This is an analysis of those schools of thought and endeavour, which formulate and develop theories and paradigms, and one of its purposes is to highlight source(s) of dissonance, whether cognitive or unknown, with special reference to the Reciprocal System of Theory.
Essentially where you read Analysis, Analyst & Analytical you may assume it encompasses any row of three items in TABLE 1 below.
| ALTERNATIVE WORDS OR PHRASES TO SUBSTITUTE IN TEXT FOR A SCIENCE | ||
|---|---|---|
| DISCIPLINE | PRACTITIONER | PERTAINING TO: |
| ANALYSIS | ANALYST | ANALYTICAL |
| THEORETICAL PHYSICS | THEORETICAL PHYSICIST | THEORETICAL (PHYSICS) |
| PHILOSOPHY OF SCIENCE | PHILOSOPHER OF SCIENCE | PHILOSOPHICAL (SCIENCE) |
| ALGEBRA | ALGEBRAIST | ALGEBRAIC |
| SCIENCE | SCIENTIST | SCIENTIFIC |
| COSMOLOGY | COSMOLOGIST | COSMOLOGICAL |
Table 1
1) THE PRACTICAL SCHOOL
Where pragmatism, realism, functionality and/or experience are the order of the day and no imagination is necessary.
The science is treated as a mental tool, by the means of which one applies rules, and there is a concomitant ease of operation.
INADEQUACIES
As a consequence of the above conditions, it is found to have limited powers, both within and without certain fields of endeavour, where it can be found, in some cases, to be useless.
A rule used successfully in some cases cannot be used in all cases.
The science can fail to produce a discovery in another field of science, when there was strong reason to believe it should have done so.
e.g. Quantum Theory
2) THE PHILOLOGICAL SCHOOL
Where the predominant thesis, supposition and/or assertion is based on the structural, syntactical and semantic analysis of the language, in which the scientific discipline is couched.
Hence it is looked upon as a language, that should produce symmetry of expression and symmetry of equations and formulae.
INADEQUACIES
As a consequence anomalies appear, such as exceptions, which break the symmetry of the syntactic, thereby disturbing the erstwhile simplicity of the notation.
This accentuates a feeling of helplessness in the analyst for this approach, when he attempts to write some equations or formulae, since great care is necessary, thereby highlighting the non-universality of the symbolism.
3) THE THEORETICAL SCHOOL
Where musing, reflection, speculation, hypothesis, conjecture, inspiration, deliberation, premises, deduction, induction, prediction, supposition, revelation, circumspection, axioms, propositions, theorems, inference, assumption, precepts, principles, conclusions, maxims, laws and rules are the order of the day.
There is clarity of thought, which in itself allows the theorems to be formulated and analysed.
INADEQUACIES
There is often a clouded issue, effecting clarity of thought.
Anomalies appear, which are dissonances, cognitive or unknown. There seems to be irreconcilable contradiction, thereby threatening one's belief in, and reliance on, either.
e.g. Two Theories of Relativity, (General & Special), and Quantum Mechanics cannot be united as one, even with Super-String Theory.
There can be a tried and true Rule, that always works, but can not be proven nor fully understood.
When a theorem is so esoteric in its presentation, that it does not lead to intuitive predictions by induction nor in any other way can one look beyond it.
| ANALYSIS (OR ANY OTHER MATHEMATICAL SCIENCE) | ||
|---|---|---|
| PRACTICAL | PHILOLOGICAL | THEORETICAL |
| Instrument | Language | Contemplation |
| Ease of operation | Symmetry of Expression | Clarity of Thought |
| Rule | Equation or Formula | Theorem |
| IMPERFECTIONS | ||
| Limited Power | Anomaly may be presented | Clarity of Contemplation obscured occasionally |
| Occasional limited application of rule within a given field | An occasional exception disturbs simplicity of Notation or symmetry of Syntax | Occasional appearance of Contradiction from reasoning, or complexity which puts strains on validity |
| Non-ability to use it in another field on some occasions | Non-universality of Symbolism sometimes apparent | Occasional inability to prove and/or understand Rule, despite its applicability or usefulness |
| Sometimes induction cannot lead to intuition nor can there be extrapolation | ||
Table 2
No scientist, cosmologist, philosopher of science, analyst, nor theoretical physicist belongs exclusively to any one of these three schools, so as to be only Practical, Philological or Theoretical. Language and thought interact, while Theory and Practice help and improve each other.
No one can be so merely practical that he eschews the beauty of the language, in which his rules are expressed, and does not care to know the reasoning, which deduces or induces them.
No one can be so simply philological an analyst, that he divorces his mind completely from entities and existents, and that he will not at some time leave the ethereal domain and ponder on the meaning of his expressions and how to apply them.
