I'm in total agreement with Kerry O. on this one.

Mathematics is a tool (or map) that describes the quantitative properties of our universe.

I'm saying that modern mathematics is actually a flawed tool in that it doesn't describe the quantitative properties of the universe correctly.

It's pretty darn close, but there are subtle areas where is is wrong.

In fact the very reason that it is wrong is because mathematicians have begun to view it as a mere mental construct of man and therefore they have wandered away from its original purpose!

Instead of refining a tool, they have decided to go down the road of making it into a toy that is totally built on the whim of man rather than being constantly checked to see if it is indeed accurately representing the true quantitative nature of the universe.

Mathematics began as a 'tool' but has ended up becoming a 'toy'. It's totally off track from its original intent and purpose.

It will eventually need to be put back on the correct track. This will happen someday inevitably. Unfortunately no one seems to be remotely aware that it's off track (other than myself).

Wow! I guess that makes me pretty special.

I'll leave the math end of science to Abra. Given a bit of time and a capable intellect, he can finesse any mind into seeing his point of view. That's what I call, his scientific charm.

Skyhook wrote:


I do understand what you are trying to get at. Descartes tried to "get to" the same points, only logically, by proving, with mere thought, that we can know we DO EXIST. "Ego Sum, ego existo" or as others say Cogito ergo sum.

Anyway, science has also broken into the realm of the brain, the mind and its called the science of cognition. From its findings science theorizes and in the form of psychology the findings are used for verifications.

You see Sky, when it come to studying the mind, the brain, there are many sciences involved and YES they don't all the 'truthes' the clear cut answers. BUT, they have a great start. We know alot more abour memory, choice, opinion, self-determinism than ever before and continue to learn more.

For example, we know a lot of people LIKE the mystery that surrounds magic and the realm of the 'unknown', and isn't that what religion is? It certainly can never be proven, but science does prove or disprove its own theories at some point.

That's the difference between the two.

The whole “math” thing went off in a different direction from what I intended. So let me just say that
I’m with both of you, 100% here. “The mathematicians” have, in essence, begun ignoring the territory that the map was originally created to represent, and started treating the map itself as a separate territory.

Ok, I have to stand up and do a jig for that one.

Personally, I think Descartes had it exactly backwards. It should be “I am, therefore I think.” It’s the difference between “I am a product of thought” and “thought is a product of me”. But I think psychology has it chopped it all up into a sort of Rube-Goldbergian anagram, effectively turning it into “I am thought”, which as far as I’m concerned, is a giant step backward.

I think this goes directly to the core of my original point. Psychology starts with the closed-loop postulate that these are all physical things. Personally, I think that is NOT a “great start” but a very BAD start. It leads only to the conclusion that there is, and can be, nothing but the stimulus-response “autopilot” mechanism of the physical universe, and that the illusion of self-determinism is really nothing but an automatic response programmed into the physical universe’s autopilot. Which is the very definition of the materialistic philosophy.

In fact, the very word “psychology” has become a self-contradiction. It originally meant “the study of the spirit or soul”, but has now degraded into “the study of the stimulus-response nature of human beings” and denies the very existence of that which it was originally supposed to be studying.

On the other hand ..... (Oh jeez, not again! )

Since math itself is just an abstraction, why would "an additional level of abstraction” necessarily be a bad thing? Why not have a “mathematics of mathematics” ("map of maps")? I admit that that’s a little too abstract for my puny mental powers. But I’m sure some of the eggheads deep in the bowels of the math departments of MIT or CalTech could make some sense of it.

Just think of it as being able to make tools that make other tools. And though recursion can drive you nuts, always remember this:

"In order to understand recursion, one must first understand recursion." :)

And the math does allow for fake fakes, but that's another topic completely.


-Kerry O.

This is a big issue Sky. Very big!

What do we mean when we say that mathematics is 'abstract'? And why do we insist that it must be abstract?

First off we need to investigate the semantics of the very word 'abstract'.

After all, if we are going to claim that mathematics is 'abstract' shouldn't we have a clear definition of that that means?

Can we even have a clear definition of the meaning of the word abstract?

First off the word itself has mutilple meanings! Is mathematics abstract by every meaning of the word? Would we even want it to be abstract in that way?


First, let me list some possible meanings for the word abstract and then we can ask whether we'd want mathematics to be abstract with respect to all these meanings.

