Yeah, Ok. I didn't rationalize that one very well did I.

I have to agree here that Rationalism (at least in my understanding of it) does indeed require a 'god concept' of some type. It's the idea that there is an 'absolute truth' that exists somewhere 'outside' of the physical universe in which we live. And that 'absolute' truths can be deduced.

In fact, this was the driving force that swerved mathematics into the Rationalism camp. Modern day pure mathematics is indeed riddled with rationalism. I hesitate to say that it is based on rationalism because I actually feel that in its early going mathematics was indeed based on empiricism more than people realized. But that changed over the millennia.

When we ask, "What is mathematics?", we really need to ask two questions: What was mathematics in its early stages, and what has mathematics become over time?

I realize this thread isn't about mathematics, but modern mathematics has indeed become based more on rationalism than on empiricism, and the very reason for this is precisely what Di said. Rationalism tries to rationalize everything from the point of view of an abstract spiritual 'mind of God'.

It's no accident that modern mathematics is called PURE mathematics verses the APPLIED mathematics of empiricism. The very term PURE came into play to mean that mathematics is now being considered to be a school of pure thought untainted by the physical world.

This is truly the greatest joke that mankind has ever played on himself. He took the concept of number which was originally an empirical adjective and turned it into a pure noun of rationalistic thought.

This was indeed a wrong turn and must be corrected. It's inevitable. It's simply wrong.

And when you think about it it's truly crazy. Mathematics is being guided, today, almost entirely by pure rationalistic thought. The science of physics is supposed to be empirical-guided thought. Yet science relies heavily on mathematics. Over the centuries, science has dealt with this by using Applied mathematics which pure mathematicians view as a mere subset of the far richer field of pure mathematics.

But this is all wrong. The very concept of pure mathematics is misguided. And mistakes have indeed been made. Number is not a noun, that exists abstractly in "The Mind of God" as an absolute truth. Number is truly just an adjective that describes the quantitative properties of the physical universe in which we live. It's not a godly notion at all. It's extremely empirical.

However it may be true that any empirical universe must be based on a quantitative nature. I can actually argue this from a purely rationalistic point of view. As odd as that may seem.

So it might be possible to make that kind of conclusion using purely rationalistic thinking. However, that doesn't help much with physics of this particular universe because it would still come down to the fact that precisely how that quantitative aspect unfolds within a universe must necessarily be dependent upon the random seeds of that universe.

In other words, Rationalistically speaking, we could say that all physical universe must have a least quantum. Our universe has Planck's constant as its least quantum.

However, every universe does not need to have Planck's constant as its least quantum.

In other words, the idea that all physical universes must have a least quantum might be an absolute truth that can be deduced using pure rationalistic thought.

However, there would be no way to deduce the precise value of that least quantum (the value of Planck's constant) in this universe without directly experiencing it (i.e. measuring it).

There's no way you could deduce what it must be using pure thought alone. And the reason (rational thought again) is because this universe is based on random seeds.

So I suppose I do use both Rationalistic thought and Empirical thought.

Rationalistic thought leads to the mind of God.

Empirical thought leads to the physics of this universe.

However, Rationalistic thought doesn't help much. Because, as I have shown in this example, all that Rationalistic thought can say is that all physical universes must have a least quantum. But there's no way that it can put a value restraint on it.

Anything goes!

In other words, God might be limited to only creating quantum universes. But they don't all need to be like this one. They can have different values for their quantum, and for other quantitative relationships within that universe as well. And all of those parameters would be completely inaccessible to someone who is attempting to deduce them using pure Rationalistic thought alone. The only way they can possible know these parameters is to measure them. Therefore the physics for each individual universe can only be deduced via empirical thought.

Because for the mind of God ANYTHING GOES!

And I actually used Rationalistic thought to come to that conclusion.

But where did it get me?

It just got me to the conclusion that I can't figure out this universe using Rationalistic thought alone. Empiricism is an absolute must.

So for me, Rationalistic thought actually proves that Empirical thought is the only one that has value when thinking about the physics of this universe.

