FIRST INVESTIGATION INTO A MAJOR CLASS THEORY OF THE POLYCALCULII NATHAN COPPEDGE UNDERGRADUATE, PHILOSOPHY DEPARTMENT SOUTHERN CT STATE UNIVERSITY I have previously been tutored by professors and a rocket scientist. The current work is an effort to realize the opportunity of this outstanding largely informal education. However, let it be understood that this is a work of philosophy of science. This paper builds on previous work, especially insights into physics, mathematics, medicine, and recently chemistry. It is part of a larger effort to create knowledge that is coherent and comprehensive. FIRST INVESTIGATION INTO A MAJOR CLASS THEORY OF THE POLYCALCULII ABSTRACT: This paper will investigate the general class theory of polycalculii, and theory originally developed and introduced on the Quora platform as a kind of philosophy of logic and mathematics. The ostensible goal at minima will be to demonstrate the exclusion of an array of class types which edicate the theorem of the polycalculus. The polycalculus is a general method for deriving equivalent calculus’s other than the traditional intelligent calculus. The domain of this discussion is not only mathematics, but also logic, philosophy, and philosophy of science, as well as philosophy of the foundations of mathematics. KEYWORDS: Calculus, Calculii, Polycalculus, Inference Engine, Higher Mathematics, Logic Theorems, Theorem-Proving, Theory of Calculation, Theory of Logic, Logic-Proving, Modes of Inference I. MISSION: The goal of this brief project is to demonstrate a variety of coherent modes of inference alluding to the expandability of mathematics and the capacity to generalize mathematics over a relatively larger logical domain. The central problem will be to elucidate a central ‘motive process’ to calculation. A motive process shall be in this case simply a more fundamental process that still allows for the respective tools of each constituent calculus without eliminating functions of any calculus. However, the full proof that functions have not been eliminated is beyond the scope of this paper. In order to be parsimonious, there will be an operant insight implicated in each calculus that its fundamental operability is retained. Each calculus (or LOGIC) will be seen as representing a fundamental operability of a distinct type, although this distinct type will not always be elucidated except by mentioning the type of calculus. II. STRUCTURE / DEFINITIONS Polycalculus was previously disclosed to have the following general structure: Physics Number Theory Qualified or Un-Qualified Thus, it is obvious that with the binding assumption that this is a correct operation, providing a permutation of appropriate elements in each part of this series would lead directly to a complete list of calculi. One other assumption assumes that each of the three parts contains all possible elements within its part, or that the mode of the part within the overall structure of calculus is understood. One should assume at this point that the formula is accurate in order to deduce the appropriate results. III. REPRESENTATION: Part 1. Physical Calculus. This may be seen of consisting of the exclusive elements of experience, which may be taken to be Infinity, Relativity, Complexity, and Infinitesimal Calculus. Part 2. Number Theory. This may be seen as consisting of Set Theory, Cardinals subsumed within Rationals, Proportional Trans-Finites, and Extended Numbers. Part 3. Qualified or Unqualified This is the distinction between Intelligent and Literal Calculus, implicating an element of calculus in both cases. Literal Calculus is for example the limit as it approaches zero, the anti-derivative, the normalized wave functions of information theory, and the change of a system (t) in chaos theory. Intelligent Calculus is for example, intuitions on advanced physics, medicine, and chemistry. The result of the permutation is 4 X 4 X 2 = 32 Calculii. Calculus 1: Infinite Set, Intelligent Applications of categories, complexity, algorithms, paradigms. Calculus 2: Infinite Set, Literal Exhaustive processing, exclusion principles, evolutionary processes. Calculus 3: Infinite Cardinals Subsumed Within Rationals, Intelligent Mathematical intuition, I.Q., functional heuristics, adaptogenius. Calculus 4: Infinite Cardinals Subsumed Within Rationals, Literal Knowledge of limits, Laplacian, Gauss curves, chaos theory, probability. Calculus 5: Infinite Proportional Trans-Finites, Intelligent A Priori, Deterministic, Ethical, Aesthetic. Calculus 6: Infinite Proportional Trans-Finites, Literal Extension, Variation, Creativity, Repetition. Calculus 7: Infinite Extended Numbers, Intelligent Absolute, Complete, Representative, Theoretical. Calculus 8: Infinite Extended Numbers, Literal Direct, Political, Magic, Natural. Calculus 9: Relative Set, Intelligent Elemental, Deductive, Formal, Semantic. Calculus 10: Relative Set, Literal Artistic, Figurative, Strategic, Physical. Calculus 11: Relative Cardinals Subsumed Within Rationals, Intelligent Large