to read the subject matter but it will be at my own discretion. Please don't take this as me being rude, I don't mean to be but I have been recommended so many books and even just essays that I have lost all interest in what others' consider interesting, informative or true. I've put too much effort into being discouraged, misinformed and bored, I don't particularly want to continue this trend.

In that case I don't think there is anything we may gain from talking about spirituality.

Perhaps not, I am open to discussion but I certainly want some kind or support, even if it's only logical support, for any claims made regarding discussions on spirituality.

 

[idea]

The way I see it, there are 3 or 4 main types of TRUTH, and though they may occasionally overlap, they may also not necessarily be the same, in term of objective and context.

1. Personal truth.
2. Religious truth or faith-based truth.
3. Logical truth.
4. And lastly, Factual truth.

you missed

5. relative truth.

what is the velocity of that car? 80 MPH - this is only true relative to the road... if you look at the velocity relative to the sun, the velocity is very different...

come to think of it, all truth seems to be relative...

 

[PolyHedral]

you missed

5. relative truth.

what is the velocity of that car? 80 MPH - this is only true relative to the road... if you look at the velocity relative to the sun, the velocity is very different...

come to think of it, all truth seems to be relative...

The speed of the car is always c, and it's direction is perfectly objective. Just because the specific value changes with a different position doesn't mean it can't be pinned down.