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NOTES FROM 2001 JOURNEY IN THE TRINITY ALPS ANIL MITRA PHD, © 2001, REFORMATTED February 2013 ADDITIONAL NOTES IN SEPARATE DOCUMENTS: Map of Mind | Map of my World | Mathematics and its Foundations | Words, Language, Metaphysics | Surface and Depth | Fundamental Problem of Metaphysics and its Resolution | The Origins of Language | The Truth Can be Known Document status: February 11, 2013 This document is the beginning of much in the way of new development relative to where I was at the time Maintain as a source; no action necessary, especially for Journey in Being The following is a possible start of a development There is much else that is interesting, especially Wittgenstein’s Philosophy but that has been absorbed to History of Western Philosophy The Fundamental Problem of Metaphysics | The Fundamental Problem of Metaphysics and its Resolution are now in a separate document I am leaving the plans and fundamental conclusions as they are; they can be left behind since the essence of this document except the fundamental problems above has been absorbed or superseded
Brief Contents Legend Fundamental conclusions Plans
These notes, written in the Trinity Alps, are currently in process. I am translating them from rough hand notes, refining them as I do so. Once complete, the notes may be critically incorporated into existing essays. As examples, The Fundamental Problem Of Metaphysics and The Fundamental Problem Of Metaphysics And Its Resolution will be incorporated into On Mind and Metaphysics; and On Inference, On Inference II, and Mathematics And Its Foundations and The Origins Of Language, will be incorporated with Kinds of Knowledge Complete this process of critical incorporation.
2.1 Is there a categorical ontology? 2.2 What is nothing, or no-thing? 6 ON THE INTEREST IN PHILOSOPHY 6.1 The constitutional requirements for an interest in philosophy 7 WHAT ARE THE PROBLEMS OF A PHILOSOPHY OF MIND? 8 THE FUNDAMENTAL PROBLEM OF METAPHYSICS 9 THE FUNDAMENTAL PROBLEM OF METAPHYSICS AND ITS RESOLUTION 10 PHILOSOPHY, SCIENCE AND LIFE. WITTGENSTEIN AND HUME 10.1 The concept of the empirical 10.3 What makes something [a claim, a study… ] empirical? 10.4 The claim that philosophy is not empirical 10.5 Hume and science – or, Hume’s brilliant error 11.1 Evolution and the Boundaries of Being 12.1 The Concept of Logic and Inference: preliminary 12.2 The Concept of Logic and Inference 12.3 Logic as the Process of Knowledge Acquisition and “Verification” 12.5 The Analysis of Knowledge 12.6.1 “Definition” vs. criteria 12.6.2 Concepts or theories of truth: 12.6.3 Relationship among and status of the theories 12.6.4 An example: the pragmatist theory 12.7 The Analysis of Thinking… Cognition… 12.8.2 On abstraction and generality 12.8.3 An example: independent universes 14 MATHEMATICS AND ITS FOUNDATIONS 15 ON YOGA: A TALK DELIVERED TO THE SKY AND THE WIND AT ENNI CAMP 18 A MAP OF MY WORLD / A MAP OF THE WORLD 19 DESIGN: HORIZONS ENTERPRISES 20 DESIGN: A JOURNEY IN NATURE BELIEF, KNOWLEDGE, CODINGSunday 8.19.01 This discussion is continued in Map of Mind In an indeterminate universe, by adaptation – in the nature of being in such a universe, one can believe and doubt at the same time. But this is inherent in the primary meaning of belief: when I say “I believe that” – this is consistent with doubt. Or, if there are a number of – exclusive – possibilities one can believe all with some weighting at the same time. But this is in the nature of being – that in truth the “state” of a being is always a superposition: a | this > + b | not this > or a | this > + b | that > Then, “I believe this” is better than “I know this” even in the usual case where / when a >> b and I say “I know this.” Belief is omnivalent and real Belief state = Σ α | x > Belief is real; knowledge is a concept Belief is what the individual has, knowledge is what the group accepts / certifies and to which the individual may adhere Certified as to: degree of certainty, intrinsic utility, truth, morality and aesthetics and combinations and degrees thereof Certainty should not be central, yet it is almost a kind of an aesthetic. To what kind of mind, or in what socio-political climate would certainty be an aesthetic? This is related to “cleanliness is next to godliness” Certified how: justification, convention, in-action – both common knowledge and science… Knowledge is flat; belief is rich. Belief takes into account knowledge, being and experience. Belief is of the universe and therefore “Belief is real and – subconsciously – omnivalent. Belief is the key to truth and full growth into potential Belief and knowledge are held, acquired