Final Statements: The Nature of Truth

I admit that I haven't read every post in the "What has become of America" thread.

But I have read enough to note that you are discussing a subject I find very interesting -- the nature of truth. Truth is divisive, because people who think they have it often look down on those who "don't." This is not only the Christian religion, but also includes many others -- all that do not concede that every religion is equally valid.

However, I cannot stomach the relativist view of looking at things, which says that not only must one respect the beliefs of others, but we must also admit that the beliefs of others are just as good.

The basis of the Christian faith is essentially irrational. God cannot be proved by scientific or philosophic means. One philosophical tenet is that the basis of all our understanding today is irrational -- everything has to come from some unproven assumption, like a postulate. The Bible explicitly states that no one can know the truth except through the Holy Spirit -- something which Juntel objected to. What! you reject the power of human reasoning and individuality! This does not mean that nonChristians cannot learn anything -- rather, that even nonChristians who grasp truth are learning, inadvertently, from the Holy Spirit.

I believe that Jesus is the only son of God and that he died and rose again, but I cannot prove this. I have to accept it on faith and act in obedience. This is, of course, unreasonable and unscientific. Who was it that said humans are rational beings?

In linear analysis, it is proved that there are infinitely more irrational numbers than rational, although rational numbers are infinite. My father has shown me the reasoning behind the proof, and I understood it, although I haven't taken linear analysis. Any irrational number can be approximated by rational numbers, closer and closer to the truth, but never exactly -- consider pi, which people have tried to calculate completely, but can't ever all the way. Let me extend an analogy to faith and reason, and say that rationally there are an infinite number of possibilities. Through reason we can come closer and closer to knowing something irrational. We must, however, move into the realm of faith and obedience, accepting things that cannot rationally be understood, to gain an inkling of the truth that is infinitely more than what science can provide.

According to the Bible, to glimpse the truth beyond the theories proven probably correct by experiments and data, we must listen to the Holy Spirit.

Thus, I, a Christian, can easily claim that the leaders of the Spanish Inquisition, Albigensian Crusade and Holy Crusades were misled in their understanding of Truth, because they tried to approximate it without the guidance of the Holy Spirit.

The old thread has the wrong heading and has gotten to the point of replies to replies where it is downright confusing. I couldn't tell who was replying to whom! I thought this would be a good place for people participating in the previous discussion to state, clearly and succinctly, their own personal views. If you wish to reply to someone else's, do so in a different post from the one in which you state your own. Keep your own post free of replies and discussion, so it will be available for referral. Does that make sense? I love this subject, but I think that to continue, we must begin afresh. Anyone interested?

hmmm... new year hasn't begun here yet (montreal)...

Let me write here, at least, about some misconceptions/misunderstandings about what I have said in other threads, especially the "What Has America Become" thread.

Firstly, I do not need - and even never use - rationality to see and say that a sunset is beautiful, or to cry when my sister in law gives birth to a child, etc.

Rationality is a tool, no more, no less.

I think I have stated clearly my position about imponderables in the "WHAB" thread. Rationality can hardly scratch the surfaces on such problems, except to make remarks here and there, but cannot provoke a clear cut decision to solve them.


"However, I cannot stomach the relativist view of looking at things, which says that not only must one respect the beliefs of others, but we must also admit that the beliefs of others are just as good"

That surely doesn't come from me. I don't think you could or should consider other beliefs as just as good as yours.
I may however recommend that you not find them ridiculous just because they are different from yours (i'm glad you didn't say such things, btw).
I may also recommend that you consider that these other beliefs have believers that are as thorough believers as you are, as fervent subjects of their deity (or deities). Therefore, a good question upon these considerations is why is that so? How can that be so? Who are these gods and goddesses, etc... that exist outside your religion, and who are adored, prayed to, etc... Judaism, Islam, Hinduisms, Mazdeism, the AmericanIndian beliefs, etc...

At most, I would ask you to admit that the beliefs of others are as admissible as yours as the possible ultimate Truth. "Possible" here being the important word.
But this is of course too much to ask to certain people, who sometimes think these other religions and gods are primitive, or blatantly a work of the "demon". (And please, I'm not pointing at ANYONE from Entmoot with that last sentence).

My personal position: yes, I do admit as a possibility that the christians' deity can exist; or the jews'; or the muslims'; etc...
And this is no easily written empty admission: it is an integral part of what I believe about this subject.
Some may try to put me in the "atheist" category; but I insist that I be put in the "agnostic" one, if I must be put in a category at all; and if one asks me what agnosticism is, I can only point them to what i've said above.

I don't think I can (or people can) know what the ultimate truth is, except maybe through a very subjective experience; and if that happens to someone, that someone should respect the fact that others may have their own personal subjective experience that points to a truth that has another deity or deities in it, that may be a different truth.
As long as each other respect that personal experiences and revelations are... well... personal.
Once one thinks all must believe in what he or she experienced personally, there the big problems between religions arise.



"The Bible explicitly states that no one can know the truth except through the Holy Spirit -- something which Juntel objected to."

Read my above comments.



"I believe that Jesus is the only son of God and that he died and rose again, but I cannot prove this. I have to accept it on faith and act in obedience. This is, of course, unreasonable and unscientific. Who was it that said humans are rational beings? "

I have no problem with your personal belief above.
Again, read my above comments.



"In linear analysis.... "

Pi. Originally, Pi is simply the ratio between the circumference of a circle and its diameter. Euclid (who's work were thankfully rescued and protected by the arab muslims during europe's dark age, were such knowledge was forgotten, and brought back to Europe when Europeans went to arabic universities...) already had proven in his great Element of Geometry that whatever cirlce you took, the ratio of the circumference to its diameter is always the same; a very elegant proof I might add (it is always a joy for me to go back and read here and there Euclid's Elements). The name given to that ratio was Pi. Euclid didn't calculate the value of that number. Later, people tried to calculate it, giving some fractions that came close to it. Ultimately, it was proven that Pi couldn't be expressed by the ratio of two natural numbers: Pi, then, was proven to be irrational.
(Ultimately also, Pi was eventually proven to be non-algebraic, putting it in another category altogether... but I digress...)

Now, let's get closer to the present time... and to why I go on about this...

In the 19th century (or around), came such brilliant people such as Gauss and Riemann. These dudes came up with strange studies, going deep into mathematics, but ended going also deeper into the philosophy of mathematics (and thus of science).
They proved that one could conceive geometrical worlds other than the one we knew about; other geometries that had other interesting particularities and consequences. Today, the "usual" geometry is called Euclidian Geometry, and other geometries collectivelly called non-Euclidian Geometries (which are in great quantities, and be further categorized...).
One of the particularities of such non-euclidian geometries was that in most of them, and considering "circle" in them (ie considering the geometrical objects consisting of the set of "points" that were to an equal distance to a single "point"), the ratio of the circumference and their diameter was different for each circles: the ratio of the circumference of a circle to its diametre was no longer a constant in non-euclidean geometry: it could be different from one circle to another

Of course, that caused tremors in the world of mathematics.