If you want to use it to explore the mind of God then fine.

But I can already tell you where it will lead if you do that.

ANYTHING GOES!

I can't even use Rationalistic thought to prove that all physical universes need to be built on a quantum. I can only use it to deduce that an infinity of universes can be built from a quantum. And for that reason alone, Rationalistic thought cannot be used to deduce this specific universe.

So as far as I'm concerned Rationalistic thought has already shown its limitations with respect to what it can tell me about this specific universe.

I've taken Rationalistic thought to the very end. It leads to the fact that anything goes. That's where it leads.

If you want to know about this universe Empirical thought is the only way to go.

Hi back to ya Sky. Can't stay long, but hey, it's philosophy, I had to stop in.



It's not so much a definition of knowledge that is the problem. It's more that you're misunderstanding how Rationalists believe knowlege is achieved.

There are three ways, according to rationalists that we attain new knowledge. Not in any order but here they are:

1. Innate knowledge: We are born with inherant knowledge, given by God. We draw on this knowledge when some event triggers our memory of that inborn information. Kind of like our mind was a computer and the progam was all-inclusive, however, we just need a trigger to help us remember what we have had all along.

2. Intuition Deduction: We have intuition or insight that suddenly makes us think about an issue or a problem or maybe a question. Then we think about it by simple deductive reasoning we will turn out thougts into knowledge. Sort of like coming up with some scientific equation without ever having had a math class. No need for testing your theory, no need for any prior knowledge, we just figure it out.

3. Innate concept thesis - we receive SOME of our knowledge innately and some through experience (our senses). The idea is that the ability to think abstractly comes from some innate knowledge that is pre-stored in our brain. The reasoning is that we can not expereince certain things, like a perfect triangle. But since we can think abstractly about a triangle it must be a priori knowledge.

But if you were blind and and you had never held, or touched anything triangular or ever heard of a triangel and never had any math what-so-ever and I asked you "What has three sides and equal angles" would you reason that it was a triangle? Would you be able to draw one? Would you be able to conceptualize a three-d triangle (pyramid)?

That's what rationalism is saying. That we are born with information (knowledge) and testing and science and even perception are not necessary to have access to that knowledge.

Now consider that the vast majority of philosophers that are considered rationalists have metaphysical concepts, and believe in the dualism of mind and body, and believe that God gave us this knowledge.

Does it become clearer why and how the philosophy of rationalism came about?

Does it make sense why empiricism is associated with science while rationalism can not be?

