Introduction to World-Making - Part Three
3.126 Possibility refers to mapping operations which entertain various facets of a logical system and treat these facets as if they might be true because nothing that is known to be true contradicts such a consideration.
3.1261 As experience, belief, understanding, and knowledge change, so, too, does the character of what one will entertain as being possible. However, what one considers to be possible may, or may not, accurately reflect what, in reality, is actually possible.
3.1262 Plausibility is a mapping operation or process that renders a judgement concerning not only the validity, consistency and coherency of a given hermeneutical space, but, as well, the degree of confidence one might have with respect to whether, or not, such a space may serve as a candidate which has congruency with some given aspect of experience and/or that which makes experience of such structural character possible.
3.1263 The foregoing sort of judgement assigns a value that is greater than mere possibility but less than certainty. Consequently, depending on circumstances, there are many values of confidence which might be assigned to such a judgement, and while all such judgements have some degree of reflective capacity or sense to them, not all such judgements are equally plausible.
3.127 Correlation involves mapping operations which seek to establish the degree to which, say, two objects, events, phenomena, processes, or contexts are manifested, occur, or appear together - either simultaneously, or contiguously, or sequentially.
3.1271 Correlation says nothing about the structural character of the relationship between such objects, events, phenomena, and so on. Rather, it is a measure of the likelihood that if one encounters one of these objects, events, etc, one also will encounter the other object, event, etc - either simultaneously, contiguously, or sequentially. Thus, although night and day have a high degree of correlation, night does not cause day, nor does day cause night, but, instead, both are related to a further set of phenomena concerning the rotation of the Earth, the movement of the Sun, the propagation of photons across a vacuum, the dispersion of such photons by the atmosphere of the Earth, and the existence of beings capable of discriminating between light and darkness.
3.128 The idea of randomness is an assumption which alludes to the presence of a principle within reality which says there are no dimensions of hidden variables governing a given system and that the structure of such a system is entirely the result of events and processes that, although caused, are not ordered in accordance with any pre-existing pattern which is imposed on those events and processes - other than the fact that such events and processes having the character which they do.
3.1281 An algorithm is a determinate array of operations which are performed on a body or set of data. Although the array of operations is determinate, the outcome may not be predictable (as in non-linear and chaotic systems) because of the synergy - both negative and positive - with which the operations feedback into themselves and the data on which they operate.
3.1282 Randomness is an assumption which can never be proved since there is always the possibility that the series or array or set of events which are being called random is a function of an algorithm whose presence and nature has not, yet, been detected.
3.129 Probability encompasses a variety of artificial systems of logic which seek to assign degrees of likelihood to expectations concerning the way a given system or hermeneutical space will be manifested over time. The manner in which these degrees of likelihood are determined and assigned depends on the structural character of the methodology governing a given framework of probability. Irrespective of the method used, the assumption of randomness is often used to establish base lines against which expectations and outcomes may be compared for purposes of analysis.
3.1291 Probability is a way of modeling certain dimensions of a system - for example, the likelihood that various kinds of event or process will be given expression at different junctures as the system is manifested during its operations or functioning.
3.1292 As with all models, the value of a given probability framework depends on the tenability of mapping processes such as assumptions, abstractions, deductions, analogs, and so on, which are being used to create the structural character of the hermeneutical space that constitutes a probability model.
3.1293 Statistics is a form of mapping which seeks to quantitatively describe, analyze, organize, and interpret a given body of data and/or information, especially in relation to issues of average, frequency, distribution, distance from some standard feature, correlation, trends, and reliability of such quantitative treatments. Statistics is often used as basis for informing, shaping, and directing various kinds of inductive, deductive, and modeling processes, as well as serving as one possible approach to the interpretation and evaluation of experimental data.
3.1294 Although related, in various ways, to probability frameworks, statistics is a different kind of quantitative description than the latter. However, statistics shares many of the same strengths and weaknesses as do mapping operations involving probability.
3.130 Information refers to the ways in which the structural character of experience is characterized, analyzed, interpreted, and organized. Information does not exist in that which is being characterized, rather the structural nature of the logical form of that which is being explored and delineated through the process of characterization serves as the focus of engagement for various processes, operations, functions, and methods which are artificially generated - each of which has its own modality for creating the data that become the points - simple or complex - from which the hermeneutical space of some system of logic is constructed.
3.131 Information may, or may not, be accurately reflective - in part or in whole - of that to which the information makes identifying reference.
3.132 Objectivity is a process which seeks to eliminate as many sources of bias, prejudice, distortion, undue influence, obfuscation, corruption, misunderstanding, and error from the construction, creation, or generation of hermeneutical spaces in conjunction with both experience, as well as that which makes experience of such structural character possible.