The subject non-euclidean geometry didn't die out of course, afterwards, but such imaginary worlds were considered too futile to be taken seriously, as Euclidian Geometry was considered the self-evident True Geometry (I HAD to use that expression, self-evident, for there is no other word to convey the situation at that time).

This story isn't finished yet... it gets better.

Now enters... Einstein.
He was already famous for his 1905 series of articles (which ultimately won him the Nobel Prize of Physics); one of these articles was about what he called "Special Relativity" (well, it eventually took that name).
But he wasn't content with this "Special Relativity", for it wasn't "general" enough...
So, in the 30's, after hard work, long discussions with friends, and tremendous help from mathematician friends (including Emmy Noether, one of the greatest woman mathematician of this century), he gave birth to his General Relativity.
Why am I relating all this?
Well, it turned out that the only way Einstein found to make sense of all he wanted to say was to set the geometry in which this world "lives" to be a... non-euclidean geometry.

All this was theoretical of course. But predictions were made, which, when compared to predictions based on euclidean-geometry-based theories, could make the scientist of the time decide which worked best. General Relativity, in all the predictions that it made for which experiences have been conducted, won hands down over any other euclidean geometry-based theories.

Today, the only geometry that can be used to described the Universe, especially in the large-scale, is a special brand of non-euclidian geometry. One in which the ratio between the circumference of a circle and its diameter isn't a constant among the set of all circles.

Even in science, what was once thought to be self-evident, had to be revised as not so evident.

Now that I've made that little foray into the history of mathematics and physics, I can comment on some of Elysha's words.

You say: "Through reason we can come closer and closer to knowing something irrational."

*That is true. However, one must not think, and many scientist agree to this, that humanity will ever reach an ultimate conclusion about the workings of nature and the universe.
But in no way this must be taken as proof, and especially not a suggestion, that nature and the universe are of supernatural or divine origins.

IMHO, the ultimate ignorance of humanity about nature shouldn't be taken as a reason (!) or proof of faith.

"I am ignorant, therefore god exists"
shouldn't be something by which to go on living, imho (and I am glad that no one here ever said something like that)


Beliefs, faith, poetry and such, are there to help us make sense of what we ultimately don't know through rational means;
I can even say they help make sense of what we know through rational means! (I have given specific examples of poeple who do so in other threads).

The error, IMHO, is to take those irrational beliefs (non-pejorative use) as the ultimate truth, not to be questioned, not to be doubted.
There lies my usual condemnation of dogmas (in religions as well as in science...)



"We must, however, move into the realm of faith and obedience, accepting things that cannot rationally be understood, to gain an inkling of the truth that is infinitely more than what science can provide."

*Obedience, acceptance: without questioning? Without doubting the origins of these things you give obedience and blind acceptance?

Let us not be afraid of not understanding the ultimate truths!
Let us not be afraid of not even knowing the ultimate truths!

If for you your beliefs help you make sense of this world, then GOOD!
I'm really happy for you, sincerely.

Just don't be surprised though that others make sense of this world through other beliefs (which in this sense only are just as good as yours, but in no other sense), or non-belief.

This is, I hope you understand and accept, a question of personal experience.



"The old thread has the wrong heading and has gotten to the point of replies to replies where it is downright confusing. I couldn't tell who was replying to whom!"

As I commented, we have reached, I think, in that thread, the limit of what EZBoard can offer us as a method of communication. We stressed it to its limit, which in turn stressed us...

"I thought this would be a good place for people participating in the previous discussion to state, clearly and succinctly, their own personal views."

To be succint takes a lot of skills. Which, then, I obviouly haven't!!


"If you wish to reply to someone else's, do so in a different post from the one in which you state your own"

This is due to the format of this board. EZBoard has many board formats. This board, Entmoot, is somewhat linear, which is just fine for Entmoot, but can be not fine for important and deep discussions.

Another format would be of the "tree" kind, where one single thread may have many branches... I really don't know if that format would have helped though. Maybe a little.

As Gil said, the best format would be around a beer and a pipe (or three); I don't smoke, so I would ask for more beer!
I might add some confortable couches in a circle...

When you see in the other's eyes that he/she is serious about what he/she says, and fervent, and full of good will, mutual respect is much more easier to create than just through these invisible avatars that we create when we surf the web...






Greetings!

Happy New Year!

Bonne Année Ã* vous tous!

It is now 1:00 AM in California. I'll reply to your post later, Juntel. I'm sorry about misunderstandings -- as I said, I didn't actually read the complete threads, only bits here and there. The thread would have taken quite a bit of time and effort to unravel, and I felt it had gone too far for me to join in!

I am familiar with the history of mathematics, although I have not studied it in as much depth as you have. Most of what I know I know through my father, who is fascinated with history and has a doctorate degree in mathematics. I agree that our understanding of the universe will never be complete; indeed, a new change that will probably cause astronomy texts to be rewritten. Satellites that have left the solar system have detected what appears to be a new force equal to Hubble's constant pulling inward in the universe. Lectures have been presented at various universities and places, including Stanford University.

Hubble's constant was originally included in Einstein's equations as the force required to keep the universe stable, without gradually expanding. Because it was purely theoretical, it was taken from the equations and scientists assumed that the universe has been expanding ever since the Big Bang. Now that the Hubble constant has been detected, a little reevaluating may need to be done. Note: this is not a post against evolution, but rather a reinforcement of your post pointing out that while absolute truth can be approximated, it cannot be absolutely reached.

Hey, you can examine religions without choosing any of them -- it's fine. Certainly, God cannot be proved. There, I agree with agnostics. He can only be known through personal revelation and experience. Everytime we take something for granted without testing it and retesting it, some new discovery comes along that shatters our little world. To me, this is a reminder that God wants us to search for truth, to seek it, and gradually to discover it. But there will always be more to find, because knowledge is infinite. In some ways, confusion is excellent, because it draws us out of our preconditioned, narrow understandings and forces us to look further.

I, too, hate the statement "I am ignorant, therefore God is." God is not simply the explanation for everything -- I do not agree with anyone who thinks that because they believe in God, they have it all. "The fear of God is the beginning of wisdom." And if one respects and revers God, one will pay Him the complement of seeking to understand Him and His creation, willing to be drawn out of one's own world and to learn new things. To me, though, the basic statement of faith I gave in my previous post is Euclid. I must begin somewhere. After all, religion isn't simply a philosophy -- it is a way of life. My religion is determined by the life of Christ, and it is not simply a way of life, but it is life.

But this is of course too much to ask to certain people, who sometimes think these other religions and gods are primitive, or blatantly a work of the "demon". (And please, I'm not pointing at ANYONE from Entmoot with that last sentence).