by individuals. More fundamental is coding. Forget about what you know about coding, the other symbols attached to “coding”. Here, coding is any structure in the individual that attunes the individual to the universe – that includes self and environment. The source of the coding could be random but usually bears the imprint of the universe. The structure and composition of the skeleton are coding. In between this basic organic level and the level of articulated belief is an entire range of coded modalities CATEGORICAL ONTOLOGYMonday 8.20.01 There is action and meta-action. Meta-action includes talk. Axiological meta-talk: it is good / bad, useful / useless, inspiring / boring to talk about… [ categorical ontology ] There is analytical meta-talk: to deduce a result within the system by looking at its structure. Analytical meta-talk is the same as analytical talk? No, the former must include a degree of intuition or some other element The categories are categories of the universe… or of our understanding. How will we ultimately distinguish? This is answered below, in THE FUNDAMENTAL PROBLEM OF METAPHYSICS Sunday 9.16.01 and THE FUNDAMENTAL PROBLEM OF METAPHYSICS AND ITS RESOLUTION Sunday 10.7.01 To not go through a process is to abort it and remain in a state of arrest. If you do not make something basic, explicit you will accept and remain in an arrest: the default position Is there a categorical ontology?Matter vs. mind? Seriously, what is matter? Something from no-thing: 0 = 1 + [-1] Some things about this: It is the empty ontology: nothing, no-thing, Φ Therefore, mind and matter are equally basic It requires an abandonment of universal causation and an abandonment of determinism. Although physics is consistent with something from nothing, there are grades of nothing-ness. As far as something from the absolute nothing there is no way out but to completely abandon, as a universal principle, causality and any thought of determinism [ there may arise pockets of causation and quasi-determinism ] What is nothing, or no-thing?No structure No form Non-existence Neither existence nor non-existence Just like infinity, are there / there are levels of Φ WHAT IS ANTHROPOLOGY?Wednesday 8.22.01 A shaman claims to fly in the spirit world Can the anthropologist [ claim to ] understand the shaman’s claim …know whether the shaman actually believe his own claim …whether the shaman believes he believes his own claim …judge the reality content of the shaman’s claims and beliefs …understand the “function” of the shaman’s claims, beliefs and practices – interpret them from “the” western worldview …learn from the culture? How? …can there be mutual adaptation WITTGENSTEIN’S PHILOSOPHYThe essence of this section has been absorbed to History of Western Philosophy Saturday 9.1.01 LANGUAGESaturday 9.1.01 Language, among its functions, bears ands permits creation of meaning. As a bearer of intended meaning, language has limitations; but a non-linguistic animal cannot communicate [ or feel? ] the range of meanings that is possible for a linguistic one Language – in one role – describes states of affairs, patterns and so expresses and communicates knowledge: knowledge by description. Knowledge by acquaintance is through the senses and may be described when there is a set of elements and meaningful combinations – otherwise this form of knowledge is communicated by shared practice and pointing [ naming ], depicting, acting out. Knowledge by acquaintance is richer, more direct, a paradigm of our experience of reality [ empiricism ]. By contrast, knowledge by description, by language, is limited: one-dimensional, flat, second hand, a poor bearer of the “real”. I suppose art would be part way between but do not see why art is not “by description”. Communication is multi-modal, the written word, however, for various reasons unconnected with the actual power of the word, dominates the scene and so gives an impression of the supremacy of the word beyond its actual capability Yet, knowledge by acquaintance requires special organs, cannot [? ] transcend its domain of application. Knowledge by description requires the facility of language but needs no special organ for each domain of application – and therefore permits not only the acquisition of new knowledge but, also, the formulation and expression of new domains of knowledge. The flatness of knowledge by description has as its reward the ability to move into new realms. That could be a limitation or a freedom. It is a limitation if it is expected that description will be a perfect substitute for acquaintance. The situation is not that flat for feeling follows description in developing [ at least ] two