Note: This post is off-topic in response to Di's comments on garlic necklaces and wooden crosses, and contains nothing on the subject of Rationalism vs. Emiricism.

~~~


Boy are you going to be disappointed in me Di!

I'm becoming a witch, or a shaman.

I'm not into garlic yet, but I am sprinkling salted holy water around my cottage in preparation to cast a magic circle to invoke the Gods for the purpose of participating in a spiritual communiqué.

Yes Di, I finally found religion.

Well, you've always known that I'm a pantheist. Although now I'm thinking more along the lines of animism. (not truly different but it has slightly different connotations).

I'm not truly seeking to meet any deities per say, but I am hoping to contact the spiritual self on a higher plane.

Although if I meet up with any Greek Goddesses who want to get naked I'm not going to complain. Aprhodite would be a welcome sight in my living room.

But on a more serious note I am looking into becoming more spiritual via religiousity (i.e. ritual).

I've begun by following the way of "Wicca" as introducted by Scott Cunningham. He introduces it with much abstraction which I totally enjoy. It's not dogmatized at all the way that he presents it.

However, there are other forms of "Wicca" that are heavily dogmatic and have strict beliefs and rules. I'm definitely not going there.

In fact, somewhat ironically, Scott points to books on shamanism for "further reading" with respect to his presentation of Wicca.

Well, I've begun looking into some of those books and they hold two things as premises. 1.) Shamanism isn't a religion. 2.) Shamanism appears to be much more aligned with animism rather than deism. (at least in the books I've been looking into).

So don't be too surprised if you see me wearing a garlic neclace at some point.

Although, I'm seriously not even thinking in terms of warding off evil spirits. I'm just thinking in terms of making some type of spiritual communiqué for the purpose of self-improvment and learning techniques of magic particularly with respect to the art of healing.

Owl let you know how it goes, but don't look for instant results. I'm not expecting instant gratification. And I'm in it for the long haul. Owl at least try it for a year or so and see how it goes.

I'm finding the religiousity (ritual) aspect of it to be useful in its own right already.

Abra:


You had me cracking up as I read your post. An insightful moment – awe no not really, BUT oh, that can’t work either…..

Let me ask you- in recent years I remember reading an article about the last mathematical equation/therum? (whatever) finally being solved and it went as back as -- was it Epicurus? OH I can’t remember? At that time I wondered, how could someone, prior to expanded theories of math, have come up with an idea that would take so long for math to advance so that another person could prove it? Did that person “Epicurus” use rationalism? But I don’t think so, if so, he would have completed the effort and not left the idea have finished.

I don’t believe – even in math – that people have inborn knowledge. If they did, we would not continue to use postulates as foundations for further experimentation. NOW – a student may be told about some postulate and the student adds the information to his knowledge base, even though the postulate has never been proven, its only proof is that it hasn’t failed yet. There are so many of these that they are taken for granted.

This is not really rationalism, it is simply trial and error. If it works, keep using it, when it doesn’t, there will be a calamity and all of the math world will have to go backwards – BECAUSE – there is no rationalism. If there were, we would not have continued to use the wrong postulates.

I’m not at all sure how this post will turn out, I’m exhausted . I hope it makes some sense, I know what I want to say – did I say it?
Oh may GOODNIGHT!

Ok one last post -

Abra, Shamanism, how interesting. I just recently met a couple people who where into shamanism.

I think there are all kinds of ways to expan the mind but only if that's what the person is acturally striving for.

Ritual has always been a part of any mind altering function - if you think about it,including education. FLASH CARDS - times tables - rhymes (i before e) and even song ABCD.

There's just something about our mind that can focus better under ritual - unfortunately it has a downside. Those who wish to manipulate the mind/thoughts of others will use ritual to do it.

Anyway - I can't wait to hear how it goes for you. I expect you'll get some intersting results.

I'll be back, but I don't know when - I've never had so much trouble with a class in my life as I'm having with math. What the heck is that about? I've got to spend the rest of the semester getting my grade up - so see ya later.
di

I believe you are thinking about Fermat's Last Theorem, and the solution given to that problem by Andrew Wiles.

First off, Fermat may have been wrong. That is to say that he may not have truly proven this theorem to be true.

Secondly, even if he had proven it to be true he most certainly didn't use the same methods as Andrew Wiles.

Finally, there still exists a possiblity that even Wiles' proof could be flawed!

He uses a questionable counting technique that uses p-adic numbers. I've been meaning to go over the proof myself. It would be good material to use in my book (if I ever write it). The fact that he had to restort to p-adic numbers for his proof causes me to have suspicions concerning the validity of his proof.