3.1321 Hermeneutical filters are used to process experience, data, information, and so on in a way that emphasizes, or brings out, some features of that experience, etc., while eliminating other facets of such experience. Photographers use various kinds of lenses to filter out certain wavelengths or conditions of lighting. In chemistry, one uses filters to eliminate certain ingredients whose size is larger than the holes of the filter. Audio technicians filter out noise to enhance the quality of sound.
3.13211 All filters have a bias to them which is inclined to some forms, or aspects, of experience, to the exclusion of others, according to the structural character of a filter.
3.13212 Sometimes such biases serve a useful function in conjunction with the quest for objectivity, and sometimes they do not. In either case, one needs to keep track of the filters in use and how they shape, color, and orient experience.
3.132121 Calibration is a process that is intended to enable some form of methodology, instrumentation, or hermeneutical activity to function in an optimal way - optimal being a function of the capabilities inherent in the given methodology, instrumentation, or hermeneutical activity, together with the skill and artistry of the individuals who are using such methodology, etc..
3.132122 Part of the process of calibration involves establishing, under specified conditions, base lines of performance and outcomes against which subsequent performance and outcomes generated through such methodology, instrumentation and hermeneutical activity can be compared and assigned meaning and significance.
3.132123 A base line is not necessarily a reflection of the structural character of some aspect or dimension of experience, or that which makes experience possible, which is independent of the base line. Rather, base lines are established in order to give one a place of known properties and conditions from which to operate and through which one can explore, probe, and experiment with various facets of experience.
3.132124 Base lines and calibration are part of a filtering process.
3.132125 Measurement is a process which seeks to quantify the extent to which some aspect or dimension of experience, or that which makes experience of such structural character possible, gives expression to some quality, property, state, activity, value, or feature in which one is interested. Generally speaking, measurement depends on the existence of some kind of standard unit that either remains consistent over time and across conditions, or fluctuates in known, regular ways according to circumstances.
3.132126 Measurement is another kind of filtering process. The properties of this filter will vary with: (a) the modality of measurement; (b) the nature of, and the problems surrounding, the 'standard unit used by a given form of measurement; (c) the extent to which such a modality interferes with the way in which that which is being measured is manifested; (d) the capacity of the modality of measurement to generate relevant data which serve as hermeneutical entry points through which one might gain insight into the structural character of that which is being measured; (e) the degree of resistance inherent in the structural character of that which is to be measured to the modality of measurement being employed (i.e., some modes of measurement are more compatible with certain dimensions of experience, or that which makes experience possible, than are other modes of measurement.
3.132127 Unobtrusive measures are those forms of measurement which do not interfere with, or influence, the way some given phenomenon, event, process, object, condition, state, or the like, is manifested during the time in which the modality of measurement engages such a phenomenon, event, etc..
3.132128 At least since the work of Heisenberg, there has been an awareness that the very act of observing a system, phenomenon, and so on, can alter the way in which the system, phenomenon, etc., is given expression during the process of observation. The nature of such alterations may mask, to varying degrees, the actual character of certain dimensions or facets of the system being observed, and, as a result, affect the quality and accuracy of the hermeneutical spaces generated with the assistance of such processes of observation.
3.132129 Quantifying a given property has at least two aspects. The first aspect is to establish a modality of measurement which is capable of reflecting relevant data concerning such a property. The second aspect involves the mathematical treatment of that data.
3.13212901 Methodology, measurement, quantification, and mathematics do not guarantee that the experience or data which is processed through such means will be understood. As Richard Feynman, a Noble laureate, is reported to have once told a student who was anguishing over the nature, meaning and significance of quantum mechanics - 'Look, no one understands it, just do the calculations."
3.1321291 Relevancy is not a matter of what is of value to a given form of methodology, measurement, or hermeneutical activity. Relevancy is determined by the actual nature, logic, or structural character of that which is being explored.
3.13212911 The ultimate baseline for all methodology and measurement is reality itself.
3.132130 Not all facets or dimensions of experience, and/or that which makes experience of such structural character possible, are amenable to processes of measurement and/or mathematically tractable.
3.133 The interrogative imperative refers to a dimension of human existence which is, on the one hand, rooted in curiosity and the desire to know the truth concerning the nature of experience and/or that which makes experience of such structural character possible. On the other hand, the interrogative imperative is rooted in the awareness that there are many ways in which objectivity can be compromised during the process of engaging, exploring, characterizing, analyzing, interpreting, evaluating, modeling, understanding, and applying experience - such awareness contains the desire to eliminate as many of these kinds of problems as possible.