1. Abstract - Vague, unclear, ill-defined, difficult to comprehend.

This is a very poor meaning of the word abstract and one that isn't even listed in many dictionaries, but it is a meaning that many people give to this word. Clearly mathematicians do mean that mathematics is vague, unclear, or ill-defined when they claim that it is abstract. On the contrary mathematicians boast that mathematics is extremely well-definite and quite rigorous in precision and logical integrity. So we can toss this definition of abstract in the trash can. This is definitely not what mathematicians mean when they claim that mathematics is abstract.

2. Abstract - concise, summary, to the point, synopsis, brief, shorthand description.

Well, mathematics is certainly a very concise and brief shorthand language. So this meaning of the word abstract could easily apply to mathematics, however, again this is not what mathematicians are attempting to convey when they claim that mathematics is abstract.

3. Abstract - intangible, non-physical, existing only in the mind, an idea of pure thought.

Now we're onto something. Unfortunately this is the definition of abstract that mathematicians prefer to use when referring to mathematics. I say that this is unfortunate for reasons I'll expand upon later when I give a fourth definition for the word abstract. For now though we can certainly see that this definition of abstract can be applied to mathematics in many ways.

Mathematics is indeed a language that describes the quantitative nature of the universe in which we live. All languages are abstractions. They are ideas of pure thought that refer to various concepts. So with this understanding of the meaning of abstract, we can see that mathematics is definitely abstract in this regard.

However, pay attention to the part I underlined above in the definition. Existing only in the mind. It his true? Does mathematics exist only in the mind? It is a total fabrication of the whim of men? Is it totally independent of the physical world? Well, let's hope not! It supposed to be a study into the quantitative nature of the universe (at least this is what it started out to be_). If it has become something other than that perhaps we need to ask why it has gotten off track and what happened to the original investigation?

This is where the map has become the object of study, rather than the original territory as you mentioned earlier. This is the kind of abstraction that mathematicians have fallen in love with.

Almost to the exclusion of the original purpose! Mathematics is supposed to properly reflect the true nature of the quantitative property of the universe. If it is completely divorced from the universe to become nothing more than the whimsical abstract ideas of men, then it has truly lost its way IMHO.

This brings us to a fourth definition of the word abstract. The most powerful and meaningful definition of all.

4. Abstract - Apply to many cases, free from a concrete example, generic, apply to cases in general.

Now we're getting somewhere! This is the real POWER of mathematics. It this the meaning of abstract that truly gives mathematics is power and versatility. It's not so much that it can be applied to intangible concepts, but rather that it can be generically applied to many different cases of tangible concepts (i.e. the quantitative properties of actual physical things).

So the real power of mathematics lies in it's flexibility to be applied to many different situation generically. This is the real notion of abstract that is important to mathematics. The idea that mathematics is abstract in the sense of it being merely intangible thought has been way overemphasized out of proportion. It's the ability of mathematics to be applied to many different cases that is the true power of it's abstract qualities.

Here's where they (mathematicians) made their mistake. (philosophically speaking).

They began by recognizing that we can quantify anything with numbers generically.

We can have,...

One dog
One apple
One night of mind-blowing sex
One dollar
One ocean
One continent
One idea
One love

Etc. In all of these cases we have recognized a generic or abstract concept of Oneness.

However, notice that in all of the above this abstract concept is being used as an adjective describing the quantitative property of something. One is always an adjective.

But then mathematics wanted to abstract this idea. They wanted to talk in terms of,...

One thing

Where we can replace thing with anything we choose.

In other words they recognized that the adjective 'One' could be abstracty applied to any thing

So what did they do?

Did they abstract the thing and leave 'One' as a quantitative adjective?

NO! THEY DID NOT!

Instead they abstracted the word "One" and started treating it as a NOUN in it's own right that is completely divorced from any thing.

That was basically when they turned their back on the universe and walked away into the la la land of pure whimsical speculation.

They actually not only abstracted the idea of number so that it could be applied to many cases, but they in fact did abstract the idea into one of pure intangible thought totally divorced from the universe from whence the idea of quantity first arose.

Because of this, they have stepped away from the connection between mathematics and the quantitative nature of the universe.

In other words, like you've suggested; This was the point at which they decided to ignore the territory and start studying the map for the map's own sake.

Even today, they still think that the number One is a noun in it's own right, completely divorced from the idea of the quantitative property of any thing. They have lose sight of it's original roll as an adjective.

So they've done more than just abstract the idea behind the adjective, they CHANGED it into a NOUN that has been completely divorced from the things that it used to describe!

Bad mathematicians! Bad, bad, bad.

Abstracting is ok. But they had no sane reason for changing it from an adjective into a noun. That was their mistake!