No one can be so purely theoretical or so exclusively devoted to thoughts and to the contemplation of theorems in Analysis, as not to feel an interest in its notation and language, its symmetrical system of signs and the logical forms of their combinations. Nor will he fail to prize those practical aids, and especially those methods of research, which the discoveries and contemplations of Analysis have given to other sciences.
Summarily, without the intention of polarising analysts, but to distinguish them one from another, it is, perhaps, correct to say that every analyst and each analysis has a leaning towards one or other of these schools, according to the individual partiality of the practitioner, thereby marking the work with the stamp of the individual, according to the particular admixture of schools to which he subscribes.
These prefatory remarks are important to prepare and aid the reader, that he may perceive more easily and distinctly what the design of a particular paper is and to what the author aspires, or at least wants, to accomplish.
Most papers on the Reciprocal System of Theory are Theoretical, in the sense already explained, as distinguished from what is Practical, on the one hand and what is Philological on the other. Their professed aim is to improve the science predominantly and not the art nor the language of the analysis. The imperfections, sought to be removed, are confusions of thought, and obscurities or errors of reasoning; not difficulties of application of a scientific tool, nor failures of symmetry of expression.
The fact that confusions of thought and errors of reasoning can still pervade the most honest paper and thereby cloud a particular analysis is, no doubt, always in mind to be eschewed by the authors.
There are some areas of research, in which properties and truths are never in doubt, there are merely different ways, perhaps clearer, ingenuous, and superior, to demonstrate them. Hence in those cases there is neither ambiguity nor confusion of thought and no reasonable ground for doubting those truths.
However in many sciences of today scepticism is not unusual, to say the least, and intra-disciplinary factions abound, some examples being tabulated below in rows.
—————————(IGNORE COLUMNS)
| INTRA-DISCIPLINARY FACTIONS | ||
|---|---|---|
| WAVE THEORY OF LIGHT | PARTICLE THEORY OF LIGHT | |
| QUATERNIONS | VECTORS | |
| UNIVERSE OF ENERGY | UNIVERSE OF MATTER | UNIVERSE OF MOTION |
| VORTEX THEORY | GEOCENTRIC THEORY | HELIOCENTRIC THEORY |
| NEWTONS THEORY | RELATIVITY | RECIPROCAL SYSTEM |
| GRAVITY FIELD | GRAVITY WAVES | RECIPROCAL THEORY |
| DETERMINISM | INDETERMINISM | |
| NUCLEAR MATTER STARS | RECIPROCAL THEORY | |
| MAGNETIC THEORY | RECIPROCAL THEORY | |
| ELECTRICAL THEORY | RECIPROCAL THEORY | |
| BOHR'S ATOM | QUANTUM THEORY | |
| SIMPLE HARMONIC MOTION | BIROTATION | SIMPLE VIBRATORY MOTION |
| 3-D UNIVERSE | 4-D SPACE-TIME CONTINUUM | RECIPROCAL THEORY |
| POPPER'S THEORY | LAKATOS' THEORY | RECIPROCAL THEORY |
Table 3
Sometimes the question arises, are we substituting or compromising contemplation, (speculation, theorising), and intuition, (inspiration, instinct), for a gain, only of skill or elegance?
As mentioned earlier the Reciprocal System of Theory was formulated by Dewey Larson as a Theoretical Paradigm, predicated on:-
- A Postulational Base, which, in the first publication was couched as `Four Postulates', but later re-analysed and reworded as `Two Preliminary Assumptions, a Definition and a Postulate'.
However, this theoretical construct had to be couched in a language, so the Philological aspect was found to be purely linguistic, being the English language, since there is no Mathematical expression in this base.
This sets it apart from Relativity, which leaned heavily upon its mathematical definitions, as do most other paradigms for the Physical Universe.
- A Syntactic, which develops this language, by logical deduction, into the assertions and theorems of the Paradigm.
Again, English is the main tool to obtain results, although Mathematics does enter into many of the findings.
This displays how the absence of Mathematics in the Postulational Base does not preclude its entry into the Syntactic, BUT it also highlights a disadvantage. A Paradigm, which includes Mathematics in its Postulational Base, is much easier to develop through its Syntactic, and has a better chance of being regarded seriously and becoming accepted.
This is the area where we students of R.S. should be looking to improve its wider acceptability, since the apparent incongruity of mathematics appearing for the first time in the Syntactic will be removed thereby.
- The Semantic, which relates this inductive theory to observations.
This, then, should give the theory the ability to predict other observations, confirming the theory, providing the theory does predict, as expected.
Obviously this is the Practical aspect of the theory, completing the admixture of the three headings in Table 2.
Summarily we have no room for factions within ISUS, since such a `luxury' would be devastating in its destructive power.