3.1331 Much of the focus of the interrogative imperative is to determine the extent, if any, to which a claimed insight is possible, plausible, probable, or accurately reflective with respect to that to which the alleged insight makes identifying reference.
3.134 Ockham's razor stipulates that one should not multiply terms, concepts, and4 assumptions beyond what is necessary to explain or account for a given phenomena. An alternative way of alluding to the same sort of principle is that when comparing two explanations, ideas, assumptions, etc., then, all other things being equal, the simpler of the two is to be preferred.
3.1341 Some of the problems with the foregoing are as follows: what is necessary is often at issue; moreover, 'all other things' often are not equal and how such inequalities affect the process of identifying what is necessary or simpler is not always easily, if at all, capable of being sorted out; in addition, finding reliable measures of simplicity which are independent of the eye of the beholder (i.e., some artificially constructed system of logic) is a complex and difficult process.
3.135 Evidence refers to the set of assumptions, data, information, facts, beliefs, values, judgements, interpretations, understandings, methodologies, mappings, questions, and so on, which have been woven into a framework of reference through which certain kinds of experiences are considered to have some degree of congruency with either an aspect of experience or an aspect of that which makes experience of such structural character possible.
3.136 The manner or modality of weaving together such evidence is often given expression in the form of a mathematical, logical, or rigorous argument, demonstration, proof, or explanation, of some kind. These 'forms' are ways of ordering, structuring, arranging, and/or relating the elements of evidence so that the structural character of such a form may be seen, or understood, to have a certain degree of congruency with the structural character of that to which the form of evidence makes identifying reference.
3.137 A tenable argument, demonstration, proof, or explanation is one which is capable of standing up under the scrutiny of the interrogative imperative over time.
3.1371 Tenable arguments, and the like, are not necessarily true, for the value and strength of a given judgement of tenability is dependent on the strength and value of the questions which are asked. If the right questions are not asked, then, a given argument or explanation is only as good as the quality and rigor of the questions which have been raised concerning it ... which may, or may not, be all that good depending on circumstances.
3.1372 Proof can be a relative thing which depends on an individual's acceptance of the assumptions, evidence, arguments, propositions, mapping operations, and conclusions contained in the proof.
3.13721 The fact someone accepts a proof as valid, adequate, consistent, coherent, and so on does not, in and of itself, confirm the proof as true, logical, substantiated, and/or legitimate.
3.137211 Before Riemann and Lobachevski, people, generally, accepted Euclid's geometric proofs and made them the cornerstone of a great deal of subsequent work in both mathematics and science.. After the work of the two aforementioned mathematicians, people approached the idea of geometric proof differently.
3.137212 Before Godel's notions of incompleteness and inconsistency arrived on the scene, many people regarded the proofs of mathematics as certain and reliable. After Godel, people looked at the idea of proof very differently.
3.13722 The fact most people believe something to have been proven does not, in and of itself, mean the proof is beyond warranted criticism. Similarly, the fact few people believe in a given proof, does not, in and of itself, negate the value of such a proof.
3.137221 Some proofs are entirely about the internal properties of a given system of artificial logic, and have little, if anything, to do with reality beyond the horizons of such a system.
3.137222 Some proofs focus on seeking to determine the structural character of various facets, aspects, or dimensions of experience.
3.137223 Some proofs are concerned with the relationship among understanding, experience, and the nature of that which makes experience of such structural character possible.
3.138 Falsification is an idea introduced by Karl Popper which, in simplified terms, stipulates that while only one contraindication with respect to some given conjecture, hypothesis, principle, or the like, is enough to falsify claims concerning the correctness or truth of such a conjecture or hypothesis, no amount of positive evidence is sufficient to prove the truth of a given conjecture or hypothesis because there is always the possibility that some form of contraindication with respect to such a conjecture or hypothesis might arise in the future.
3.139 Human beings seek out certainty, but, in general, are immersed in uncertainty, unanswered questions, inconclusive evidence, and problematic proofs.
3.140 Hermeneutical spaces can be divided up into linear and non-linear systems. Linear systems are those that tend to be tractable to mathematical treatment because of the regularity or repetitive nature of the patterns and features to which such a system gives expression The task, then, becomes one of trying to establish some degree of congruency between the structural character of some form of mathematical system of logic and the structural character of the facets of hermeneutical space and/or phenomenology of experience which one seeks to understand. One uses such congruency as the manifold of commonality through which one generates abstractions, models, logical frameworks, and so on, as a basis for mirroring the properties, structure, and logical nature of a given linear system.
