What is an axiom? can any theory based on axiom solve all that science is looking for?

[neil2366]

dictionary shows Axiom can not be disproved. do we need any arbitary derived constant or experimentally measured value or emperical derivation to form theory if theory is based on axiom. Is there any theory out there based on axiom?

 

 

[ydoaPs]

Axioms are assumptions of formal systems. They are true within their system by definition. They may or may not, however, accurately reflect reality. The fun thing, though, is we need not concern ourselves with reality when making formal systems such as mathematics or logics. The axioms along with the rules sort of define what is true in that system. Formal systems are created, but the relations that must hold for the system to be consistent are discovered and the axioms and rules used to create the system determine what those relations are.

 

Now, there is another type of assumption that you might be thinking of called a "premise". Premises are the foundation of deductive arguments. Premises can be either true or false and the arguments in which they occur can be either valid or invalid. If the premises are true and the argument is valid, we say the argument is "sound".

[neil2366]

"The fun thing, though, is we need not concern ourselves with reality when making formal systems such as mathematics or logics" -- if theory based on mathamatics & logic brings accurate result what science has discoverd through practical approch ,without using any arbitary constant or emperical value , for all phenomena from within the axiomatic principal ,valid? If theory on axiom proves everything what sciencehas discoverd so far and much more where science is having questions ,without practicla approch,consider valid? sure it should have practical varificatin after that.

[ydoaPs]

"The fun thing, though, is we need not concern ourselves with reality when making formal systems such as mathematics or logics" -- if theory based on mathamatics & logic brings accurate result what science has discoverd through practical approch ,without using any arbitary constant or emperical value , for all phenomena from within the axiomatic principal ,valid? If theory on axiom proves everything what sciencehas discoverd so far and much more where science is having questions ,without practicla approch,consider valid? sure it should have practical varificatin after that.

 

Science itself is not a formal system. It is an empirical process which utilizes several formal systems such as deductive logics, calculus, and set theory.

[Ronald Hyde]

I don't know who he is or what he does, but ydoaPs is dead right on this one. I would just add that as much as possible, good Physicists try to turn Physics into a formal system, so

that axioms will become true laws of Nature.

[neil2366]

This is quite constructive explanation indeed for oneself from both of you and perhaps for many on this forum.Ronald indeed put in right words.Now the formal system so far been used don't have all questions answerd form scientific point of view and we are all left with many anomalies unanswered ,aren't we? like pioneer .dark matter,red sift ,neutrino faster than light etc..etc. list goes down to more than 30 anomalies in wikipedia and many scientific journals. so can we say that something is seriously missing in formal system so good physicist are not be able to turn physics where axiom can become true laws of nature? One has try to understand Nodal and few others talked about axioms ,but couldn't grasp them.

[ydoaPs]

neutrino faster than light

 

The only anomaly there was a loose cable. The neutrinos weren't superluminal.

 

I don't know who he is or what he does, but ydoaPs is dead right on this one.

 

I'm a former nuclear machinist mate and current philosophy student at Purdue with focus on formal systems, philosophy of science, consciousness, and language. I've also been on this site since 2004.

[studiot]

can any theory based on axiom solve all that science is looking for?

 

No, you should study Godel.

[ydoaPs]

No, you should study Godel.

 

Perhaps you should study Gödel. Presumably, you're talking about his result which is oh so often mangled by those who don't know really anything about formal systems. What Gödel showed is that certain formal systems (like most of mathematics) cannot be both consistent and complete. A formal system is said to be consistent iff all provable theorems are true. A formal system is said to be complete iff all true theorems are provable. So, Gödel flipped the world on its head by showing that you can prove things which are false in most mathematics ior you cannot prove all true things in most mathematics. The part that is so often left out is that the proving he was talking about is proving things from within the system. We need not limit ourselves to the confines of a formal system to prove things about the system. In fact, it's often far easier proving things from outside the system. For instance, it's extremely difficult to prove just about anything about Smullyan's Machine from within the system. We need to work from outside of the system using things like conditional proof, indirect proof, mathematical induction, Modus Tollens, etc. In fact, Gödel got his result from working outside of the formal systems he was studying!

[studiot]

As I understand it, he was saying that you can't use the axioms to prove themselves.

 

So if you have axioms you have, perforce, something unproven.

I am taking unproven to mean not explained or derived from something else.

 

Is this not so?

Edited September 20, 2012 by studiot

[ydoaPs]

As I understand it, he was saying that you can't use the axioms to prove themselves.