Although, I personally believe that the theorem is true whether his proof is flawed or not.

I mean, just because a proof is flawed doesn't necessarily mean that the conclusion is necessarily false. It would simply mean that it hasn't been correctly proven.

But the main point here is that Fermat would have necessarily used an entirely different method of proof.

In fact, Wiles actually proved Fermat's theory indirectly by proving something else entirely that, if proven, would then imply that Fermat's theorem must also be true.

So it's not even close to being the same proof.

Andrew Wiles actually proved something entirely different. But in proving that he showed that Fermat's last theorem must also be true.

So it was a totally different line of thinking altogether.

This is true, but as you point out, it can be the basis of education as well.

I think of it more as gymnastics for the spiritual mind. I'm not concerned about being brainwashed into believing weird things. I'm more concerned about having spiritual experiences, and with being able to improve my health.

If I feel better and it's just due to a mental attitude who cares?

Feeling better is feeling better right?




Yes, this is why I don't support the organized religion or dogmatic aspects of it.

If a person can obtain better health, a more organized lifestyle, and feel more purpose-driven and productive then this is a good thing.

But if they end up being oppressed or used by charismatic spiritual leaders then it's a disaster.

I'm totally against dogmatic religion, but 'religiousity' (i.e. devotion to methodic improvement via the consistency of ritual actions) then I'm all for it.



Too bad I'm not there. Owl bet I could make it so much easier for you.

Presentation is everything!

Math is one of the worst-taught subjects in all of academia. They tend to teach number-crunching rather than forms and abstract relationships.

It's so sad.

If I could teach everyone math they would all love it.

I once had a girl student in one of my math classes that was totally under the belief that she could never comprehend math.

By the end of the course she was so excited about math she was actually talking about becoming a mathematician.

Ok. I'll shut up.

Sky,

Don't ever shut up. Your input is valuable and you always make me think. I know the information from the link was ALOT of reading and if someone is not familiar with that kind or terminology the information is especially hard to digest. So I was just trying to simplify it, I hope it wasn't taken offensively.

BUSHI - science and philosophy really can get along, in fact philosophy has a new angle and philosophers have made themselves the new watchdogs of the scientific community. I think that's a good thing, complacence is possible in any group.

Abra:
I really do agree with you idea that what we do should be about our health, whether its physical or mental, feeling good physically and metally is not a gift, it takes our caring about ourselves.

My ritual is a morning work out good for mind, body and soul.

later all
di

Cantor's theorem di. People are still arguing over it, even though it works.

_____________________

'rationalism'
"any view appealing to reason as a source of knowledge or justification" (Lacey 286). In more technical terms it is a method or a theory "in which the criterion of the truth is not sensory but intellectual and deductive"

I don't really see where rationalism has anything to do with god. To me it is a function of analytical thought.

I agree that no knowledge can be gained by a processing unit with no data.

But if all processing units where equally adept at restructuring data to make simply rational logical concepts then everyone could be an Einstein.

I feel that rationalism is the tool by which all data is interpreted.

I feel we let out definitions of words sit in antiquity past there expiration date.

"In philosophy, empiricism is a theory of knowledge which asserts that knowledge arises from experience."

A data collection device would have no understanding of light waves beyond being able to bring forth regurgitation style every example that is tagged within its data base as light.

It could no more explain it then by showing you.

I see these two variables as one function called analysis.

____

Di I agree, they get along fabulously, but like a marriage when someone gets grumpy they can take things out of context, and you see poor lill scientist all in a huff over definitions heheh.


I enjoyed the article and this thread immensely.

Billy,

I think the major problem associated with the terms, Rationalism and Empricism, is indeed a bit murky and before any meaningful discussions can be had regarding their relative credibility their precise definitions would need to be clarified.

I think it should be pretty clear that Empircists use reason and rationalization. Otherwise they wouldn't be 'thinking' at all.

I mean to imply that Empiricists only go by what quite literally hits them in the face without using reason at all is a bit absurd.

I personally believe that the difference between pure mathematics and science is an excellent example of the difference between pure rationalism and pure empiricism.

The scientific method is based on pure empiricism, but at the same time it doesn't reject creative thinking. It simply states that creative thinking must be verified by experience before it can be accepted as being 'truth'.