3.141 Non-linear systems refer to contexts in which the forms, patterns, and structures to which such systems give expression tend to be irregular in character and oftentimes exhibit anomalous behavior of one kind or another. The properties manifested by such systems over time are said to be self-similar rather than self-same (as in the case of linear systems), and, consequently, such systems are not easily, if at all, tractable through most mathematical systems.
3.142 Non-linear systems are determinate in nature - that is, they are governed by a set of principles of identifiable nature, but they tend to be unpredictable because of the manner in which the various dimensions of the system are extremely sensitive to fluctuations taking place within that system (as well as around the system) and, therefore, exhibit complex forms of feed-back loops which are not readily amenable to mathematical treatment, and even when such treatments are available, the latter tend to be limited to very specific contexts and subject to a considerable amount of constant manual adjustments in the formulae and equations of such treatments in order to keep up, somewhat, with the changes being manifested in non-linear systems.
3.1421 Most of life consists of non-linear phenomena.
3.15 Mathematical formulae and equations are expressions of different facets and dimensions of the structural character of the artificial systems of logic to which they give expression.
3.151 The value of a formula, equation, or set of formulae and equations, lies in the degree of congruency which can be established or exists between the structural character of a formula or equation (or set of them) and the structural character of the aspect of experience to which such mathematical forms make identifying reference in a given context.
3.1511 Mathematical and non-mathematical languages, alike, seek to establish congruency among understanding, experience, and that which makes such experience possible.
3.1512 In some instances, mathematical language accomplishes this far more precisely and rigorously than does non-mathematical language. In other instances, the reverse may be true (e.g., in the realms of, say, creativity, love, emotion, morality, spirituality, poetry, identity, justice, faith, art, community, belief, purpose, parenting, psychological therapy, and so on).
3.16 All methodologies are subject to the limitations of incompleteness. In other words, no methodology is self-contained and self-sufficient, but, instead, one must journey beyond the horizons of any given methodology in order to discover the value of that methodology.
3.161 Among other things, methodology stands in need of, and presupposes, experience and/or that which makes experience of such structural character possible.
3.162 Although methodology arises out of experience, not all experience is necessarily reducible to such a methodology or capable of being grasped through such a methodology.
3.163 Methodology, like language, and systems of logical, in general, do not move themselves. They require the presence of consciousness (both basic and reflexive) and intelligence to invent, generate, create, construct, apply, understand, and critique them.
3.17 Frames of reference, belief systems, hypotheses, theories, models, paradigms, and world-views are the hermeneutical spaces created or constructed by intelligence as it engages experience through the phenomenological field - which is the point of conjunction of understanding, experience, and that which makes experience of such structural character possible.
3.171 A hypothesis is a conjecture concerning the way in which certain facets of experience, or that which makes experiences of such structural character possible, are related.
3.1712 Often times, the nature of this relationship is expressed in terms of independent and dependent variables.
3.17121 Something is considered an independent variable when: (a) it can change in value under different circumstances, and (b) the value is not affected by changes to the dependent variable with which it is associated by means of the hypothesis.
3.171211 Among various possibilities one might cite, global economics, chaotic systems, and mysticism as tending to suggest that few things in the universe may actually be fully independent of changes elsewhere in a given context or system. As such, there are degrees of relative independence and relative dependence.
3.171212 Causation refers to the idea that the relationship between two events, objects, contexts, states, and so on is governed by the manner in which one pole of the relationship is prior to (both logically and physically), as well as, directs, shapes, orients, alters, transforms, changes, and/or helps give rise to the other pole of the relationship.
3.171213 The interdependent nature of many facets and dimensions of experience and/or that which makes experience of such structural character possible - as is suggested by, among other things: life, Bell's theorem, quantum physics, the stock market, politics, gravitation, education, peace, cybernetics, ecology, jurisprudence, consciousness, intelligence, understanding, illness, and happiness - indicates that isolating something as 'the', or even 'a' cause, may not be a straightforward matter, and may be, in many instances, quite arbitrary.
3.1713 A theory is a belief or set of beliefs concerning the structural character of some facet of experience and/or that which makes experience of such structural character possible.
3.17131 Some theories are more rigorous than others in the sense that the former: (a) tend to be supported by more well-considered evidence than the latter; (b) may be more coherent and consistent; (c) may have been subjected to closer and more exacting scrutiny through the interrogative imperative than have weaker theories; (d) are more likely to be accepted as heuristically valuable guides to subsequent exploration by the prevailing community of experts who deal with such matters; (e) tend to have a more precise, and less problematic, ability to describe and/or account for certain phenomena than do weaker theories.