Perhaps you will be surprised to learn that I not only believe that there is a God, but I also believe in the supernatural realm of angels and demons, and that there are certain pagan rituals, human sacrifice among them, which I do consider barbaric and even demon-inspired. While I can care about the people who participated, I cannot respect any "god" that would request such rituals. If one believes that there is a supernatural realm of good and evil, angel and demon, then there is no reason not to believe that such a realm can interfere with our personal lives. It is, of course, perfectly natural for you to consider such a view ridiculous, as you consider all religions equally valid.

I said I'd reply later; well, instead I replied just now!

hehe... I also sometimes want to begin with a small post, but end up writing one of those big ones...

As regards to "human sacrifice", I consider religious warfare and savagery as not much different than human sacrifice, where the other, the one with a different religion, or who threatens your religion (by similar means) is then taken as the "sacrifice" to one's god...

As an very good example of this, do consider the quote I took from I Samuel 15 in the WHAB thread, or in your bible (for context).

There it is written that your god explicitely gave an order in which children had to be savagely murdered for the "sins" of their parents (or in this case, in fact, of further ancestors), and he "got away with it" (if I may say so...)
One doesn't need to go into other religions to see a deity's "sins"...

I do not doubt that christians would not condone such an "action" coming from another religion's god; nor in fact from their own god. One could call upon an explanation based on symbolism, saying that what the text was referring to never really happened, and was only written for symbolic purposes, to teach some kind of lesson to the reader/believer...

Well, i don't know, for it's not my problem after all, it's not my bible. There are many bible studies that I could find at the university, for example: some for the general public/believers, some for more knowledgable bible students, and others for scholars. None of these has given me much, upon reading, an explanation that would exempt that god from the crime of genocide... but overall, i've seen that this passage isn't much talked about; it's usually dismissed quite rapidly, even sometimes with antisemitic undertones (in the more vulgarized bible studies, unfortunately... or fortunately... i don't know...)

I guess then that it is for each christian, and jew, and muslim (although the later always end up saying the earlier scriptures are too manipulated and altered to be relied upon) to make for himself/herself an opinion about that passage... as well as other passages...
In context of course: litterary context (within and out of the TaNaK), historical context, cultural context, etc, etc...

If you (and others) have already an opinion about this passage, I am genuinly interested to know your view about it.


Also, regarding the use of the word "paganism", one must be carefull with it, since it may mean several things: some are neutral, some not, and some are very bigoted and have been used by christians (and others) to justify their murders and hate propaganda.
I'd like you to tell me what exactly you intended to mean by using that word, please, so that I know where you stand (but i'm sure you're not part of the later kind).

I do not doubt however that there are human groups with very gruesome habits; but even here I don't need a supernatural explanation. We don't need to burn witches anymore.

For me, something like Charles Manson, for example, has more to do with grave mental illnesses than with demonic manipulations; not knowing exactly what ails him in his brain, our ignorance, isn't in any way a reason to call for demons, in my opinion. You may disagree (i don't know), but at least we can agree on this: this guy should be stayed locked up; and, while he's in there, why not try to understant what's up with his brain (who among you stayed up at night many years ago, to see the interview Tom Snyder had with him!)
But of course, ultimately, I can't really say that I'm 100% sure Manson was not demonically manipulated by a demon or whatever...
And one could always say that the Demon gave him these grave mental illnesses... etc, etc, etc,...

Imponderables.........


There... already this post is longer than at first intended... (and I always adding things up, edit after edit... hehe)

*** Hubble constant not constant? Heck, even Newton's G was once considered to be not so constant, if not still today... The thing is, what were thought to be constants may come up to be very very very slooooowly changing values, over a large time-scale, over billions and billions of years - how do you like my Carl Sagan impersonation!?
Just as, in non-euclidean geometry used for General Relativity, space is somehow "curved", but only over very large scale can this "curvature" be noticed (or near very massive objects) - locally, geometry seems "flat", ie Euclidian (just as we may think that earth is flat just by looking around... for example, we don't build houses, skys****pers, etc.. by taking account that the earth is round!)

It's 6.40am here in Mtl... I guess that by now everyone is in 2001 (except maybe Easter Island?!)
hehe...

Well, I have been drawn into this conversation now. Your idea of I Samuel 15 made me go back and read it. And here is what I found.

It is true, that God sent Saul out to destroy the Amalekites for what they had done to the Isrealites when they were coming out of Egypt.

BUT, and I stress that but alot. If you read it carefully you will have seen a little bit more to it. I am not saying you didn't read it carefully, which I assumed you did before commenting on it. In verse 18 Samuel is scorning Saul for keeping certain things that were still good, like cows and sheep. Which Saul said were for sacrifice to God. And Saul says to him, "..And he sent you on a mission, saying, 'Go and completely destroy those WICKED people...."

There it is clearly stated that the Amalekites are still a wicked nation. So there is more to it than just what they had done in the past.

But, after Jesus Christ died and rose from the dead, breaking the gates of hell, our sins were forgiven. Sacrifices of animals and destroying wicked people was no longer necessary. Now, our(Christians) duty is to lead people to Christ, so that they can spend eternity in Heaven with us.

Now, along the topic of truth and absolute truth. I believe the human quest for absolute truth finds its fullfilment in Jesus Christ. Because Jesus came to bring truth into the world.
John 18:37
Jesus said..."I came to bring truth to the world. All who love the truth recognize that what I say is true."

And as for by belief in whether or not Jesus Christ rose from the dead. Well, I don't believe it happened. I KNOW it happened. I trust the New Testament's claim of Jesus' resurrection because the story is told by EYE-witnesses.
I John 1:1
We saw him with our own eyes and touched him with our own hands.

I would suggest reading I Corinthians 12:1-11. It speaks on spiritual gifts and how these gifts get rid of ignorance. Because Christians are not to be ignorant. I am not saying all Christians are not ignorant, cuz fact is, probably a lot of them are. But they should strive to not be. Cuz I can admit that at times I am ignorant too, I think everyone is, but people should try to not be.

Well, now I know what you mean by these messages end up being really long even when you didn't intend it.
Hopefully this helps, if anything isn't clear or needs more explaining, just tell me. And I will try to explain it better. Next post I will go into wisdom, most of that will be from Proverbs, if you wanna read it.
He he, its not as long as I thought it was, it just felt long as I typed it. lol.

Well... indeed i've read more than what i posted on I Samuel 15...

Saul did disobey...
"He took Agag king of the Amalekites alive, and all his people he totally destroyed with the sword.
But Saul and the army spared Agag and the best of the sheep and cattle, the fat calves and lambs--everything that was good. These they were unwilling to destroy completely, but everything that was despised and weak they totally destroyed."
- I Samuel 15...

So, the big sin Saul seems to have commited, is not having mudered children, but having spared the king of the other tribe, as well as some cattle...

