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Author Topic: Science and mathematics end in meaninglessness-nothing but mythology  (Read 18379 times)

Offline bettybop

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The Australian philosopher colin leslie dean argues that mathematics and science have paradoxes at there very heart that collapse them into meaninglessness. Even though they work the explanations as to why they work end in meaninglessness ie contradiction-thus we have a mystery namely seeing they are logically not true how is it they work. Thus there explanations are just myths which will keep changing as time goes on ie from the Bohr atomic structure we have modified that myth to its current mythology

from his book

http://gamahucherpress.yellowgum.com/books/philosophy/Absurd_math_science4.pdf [nofollow]
"The absurdities or meaninglessness of mathematics and science: paradoxes and contradiction in mathematics and science which makes them meaningless, mathematics and science are examples of mythical thought, case study of the meaninglessness of all views"

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In the so called most rational of endeavors mathematics, absurdity or  paradox and self-contradiction goes right to the heart of it. In 1930 the mathematician Hilbert began a program to prove that mathematics was consistent. With the discovery of such mathematical paradoxes as the Burli-Forti paradox, Russell’s paradox, Cantor’s paradox and Skolem’s paradox by early 1930’s as Bunch notes, Hilbert’s program did not succeed such that “disagreement about how to eliminate contradictions were replaced by discussions of how to live with contradictions in mathematics."  Attempts to avoid the paradoxes led to other paradoxical notions  but most mathematicians rejected these notions.  Thus the present situation is that mathematics cannot be formulated, except in axiomatic theory, without contradictions without the loss of useful results. With regard to axiomatic theory, this cannot be proven to be consistent with the result that paradoxes can occur at any time. As Bunch states:

“None of them  [paradoxes] has been resolved by thinking the way mathematicians thought until the end of the nineteenth century. To get around them requires some reformulation of mathematics. Most reformulations except for axiomatic set theory, results in the loss of mathematical ideas and results that have proven to be extremely useful. Axiomatic set theory explicitly eliminates the known paradoxes, but cannot be shown to be consistent. Therefore, other paradoxes can occur at any time [i.e. the Skolem paradox].”   


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Heisenberg notes that “ the strangest experience of those years was that the paradoxes of quantum theory did not disappear  during this process of clarification; on the contrary they have  become even more marked and exciting.”   

In regard to the paradoxes and contradictions of quantum theory  Wick state the orthodox view when he says  “here my opinion of the orthodox quantum mechanics, like Bohr, comes down to the meaning of words. “Classical” and “complementarity”, insult and commendation, are euphemisms; the belief concealed is that Nature has been found in a contradiction. But quantum physicists are not simpletons. In their hearts they know such a claim is philosophically unacceptable and would be rejected in other sciences.” 
Wick notes “ I believe orthodox quantum theorists [slates] reason, consciously or unconsciously, something like this. The microscopic world exhibits paradoxes or contradictions and this fact is reflected in the best theory describing it.”

Now even though quantum mechanics is paradoxical no experiment has contradicted quantum theory predictions and quantum theory is the most successful that has ever existed in science. Thus it is a mystery how our scientific and mathematical theories have the success they do seeing that in terms of Aristotelian logic they are absurd , or meaningless or in other words not ‘true’.



 

Offline rosy

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Depends what you think the point of science and maths are.
Pushing back the boundaries of understanding, sure, it's fun... but actually the reason people get paid to do it is that quantum theroy has lead to all manner of incredibly useful technology. Anything with a laser in it for starters (CD players etc), MRI scans, LEDs, and many, many more banal things that I can't think of because they're so obvious.
Don't know about maths, to be honest I think high end maths is rather dull (probably because I come nowhere near understanding it).

Bettybop, I'd be interested to know your take on this as at the moment all you're doing is quoting Dean (and I think quoting Dean quoting others). What Dean has to say may be interesting, tho' to look at that quote my knee-jerk response is that in terms of meaningless he wins hands down.
 

another_someone

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That Hilbert did not succeed does not prove anything, that Gödel proved he could not succeed is more the issue.

http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems
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In mathematical logic, Gödel's incompleteness theorems, proved by Kurt Gödel in 1931, are two theorems stating inherent limitations of all but the most trivial formal systems for arithmetic of mathematical interest.

