COHERENT ALGORITHMS NATHAN COPPEDGE UNDERGRADUATE, PHILOSOPHY DEPARTMENT SOUTHERN CT STATE UNIVERSITY A paper concerning math, philosophy, and evolution, or computer science and information theory, as requested by Igor Schagaev, member of the Life Science and Computing Department of The London Metropolitan University This paper builds on previous work, specifically coherentist philosophy and logic, and arguments which Schagaev considered ‘perfect’, on the subject of a discussion paper by Schagaev, found at: https://www.academia.edu/s/4cd5ae8775 COHERENT ALGORITHMS ABSTRACT: This paper concerns a deceptively simple, purposively new logical technique, a technique that may have implications for computers and the information sciences. It may be considered a by-product of my own work in philosophical logic (coherency theory), developed since 2002 and widely publicized on the internet. It is the subject of several of my books, including The Dimensional Philosopher’s Toolkit, Coherent Systems Theory, The Ninesquare Notebook, Coherent Logic, and others. The logic has earlier roots in algebra, deductive logic, Cartesianism, and hyperbolic geometry and other logical tools, etc. Part I. concerns the algorithmic formulation of my coherent categorical deduction method as expressed for computer science. Part II. briefly describes the implications of my work. I. THE ALGORITHM This material I am presenting with the encouragement of Igor Schagaev, a member of the Life Science and Computing Department at London Metropolitan University. Before I get into the material, it would be appropriate to mention that the material is (at least, for the time being) heavy on philosophical jargon and light on math. The clear qualifications which differentiate the method from many similar methods, such as methods from formal logic and philosophy, are not obvious on the surface. However, if we analyze that the output of the deduction is coherent through use of the Cartesian Coordinate System and take a different technical form, then those concerns are no longer an issue. The basic algorithm expressed by the deduction is shown in the following diagram: ABOVE: The feedback loop of the coherent deduction algorithm. As I state later, the ‘query’ aspect is not essential. It can be run automatically. However, the algorithm expressed in that way does not reveal completely how it works. The investigation of what is meant by a neutral system, for example, could span multiple books. So, we will focus on the steps beginning with ‘QUERY’. Steps involving ‘user preferences’ only get involved at the level of applications. 1. Query A query that takes place in terms of a coherent algorithm is conveniently simple. It simply involves subjects of interest (a logical sentence, or more commonly a single word), and related opposite terms. That is what is meant by ‘categories in CCS’ so we are already on to our next step of the analysis. (The query could easily be generated automatically on a wide variety of subjects. One of the only major necessary technical requirements of the algorithm, so far as programming is concerned, is a list of conventional polar opposite terms. As I mention later, ‘cat‘ and ‘dog‘ as well as ’black person’ and ’white person’ do not qualify without placing unnecessary restraints on the system). 2. ‘Categories in the CCS’. ‘CCS’ stands for the Cartesian Coordinate System. Here it will be used unconventionally, but it will retain many of the same properties. Opposites I argue opposites are any category in existence except for neutral systems and systems-neutral terms or problems expressible in multiple terms. Also, multiple-term expressions may serve as valid categories also. Thus, in part, the system’s coherence. are assumed to express, in a linguistic comparative form, all available data between extremes. True neutrals amount to one idea: ZERO, which for our purposes does not bear on anything except system-forming. System-forming is unessential to the basic operation of the system, just as ‘query’ and ‘user-preferences’ are unessential. By this point the process has been simple. We simply have opposites expressed in a CCS, and there is one important thing to remember: opposites always occupy the furthest possible distance from each other, which signifies that they are opposed DIAGONALLY. So in a standard CCS (other typologies are possible, incidentally, using similar logic), category A is opposed by category C, not categories B or D. Category B is opposed by category D, not categories A or C. This produces an important efficiency. All of this may be considered necessary for coherence, apart from the size and complexity of the set For formal purposes, ‘size of the set’ will always be determined to mean the number of exclusive categories (opposites).. 3. ’Arbitrarily asymmetric’ Although necessarily any given bounded CCS so expressed amounts to a neutral relationship (when multiple axes are involved, the relationship is actually double-neutral), in terms of any of the specific data, specific relationships are involved. This signifies that the data is in fact coherent through multiple incoherence. But since the system is always neutral, the incoherencies cancel out. We already covered neutral systems a little bit. That’s the high-level systems stuff, and typically does not affect the workings of the system. For example, neutral systems may concern symbolic functions for larger numbers of opposites, or in more than two dimensions. Now we move onto the logic itself. 