True, the Amalekites were probably a gruesome people... at least lets suppose it for the sake of this conversation.

But would that be a reason to murder the "children and infants"?

Would you, for example, have followed such an order from your god, if it came in some sort of revelation, some sort of personal experience?

[This of course makes me think of a much earlier episode in "Genesis", about the god asking Abraham to sacrifice his son; Abe did accept in the end to sacrifice his first born, I guess after much internal pain (if this story has any litteral truth to it)... but it turned out to be just a test (great scene that ends the movie "The Bible", with GC Scott as Abraham...)
...In this case of Saul, however, Saul failed the test by not having eradicated all from the Amalekites; he slaughtered the children and infants as his god ordered... but kept some wealth (cattle) and pride (opponent king...) ]

Yes, I know, god sent jc, the ways of things changed with the new covenant, etc...
But the past is still there. The order to slaughter children and infants is still there, alledgedly by the same god, that same god you believe in...

If Charles Manson had a child (brrrrrr!), should that child be murdered for the crimes of his father? Same question if Hitler had had children.


As for the proposed readings, I thank you.
But do not suppose I've never read the book; it's just that I've never read it while presupposing it was the ultimate book, that it contained the ultimate truth.

Nowadays I prefer such things to get to me through friends and people, through their experience of their religion (christianty, but also islam, judaism; i've never had the honor of meeting a friend that turned out to be hindu or buddhist, except for very brief time, and the exchange was quite beautifull).



As for the length of posts, it may tend to grow exponentially at times, when comments about comments about comments pile up (fortunately, or unfortunately, some details get forgotten, and the growth slows down a bit...)

Since for now I'm still on fast conextion (well, adsl), I can still view a thread as one big page, rather than many smaller pages; easier to search through...

I like the posts that Juntel and Elysha have made on this board. Allow me to add my own comments.

Juntel:
>> The error, IMHO, is to take those irrational beliefs (non-pejorative use) as the ultimate truth, not to be questioned, not to be doubted.
There lies my usual condemnation of dogmas (in religions as well as in science...) <<

This statement is grossly prejudicial and betrays a lack of understanding of irrational knowledge. As a mathematician, I accept the validity of the Commutative Laws of Addition and Multiplication on faith. I see no need to endlessly try to question or doubt it. It is irrational knowledge that is also a firm conviction.


Elysha:
>> "We must, however, move into the realm of faith and obedience, accepting things that cannot rationally be understood, to gain an inkling of the truth that is infinitely more than what science can provide." <<

Juntel:
<<*Obedience, acceptance: without questioning? Without doubting the origins of these things you give obedience and blind acceptance?

Let us not be afraid of not understanding the ultimate truths!
Let us not be afraid of not even knowing the ultimate truths! <<

You seem to think that irrational knowledge can only be understood by being questioned and rationally dissembled. Yet you acknowledge that all rational truth is built upon irrational presuppositions. Hence, is not the rational analysis of one person’s irrational knowledge by another person only the prejudicial judgement of that knowledge based upon the other person’s irrational preference? Rationality is useful if it is used to assess the consistency of different irrational beliefs, but it will not decide which irrational belief should take precedence if two irrational beliefs conflict.

Many people think that irrationality is the primary cause of wars and oppression. Actually, it is rationality seeking to exclude irrational sources of knowledge that causes most conflict. The Church persecuted Galileo because his truths were rationally inconsistent with their theological beliefs. The Germans persecuted Jews because the rational conclusions of their irrational beliefs – evolution and the fact that Jews were bad – led them naturally into following these horrible practices. British exportation of fish and other goods from Ireland during the Irish famine was a result of their rational conclusion (called political economy) that any support to Ireland would result in the development of a dependant state.

The rational conclusion of the fact that there is one law and therefore all people should be judged by that law led Moses and Joshua to unleash the sword on all of the people in the land of Canaan (after first unleashing the sword on themselves). Even the destruction of women and children might be deemed rationally necessary for establishing a country guided by one divine truth in order to prevent future terrorism or infection by their gods and their truths. The irrational conclusion of David that God is merciful led David to absolve Absolom of all punishment for his treasonous actions even though it hurt the stability of his own kingdom. Jesus’ rationality took into account both justice and mercy by forgiving an adulteress and declaring to her judges that the one without sin should cast the first stone. He rationally reconciled justice and mercy by changing the law – an eye for an eye – into the golden rule – do unto others as you would have them do unto you. When rationality excludes irrational beliefs, it becomes oppressive. When rationality seeks to understand and incorporate the irrational beliefs of others to whatever degree it can both comprehend and include, it edifies. When irrational knowledge presents itself as a firm unbending conviction, there is generally a valid source for the irrational knowledge. It is the simplistic logical deductions of irrationally held convictions - which do not encompass or comprehend other irrationally held convictions - that can mislead.

Truth is irrational, but it is perceived through rational means. The very process of defining it in human language also rationalizes it. Rational perception requires revelation by degree, in stages, rather than complete instantaneous revelation. Even when Jesus came to earth, he told his disciples that he must leave so that they can better comprehend his nature, which implied that his physical presence was an obstacle to their further understanding. And he told them that the Holy Spirit would teach them, which also implies that their understanding of God would continue to grow by degree. It is as impossible for a person to claim complete knowledge of the truth as it is to rationally comprehend God. But it is possible for a Christian to say that he or she perceives truth. Perception of truth is not the same as complete understanding of truth. Just as I can perceive the existence of another person without completely understanding him or her, I can also perceive truth without completely understanding it.

Welcome, Ptah! (if I may use that shortened version of your name)

Your comments are welcomed!

Let me try to add my two cents about some of them:


". As a mathematician, I accept the validity of the Commutative Laws of Addition and Multiplication on faith. I see no need to endlessly try to question or doubt it. It is irrational knowledge that is also a firm conviction"

As a mathematician, you should know that those "laws" of commutativity you mention are rules within a formal system, a construct of the human mind.
And that the simple formal system that is ordinary arithmetics as not yet been proven to be consistent.

(and, if you have some knowledge of physics, you will also know the need and usefullness of a non-commutative algebra is not only ackowledged, but impossible to do without... Hint: quantum mechanics...)

As a mathematician, I have no faith in such "commutative law of addition and multiplication"; for it is our creation, and does what it does because we want it to do so; we can change these rules, if we need so... and as I just commented, we do need so, to create other tools, other algebras, other mathematical worlds.
These tools we create, wether it is a non-commutative algebre (where A x B doesn't necessarily equals B x A) or a world in which the sums of the interior angles of a triangle can be different than 180 degrees, are not futile mathematical musings, they are important tools that give us today a better understanding of the physical universe we live in, better than if we didn't doubt the existence of these other "truths".