Sums, Economics, Prophecy, Number Theory. Calculus 12: Relative Cardinals Subsumed Within Rationals, Literal Variables, Arithmetic, Spatial Reasoning, Conjunction. Calculus 13: Relative Proportional Trans-Finites, Intelligent Meta-Mathematics. Calculus 14: Relative Proportional Trans-Finites, Literal Vector Analysis. Calculus 15: Relative Extended Numbers, Intelligent Medicine. Calculus 16: Relative Extended Numbers, Literal Conjectural Analysis, Meditation, Un-Attachment, Parsimony. Calculus 17: Complex Sets, Intelligent Invaluable Proof & Refutation, Computational Inference, Noble Deduction, Cutting the Gordian Knot. Calculus 18: Complex Sets, Literal Problematics, Stating the Problem, Case Studies, Prior Art, Critical Methodology. Calculus 19: Complex Cardinals Subsumed Within Rationals, Intelligent Mazery, Dialectical Reasoning, Guesswork, Emergent / Emergency Thought. Calculus 20: Complex Cardinals Subsumed Within Rationals, Literal Exploration, Adventure, Procedural Reasoning, Empiricism. Calculus 21: Complex Proportional Trans-Finites, Intelligent Recursive, Operational, Synchronizing, Retrofitting. Calculus 22: Complex Proportional Trans-Finites, Literal Organizational, Informational, Neutral, Symbolic. Calculus 23: Complex Extended Numbers, Intelligent Transcendental, Visionary, Impresario, Beautiful. Calculus 24: Complex Extended Numbers, Literal Exceptional, Significant, Inherent, Complex-Ordinary. Calculus 25: Infinitesimal Sets, Intelligent Egregious reasoning. Calculus 26: Infinitesimal Sets, Literal Formal Aesthetics, Minimalism, Justice. Calculus 27: Infinitesimal Cardinals Subsumed Within Rationals, Intelligent Data, Proto-Semantics, Notation, Lemmas. Calculus 28: Infinitesimal Cardinals Subsumed Within Rationals, Literal Formatting, Computer Language, Markup, Legal Style. Calculus 29: Infinitesimal Proportional Trans-Finites, Intelligent Essential, Potential, Demonstrative, Elective. Calculus 30: Infinitesimal Proportional Trans-Finites, Literal Mechanical, Psychological, Spiritual, Animation. Calculus 31: Infinitesimal Extended Numbers, Intelligent Broken, Ugly, Conceptual, Universal. Calculus 32: Infinitesimal Extended Numbers, Literal Situational, Synthesizing, Found Object, Emotion. To summarize: 1. Algorithm, 2. Exclusion, 3. I.Q., 4. Limits, 5. A Priori, 6. Extension, 7. Complete, 8. Direct, 9. Formal, 10. Artistic, 11. Number Theory, 12. Variables, 13. Meta-Mathematics, 14. Vector Analysis, 15. Medicine, 16. Conjectural Analysis, 17. Gordian Knot, 18. Problematics, 19. Emergent Thought, 20. Adventure, 21. Operational, 22. Symbolic, 23. Beautiful, 24. Complex-Ordinary, 25. Egregious, 26. Justice, 27. Lemmas, 28. Formatting, 29. Essential, 30. Psychological, 31. Conceptual, 32. Synthesizing IV. PROPERTIES: If it is seen that one calculus transforms into the next due to their related properties, then when X calculus follows Y calculus we can say Y has a property of vector X or VX. If X calculus precedes Y calculus we can say X has a priority on Y, or Y has a property of PX. So, the 32 calculi can be expressed in this form as follows: 1 Synthesis P Algorithm V Exclusion. (The principle of an algorithm is to exclude synthesis). 2 Algorithm P Exclusion V I.Q. (The I.Q. of an exclusion is not an algorithm). 3 Exclusion P I.Q. V Limits. (The limit of an I.Q. is not an exclusion). 4 I.Q. P Limits V A Priori. (The A priori limit is not I.Q.). 5 Limits P A Priori V Extension. (The extension of the A priori is not the limit). 6 A Priori P Extension V Complete. (The completeness of extension is not A priori). 7 Extension P Complete V Direct. (The direct reason of completeness is un-extended). 8 Complete P Direct V Formal. (The formalism of directness is not complete). 9 Direct P Formal V Artistic. (The artistic formalism is not direct). 10 Formal P Artistic V Number Theory. (The number theory of art forms is not formal). 11 Artistic P Number Theory V Variables. (The variables of number theory are not artistic). 12 Number Theory P Variables V Meta-Mathematics. (The meta-mathematics of variables is not number theory). 13 Variables P Meta-Mathematics V Vector Analysis. (The vector analysis of meta-mathematics is not variables). 14 Meta-Mathematics P Vector Analysis V Medicine. (The medicine of vector analysis is not meta- mathematics) 15 Vector Analysis P Medicine V Conjectural Analysis. (The conjectural analysis of medicine is not vector analysis). 16 Medicine P Conjectural Analysis V Gordian Knot. (Cutting the Gordian knot of conjectural analysis is not medicine) 17 Conjectural Analysis P Gordian Knot V Problematics. (Problematics of Gordian knots is not conjectural analysis) 18 Gordian Knot P Problematics V Emergent Thought. (Emergent thought of problematics does not cut a Gordian knot) 19 Problematics P Emergent Thought V Adventure. (Adventure of emergent thought does not have problematics) 20 Emergent Thought P Adventure V Operational. (Operations of adventures are not emergent). 21 Adventure P Operational V Symbolic. (Symbolic operations are not an adventure). 