4. The efficient logic which I hinted at already, is the relation of opposites on the immediate level to non-opposite terms. This means comparing opposites with terms that are not located across the diagonal from the initial term. To yield a coherent set, one need only compare the terms using all-neighboring terms. As it turns out, this yields a cyclical relationship in the CCS. But, it requires using polar extremes. It doesn’t work with relationships like Cat and Dog, because those terms are not true opposites (Cat and Dog are both animals, so they can’t be opposites. It also doesn’t work with black person and white person, since both terms are people) One stipulation is that often the direct comparisons are clearest when expressed as a quality-to-state relationship. Although this type of relation implies an additional assumption, it is not necessary for the mathematical validity of the system.. Since any given cyclical relationship is identical to every other order of the same cycle, the cyclical expressions (ABCD, BCDA, CDAB, and DABC in the CCS) can be standardized to always refer to the first category first. This is similar to the arbitrary assignment of set-order in mathematical matrixes. Thus, it is possible to orient the data towards specific hierarchical evaluations without compromising objectivity, and therefore TWO possible coherent deductions on FOUR categories are possible: ABCD and ADCB. The second deduction-form involves reversing the order of the terms. It may be important to note, that unlike in more conventional systems, given a fixed set of all pre-conditions X, both parts of the deduction are equally valid ALWAYS so long as the data remains coherent. Thus, the first pointer to valid terms that are contradictory is the incoherence of empirical data, in other words, the assignment of exceptional cases to the pre-conditions of the test case. Another possible option is that something problematic is involved in the data. But again, it is the data, and not the system, that is implicated in this. For, by definition of the system, there is no alternative to comparing opposites with non-opposite pairs, other than accepting either outright contradiction, or naïve realism. Naïve realism is unacceptable because it raises Hume’s Arrow, a problem in which nothing can ever be concluded from the data. Thus, this type of data (explained later) is highly significant, and might even be called a non-causal form of inference. II. IMPLICATIONS 1. Deductions can be drawn on any subject expressible in words, and conceivably even with non-linguistic (or ‘larger-linguistic’) entities that are expressible as opposite terms. As I have already argued, this means that what is encompassed is all entities expressible in language and all symbols conceivable in the mind. Conceivably all knowledge related to them can benefit from this form of knowledge, making it a highly-qualified rational system comparable to mathematics. 2. The results are efficient and coherent, meaning they express data that is not inherently obvious, yet is potentially absolute. This serves as a valuable tool. In this way, a coherent system is analogous to other major systems, such as Venn diagrams, flow charts, and any other organization involving differentiated categories. 3. Because the system is ostensibly coherent E.g. because no other relationships are ultimately possible without re-defining the context or the extremism of the opposites, or by relating to the truisms found in the deductions., and is expressed in terms of a bounded Cartesian Coordinate System, the results are potentially analogous to equations from social sciences or even formal mathematics, and any other context in which the CCS is implicated. In mathematics, it is conceivable that ‘spirals would be found in the data’, however these spirals would generally collapse to axial or radial-type relationships. One alternative is that the relation would be subtle and super-possessed. Super-possessed is a term that refers to the symbolic importance of contradicting the assumptions of this form of coherency theory. Arguably, since each bounded Cartesian diagram refers to not just negatives, but opposites, each in fact represents greater coherence than mathematics. Its position for analyzing abstract mathematics is thus maximized, if math is taken as a relatively strong example of coherence. 4. The importance for computer science and information theory is thus very certain and verifiable. The implication is for investigations of knowledge and data-presentation. The one problem that may arise is that the system is not 100% formally compatible with mathematics, due to its adoption of non-mathematical terms. In that case, the conclusion, surprisingly, is that math is incoherent, as has already been proved. It does not mean that coherent deduction is not compatible with mathematics. (If the two systems must be used separately, so be it. But since this system is easier to use than mathematics, it is likely to be treated as less serious, out of habit rather than truth). Coherent deduction can be used to supplement empirical data, to acquire relevance for data, in determining user preferences and investigating relevant data-points. It can also be used for determining the shape of a hypothesis, or to eliminate theoretical dead ends. Thus, coherent data is highly useful, and this paper is just a precis to the wealth of insights and corollaries made possible by the system. There are many other possible implications of the system, such as its application to computer hardware efficiency, its application to interface design efficiency and semantic knowledge in virtual reality, but I do not have time to discuss those possibilities here. I will leave the real implications of this writing to the imaginations of my readers. ----Nathan Coppedge / Student SCSU REFERENCES Coppedge, Nathan. Books -------. Coherent Logic. CIP, 2014. ------. Coherent Systems Theory. CIP, 2015. ------. The Dimensional Philosopher’s Toolkit. CIP: 2013 - 2015. ------. The Ninesquare Notebook: An Objective Knowledge Manifesto. CIP, 2014. Papers -------. “A Complex View”. Academia. -------. “A Future for Categorical Knowledge”. Academia. -------. “Coherent Data Project”. Academia. -------. “Exceptional Venn”. Academia. -------. “General Implications of Dimensional Knowledge”. Academia. -------.”How to Construct A Variety of Typologies”. Academia. ------. “Ideas to Change the World”. Academia. -------. “A New Invention: Axiometry”. Academia. -------. “On Higher-Informational Philosophy”. Academia. ------. “Problems in Nathan Coppedge’s Philosophy”. Academia. ------. “The Only System”. Academia. ------. “(The) Solution to All Paradoxes”. Academia. ------. “Valuative Language of Categoric Entities”. Academia. ------. “Work on Truth and Philosophical Irrationality Vis. Absolutism”. Academia. 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. Nathan Coppedge, / SCSU 11/29/2015, p.