kinds of intuition: physical and analytic Physical intuition is intuition of the world, analytic intuition is intuition of symbols – and language and of the kinds of structures and patterns of symbol systems. We could have intuition about all kinds of knowing. In that symbols are in the world, the distinction between analytic and physical intuition breaks down but in that they call upon different mental abilities, the distinction is valid and useful. Physical intuition, pictorial imagination and analytic intuition are all “pictorial”, involve, more, the “right” brain hemisphere It is natural that language users will be confident in its use. But that confidence in new domains has been called “bewitchment.” In moving into new domains, however, although bewitchment is a motive, trial and error [ criticism ] is the way. It is through bewitchment that [ slow ] forward motion is possible. The pessimists say no; but think of a time in hominid evolution when language was about to emerge but did not yet exist. Critical philosophy in turning its own viewpoint into a paradigm takes a moment, a slice of history and sees a universe God, of course, as being itself would require neither words, nor patterns, nor concepts, nor senses, nor immersion On the origin of languageOrigin / origins I would like to write an hypothetical analysis of the evolutionary origins of language which does justice to its subjectivity, objectivity [ realism and not mere conventionalism ] and to its power to immediately communicate [ despite flatness of dimension ] and the dependence of this on context and non-linguistic modes of communication [ is the distinction between language and non-verbal communication artificial? ] There is a beginning of this in Kinds of Knowledge. Combine with The Origins of Language and. The beginning of this in Kinds of Knowledge. ON THE INTEREST IN PHILOSOPHYSunday 9.29.01 When I talk to others naturally, I find, almost invariably, an interest in philosophy. What is natural? That depends upon the audience. Problems, issues, ideas arise naturally; there is interest. It is different if I were to introduce a philosophical problem and thoughts out of context. There is a context to the “theoretical” issues; that requires building up The reaction depends on when “philosophy” is brought up… I do not begin talking about some issue unless there is an occasion: a life context, an issue, some one mentions a course they took, a puzzle And how… I could say that the argument is a form of transcendental analytic from the facts of existence and sentience to the idea of matter. Or, one could say: Science teaches that the world, including minds, is made up of material particles. If that is true, the fact that we think, see, have minds must tell us something about matter. Here’s one way to look at the situation… Just in the way that “algebra” is more interesting if you start with a real life situation, solve a problem and then say “By the way, that was algebra.” Part of the problem: life is continuous with the disciplines; it is very easy to lose sight of that There are, certainly, reactions against philosophy. Mostly, the reactions are reactionary: fear, control, anger. Then there is politics: philosophy is the province of the elite, it is anti-democratic. And, surely there is confusion of motives – how often do we find that people have moral reactions as defenses? But, mostly, apart from “pathology”, I find that the interest / lack of interest in philosophy depends on when and how the topic is introduced – including whether it is presented as an isolated academic exercise or as continuous with life. It is different in writing; and it is different when talking to someone who has a mutual knowledge and interest in the discipline I do not open a discussion of philosophical issues with, say, a discussion of “solipsism” – unless I am talking to someone who is interested in the tradition of philosophy First, this depends on what is philosophy – a method, accumulated ideas and arguments, an activity… Second, I am not a philosopher if you mean someone who is interested in philosophy for its own sake. [ Some rambling stuff. There is some of that because some very creative [ and some rather dull ] minds have contributed. But, primarily, philosophy is the main ingredient of gñana yoga. Here, philosophy is understood in a general sense of an umbrella discipline; and it includes art – I could say humanities but philosophy in its general sense is better. That will confuse those who cannot for a second give up the picture they have in their minds; that contradicts what may be said about the arbitrariness of definitions. What is yoga? It is the “union” with