The theorems are also of considerable importance to the philosophy of mathematics. They are widely regarded as showing that Hilbert's program to find a complete and consistent set of axioms for all of mathematics is impossible, thus giving a negative answer to Hilbert's second problem. Authors such as J. R. Lucas have argued that the theorems have implications in wider areas of philosophy and even cognitive science, but these claims are less generally accepted.

Gödel's first incompleteness theorem, perhaps the single most celebrated result in mathematical logic, states that:

    For any consistent formal, computably enumerable theory that proves basic arithmetical truths, an arithmetical statement that is true, but not provable in the theory, can be constructed.1 That is, any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete.

Gödel's second incompleteness theorem can be stated as follows:

    For any formal recursively enumerable (i.e. effectively generated) theory T including basic arithmetical truths and also certain truths about formal provability, T includes a statement of its own consistency if and only if T is inconsistent.

« Last Edit: 21/09/2007 12:38:32 by another_someone »
 

Offline Soul Surfer

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This is a reply to both your recent posts

Paradoxes and a degree of uncertainty are part of the universe that clearly exists and functions in a largely understandable and predictable way.  You seem to have some fixation that everything must must have a "meaning" could you please explain meaning in this sense because superficially to me it seems to be completely non essential.
« Last Edit: 21/09/2007 14:36:41 by Soul Surfer »
 

Offline bettybop

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quote
"That Hilbert did not succeed does not prove anything, that Gödel proved he could not succeed is more the issue."
dean shows in another thread that godel is wrong because he used flawed and invalid axioms-even godel ends in meaninglessness
 

Offline neilep

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Should this be in ' New Theories ' ?
 

Offline bettybop

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You seem to have some fixation that everything must must have a "meaning" could you please explain meaning in this sense because superficially to me it seems to be completely non essential.

in terms of what dean is getting at meaninglessness = contradiction paradox

if something is illogical then it = meaninglessness
 

another_someone

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in terms of what dean is getting at meaninglessness = contradiction paradox

if something is illogical then it = meaninglessness

Are you saying that you think that all systems or concepts that include some paradoxical component are meaningless, or are you simply saying that you are applying a very specific (and idiosyncratic) definition of meaningless to mean something which contains a paradox?
 

Offline bettybop

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"Are you saying that you think that all systems or concepts that include some paradoxical component are meaningless, or are you simply saying that you are applying a very specific (and idiosyncratic) definition of meaningless to mean something which contains a paradox?"

the two questions in your statement are really the same statement expressed in different words

axiomatic set theory contains the skolem paradox which reduces axiomatic set theory to meaninglessness

The banach-tarski paradox means that naive notions of space  and time are meaninglessness ie paradoxical or contradctory
by meaninglessness i mean paradoxical or contradictory ie logical not semantic


i am saying all systems end in paradox or contradiction and thus are meaninglessness
 

sooyeah

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i am saying all systems end in paradox or contradiction and thus are meaninglessness

Like a blackhole? Everything breaksdown into meaninglessness and contradicting, the closer you get to the center?

Ok, so thats a problem, what would the solution be? Is a solution possible? Does axiomatic set theory also breakdown into meaninglessness?
 

another_someone

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As someone who is not a specialist mathematician, I will try and give a laymean's interpretation of what I see Gödel as saying.

Mathematics is a language, like any other.  It tries to remove some of the ambiguity of other languages, but essentially is just another language.

In any language that is sufficiently expressive, one can also express nonsensical ideas.  If the language is not expressive enough to be able to express nonsensical ideas, then the language is clearly incomplete in some way.  The fact that you can express nonsensical ideas in a language does not make the language meaningless, but merely proves that it is complete enough that it can even express ideas that are illogical or paradoxical in some way.

As for the Banach-Tarski paradox (which I had not come across before - but then that is what makes life interesting), it is an exploration of the use of the language of mathematics, but in no way does it pretend to be a description of the real world.
« Last Edit: 21/09/2007 17:10:00 by another_someone »
 

Offline Soul Surfer

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Most of the analysis techniques that we use to understand our universe are based on models,  frequently mathematical models, that accurately predict behaviour (to the limits of practical prediction) within their range of validity.  The fact that a particular model is not valid for parameters outside a particular range does not reduce its value as a model in any way and does not render it without meaning. for example.  Newton used great insight to describe the inverse square law and motion under gravity.  The fact that Einstein later showed this to be an approximation that was only valid as long as the velocity was small with respect to the velocity of light does not mean that Newtons laws of motion are not valid for most of the situations that we are likely to encounter every day.