If you really want to have firm convictions on irrational knowledge, may these be about love and compassion, not "commutativity": we can construct whatever formal system we desire by changing the axioms and the rules of a formal system, whereas such imponderables as love and liberty, for which we must fight, cannot be put in a formal system of axioms and rules (fortunately)...

Making comments on my understanding of irrational knowledge is allright, but in return I suggest you brush up on your understanding of rational knowledge...



"Rationality is useful if it is used to assess the consistency of different irrational beliefs, but it will not decide which irrational belief should take precedence if two irrational beliefs conflict"

Rationality, I think I was clear about that, is a tool, no more, no less.
When imponderables come into the scene, again I've made it plain that rationality can be very limited in this area.


"Many people think that irrationality is the primary cause of wars and oppression. Actually, it is rationality seeking to exclude irrational sources of knowledge that causes most conflict"

One can "help" the other.
Beauty as an irrational "quality" may very well smooth the metallic harshness of cold misused rational logic.
And the importance of rationality in methodology may very well remove the veil of irrational superstition from people's mind.
I don't think there's a straitghforward exclusive condemnation that can be given to either view, the rational or the irrational.
Both are necessary parts of our lives.

It is when one holds as the only "Truth" one's own irrationality that problems will occur. Or when one thinks one's rational deductions are the only ones possible.


"Jesus’ rationality took into account both justice and mercy by forgiving an adulteress and declaring to her judges that the one without sin should cast the first stone"

Hmmm... I'm no christian, but I would tend to think it was J's love, not his rationality, that forgave that woman...


"When rationality excludes irrational beliefs, it becomes oppressive"

I would personaly word this as : "When rationality thinks it's the only "king of the mountain" in human's lives, and denies irrationality the right to be in a human's life, it IS oppressive"

It's a longer sentence, I admit (hey, it's me!).
I don't think anyone on this board, in the many debates that we had, ever excluded irrationality as being totally bad.

... "Throw away the ladder..." like good ol' Ludwig said...




"Truth is irrational, but it is perceived through rational means"

Truth is neither irrational, nor rational.
Just as an apple in neither irrational, nor rational.
IMHO, that's how I see these things.
It's open to debate, of course...
But of course, "truth" is also one of these words that have so many meanings, wether capitalized or not... so, we better be sure we're talking about the same thing first, rigth?

( "Neti, neti...", as is said by some hindus...)



"It is as impossible for a person to claim complete knowledge of the truth as it is to rationally comprehend God"

... or gods, goddesses, fairies, etc... Your statement can be right, as long as it can be applied to any religion or myth or belief.



"But it is possible for a Christian to say that he or she perceives truth"

... and why not a muslim, a jew, an hindu, an american indian with his/her beliefs, etc...
I have no problem with your claim, as long as you acknowledge it's universal quality, accross religions...
(this isn't about "all religions are equal" thing... it's about respecting other's irrational beliefs...)



"Just as I can perceive the existence of another person without completely understanding him or her, I can also perceive truth without completely understanding it."

I agree.
And that "truth" may have a wider quality to it than first expected, and can ultimately transcend religions and their limited regional dogmas...
Not unlike Gandhi's attitude towards religions...

Often, the problem is when different "truths" from different religions clash, and each hold tight to their own truths, never ever wanting to maybe see that the other's truth could be just be the same one but with a different shade or hue...

I think the main communication problem we may be having is the definition of rational and irrational knowledge. I claim that the commutative law of addition (or multiplication) is an irrational form of knowledge that is also a conviction and not just an arbitrary belief or superstition. You refer to it as simply an artificial construct. However, if you show me 1400 rows of pennies with 72 pennies in each row located in one corner of a room, and you show me 72 rows of pennies with 1400 pennies in each row located in another corner of the room, I will be convinced (through my irrational knowledge) that both groups of pennies are of equal number. It is not simply because I have defined truth to be that way. Mathematics is constructed within the concept of definitions to allow versatility of its applicability to different circumstances. But commutative properties of ordinal numbers do have real world applicability, and within that context the knowledge is irrational. I gather from your post that you think of irrational knowledge as something rather arbitrary and esoteric. I think that valid irrational knowledge should be a strong personal conviction.

As regards the slippery word called truth, you are right that truth can have many definitions. However, I hold to an irrational conviction that there is such a thing as absolute truth. It is something that I perceive, though admittedly my powers of observation regarding its qualities are not always perfect.

I do not doubt that an A x B array of pennies
would contain as much pennies as an array of B x A.



Through experience, this "A x B = B x A" knowledge about numbers, that commutativity of multiplication, does become somewhat like an everyday truth, that one can believe blindly without proving it experimentaly for all cases (for that would be simply impossible, since it would need an infinite amount of time).
Irrational faith in it may be, therefore, somewhat important to go on...
As long as that doesn't prevent one from pursuing investigations...

The prevention of such investigations by the derision of peers fortunately didn't stop open minds to look for other avenues of mathematics, other kinds of mathematical truths.

When dealing with real-life applications of math (if i may say so), one can be forced to use induction:
it has always worked (in similar conditions), and we see no reason that it won't work again (in similar conditions), therefore we make it law.

Induction: an age-old problem.

So, should we accept induction as an acceptable tool for us to get to truths?

Well, it has always worked, and we see no reason that it wouldn't work again, therefore...

Hmmm.... Bummer... that's circular reasoning... justifying induction by induction...



Nevertheless, induction is used everyday, by you and me. And we still live! hehe...

So, again, A x B = B x A for everyday numbers is something I wouldn't go on doubting very long, for practical purposes.
But wether we can make even this "law" fit into a consistent number system (ie a system that we can show has no internal contradictions) is still an open debate, a problem not solved in mathematics.
But it doens't stop one from doing math! (and math homeworks!)

The "irrational" belief is to a certain point commendable, if only for its practical purposes; but it shouldn't make us evade the very real concerns about the nature of math, it's inner workings, the different ways of approaching it...
(this isn't about politics or religion, anyways! it's only math! much, much simpler...)


Yes, we must use commutativity, for real-life applications need it, as other real-life applications need non-commutativity.



I'm from the old ordinary school for whom the Axiom of Choice is acceptable (I speak in this paragraph directly to Ptah, for he probably knows about this, and may be the only other one here who does; so, sorry to other folks, for now...). As you might already know, there is other schools of thoughts inside the mathematical world, with very justifiable concerns about the way math works and is used; for example, those for which the Principle of Excluded-Middle shouldn't be accepted unless proven from other axioms (one of these schools of thought is called the Constructivist School).
You may think these guys and girls are splitting hair, but in fact they have very important concerns, especially regarding such things as the Axiom of Choice.

Now, personally I'm of the conservative school ( !!!!), but I do admit that their concerns are valid, even though what they are against seem so self-evident(!) (eg. excluded-middle in logic, axiom of choice in set theory, etc...).