As usual, i love the way you exlain your concepts james - is that james watt's by chance -[joking]

and i can't help agree with you on this not that i understand all that you and others do - but i've seen things like this on TV that were not explained as well as you have hear.

thnx for that -

Abra, I love feeding you these straight lines ‘cause yer jus’ so dang good at speechifyin’

However, if I may hijack my own thread back ……

Might we use a sort of inverse of that analogy to apply to what the “cognitive sciences” have done?

“Self” is a subjective thing. In fact, it is, by definition the MOST subjective thing. But this subjective thing has been “de-abstracted” into an objective thing. And in doing so, the very nature of that subjective thing has been denied. Although the map/territory analogy gets very flimsy here, it’s almost like saying “there can be no map, only territory” (Or maybe “the territory is the map” )

The simplest example is the experiment where portions of the brain were stimulated with electricity. The resulting subjective phenomenon was “memory recall”. The conclusion was then drawn that “memories must be stored electro-chemically in the brain”.

I see that conclusion as being about as logical as concluding that the images viewed on a television screen must be stored inside the television. That is to say, VERY logical if you have no concept of the principles of electronics. Likewise it is logical to conclude the “electro-chemical memory storage” theory if you deny the possibility of any extra-physical agent.

Well, see, that was the issue at the time. How to get away from the metaphysical view that stated the whole realm of the physical was totally illusion.

That meant, we did not have a physical existence at all. But without proof that we exist physically, how could be prove the existence of that thing called ‘self’ or ‘thought’?

So Descartes set out to “prove” that we do, in fact, exist. He did so with a dualistic approach that separates the physical (substance/body) from the mental (non-substance/soul).

He reasoned that if he could debate with himself and persuade himself of ‘anything’ than he must exist. He took the view one step further by indicating that if any other deceiver of unknown origin was attempting to deceive him (implicating the devil) then he most assuredly exists – for who or what entity would attempt to deceive that which does not exist.

Remember, at the time, religion ruled the world and prior to this time, theology along with political philosophies were about all that existed in the world of philosophy.

Since that time, philosophers have struggled with various theories from the dualistic, to monistic, mechanistic, functionalism and so on.

Only in the last 30 years or so, have philosophers taken a new direction. Part of that direction includes the scientific theories of “cognition”. As I stated:



Your reply


Actually, your perspective lacks analysis. No offence, for you have summed up, in part, one particular theory, the mechanistic one and in part a second theory that of biological correlations of human thought & emotion in the neurochemistry of the brain.

But there are about a dozen others, and YES they attempt to dispel the dualistic nature that says body and mental are separate.

How they do this encompasses several different scientific fields. At this point, most people admit that pinpoint precision in predicting mental processes or behavior due to any causal effects of the physical (brain/body functions) are likely never to occur.

Our environment, our genetics, the way in which we gain and store our experiences and then the way we connect to those memories are unique and this is the reason we have been so limited in understanding the functioning of mind/thought/brain/cognition – whatever you want to call it.

To separate the two functions into separate entities, is to open the philosophers proverbial can of worms. The arguments are many, and so far, science is winning – religion and belief systems have all but lost. Current philosophies AND philosophers have hedged toward the scientific, leaving the mysticism and the dualism to those who dwell in the realm of the religious, where faith demands no proof.




In some respects you are right, however, there were various words used for the spirit, soul, including psyche which was used as early as Plato.

Plato did not equate soul with psyche, in fact, from the age of enlightenment (17th century) philosophers began getting away from using the word soul. You can imagine this made many religious leaders uncomfortable.

So by the time ‘psychology’ was used to indicate a science, it was used in reference to Watsons’ structuralism, and Freuds’ psychoanalysis – which both explored the “psyche” which has meant the mind for over 150 years. So Psychology is the scientific study of the mind. Unlike philosophy, it uses scientific methodology and doesn’t rely on an individual persuading himself that what he sees is empirical evidence of ‘any kind’.

I've always taken his qoute and stated - I am capable of thinking, therfore I am - and then added: capable of thinking wrongly -

Abra,

How is "one" a noun? How would you use it as a noun?

Even if I said, "You are the one." There is an implied noun in that statement. As in "You are the one person."

"Person" being implied.

Or else If I said, "I am the one." The question would be "One what?" "You are the one what?"

"I am the one who they are looking for."

So can you give me an example of how you would use one as a noun rather than an adjective?

Jeanniebean has been this way since "day one"

as a noun and in league with another supportive noun - day

I think you misunderstand Jeannie.

