Metamathematics and Metaphysics: - A Modern approach of Moral Education

Metamathematics and Metaphysics: - A Modern approach of Moral Education.

Dr .Jai Shankar Prasad Yadav
   M. Sc(Maths), M.Ed, Ph .D (Education);D.Litt (Education)-R

Jawahar Navoday Vidyalaya Wafapursarma Vaishali,Bihar

Email  : yadav48mathslab@gmail.com;

 Mob   : 09473162311

Metamathematics is a philosophy of mathematics which might be revamping mathematics education and providing a mathematical frame work for studying a wide range of philosophical issue and term revamping means to improve, to patch up, or think about a plan, idea again in order to change in a new way  of teaching learning process ; especially mathematical technique for investigating a great variety of foundation problems of mathematics and logic  among which the consistence problem and systematization of mathematics arising from the  logicistic  and semantic purpose in intuitionist  school  as well as  n- dimensional Hilbert Space , proof theory and Maths lab activity would be correlated from our daily life situations. As proof s are simply finite sequences of formulae. But Metaphysics is deals about the nature of existence, truth and knowledge of human life. According to A.J. Ayer the futility of metaphysics becomes transparent ,if we remember that “ The fundamental Postulate of metaphysics is that there a supper phenomenal reality, “and whatsoever the supper phenomenal reality may or may not be one thing is quite clear ,namely that the statements pertaining  to “this reality” cannot be analyzed  in to simple proposition or protocol statements .The metaphysical problems are due to conscious or unconscious; everything happens according to (Prarabdh) Karma (the result of one’s act in the past) and it concern`s only the out turned ,not the in turned mind. One who seeks his real self will not be afraid of any obstacle. Thought of an obstacle is itself the greatest obstacle-(Raman Maharshi) .The more important formulations of the Univesalization of Metaphysics by German Philosopher Immanuel Kant.  In  Metamathematics  David Hilbert  try to proving  the consistence of mathematical theories  by proving a proportion a theory itself . i.e specially about all possible proofs of theorem in theory  in particular both apposition  A  and  its negations not A Should not be theorems Kleene (1952,p-55) .Morality may be comes from within which means it has to be part of the nature of an individual; It cannot be taught but by livening through tradition of values. Now the basic question`s is who a teenager can be initiated into a living through traditional value? Mukharj Asha(2014).Is theological or religious way of living included here? This is serious question and in modern world we people believe in democracy and secularism and secularism means equal respect to all religions but not having no religion at all.

Introduction:- Metamathematics is a philosophy of mathematics which  might be revamping mathematics education and providing a mathematical frame work for studying a wide range of philosophical issue ; especially mathematical technique for investigating a great variety of foundation problems of mathematics and logic  among which the consistence problem and systematization of mathematics arising from the  logicistic  and semantic purpose in intuitionist  school  as well as  n- dimensional Hilbert Space , proof theory. As proof s are simply finite sequences of formulae. In Introduction to Mathematical philosophy, the great mathematician Bertrand Russell wrote in 1920 “Logic has become more mathematical and mathematics has become more logical...”G.W.Lebniz an outstanding thinker(1646-1716)even dreamt of discovering a universal algorithm for solving all mathematical problems. A great contribution to development of theory of algorithmic problem has been made by .E.L.Post and Soviet mathematician A.I. Maltsev , P.S.Novikov . A.A.Markov and later on algebraic analysis might be A.Tarki and A.I .Maltsev.  Metamathematics provides a rigours mathematical technique and tools for investing a great variety of foundation problems of mathematics and logic among which the consistency problem a only sone. (Jim L Loyd).  Actually absolute reality exists unconditioned by time or space or our states of waking, dream and sleep .So Metamathematics is about logical foundation of mathematics, since mathematics is itself philosophy. The Herbert Spencer lecture, delivered at oxford June 10, 1933 published in Mein weltbid ,Amsterdam :Queridi Verlag 1934  , “The physical world is represented  as a four – dimensional continuum .The modern quantum theory in the form assouated with the names of de Broglie with continuous functions. An atomic theory in the true sense of the world, without localization of particle in mathematical model is perfectly thinkable. The theory of relativity is a fine example of the fundamental character of the modern development of theoretical science and initial hypothesis become steadily more rationale and remote from experience .The theoretical scientist is compelled in an increasing degree to be guided by purely mathematical because the physical experience, of the experiment cannot lead him up to the region and highest abstraction. Thus a growing number of scholars to question the universality absoluteness and perfectibility of mathematics and mathematical knowledge (Davis and Hersh 1980 ,Lakatos 1976,Tymoczko1986,Kitcher 1984,Ernest1997).This is still controversial in mathematical and philosophical circles ,although less so in education and in the social and human sciences. Hersh(1993)and Lakotos(1976).I elaborate further on the persuasive, epistemological role of proof in mathematics.”Boolean algebra in honour of George Boole (1815- 1864) and English mathematician and logician whose book An investigation of the laws of Thought appeared in 1854. The  work of B. Bolzano. Dedekind, and G. Cantor to the creation of new mathematical discipline., the thory of set ,the beauty and force of whose construction and prospects’ of using it in the foundation of mathematics attracted the attention  of many leading mathematician of that time.  In modern mathematics after a departure from the Euclidian tradition during the seventeenth and eighteenth centuries, there has been an increasing penetration of the axiomatic method in to every field especially in digital world or IT sector or computer Education. One of the most recent result has been creation of new discipline , Mathematical logic, Metamathematics, Bisomathematics.  Metamathematics provides a rigours mathematical technique and tools for investing a great variety of foundation problems of mathematics and logic among which the consistency problem a only sone. (Jim L Loyd).  Actually absolute reality exists unconditioned by time or space or our states of waking, dream and sleep .So Metamathematics is about logical foundation of mathematics, since mathematics is itself philosophy.