So, if I may be brief (but it's obviously too late for that! :lol: ), I may comment on your statement: "I think that valid irrational knowledge should be a strong personal conviction."

Seeing in this "irrational knowledge" the consequence of induction (but i'll also wait for your comment on this), I may agree that one may be safely convinced, for pratical reasons, to accept such knowledge; but I would disagree strongly that this knowledge be taken as an ultimate truth, not worthy of further investigations.
(NO! I'm not saying that the penny count will change! :lol: )



"I hold to an irrational conviction that there is such a thing as absolute truth. It is something that I perceive, though admittedly my powers of observation regarding its qualities are not always perfect"

We do have to start somewhere, everyone of us. It is in no way unhealthy for you to hold that point of vue.

As long as that conviction doesn't prevent you, in principle, from seeking other explanations, others' convinctions' truth-value.


Of course I may have misunderstood again yet your use of the word "irrational knowledge" in this conversation; so please do elaborate if you feel i didn't understand what you meant by it, in this thread.

So...

...what have I got in my pocket?


[c] ~~~[/c]

Really enjoying reading one of these for a change! Keep up the good work guys. I'm learning a lot! (Well, actually most of it is review of material not particularly appreciated the first time it was "learned.")

Nevertheless, it explains to me a lot of the communications failure in the "What Has America Become" thread.

Not really to join in this argument (since I am not qualified due to my lack of specialization), but I could not help but notice that there might be something of a sticking point in acceptance of inductive reasoning when applied to situations outside of mathematics. (As we self-evidently must, to make it through the day...)

I have a further consideration, stemming more from my history background than my scant mathematical preparation. When in school, we had a "summit meeting" of the History Department and the Biology Department, each representing different methodologies of arriving at conclusions. On the one hand, there is what I would call the judicial method, and on the other the scientific method.

Now, both are tested methodologies for arriving at the "Truth." One is used in the courtroom/study, the other in the laboratory.

Both use logic. Both try to "control" for other causes or explanations. One method is concerned with deriving the truth about a past event, which can never be repeated. The other is almost entirely concerned with repeatablility.

When we reach the realm of Astrophysics (I can then no longer follow the math...), it seems to me that the Scientist is reduced, at last, to the other methodology.

One cannot repeat the observed celestial event. The data is not repeatable and therefore not verifiable, except in the inductive sense.

This is similar, though not the same, to the sort of point that I was making regarding the subjective experience of the 'born-again' Christian.

St. Paul reports an extraordinary event on the road to Damascus. 2000 or so years later, Gilthalion reports a similar (though less extraordinary) event. In the interval, there are many other such reports.

Inductively, one must conclude that SOMETHING is going on, even without one having had the same subjective experience.

Given the nature of the SOMETHING, what's a poor scientist to do, if she/he wants to know the "Truth?"

"Given the nature of the SOMETHING, what's a poor scientist to do, if she/he wants to know the 'Truth?'"

These kinds of matter, imponderables, aren't touched by science itself; but the scientist, as a human being who is more than a thinking machine, has his/her own beliefs.

In the Creation/Evolution thread (now probably in the Entmoot Archive), i've given names of scientists who had both faith and science.
I'll just named them again: Pierre Teillhard-de Chardin, a jesuit archeologist (on whom WP Blatty bases himself for the character of Father Merrin, in his novel The Exorcist, at least for the scientific mind/profile), who believed in a god-driven evolution over billions of years; and Trinh Xuan Thuan, an astro-physicist who impressed me in one of his book, in which he "destroyed" one by one the traditional arguments invoked for a scientific or logical justification of god, afterwhich nevertheless he admitted he did, as a man of faith, still believe in his god (he's a buddhist, but of course by "god" he didn't mean the Buddha...).

And all of this reminds me of ol'Ludwig W.'s words towards the end of his Tractatus Logico-Philosophicus:

"How things are in the world is a matter of complete indifference for what is higher. God does not reveal himself in the world.
The facts all contribute only to setting the problem, not to its solution.
It is not how things are in the world that is mystical, but that it exists. [...]
When the answer cannot be put into words, neither can the question be put into words.
The riddle does not exist.
If a question can be framed at all, it is also possible to answer it.
Scepticism is not irrefutable, but obviously nonsensical, when it tries to raise doubts where no question can be asked.
For doubt can exist only where a question exists, a question only where an answer exists, and an answer only where something can be said .
We feel that even when all possible scientific questions have been answered, the problems of life remain completely untouched. Of course there are then no questions left, and this itself is the answer.
The solution of the problem of life is seen in the vanishing of the problem.
(Is not this the reason why those who have found after a long period of doubt that the sense of life became clear to them have then been unable to say what constituted that sense?)
There are, indeed, things that cannot be put into words.
They make themselves manifest . They are what is mystical. [...]"


Obviously, as you've seen in the WHAB thread, I don't agree with everything in that quote, but it is a point of vue that I visit regularly.
[This little treatise of him sparked a new generation of philosophers, most importantly the (in)famous Vienna Circle, with whom he nontheless did not associate with.
The V.C. invited him one day so that he could make lectures to the Circle; it is said that he accepted, but when he came and gave his lectures, all he did was to read to them Rabindranath Tagore's poetry...]

He concluded his above treatise ( Tractatus...)by these words:

"My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them - as steps - to climb up beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.)
He must transcend these propostitions, and then he will see the world aright.

Whereof one cannot speak, thereof one must be silent."


[Please note that these quotes from the Tractatus... are maybe the only intelligeable parts of that treatise! So many "interpretations" have been given...]


So, "what's a poor scientist to do"?
Keep his/her eyes, ears and heart open, for things even out of science's limited realm.
But at the same time keep clear of so-called logical justifications for religion: they are a disservice to both faith and reason.




As for induction, my point in the previous post was that, even if its seems we can't escape its use, the justification of this use is not altogether clear, if one wants to avoid a vicious circle.

As Gil mentionned somewhere else, it's not because we've seen all our lives only black crows, that there are no purple ones (ok, ok... the classical reference is to a white crow, but a purple one seems, to me, more usefull to make the point... )

Good Post!

In the final analysis, faith can be reported but it cannot be logically derived or measureably observed (else it would not be faith!).

Christians hold that our Faith (divine caps), is a gift from God, not an achievement of Reason (archetypical caps), nor yet a self-evident matter of observation.

[A recent meeting of Roman Catholic and Southern Baptist clergy finally found some agreement on this point, though there is disagreement about what was actually meant by the agreement...]

"What is truth?" Pontius Pilate asked Jesus of Nazareth.

This wisest of men, refused to answer.

I've often wondered why that was.

"Now, therefore, the description of Brahman: 'Not this, not this' (Neti, Neti); for there is no other and more appropriate description than this 'Not this.'"