In English we typically use One (and all numbers) as adjectives. But in mathematical formalism the concept of "One" (and all numbers) is formally defined as a noun. Although they don't call it a 'noun' in mathematics, but none the less they treat it as such.

'One' exists as a number in its own right without the need to be assocaited with any 'thing'. And this is true of all numbers in math.

They have completely detached the concept of 'number' from the concept of the quantitative properties that they original described.

In fact, this is why it is called 'Pure Mathematics'. It is pure because the concept of 'number' has been divorced from the concept of the thing that supposedly have the quantitative properties.

This was done formally by a man named Georg Cantor.

The result that follows is that there now must be different sizes of infinity. In fact, Cantor proved that this must be the case (based on his formal definition of the number One).

But his formal definition is far-removed from having anything to do with the original quantitative properties of things.

Because of this (and the work of other mathematicians as well), the very idea of number is no longer an idea of quantity, but rather it is a stand-alone idea in its own right.

It would be difficult to find examples in English that could clearly demonstrate the significance of this.

Most of the mathematics that is affected by this would not affect that layperson. In other words, it's not going to affect bank tellers or even airplane engineers.

The things that would change would have to do with idea of infinity, Group Theory, and abstract aglebraic notions concerning the mathematics of differential manifolds in higher-dimensional spaces.

In other words, it only affects that mathematics of very high-level mathematical concepts and theories.

It's not going to change the amount you're due back on your Income Tax Return.

Sorry about that.

Very articulate refutation! Kudos!

I freely admit that my arguments were mostly rhetoric.

So lets take a concrete example. I had what is commonly called an out-of-body-expereince. Specifically, I observed my body and it's surroundings from about six feet in front of it. Now, all the "scientific" explanations for that, that I have ever heard, are not explanations at all, but simply denials that it is an accurate account of what happened. Essentially assigning it the label "delusion".

So getting back to the original point of this thread, I can have faith in the "scientific" viewpoint, in which case I am "delusional", or I can have faith in a "dualistic" viewpoint, in which case I am "enlightened". But in either case, it is based on faith in an unproven (and as you said yourself) probably unprovable assumption.

I too have had 'out of body' experiences. The most profound was when I was a very young child. I once left my body and hovered directly overhead looking down at myself. I could see what was going on behind me.

How 'real' was the experience? How much might it have been a delusion?

I have no clue. I can't even prove that life itself isn't a delusion, so I guess I'm in pretty bad shape.

The only thing that I know is that I can't recreate out of body experiences at whim.

Whether they are real or delusions I cannot say.

When it comes to science, I am no more a 'believer' in science than I am a believer in any religion.

At least not in all aspects. I don't just take the scientific view as fact. Especially when it comes to things that science has yet to disprove.

I don't believe that science has ever proven that it's impossible for us to have a spiritual element. If it has, then I suppose I'm behind the times.

Science doesn't know everything. I accept what it does know (like evolution). Clearly I don't need to accept what it doesn't know.

You seem to be suggesting that science is claiming that your out of body experience was indeed only an illusion.

I beg to differ with you.

I think that all science is actually saying is that based on what it known at the current time it appears that "delusion" is the most likely explanation.

I don't believe that science can say with certainty that this is all that it was.

In other words, science isn't saying, "You were deluded and we can prove it!"

Not at all.

Science is merely saying, "Based on the information we currently have, delusion is the most likely explanation"

That's not the same as claiming that this is the explanation.

Do you see what I'm getting at?

Yes I do, but I don't think you see what I'm getting at, because of this statement... That simply says that they do not have all the information. Which simply admits that the "scientific" conclusion of "delusion" is no more "likely" than is the "personal" conclusion of "enlightenment". Which is the exact point of my original post.

Well, in this respect I agree with you 100%.

Science is not complete. It does not have the answers to everything and doesn't even claim that it does.

To worship science as though it has all the answers would be foolish IMHO.

I don't personally view science as a religion. I don't have 'faith' in science as an absolute knowledge base. Nor should I! To the best of my knowledge science is not finished, by far. It's an on-going quest for knowlege.

I do put my 'faith' it what it has accomplished to this point.

At least with respect to certain conclusions!

I do not just blindly accept every theory that scientists are working on or proposing.

I believe in Einstein's Relativity because it's been experimentally verified (not simply because it was proposed as a so-called 'scientific theory') Time dilation has been measured. Time really does dilate in this universe. It's no longer 'just a theory', it's an observed property of the universe.


Einstein doesn't even explain why time dilates, he simply points out that it MUST dilate.