3.17132 However, rigorously developed, a theory is still a belief system which embodies a certain amount of knowledge and has, within limits, a capacity to accurately reflect various facets of experience and/or that which makes experience of such structural character possible.
3.17133 Hypotheses are used to help confirm or refute various dimensions of a theory by stating issues in a narrow fashion which is both capable of being operationalized in the form of testable proposition (or set of them), and, as well, is likely to lead to results that provide data which can serve as evidence to help confirm or refute some aspect of a given theory.
3.17134 Theories rarely stand or fall due to the outcome of a single experiment which is devised to test a given hypothesis. Often times, if experimental results are inconsistent with a particular theory, the theory may be revised or re-interpreted in order to accommodate the new data.
3.17135 Theories, however, may come into disfavor as the result of a series of contraindications which arise from experimental data. A certain theory also may come into disfavor because there some other theory, seeking to account for similar phenomena and/or data, which is considered, rightly or wrongly, to be more heuristically valuable, in some sense, than is the previously accepted theory. One theory may gain in general acceptance over a competing theory because of the influence of certain centers of learning in setting hermeneutical trends that tend to propagate such perspectives to the next generation of researchers. The popularity of one theory may increase at the expense of a competing theory due to the politics of hiring and publishing. Finally, one theory may gain in ascendency relative to a competing theory because the proponents of one theory die off, leaving the field relatively clear for another theory to establish itself and begin to flourish through the activity of its still living proponents.
3.17136 A paradigm is a theoretical framework which serves as a work in progress that shapes the methodology, experimentation, interpretation, understanding, politics, and education of those who come under its influence. A paradigm is the hermeneutical filter through which certain facets of experience, and/or that which makes experience of such structural character possible, are engaged, processed, and understood.
3.172 Some people argue that one cannot derive 'ought' from 'is'. In other words, just because some dimension of experience, and/or that which makes experience of such structural character possible, has a certain nature does not, in and of itself, necessarily warrant the inference that one ought to behave in certain ways which are said to follow, or are derivable, from experience or things being the way they are.
3.1721 Whether, or not, the foregoing contention is correct really depends on the extent to which some form of 'ought' is inherent in the logical character of that which makes experience possible.
3.17211 If there is a dimension of 'ought' to what is, then, there is a directional potential which is built into being and existence.
3.17212 In one sense, there is such a directional component inherent in being - namely, reality is what it is, and if one wishes to have any hope of understanding various facets and dimensions of that reality, then, one ought to seek generating hermeneutical spaces which have a structural character that has congruency with the structural character of the aspect of experience to which identifying reference is being made through the hermeneutical space and/or the structural character of that which makes such experience possible.
3.17213 If there are one, or more, dimensions of ought to being, then, this, in and of itself, does not necessitate what one will choose to do with respect to such an 'ought'. Ought is a suggestion with a certain degree of moral direction and force (or warrant) with which one complies or ignores at one's own risk - just as truth, knowledge, and understanding (of whatever kind, and on whatever level) are hermeneutical vectors with a certain degree of moral direction and force (warrant) with which one complies or ignores at one's own risk - the risk one runs in the latter case is ignorance, misunderstanding, error, bias, or the like.
3.18 The primary task of education is to provide a means for individuals to explore, gain facility with, learn how to critique, and generate (or adopt) useful applications as a result of the capacity, and inclination, of human beings to generate hermeneutical spaces. The essence of this generation process is a function of the interplay of the following processes: identifying reference; characterization; the interrogative imperative; mapping operations; and establishing congruencies.
3.19 As such, facts, per se, are less important than understanding the processes which gave rise to, shaped, colored, and oriented those facts. Information, per se, is less important than grasping the structural character of the processes that generated data of such structural character. Facts and information, together with their perceived value or reliability, often change over time, but the general features of the structural character of generating and evaluating the nature of hermeneutical spaces do not change with time.
3.21 Logic is an expression of the manner in which the different, aforementioned components involved in generating hermeneutical spaces are employed by a given intelligence within the context of engaging the phenomenology of the experiential field in the attempt to understand that which makes experience of such structural character possible.
3.211 There are many kinds of logic and one of the challenges with which all human beings are confronted - and with which education ought to be concerned - is to try to discover which system(s) of logic is (are) most congruent with, or reflective of, the structural character of various realms of experience, together with the nature of that which makes experience of such structural character possible.
3.3 Education is a medium for learning about the possibilities, problems, and methods that are associated with trying to understand the logical nature or structural character of hermeneutical spaces which arise in conjunction with various kinds of experience, together with that which makes experiences of such structural character possible.
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