- Brihadaranyaka Upanishad

Your quote from Ludwig W. "God does not reveal himself in the world." I find to be highly untrue. God reveals himself in the world in so many ways they are uncountable. But for a few examples there are the mountains. When I see the mountains no one can tell me that God does not exist. The beauty of them is almost intoxicating. Also, the way the whole world works together. It was not a simple way of evolution that the world can work together so well, it was made that way.

But now, back to I Samuel 15. You asked why even the children and babies must be killed too. Well, its like this. If someone says they are gonna quit smoking but will have just one tiny cigarette a week, just ONE a WEEK. Sure, he has basically quit and it is hardly noticable anymore, but it is still there. It is the same way with what happened in I Samuel 15. As long as there was anything left of those wicked people there would still be the reminder and the temptation.

Tell me this. If one player continually screws up in a basketball game and costs there team the game. Is it not mostly his fault? yes, it is. Does the rest of the team still suffer from what he did? yes, they do. So even though it was a only a small amount of the team that cost them the game, the whole team still suffered.

In a war, do people who don't want the war still suffer? yup, they do. Mother's childrens get forced to go to war and die, the whole family grieves. When countries drop bombs does it kill children? it sure does. But does it stop the war? uh huh. I have seen pictures of when the USA dropped nuclear bombs on Japan and those pictures of children with clothes and skinned burnt on there bodies running and screaming are permanently etched in my mind. But it helped stopped the war and end further slaughters.

Do I agree with what all happened? no, I don't always. But I do find that it is necessary to prevent further corruption or death.

He he, sorry about all the questions and then short little answers. Just one of those themes you get into. lol

So, if your god asked you, rigth now, in some exceptional spiritual experience, you would go and kill babies? infants, still suckling at their mothers' breasts, like the god did in that passage?


With your statement:

"As long as there was anything left of those wicked people there would still be the reminder and the temptation",

these questions arose in my mind:

"When does a person become 'wicked'? Is 'wickedness' in the blood, genetically inherited? Is a suckling child, not yet a year old, so 'wicked' that the god of the bible condemn him to be murdered on his orders, just because his parents where branded 'wicked'?"

How far one is to go to defend one's god, when that god explicitely ordered the death of innocent born individuals?

As for WWII, etc... these wars, as far as I know, weren't orders from an almighty deity; it was a consequence of human absurdities.
And the Abomb (and other massive bombardments on Tokyo or Dresden, etc..) were made with tools of mass destruction, that required so little human one-on-one contact (therefore making war less human, less prone to settlement and peacemaking...).
Whereas, in the context of I Samuel 15, the order came directly from the Big Dude himself, and the killings were made mostly with swords that cut the throats of the people.


As for LW's quote, I was less concerned with his views on god(s) than on what he said about ultimate truths; and I did not quote him because I believed what he said, but because I found what he said interesting and worthy of consideration.


/Edited: I'll go check back what is taught in the Yeshiva's about that passage; sometimes explanations from jewish religion can be much different than from christians...

OK. I’m back. Sorry for taking so long to reply. First I agree with you on the problem of induction (induction does not imply truth), even though induction is used all of the time in science. It is obviously clear that just because something works 100 times, 1000 times, one million times, or a trillion times, does not make it true. In fact, if one could put a probability of something being true after repeatable demonstration a finite number of times, I would put the probability of it being true at zero. Nevertheless, do not confuse faith in the commutative laws of mathematics, even as applied to discrete items in the universe, as being inductively discerned. It is true that we look at examples to understand, but this is not the same as proving its truth by how many examples we have looked at.
Let me illustrate with two different examples. First, I believe, irrationally I might add, in the principle of mathematical induction, which is not the same as inductive logic as used in science. In mathematical induction, we conclude that if a formula involving a variable n is true if it is true for n = 1 and if we can show that whenever it is true for n it is also true for n+1. Obviously, if it is true for n=1 then it is true for n=2, and if it is true for n=2 then it is true for n=3, and so on. Yet I don’t have to pursue this 100 or 1000 times in order to believe this. You may pursue it a few times until you can clearly see its validity. On the other hand, if you ask me whether I can find integers for which
n*n*n + m*m*m = k*k*k, then even if a computer demonstrated that for all integers less than one million the above cannot be found, I still will not have confidence that there are no solutions. Hence, my belief in mathematical induction (or the commutative laws of mathematics) is not based on inductive logic. It is an irrational belief, yet one for which I am firmly convinced of its validity.


<<< Yes, we must use commutativity, for real-life applications need it, as other real-life applications need non-commutativity. <<<

Obviously some things are commutative (such as addition and subtraction of ordinal numbers) and some things are not commutative (such as matrix multiplication). It can often be easy to prove (by counter-example) that something is not commutative. Generally the acceptance that something is commutative is either irrational or a consequence of definition, logic, and the acceptance that something used in its definition (like the commutative property of addition of ordinal numbers) is irrational.


>>>Seeing in this "irrational knowledge" the consequence of induction (but i'll also wait for your comment on this), I may agree that one may be safely convinced, for practical reasons, to accept such knowledge; but I would disagree strongly that this knowledge be taken as an ultimate truth, not worthy of further investigations. <<<

As said above, I do not believe that all irrational knowledge is a consequence of induction. Induction is the principle by which science accepts things as truth. It has practical value since if one cannot find counter examples after many repeated trials, the chances of other people finding counter examples are diminished. But is far from being philosophically reassuring.
There are many things for which we can have irrational knowledge. Mathematics is but one example that I mentioned because it is something for which many people can relate, although I recognize that it mystifies a much larger crowd. I already mentioned that a belief in the existence of absolute truth is another example. Of course there are many more examples. My assertion is and was only that we should not feel a necessity to doubt or question an irrational belief simply because it is irrational. If we do hold an irrational belief and we perceive something in nature or wherever that makes us doubt it, then we should feel free to question and examine what we believe. It is healthy.
I appreciated Gilgalthion’s comment, too. There are many types of truth, and many different ways of trying to determine truth. Most of our methods are imperfect. Truth can be complicated (even in a legal case when it is not only deeds, but motives that are at question), and we must live with our imprecise knowledge. Irrational beliefs or knowledge is fundamental to our understanding of truth. It should not be discounted, and it should be re-examined whenever the conviction of its truth is either no longer a conviction or opposes some other irrationally held convictions. In the last statement I make use of the fact that all rational convictions are deduced from irrational convictions. Rationality is a good tool to test irrationally held beliefs against each other.
I think you unfortunately also brought into question the Axiom of Choice. It is a controversial axiom. I personally have no problem with the idea that in a collection of nonempty sets each set can be associated with an element in the set, but I am leery about how we can sometimes be too careless in defining a set (such as the set of all sets). Anyway, I am aware that it leads to some surprising conclusions, but it does not in any way challenge any of my other irrationally held beliefs, so right now I tend to accept it on faith (though perhaps less than a firm conviction). I never meant to imply that one has to believe everything with firm conviction.