I believe in the evidence for evolution. Uneducated people will often say that evolution is 'just a theory'. That's hogwash. There is as much evidence to support that evolution must have occurred as there is evidence to deduce that the earth orbits the sun. It's not even in question anymore. Science has uncovered this TRUTH.

I appreciate science for what it can reveal. It has proven itself in many technologies, of medicine, disease prevention, and the ability to design and build great tools and toys.

Clearly there are many truths that science has revealed to us. But that doesn't mean that everything that is being studied under science is true.

I don't necessarily believe in String 'theory' for example. On the contrary I would even argue that it doesn't even qualify as a valid theory yet. At this point is't just a guess that could be wrong.

I think they toss the word 'theory' around pretty loosely in the world of Science. (unfortunately)

I'm currently studying Alan Guth's Inflationary theory of the Big Bang. He has a lot of convincing arguments. He presents a really good case. He may even be right. That's certainly as far as I'd go with that. I don't think he's in a position to say that this is precisely how it happened. But, in truth, I don't think it makes much difference to our everyday life. It doesn't matter much how the universe came to be, it doesn't change what it is today.

When you speak about the science of psychology I think that is probably the weakest area of science. That would be one area of sceience where I'd place the least amount of faith.

Especially in something like you've described concerning out of body experience.

Show me where science has a theory that actually states that's not possible?

I'm not aware of one. But then again I haven't been focusing on the science of psychology so I'm not sure what they are claiming to know.

With respect to placing 'faith' in science, that would be entirely up to you. Science isn't requesting people to follow it like a cult as far as I known.

All that science does is offer its results and explains how it came to those conclusions. It's up to you to decide whether or not you agree with it's conclusions and methods.

I wouldn't advise anyone to 'follow' science as a religion. It's not even meant to be a religion!

I must also stress too that science itself neither claims atheism nor supports atheism (although individual atheists might point to science to support their atheistic views). So you need to be careful not confuse the scientist with science (just like you can't trust a religious person to speak for their religion )

There are many scientists who are also pantheists of one sort or another. Science does not rule out a spiritual world, it's just that no one has yet been able to provide any scientific evidence for it. But non-evidence doesn't mean that something can't exist.

Why put your faith in anything like sceince or religion?

Maybe we were better off as cavemen when we had no choice but to just put faith in life itself.

Is it really necessary to have some 'logical construct' to believe in?

I think religions sometime cause us to feel this way because they hold that God lusts to be worshipped and get's peeved if not worshipped.

This makes people 'subconsciously' feel that they need to believe in something if only to appease the gods.

I thank God that I'm past all of that.

I put my faith in one thing and one thing only,...

God must be nicer than me! Period.

As long as that's true I'm in great shape! If it isn't true, then does it really matter? What good is a God that isn't even as nice as a mortal man who lives like a hermit in the woods?

If God is as nice as me then God could never allow anything bad to happen to me. (I'm talking seriously bad). And it most certainly woudln't send me to some stupid place of eternal damnation. It would be an extremely lesser being than me if it even permitted that to happen much less took part in arranging it.

Therefore the only thing I need to have faith in is that God is nicer than me. Anything less isn't worthy of my attention. Even if true there wouldn't be much I could do about it but try to appease the 'demon God'.

But that would be like worshiping Hitler just because you're afraid he'll send you to a concentration camp. If God is like Hitler I'd rather be sent to his eternal concentration camp than to worship him. Such a God would a far lesser being than me, even if it had more physical or spiritual power.

So that's the only think I would put my 'faith' in.

And, of course, if the atheists are right and we just die when we die then it really doesn't matter what we believe.

So either way, there's no need to have faith. Whatever will be will be.

Either God is nice, or God isn't nice.

What you decide to put your faith in isn't going to make much difference.

Abra,

I am not really familiar with evolution at all and I wonder if you can give me the best possible example of the proof of evolution. I don't doubt that creatures change and adjust to adapt to their environment while remaining within the same species. But do scientists have any evidence pointing to changes of one species to another?

If so, does this change happen gradually or all of a sudden? If gradually shouldn't there be an abundance of fossil evidence? If there is, can you give me the best and most convincing fossil evidence?

As you see, I know nothing about the theory of evolution, but I am curious why if it is so cut and dried and obvious why is the controversy still raging other than stubborn religious ideas?

Religion finally had to admit the earth was round, and that the sun is in the center of the solar system. Why have they not admitted evolution is true if it is so iron clad?

ps: Does one species change into another, or does each species evolve in their own line from the very beginning? If so, does science theorize that DNA changes in these cases?

JB