It is always possible to take any idea to the limit where it will break down.  to expect an idea or model to have total validity under all circumstances before it has any value is to insist that the universe is a simple totally mechanistic structure and not the vast complexity that we know it to be.  Such thinking is naive in the extreme and not worthy of serious philosophical discussion
« Last Edit: 21/09/2007 20:05:25 by Soul Surfer »
 

Offline Soul Surfer

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I have taken the trouble to have a look at some of the other work of Colin Leslie Dean and see that he seems to start where Nietzsche left off.  OK it is valid to discuss and think of concepts of the ideal predator who destroys what it cannot consume but this has no place in a world where all the greatest achievements have been made by co-operation and not conquest.  I would also go almost as far as to say he should consider the example of his predecessor Nietzsche bearing in mind that he eventually went insane.

Bettybop I am concered that you are being seduced by a mind that wishes to destroy science.  Science has its failings and its weaknesses but like democracy  (quote: a bad form of government until you consider the alternatives)  you must first find something better before you replace it.
« Last Edit: 21/09/2007 20:22:13 by Soul Surfer »
 

Offline bettybop

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yes axiomatic theory breaks down into meaninglessness due to the skolem paradox
godel is a complete failure what he said is wrong due to using invalid and failed axioms-see the thread on godel

no dean is not destroying science he is regenerating it
because
by seeing it logically cant be true  but it nevertheless still works we have a mystery
how/why does it work when it cant be logically true


 

another_someone

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no dean is not destroying science he is regenerating it
because
by seeing it logically cant be true  but it nevertheless still works we have a mystery
how/why does it work when it cant be logically true

Do you not think it a paradox to suggest that something works and yet is not true.

That it is incomplete is without question - but this is not to say that it can per se be regarded as wholly untrue.

Clearly, there can different views of the truth, and you can certainly suggest different perceptions of the truth, if you are able to put forward theories that do better than the existing theory, but merely suggesting that existing theory is completely broken because it is imperfect is rather like saying a motor car is broken because it cannot fly - if you don't try and fly in a motor car, then it performs the functions required of it, and it is not broken.  You want to fly, you design an aeroplane, but simply protesting that the motor car is broken because it does not fly is not particularly constructive.
 

Offline bettybop

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"Do you not think it a paradox to suggest that something works and yet is not true."
no
the Ptolemaic model of the universe worked for the ancient world but it was not true
the Bohr model of the atom worked but it was not true
read kuhns books "the structure of scientific revolutions" to see many models theories that worked but where not true
take calculus when newton presented it philosophers said it collapsed into contradiction ie it was logically not true

quote from deans book

http://gamahucherpress.yellowgum.com/books/philosophy/irrationality.pdf [nofollow]
    Absurdities or meaninglessness or irrationality is no hindrance [sic] to something being 'true' rationality, or, Freedom from contradiction or paradox is not a necessary an/or sufficient condition for 'truth': mathematics and science examples
"
“Newton and Leibniz developed the calculus…. Their ideas were attacked for being full of paradoxes.”  Newton’s formulation of calculus was self-contradictory yet it worked. Newton worked with small increments going of to a zero limit. Berkeley showed that this leads to logical inconsistency.   The main problem Bunch notes was “that a quantity was very close to zero, but not zero, during the first part of the operation then it became zero at the end.”     These paradoxes where resolved by the time old expediency of mathematics by defining them away in the nineteenth century by Cauchy and Weierstrass.  Up until then calculus was used pragmatically such that “instead of having demonstrations justify results, results were used to justify  demonstrations.” "
 

another_someone

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quote
no
the Ptolemaic model of the universe worked for the ancient world but it was not true
the Bohr model of the atom worked but it was not true

Maybe you and I have different notions of truth.

We cannot know absolute truths - it can be demonstrated that all knowledge must be based upon some assumptions that cannot be proven, and so we cannot say anything is true in absolute.