 

The name of Metaphysics have derived from ancients Aristotle Works, his treatise on first principles Physics and was marked “Meta ta physika” following the physics; the name has now become attached to the science itself.  Halebi Douglas (2013)In “ Life, the Most Precious of Gift ‘’-As In ancient Greece there was the incendiary critic, Socrates, the metaphysician  .Plato, and the polymath and encyclopaedist, Aristotle. Two thousand years passed and the world was given a new gift, the critic Rene Descartes (1596-1650), the metaphysician Spinoza and the polymath, Leibniz;” and metaphysics is philosophy of physics  in which both of them  give a meaning  correspondingly and Agata Sagan , Peter Singer “The moral status of Stem cell “ Metaphilosophy.   The term moral derived from Greek letter “ Ethikos”  “ Ethical” to denote  the typical or Proper behaviour of human beings in society  or in others words moral  principles  that  control or influence of men’s  behaviour especially in careers  and character building  of teenagers . . Let us now turn to take a peep into the main trends of the Indian history and culture  of ancient text  “ The quarrel was mainly over the fundamental s of metaphysics among ancient Jain –Buddhist  thinker and in Upanishad. During the time of Hiuen Tsang six jewels Asvaghosha, Aryadava,Nagarjun ,Kumaralabdha, Asang, Vasubandhu ; and time of the Great seven pals budhism  widely  spread in  Magadha, Bengal , Odhisa,Nepal and in Kashmir; and Modern thinker of Aurobindo Ghosh, Vivekananda, Raman Maharshi, and Japanese Philosopher  and scientist  Dr. Motoyama(1963) . Motoyama has done extensive research using various scientific instrument s (polygraphs and electro- cardiograph)on the yogis in India and abroad.

 Mathematician John won Neumann first introduced the idea of consciousness collapses transforms the quantum wave of possibility by choosing one of its facts that becomes actualised, it prompted in the nineteen seventies the physicist Fred  Alam wolf to create   the evacuative phrase, we create our own reality. For Aristotle, Metaphysics was ontology in which the study of being as being, a science that attempted to set down the common character of ever thing that existed.  Ontology is the division of Metaphysics that deals with the nature of reality and division known as (i) Rational Psychology (ii) cosmology (iii) Theology. German Philosopher Immanuel Kent had three fundamental notions of metaphysics as (1) Self (2) World (3) God. Metaphysics deals about the nature of existence, truth and knowledge of human life and conscientious approach also. Metaphysics exist due to quantum Mechanisms; EUGENE WIGNER Nobel Laureate Physicist who first approaching a quantum traffic light with two possibilities, red and green; at the same time his friend is approaching the same light from the perpendicular road. The counterpart of a metaphysic of morals, and the other member of the division of practical philosophy, would be a moral anthropology, as the empirical science of the moral nature of man. This science would contain only the subjective conditions that hinder or favor the realization in practice of the universal moral laws in human nature, with the means of propagating, spreading, and strengthening the moral principles — as by the education of the young and the instruction of the people — and all other such doctrines and precepts founded upon experience and indispensable in themselves, although they must neither precede the metaphysical investigation of the principles of reason, nor be mixed up with it. For, by doing so, there would be a great danger of laying down false, or at least very flexible moral laws, which would hold forth as unattainable what is not attained only because the law has not been comprehended and presented in its purity, in which also its strength consists. Or, otherwise, spurious and mixed motives might be adopted instead of what is dutiful and good in itself; and these would furnish no certain moral principles either for the guidance of the judgement or for the discipline of the heart in the practice of duty. It is only by pure reason; therefore, that duty can and must be prescribed. The higher division of philosophy, under which the division just mentioned stands, is into theoretical philosophy and practical philosophy. Practical philosophy is just moral philosophy in its widest sense, as has been explained elsewhere.* All that is practicable and possible, according to natural laws, is the special subject of the activity of art, and its precepts and rules entirely depend on the theory of nature. It is only what is practicable according to laws of freedom that can have principles independent of theory, for there is no theory in relation to what passes beyond the determinations of nature. Philosophy therefore cannot embrace under its practical division a technical theory, but only a morally practical doctrine. But if the dexterity of the will in acting according to laws of freedom, in contradistinction to nature, were to be also called an art, it would necessarily indicate an art which would make a system of freedom possible like the system of nature. This would truly be a Divine art, if we were in a position by means of it to realize completely what reason prescribes to us, and to put the idea into practice..