 

That doesn't really have anything to do with Gödel. As I said before, axioms are automatically true within the formal system.

[imatfaal]

My first engagement with Godel (like many others) was Godel Escher Bach - by Douglas Hofstadter, it's a non-technical romp through recursivity, self-reference, and (formal) systems in logic music and art. I am not sure the academic logician would approve of it - it is very light-hearted at points - but for a layman it is a superb introduction and a fine read.

[Dekan]

Is there any theory out there based on axiom?

 

Isn't there one modern theory which appears axiom-based - the Theory of Relativity? It seems to rely on this axiom:

 

That the Laws of Nature should be the same, for all observers who move with constant speed relative to one another.

Which produces, as a kind of consequential axiom: That the speed of light should be the same for all such observers.

So Relativity Theory looks at heart - axiomatic. It started from an intuitive idea of what should be the case. Later it got apparent support from facts - like observations of solar eclipses, an explanation of the anomalous Mercurian orbit, and in our time - workability of GPS satellites.

 

But these facts didn't generate the Theory - it came from an axiom.

[neil2366]

Friends,

 

question is stiil there that ANY theory based on axiom which is not using any arbitary constant,emprical value,experimantal value and still produce result with great precision, what science has so far produce through experiments & arbitary constant . Also It can apply to all unsolved anomalies and unify everything eternaly from axiomatic principal.Here are some points on axiom based theory Sankhya(means logic of counting/process of counting).Pls kindly look at it objectively who are interested.

 

 

 

ankhya, as a holistic theory is correct and complete whereas Science, comprising Physics and Cosmology has no answers to the anomalies that have been found by its Physicists and Cosmologists?

 

1. Sankhya is based on axioms that are precise whereas Science is based on experimentally detected inputs that have built in errors.

 

2. Sankhya uses time, as the interval of an axiomatic cycle, which enables the derivation of parameters accurately and proportionately, while in Science all parameters are defined in an arbitrary manner and leads to errors.

 

3. Sankhya treats all phenomena exactly as humans experience events locally, whereas Science depends on created hypothesis based on detected evidence.

 

4. Sankhya depends on a logical and unified model of phenomenal activities that are intellectually acceptable whereas Science creates models based on experimental findings and creates theories to unify these.

 

5. Since Sankhya has a intellectually defined model it is able to treat detectable and hidden phenomena accurately whereas Science depends on detection first , hidden phenomena get treated as anomalies or unexpected behaviour that cannot be defined by its theoretical findings.

 

6. Axiomatic derivations based on numerical logic in Sankhya gives precise and definite results always whereas in Science experimentally formulated numerical logic has to be equated by creating arbitrary constants.

 

7. As Sankhya depends on axiomatic logic to understand phenomena it is able to predict experimental results accurately and hence is effective, whereas in Science there is always uncertainty that makes it depend on statistical verification as measure of accuracy.

 

8. In Sankhya, the axiomatic base dependant on a single variable as cyclic time provides verifiable and dependable internal numerical theoretical proof whereas in Science it is entirely dependent on observable experimental detection from which a theory is deduced and has no definite or alternate method of verification except through statistics.

 

9. Sankhya theory based on axioms is objective and its combinatorial mathematical logic enables the derivation of both maximum and minimum limits, which defines its limiting boundaries with certainty whereas in Science the observable experimental limit severely curtails its ability to be precise, certain and complete.

 

10. Sankhya being axiom based and complete with internally generated proof it forms a permanent theory whereas Science has necessarily to change continuously depending on its experimental findings and the consequential evolution of it’s dependent theoretical logic.

 

[imatfaal]

!

Moderator Note

Neil - if you wish to discuss the school of Hindu Philosophy please do so in the philosophy forum. If you wish to demonstrate the power of Sankhya to correctly predict real world events then do so in Speculations. This is the physics main board and we restrict these boards to knowledge gained through the application of the scientific method and to hypotheses that flow from that knowledge.

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[neil2366]

This is an attampt for everyone to objectively look into without any conclusion and points mentioned are applies to axiomitic logic .Also let me correct the error one has made you can look at it at original source. http://www.kapillavastu.com/index.html?r=20120707024127

http://s1.webstarts.com/Sankhyakarika/index.ht

 

The only anomaly there was a loose cable. The neutrinos weren't superluminal.

 

 

 

 

 

Cern Experiment: Detected Neutrino velocity is greater than light speed.