Given that, can we say that the Bohr model is any less true (in an absolute sense) than anything else we can suggest.  Ofcourse, in a relative sense, modern notions of quantum physics is incrementally more accurate than the Bohr model, but it is wrong to judge either model as being either absolutely false or absolutely true; and I would challenge you to show there can ever be any theory that can ever be shown to be absolutely true.  Thus, is it not rather unfair to label the Bohr model as untrue, as if we can draw a line between a true and untrue model?
 

Offline bettybop

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quote

Thus, is it not rather unfair to label the Bohr model as untrue, as if we can draw a line between a true and untrue model?

so you are going to take a trip to mars based on the Ptolemaic model
 

another_someone

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so you are going to take a trip to mars based on the Ptolemaic model

That is not really the point.

As you say, the Ptolemaic model was sufficient for their time, but they were not taking trips to Mars.  We have incrementally improved on the Ptolemaic model, but that does not make our current model in absolute sense a true model, merely an incremental improvement.  It suffices for our immediate needs, as the Ptolemaic model sufficed for their immediate needs.  In 2000 years time, no doubt they will look at our models with the same disdain that we look at the Ptolemaic model, but each model is merely an incremental improvement upon that which went before.  There are no absolute truths, so to condemn a model and being 'false' merely because it is more primitive than the latest model does still seem somewhat arrogant.
 

Offline macrocosmos

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If as i suspect that space itself is actually infinite, then anything based on mathematical principles is invalid other than as local phenomenon.
In so much as to measure anything and achieve a constant or datum would be impossible in a space that has no finite dimensions and since time itself is dependant on such a relationship between motion, velocity and distance time is truly relative as stated by Mr Einstein
« Last Edit: 22/09/2007 10:12:27 by macrocosmos »
 

Offline Andrew K Fletcher

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Bravo Macrocosmos and welcome to NS

I also believe that space is infinite and that there was never a big bang, or a black hole for that matter. More a continuity of evolving planets and decaying old planets shedding their mass into space while radiating light to other planets as they gradually fade to the point where they cool down and begin to attract mass again while other virgin planets are formed as particles connect with each other in the same way magnets connect to each other.

Infinity does indeed pose many problems for our leading scientists
 

Offline macrocosmos

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Thank you andrew
I enjoy debate that incorporates ontology as well as cosmology.
However my own personal view is that space is indeed infinite with infinite possibility built in.
That a Universe is formed from a mass that is pure matter that exists within space as all things must, yet does not have space as part of its composition, this means that its gravitational force is at its ultimate magnitude. this mass in turn is surrounded by a field of unified energy.
I also believe that Gravity fluctuates periodically although that period is billions of years on a local scale.
As to particular attraction there is a physicist called Helen Fraser who bangs rocks together at simulated zero "G" So far all that she has achieved is more smaller rocks and an increase in localised kinetic force.
 

Offline bettybop

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"As you say, the Ptolemaic model was sufficient for their time, but they were not taking trips to Mars.  We have incrementally improved on the Ptolemaic model, but that does not make our current model in absolute sense a true model, merely an incremental improvement"

thus as dean says science maths are nothing but  mythology
 

another_someone

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thus as dean says science maths are nothing but  mythology

It depends on what you regard as a myth?

Most people would interpret the assertion that something is a myth to imply it has no truth, but if you are regarding a myth as merely an incomplete truth, then I suppose there may be a valid point to that, but it is a point that can be applied to all believed knowledge, since all knowledge is, and of necessity must be, an incomplete truth.
 

Offline bettybop

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"Most people would interpret the assertion that something is a myth to imply it has no truth, but if you are regarding a myth as merely an incomplete truth, then I suppose there may be a valid point to that, but it is a point that can be applied to all believed knowledge, since all knowledge is, and of necessity must be, an incomplete truth."

dean is saying what you take for truth is a myth
science maths has no truth it is all mythology in 100years what you think is truth or partial truth will be just discarded theories of no truth value like  the theories of 100 years ago -all myth
take astronomy
up till this year there where 9 planets now there are only 8 -because pluto is now not a planet-so now the nine planet solar system is a myth
truths are built upon definitions we once had truths built upon the ether theory now all them are just myths
the thing is a present generation cannot see that its truths are myths
 

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