Grin berg in 1993 was trying to demonstrate quantum non locality for two correlated brain .Two people mediate together with the intention of direct communication. After twenty minute, they are separated placed in individual faraday  electromagnetically impression chamber and each brain is wired up electroencephalogram machine at that time alpha wave emits and such frequency may be 8-12 hertz which can be measured by EEG. But Boddha and Raman Maharshi views of science and spirituality as quantum consciousness and we people rediscovered GOD within science.

  Axiological views of Metamathematics:-  Axiology is a part of educational philosophy which deals about moral and aesthetic  values among society and in metatheory .Metamathematics  is  also a scientific enquiry in to the nature of mathematical theories and scope of mathematical methods and scholasticism views knowledge as three storeyed building in which the ground floor is represented by science and the first floor by philosophy and it collates and correlates the fundamental operation of mathematics ;science and establishes principle of universal application and validity. As we people live together in universal math’s lab. Pi is unique mathematical constant which is looks like a rational number in the form of 22/7 but it is not satisfying Quadratic functions  due to contradiction this universal constant kept in irrational number in other words   its value cannot be  expressed exactly in the form of numerator and denominator  ;  On earth here & there, everywhere looks like a   lab equipments in the form of circle, circular  objects, ball , Sphere, elliptical Path , sun, moon, spiral galaxy   or  total galaxy ( As per Sukanya chkakrabarti  10 24  stars Nasa – Scientist) ) in others words  Pi Lab equipments available In your class room, bedroom, walls, doors, fans, computer room, learning temple,  various such places, shape  and design of everything all these things developed aesthetic model of metamathematics.   In the comparisons of universe our earth is likely to dust ,particle which is moving around elliptical or circular path in solar system and seems to be spherical, and  have to  constant diameter , circumference. Mathematically the ratio of circumference and diameter of circular path is called pi or  which is always constant and numerical value of  is equal to 22/7 or 3.141592.... ; Now a day 14th march celebrated as  day every year; which is the sixteenth letter of , Greek alphabet corresponding to the English P, Pi and Greek pronounced it pie.. दृश्य  दृश्यन्ते दर्शना-ज्ञानदर्शन चारित्रोपचारा.... Axiological aspect of Maths lab education in the light of Higgs –Boson: the “God particle” reported dislike of the term is understandable. Science and philosophical atheism –the denial of God not out of sense of personal grievances. The proof of the Higgs -Boson is only the beginning of a new search of what lies further in the infinite mystery that is, the cosmos. Singer peter (2011) treated ethics entirely independent of religion , some theist say that ethics cannot  do  without  religion because the very meaning of good  is nothing other than “what God approves”. According to National Research council 1989 ,USA ,page No-70 ,”As we need standards curricula so we need standards for assessment .we must ensure that test measure what is of value, not just  what is every  to test. If we want students to investigate, explore, and discover assessment, must not measure just mimicry mathematics. By confusing means and ends, by making testing  more important than learning present practice hold`s today’s  students hostage to yesterday `s mistake Actually mathematics is a science of structure, order and relations and that has evolved from counting, measuring and describing shape of objects. It deals with logical reasoning and quantitative calculations. The Orphic myth of Zeus “Who swallowed phanes, the offspring of the Great world egg and then formed the universe within himself”, also closely resembles the tenth book of Manu Dharma Sastra where the supreme soul produced the golden egg Brahmand by thought and appears as Brahma.

 In Vedic mathematics``Sunyam Samya Samucchaye”.

``Anurupye Sunyamanyat.”

As we know that the number of counting is a natural number which is co-related to the nature giving the shape of these numbers. Indians says zero by circle and one be attached by line with circle. That is binary operation system (0,1) which controls digital world of computer system. Charles Babbage (1791-1871) an English mathematician is called father of computer science. Actually a computer is also based on two digits 0 & 1 that is binary operation itself by this 0, 1 that God and nature in the form of Mulprakrati and  Purush prakriti and zero’s paradox  as metaphor of the met-mathematical times.