Pure mathematics, on the other hand, does not require the universe's permission to accept something as 'truth'.

In fact, Georg Cantor is a perfect example of this. His formalims of set theory is entirely an invention of pure subjective thought. In fact, I hold that it is indeed 'false'.

By that I mean that if we ask the unvierse if it agrees with Georg Cantor the universe will say, "No".

Cantor's set theory is actually wrong.

This is what I present in the book I never write.

Actually I have quite a bit of it written, I just haven't published it yet.

Cantor rejects the universe and turns to pure subjective thought instead. He reasons (via pure rationalization) that he can begin a mathematics based on nothing. And thus he begins with the concept of zero. He calls this concept The Empty Set.

He then goes on to use this concept of zero to define the number One. Formally the number One is defined as the set containing the empty set.

And off he goes,... blah, blah, blah.

He ends up with an infinity of different sized infinities.

That's right. According to modern mathematical formal infinity comes in different sizes. In fact, it can be "proven" via modern mathematical formalism that there are an infinity of different "sized" infinities.

This is bull sh!t.

It's wrong.

Cantor's set theory is entirely a humanistic subjective whim. It has nothing to do with the universe.

In fact, mathematics can indeed be based on the actual universe. We can actually test our definition of the number One against the universe and get an empirical answer!

Cantor's definition flunks the universe.

There is a better way to start mathematics. There is a better definition for the number One.

Once corrected that defintion (based on epiricism) leads to the fact that there can be only ONE infinity. Period.

Infinity in that empirical system represents the concept of endlessness (an intuitively comprehendable notion actually).

Modern mathematics is actually wrong. And the reason that it's wrong is because it's based entirely on pure rationalism without appealing to the universe empirically.

Mathematics can be defined and structured within empiricism. It is not only possible, but it will lead to more 'rational' conclusions.

I really need to publish my book. I was kind of hoping that someone else might discover this and bring it to the attention of the scientific community, but I guess I'm the one who was chosen to write this book.

And yes, it has everything to do with the difference between pure rationalism, and empirical thought.

Rationalism is a 'spiritual' or 'godly' idealism as Redy suggests.

It was indeed a desire to make mathematical formalism 'PURE' that led to Cantor's work.

In fact, at the very same time Giuseppe Piano actually offered the empirical definition of the number One that I support. So it's not like some people weren't thinking this way.

The mathematical community arbitrarily chose to favor Cantor's idea of starting with nothing. They reasons are complex.

However to make it short, Cantor's idea allows the concept of number to be 'pure' (an independent noun). Dependent on nothing (i.e. It's defined on the very concept of nothing!)

Cantor started with nothing and ended up with more than everything! (i.e. Infinities larger than infinity!)

Giuseppe Piano's concept of number begins with the concept of "oneness".

But that concept is dependent on the quantitative property of the thing that is being quantified!

In other words Giuseppe Piano's idea is an empirical adjective rather than a pure noun. It is directly related to the thing that is being quantified.

And that would 'taint' mathematics with empiricism, and it would no longer be 'pure' thought.

This actually a totally erronesous way of thinking.

It is the very quantum nature of the unvierse that gives rise to the very concept of quantity in the first place!

Mathematics is actually an empirical property of this universe.

Plato was wrong!

There is no such thing as a preexisting "mind of God" in which some 'pure' mathematical formalism resides untainted by physicality.

The very concept of quantity itself is a physical property of this universe.

In fact, the value of PI may not even be valid in other universes!

We already know of geometries that exist within this universe where the quantitative relationship we call PI is not valid!

It's a maleable concept!

It's neither carved in stone, nor is is carved into the mind of God.

Mathematical formalism not only can be empirical but it should be empirical!

That's the thrust of my book.

The title of my book is, "Mathematics as a Concrete Abstraction".

It's partial written, and I really should bite the bullet and just finish the damn thing and publish it.

There isn't any technical hold up. I'm just too damn lazy to buckle down write it, that's the only problem.

When we came up the with words Empirical, and Rational, we had limited understanding of how information systems work. Developing computer programs, data bases, and decoding how the human brain works has expanded our understanding of how each of these lines of thought work at a more fundamental level.

This to me is a perfectly good reason to dump a lot of the garbage that muddles these two (not so exclusive) lines of thought. New insights allow us to filter the crap of previous generations.

I see empiricism as a set of analytical tools that overlap rationalism.

Rationalism without empirical data is a tool unused.