 

The conclusion arrived at from that experimental result is correct. Neutrinos must transmigrate faster than light or electromagnetic wave photons, due to axiomatic reasons. Neutrino mass is 9.5287340542E-35 kgs or 53.4522547393 EV. Its frequency of oscillation is 2.9657596692E+8 at a meter wavelength / sec and is an axiomatic rate of harmonic oscillation. It cannot change. Seven Neutrinos accelerate and radiate as a simultaneous wave front forming the magnetic state as the wave crest that then creates the photon with 374.165 EV. The Planck’s constant h = 6.6260755E-34 is 371.69 EV of equivalent energy carried as radiation in seven spectral ranges. Hence 374.165 – 371.69=2.47 EV, which is the work function involved in the accelerative process. It is measured as (1-.259921) x 2.47=1.8283 EV.

 

On an accelerative interaction the Neutrino stream acts as the advanced wave function and the photon subsequently accelerates as a set of retarded waves of seven energy levels thus losing 2.47 EV. The Neutrino mass in the hydrogen spectrum is in resonant balance and its EV value of 53.45 is measured at the 2

 

 

nd harmonic oscillatory boundary across a gap of .25991 (as ratio of its radius) at a resonant level of 98/100 and hence 53.45 x .98 /0.259921 is 13.605 EV. When the acceleration of Neutrinos takes place as a photon the gap of .259921 is traversed by it as a dense wave front and is therefore slower. The compressed part of the wave has a frequency of 172200 and the expanded wave front has 1722. So the ratio of the difference is 100. The gap covered by the ‘to and fro’ motion of the oscillating wave front then has a value of (100 x .98)/.25992= 377.037 which is the impedance ratio value measured in space. Hence the total displacement covered as a ratio per oscillatory cycle is 1.259921 of radius and so the ratio of difference between advanced and retarded wave front is 100 × 1.259921 = 125.9921. But as 7 neutrinos accelerate together simultaneously or merge at the crest, the value reduces to 125.99/7 =17.9988. Therefore the photon will be slower by 17.9988/ 2.9657596692E+8 = 60.68 billionths of a second. Hence in 730000 meters (tunnel length) it would be delayed by 0.1478 billionth of a second and that would the detected delay.

 

Further Neutrino oscillation rate is axiomatic in space at 296575966 cps whereas light is 299792458 cps at 1 meter wavelength. The difference is exactly 1.010845 or log 1/213.459 as the ratio of solar radius and earth orbital radius. Hence that provides proof for the composition of space as a real continuum and not an empty or vacuous entity. The advance / retard potential ratio is given by the neutrino beam as 1.010845 or the blue shift in the frequency of EMW transmigration rate from 2.9657596692E+8 to 2.99792458E+8 as measured by Michelson Morley etc. Hubbard too saw this difference but interpreted it as a red-shift for he compared the observed frequency with 2.99792458E+8 (Michelson) and not the axiomatic rate of the Neutrino at 2.9657596692E+8 which actually provided the advanced potential. Feynman and Wheeler anticipated the advanced / retarded concept and Narlikar &Hoyle too saw it as the base for an absorber of energy in space

 

The Pioneer anomaly too (for the same reason) is 0.259921/299792458 = 8.67 E minus 10 . Hence the distance covered by the EMW waves from spacecraft will be shorter by 1 meter in 36.15 years of orbital time. Pl see web site below for proof in Sankhya theory. http://sankhyakarika.webstarts.com/?r=20120214083051

 

G Srinivasan. Kotagiri.

 

 

http://sankhyakarika.webstarts.com/?r=20120214083051 http://sankhyakarika.freelancereporter.org/ http://www.mullerpower.com/Srinivasan/Srinivasan.php? http://www.magnetricity.com/Srinivasan/Srinivasan.php

 

 

 

 

I'm a former nuclear machinist mate and current philosophy student at Purdue with focus on formal systems, philosophy of science, consciousness, and language. I've also been on this site since 2004.

[ydoaPs]

It's a fact that neutrinos aren't superluminal. There was a loose cable. They fixed it, ran the experiment again, and got a velocity <c. You're wrong.

[neil2366]

respectfully and in all honesty post is not about proving anyone wrong or right but for one to share, unlearn & learn.All mathamatical numbers are derived through axioms with accuracy and verified and perhaps provide some clue to understand objectively more about axioms. Also shows how seven neutrino when radiate simultaneously becomes photon. This is just to point out if anyone is interested in looking further to axiomatic principal has derived all values & more from within , without using experimental input or any arbitary constant.

 

http://www.kapillavastu.com/index.html?r=20120707024127

http://s1.webstarts.com/Sankhyakarika/index.html.