त्यागोपा दान शून्य ---तत्वार्थ सूत्र

अत्र च शिक्षितान;.....यदुक्तं मार्यमहामेघे- निरयगति चितनित्यसमाधान शिलाश्वच-----------

चरमविज्ञानं चरमविज्ञानैन शून्यम. कर्म कर्मणा शून्यम. प्रथमविज्ञान प्रथमविज्ञानेन शून्यम.च्युतिश्चयुत्या . शून्या..कर्मणा चाव्न्ध्यता प्रज्ञायते ; विपाकस्य च प्रतिसंवेदना . ‘शिक्षा – समुच्चय’’..­पृष्टसंख्या-१३५  (बी -२५४ ).This siksasmuccaya is founded is founded translated in Tibeatan(Tanjor ,mdo XXXI) and it prepared by Ye-Ses-Sde-during 816 and 838 A.D .

 Conclusion:-Metamathematics is really philosophy ;especially area covering  with mathematical logic and provide us  semantic approach of enrichment  of Mathematics Education ,who also might be given emphasis on Hilbert space, Axiomatic Set Theory ,Boolean Algebra ,Topology, Paradoxical concept of mathematics and utilise its in computer application as well as axiological views of mathematics laboratory. Moral law tells us what he ought to do existence consistency our consideration; it gives us a will that a good will for it is not based on desire and impulse but on moral reason; if man is free who is morally free and who enjoy the autonomy of moral freedom and this freedom might be qualified respect for others and controlled by universal metamathematical  lab. Ultimately we people must be accepted that everything which happens from our spiral galaxy to atom or God –Particle does not move without prior permission of the divine will.

References:-

  1. E.A.Palyutin; Yu.L..Ershov(1984) : Mathematical Logic ,Translated by from the ,Russian By Valadimir  Shokurov ; Mir Publishers; MOSCOW; page no:- 9-14,52,198-199, 234,237,
  2. Bhandari.D.R.(1937): History of European political Philosophy published by : The Banglore  Printing and publishing co.ltd.Mysore Road  Bangolre -18, (1986) page no. 439.
  3. Courant Richard, Robbins, H, S. IAN (June 1995) : What is Mathematics? Oxford University Press, UK page no – 274-276.
  4. .  N.A.Mohan Rao( 2014):Concept of intermediate reality: The Mountain path :April -  June 2014 ,page no71-81, and Alan Jacobs July –Sept 2012 page no09-14; Sri Ramanasramam ,Tiruvannamalai, Tamil Nadu -606603

 5.       Singer Peter (2011) Practical Ethics, Third edition page no.03, 33 Cambridge University                Press.

6         Yadav .J.S.P (2014): Revamping Mathematics Education: Active learning through lab activities, IOSR_(JRME)  e-,ISSN :2320-7388,p-2320-737X volume 4 Ver. II(Jul-Aug -2014),P.P 26-29  ,www.iosrjournals.org , Editor .Dr. Rachel Granger Ph.D, UK.

7         Yadav J.S.P(2013),Mathematics Laboratory :Philosophical background  ,44(2) :212-215, Editor  :Singh  R P. Indian Journal of Psychometric and  Education(IJPE) Patna ,Publisher :Indian Psychometric and Educational Research Association, Raman Tower Sanjay place ,Agra-2

8         Yadav.J.S.P(2014):Globalisation of Maths Lab Education: Urgent Need of Nationwide Pedagogy of  Mathematics Teacher, IJPE;Patna (ISSN:0378-1003)  45(1):P-P 33-36 and 45(2)

P-P 135-138.

        9. Yadav .J.S.P (2014):   Revamping  - Lab : Psycho-Lingua,(ISSN:0377-3132) 2014,44(2): 125- 128  Publisher  Psycho- linguistic Association of India(PLAI)6/5,H.I.G.Flats,Sanjay Place,Agra -     282002.

10.Htt:www.Sorities.org  ;SORITES,  ISSN 1135-1349

s11. Immanuel Kant (1785) General Introduction to the Metaphysic of Morals Source: Steve Palmquist’s web site; Translated: by W. Hastie.

12. बुद्धिस्ट- संस्कृत ग्रन्थावली-११,शान्तिदेव विरचित ‘’ शिक्षा – समुच्चय’’ तिब्बती अनुवाद (८१६ -८३८ ई) पेज-१३४,१३५,१९७-२०६ ,मिथिलाविद्यापीठप्रधानेन  प्रकाशित (१९९९ ) दरभंगा ,बिहार .

Submitted by: Dr Jai Shankar Prasad Yadav

Ph.D in Mathematics Education

At+ PO  :  Kabirchak, Beside Engineering Gas Go dawn ,Vai- Lalbag  ,Distt-Darbhanga,Bihar-846009,Mobile no.09473162311,Email: yadav48mathslab@gmail.com.

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