Rationalism is a tool within the set called empiricism.

I like to simplify things, not make them bigger to included all past blah blah blah.

"Any intelligent fool can make things bigger, more complex, and more violent. It takes a touch of genius -- and a lot of courage -- to move in the opposite direction."

Albert Einstein.

Well, based on that perspective alone I would say that any thinking person uses both.

So the very idea of "Rationalism vs. Empiricism" is a moot point when viewed in this way doncha think?

I do. take out the Vs. and ask instead to what degree, and perhaps in what situation. Now there is a conversation.

Well, I try to rationalize everything, but I also place great value in the empirical.

As I've said, there are people who truly believe that pure thought alone has value without any empirical imput at all.

In fact, Plato, Descarte, Aristotle, and many more famous names can go on the list of philosophers who believe that everything could be known via pure thought alone.

Many modern mathematician still think this way today. They believe mathematics to be based entirely on pure thought.

In fact, many times the question arise as to whether mankind 'invented' mathematics, or 'discovered' it.

In other words, is it based on pure rationalism or does it have an existence of its own (which I would claim is empirical). However, men like Plato would claim that the pure math exists in the "mind of God", or at least some "other world that is pure psyche and non-physical".

I personally would say that today our modern mathematics is based on both empirical observations, and pure rational thought.

However, I would hold that the parts of it that are indeed based on pure rational thought are actually wrong.

They are wrong in the sense that they don't apply to the quantitative nature of this unvierse. And if they don't apply to the quantitative nature of this univese, then what do they apply to? In what way can they said to be 'truth'?

Only with respect to the axioms of the formalism?

But where did they come from? The arbitrary whim of man? "Let there be an empty set", proclaimth Georg Cantor.

Did he make that up?

Or is there such a thing?

Is there such a thing as a boogieman, just because we can imagine the concept?

Pink flying unicorns?

Faeries and leprechauns?

In what way do these pure ideas represent 'truth'?

We can imagine anything we want.

But how is it 'truth'?

Or more to the point, how can those pure ideals be used to deduce anything specific?

Anything goes is truly the bottom line.

In mathematics a pure mathematician would say, "No. Anything doesn't go, it must be based on the axioms".

But what if they axioms are faeries and leprechauns?

I think that's the key right there.

An empiricist isn't saying not to use rationale, but rather to only apply it to known premises. And the only way we can know premises are by observing them to be true. Otherwise they're just guesses and anything that is built atop a guess is still just a guess.

I think that's the bottom line that empiricists are trying to get at.

At least the premises and axioms should have some foundation in verifiable "truth", and the only way to verify truth is to experience it.

If it can't be experienced, then it's just faeries and leprechauns.

I think that's the basis of the ideal that Empriricists are attempting to get at.

Pure Rationalists seem to be saying that faeries and leprechauns are valid thoughts as long as they can be rationalized with suitable axioms. But they don't require that their axioms be empiricial.

In other words to simply say,...

AXIOM: There exist a Faerie World.

That's a sufficient foundation for a Rationalist to begin to build upon.

But the Empiricists would say, "What faeries? Show me."

By the way, Billy, this is a great thread. I'm glad you started it because these are the kinds of arguments I need to make in my book. So you're inspiring me to go back to writing on it again.

I need to show why I believe that Cantor's empty set is a 'faerie', and can't be proven to exist.

And why Giuseppe Piano's orginal definition of the number one is not a 'faerie' at all but can indeed be supported empirically.

Yes, I need to go write up that book. FINALLY!

Thanks for starting this thread, you've given me fresh ideas for a new presentation.

I have to disagree with your view that pure rational thought has no value.

As I see it, there is really only one type of knowledge that is based on 100% pure, no observation involved, rational thought.

It is called "free-will" - aka "self-determined decision".

It's not "a conclusion" as in "After doing a taste test, I've decided that this food tases better than that food".

It's not "the result of a calculation" as in "I've decided to take that that route because it's shorter."

It is a "self-determined goal" as in "I've decided that I want to feel good."

So contrary to your proposal about the value of purely rational thought, I think this type of purely rational knowledge is the most valuable of all because it is what determines the relative value of everything else. It is the source of "value".

Ok Sky,

I surrender to your pure rationale.

Owl give up on the math book and go back to writing pure poetic incantations for the spiritual shamans who just wanna be.

Aw c**p! Shot myself in the foot again. I was really looking forward to that book.

Wouldn't you say that to want to be happy is to have known sadness.

Empiricism rears its ugly head!