22 Operational P Symbolic V Beautiful. (Beautiful symbols are not operations). 23 Symbolic P Beautiful V Complex-Ordinary. (Complex-ordinary beauty is not symbolic). 24 Beautiful P Complex-Ordinary V Egregious. (Egregious complex-ordinariness is not beautiful). 25 Complex-Ordinary P Egregious V Justice. (Justice that is egregious is not complex-ordinary). 26 Egregious P Justice V Lemmas. (Lemmas that have justice are not egregious). 27 Justice P Lemmas V Formatting. (Formatting of lemmas is not justice). 28 Lemmas P Formatting V Essential. (Essential formatting is not lemmas). 29 Formatting P Essential V Psychological. (Psychological essentials are not formatting). 30 Essential P Psychological V Conceptual. (Conceptual psychology is not essential). 31 Psychological P Conceptual V Synthesizing. (Synthesizing concepts is not psychological). 32 Conceptual P Synthesizing V Algorithm. (Algorithms of synthesis are not concepts). To summarize again, full knowledge of the 32 poly-calculii might amount to: The principle of an algorithm is to exclude synthesis. The I.Q. of an exclusion is not an algorithm. The limit of an I.Q. is not an exclusion. The A priori limit is not I.Q. The extension of the A priori is not the limit. The completeness of extension is not A priori. The direct reason of completeness is un-extended. The formalism of directness is not complete. The artistic formalism is not direct. The number theory of art forms is not formal. The variables of number theory are not artistic. The meta-mathematics of variables is not number theory. The vector analysis of meta-mathematics is not variables. The medicine of vector analysis is not meta-mathematics. The conjectural analysis of medicine is not vector analysis. Cutting the Gordian knot of conjectural analysis is not medicine. Problematics of Gordian knots is not conjectural analysis. Emergent thought of problematics does not cut a Gordian knot. Adventure of emergent thought does not have problematics. Operations of adventures are not emergent. Symbolic operations are not an adventure. Beautiful symbols are not operations. Complex-ordinary beauty is not symbolic. Egregious complex-ordinariness is not beautiful. Justice that is egregious is not complex-ordinary. Lemmas that have justice are not egregious. Formatting of lemmas is not justice. Essential formatting is not lemmas. Psychological essentials are not formatting. Conceptual psychology is not essential. Synthesizing concepts is not psychological. Algorithms of synthesis are not concepts. V. PREDICTIVE POWER The model only holds under the condition that the relevant observations can be explained within limits, or the extension of limits into other calculi. The model does not account for anything except calculus, and even then only the calculus defined as knowledge of mathematical limits and their extensions. Nor does the model yet provide for the exact mathematics of these derivatives, if they are indeed mathematical. Likely a much wider range of mathematical operations would be necessary to express the full set of calculi. VI. EXAMPLES The application of the knowledge is somewhat self-evident, although in its present state it might take the form of a heuristic. VII. FALSIFIABILITY If the permutation is exclusive, and with sufficient insight, then the entire set is indeed a type of complete description of calculus. I invite readers to investigate any shortcomings of the analysis. However, doing so may require creativity. VIII. BACKGROUND The original, very short formula for Polycalculus was created on March 10, 2017 by Nathan Coppedge after a series of inspirations. His writing on Polycalculus appeared on Quora on that day. REFERENCES Coppedge, Nathan. COHERENT PHILOSOPHY SYSTEMS. Amazon. -----. Intuitive Calculus. Nathancoppedge.com. -----. The Logic of Coherence. Academia. -----. SYSTEMS THEORY. Amazon. Farlow, Stanley J. Paradoxes in Mathematics. Dover Books. Frege, Gottlob. On Sense and Reference. Max Black, trans. Godel, Kurt. On Formally Undecidable Propositions of Principia Mathematica And Related Systems. Martin Hirzel, Trans. Golumbia, David. “CORRELATIONISM”: THE DOGMA THAT NEVER WAS. Academia. Hájek, Alan. “Philosophical Heuristics and Philosophical Creativity.” The Philosophy of Creativity. Elliot S. Paul and Scott B. Kaufman, Eds. Oxford U. Korbmacher, Johannes. AXIOMATIC THEORIES OF PARTIAL GROUND: THE BASE THEORY. Academia. Lundberg, Chris. REVISITING THE FUTURE OF MEANING. Academia. Peirce, Charles. Reasoning and the Logic of Things. Cambridge, Mass. Popper, Karl R. Objective Knowledge. Oxford U. Rescher, Nicholas. The Coherence Theory of Truth. Oxford U. Schagaev, Igor. Evolving Systems. Academia. -------, Nibojsa Folic and Nichoals Ionnides. “Multiple Choice Answers Approach: Assessment with Penalty Function for Computer Science and Similar Disciplines”. Academia. Tarski, Alfred. “The Concept of Truth in Formalized Languages.” J. H. Woodger, Trans. Williamson, Timothy. MODAL SCIENCE. Academia Coppedge, Nathan / SCSU 2017/06/10, p.