"do not confuse faith in the commutative laws of mathematics, even as applied to discrete items in the universe, as being inductively discerned. It is true that we look at examples to understand, but this is not the same as proving its truth by how many examples we have looked at"

Induction, as a technical tool, is just this daily tool everyone of us uses: this thing in us that tend to generalize, from a small group of observations, and then to make statements about larger things.

Counting, and numbers and some of their properties, are indeed among these "rules" that have been widely accepted for millenia.

They work, so why go on doubting about them?...

Well, arithmetic has been studied at its roots, and so did mathematics in general, and there has been found very good reasons not to take them for granted.


You have said before: "As a mathematician, I accept the validity of the Commutative Laws of Addition and Multiplication on faith".
When I replied to you, saying that these Commutative "laws" were within a human construct, you replied with a real worl example (the "array of pennies" example).
There was my reason of talking about (logical) induction: in your example of the pennies, are you using logical induction, or mathematical induction? Which of these two are you appealing to in your real world example?
If you say you are appealing to the later, then tell me, how do you set about placing n number of pennies? What is n?!
Whenever you abstract these pennies, you get into the constructed world of mathematics, which often tries to modelize what is in nature.
But if you don't abstract these pennies, then you use "common knowledge", or "common experience", which rely/depend more on logical induction.



"First, I believe, irrationally I might add, in the principle of mathematical induction, which is not the same as inductive logic as used in science."

Nevertheless...

Would you put, presently, your "irrational" belief in Euclid's Fifth Postulate?
Are you "firmly convinced of its validity"?

Of course, in its properly built world, like the usual system of arithmetics, commutativity holds; just as in Euclidean geometry, the fifth postulate holds (by definition).

The problem arises when we speak of the "real" world, ie the physical world we want to describe mathematically.
To say that "nature" "tells" us there is such a thing as commutativity, or euclid's postulate, is clearly a Platonist point of view... which is another of these imponderables in life!

These Axioms, Principles, Postulates... are there as axioms, starting points that indeed one must start from, for we wouldn't start at all.
But to question them is incredibly healthy.
To assure ourselves that the axioms we choose do not lead somewhere somehow to contradictions is important.
But if we would take them as absolutely valid (which I hope you do not do), then mathematical inquiry would be useless, and with it mathematics itself.

Intuitions have been know to fail.
(and so did science...)


"Irrational beliefs or knowledge is fundamental to our understanding of truth"

Well, probably fundamental to our understanding of what one believes as truth.


"If we do hold an irrational belief and we perceive something in nature or wherever that makes us doubt it, then we should feel free to question and examine what we believe. It is healthy"

Good.
Same can also be said of a rationally based beliefs, or a belief in rationalizations.

But if we don't perceive any wrongness in our beliefs, should we just take them as true, and not dig deeper in its truthfullness or reality?
Should we stay confortable in complacent beliefs?

I am glad that this was not the view taken as a whole, at least as time went by, in science (although many scientists were indeed complacent).

It's not because it "feels" right that it is right.
Just as it's not because it computes rigth that it is right.

Rational thought, but also Non-Rational thought (which i think you call irrational thought), are both usefull, but yet unsufficient to this day to encompass the whole understanding of nature.


"I think you unfortunately also brought into question the Axiom of Choice. It is a controversial axiom....(...) "

I brought it up for good reasons. And fortunately.

The Axiom of Choice, upon reading it, is so simple, that one hardly would take it as an axiom: one would be tempted to take it for granted.

That such an axiom be so controversial to be specially called an "axiom", to be used or not in one's proofs, is, imho, a quite formidable example of what intuition (and reason) have difficulty to attain.

And as you pointed out, the difficulty in totally accepting it in the math community is related to the definition of set.

But because of these questions, these problems, these doubts, the notion of "Set", once thought to be quite intuitive and natural and unproblematic, has been revised, more than once, and strengthened (for most mathematicians anyways); but even now not all problems are solved.
(Others even prefer using the notion of category, which presumably avoids the notion of sets.)

"(...) but it does not in any way challenge any of my other irrationally held beliefs"

... it was not there to challenge, but rather to give an example.
An example of how something so intuitively clear can be not so clear at all.

perhaps this is not the best thread to post in after a long retirement. i've read it very quickly and i'm sure i haven't digested it properly, but i'd like to add my 2 cents on what you have written about that passage.

well, in fact i don't want to comment that passage, but the human sacrifice made by Jefte (i don´t know his name in English. he's one of the Judges. about chapter 12 or so of that book). i'm sure no christian (nor jew) will say that was a good action, but in that moment of the history of his people they took it so.

i've been reading a bit about the development of jewish religion. i think it's interesting to take the Bible not like a single book written all in a rush. not all the books were written at the same time: the oldest i think it is the Deuteronomy (about 8th century b.C.) though it was probably completed lately. most of books were written after the babylonian deportation (that's 6th century b.C.).

That means that almost all their history till that point must be interpreted without those books. the release of new books brought new conceptions of how religion should be interpreted and lived.

we christians, used to say that God showed himself progressively till the highest point: the coming of his Son (the Truth, Gil ). so, i don't think nobody need to justify yor Samuel 15 or my Judges 12(?) either.

well, i'm not sure to have explained me clearly <img src=http://www.ezboard.com/intl/aenglish/images/emoticons/ohwell.gif ALT=":\"> now i'll reread your posts

I haven't read all this thread, but sort of glanced through it and thought I would add my views.
I'm not a Christian, though I was brought up to be Church of England, if I was anything. At the moment I'm still searching for something such as a religion to believe in but I find this absolute faith thing very hard.
I feel that it is important to respect other believes and cultures, religions, it is very sad to see so many wars and hatred in the name of religion. Many religions worship the same or very similar Gods, Catholic and protestant both worship same God but, in different ways. Therefore use the fact that you worship same God as a bridge between people that leads to understanding and respect. To me all peoples are citizens of the world, therefore we should try to get along.
Obviously there are many cults that aren't true religions and are dangerous, I'm not saying respect them. Also just because you try to respect and understand different cultures, religions doesn't mean you neccessarily think they are better than yours. To me all religions and beliefs are interesting.
There are many things in this world, and maybe on other planes of existence, that can't be proven to exist, or not, by scientific means. But just because science can't prove the existence of something does'nt mean it does'nt exist. When it comes to personal beliefs and religion, spirituality, science is very largely irrelevant, as such decisions are made either instinctively or, because of a persons culture. For example certain things I believe in but cannot explain rationally why or how they might exist or why I believe in them. If I am correct it is a zen philosophy that many things cannot be explained, but can be understood on a level that needs no explanation.
Though in many things I am very rational, when it comes to thinking about life, the universe, and all that then I am completely instinctive. Just as someone said above you don't need a scientist to tell you it is a beautiful day or that a tree is lovely.