all being; yoga is “yoke”. I mean union somewhat metaphorically; it includes all ways to approach it including “design, evolution, construction.” And gñana is, of course, knowledge [ sometimes wisdom but knowledge will do. ] So, study of philosophy is a tool. What can I be? How can I know that? Here, a little comment on yoga. The kinds raja – the way of intuition and insight, exploration of space – space? Yes, but I mean the spaces that the mind can cover; then: bhakti – worship, devotion; karma – work, action; and gñana. It is claimed that raja is the highest; I often think that gñana and bhakti are the lowest; but that is all on slanted ideas of what these are; one can “do” karma with the mindfulness of raja, the attitude of bhakti without bloated ritual, and infused with gñana; and each reinforces the other. All words become slanted weighted with oppression; to be free release the ultra-secular meanings the meaningless meanings; let meaning flow amid the reality of space and self. The discipline of yoga is an idea; absorb; go beyond… naturalize, avoid word and slant ] So, what about solipsism. How interesting is that? Firstly, about a lot of “isms.” The “isms” represent philosophical positions. But more than that. No one goes around saying “I am a solipsist.” But many people have a covert solipsism: the “privacy and incommunicability of my phenomenal bubble.” And as a result a covert sense of separation. These things are real. Alienation is at the heart of human beings as is being-in. This is distinct from any fashion. So, Wittgenstein says something about that when he talks of solipsism. He shows, logically and not scientifically, how solipsism contradicts its own underpinnings. His argument shows the depth of the connection. And what of autism? That is a form of psychological solipsism. There is a theoretical approach through Wittgenstein’s argument. In philosophy the interest of solipsism is not a mere academic exercise; fundamentally, resolution of the paradox sheds light on “what is knowing”, “how am I tied in to the world”, “knowing is of the world even when it is someone’s creation”… it is a gñana yoga… What kind of activity is philosophy? The constitutional requirements for an interest in philosophyThe following are not meant to be definitive: they are “just some” thoughts Consider classing persons as ectomorph, endomorph, and mesomorph. The ectomorph does not have sufficient patience; the endomorph does not have sufficient passion. Therefore, about 1 / 3 of the population is constitutionally suited to do philosophy. Of course 1 / 3 is a rough estimate. And this refers, only, to temperament and not to ability or circumstance Can we make the correspondence: Ectomorph ® Vata Endomorph ® Kapha Mesomorph ® Pita What of the Jungian types: Judgmental vs. perceptive Sensing vs. intuitive Thinking vs. feeling Extravert vs. introvert? Or, birth order, and the reasoned and empirical study of Frank Sulloway? This is one of the best reasoned studies I have seen. Why? It does not refer so much to kind of person but what kind of activities the individual pursues. Therefore, it is possible for the study to be empirical. Sulloway makes it empirical by studying history. He considers politicians, scientists and others; he asks what their birth order was; and he looks at whether they were keepers of tradition or “revolutionaries.” Of course, he provides a rationale for his conclusions – that is necessary, but anyone with an armchair can do that. There is no other birth order typology that I have seen or heard of – formal or informal – that does that The above typologies refer, to some extent, to different dimensions To what extent do they affect the suitability of the individual to do philosophy? Or, to have an interest in philosophy? And to what extent do they affect the kind of philosophy that an individual does? E.g. what makes for a rationalist vs. an empiricist, “tender” vs. “tough”, policeman or poet [Freeman Dyson thought that one up.] What of historical or circumstantial factors? Leisure, being in the right place, having a mentor, culture… WHAT ARE THE PROBLEMS OF A PHILOSOPHY OF MIND?Monday 9.30.01 Combine with MAP OF MIND? Mind – not a definite thing or a group of things. Notice the tendency to return to objective language. Again, not a definite thing or group of things, at least in that our ideas of it and what “kind” it is are not clear; but it is not also clear that anything definite is being named; it is not clear that a [ potential ] area of use is being precisely circumscribed So, to begin, there is the dual problem of a incompletely defined concept and [ of a ] hazy object. However, it is not as though there are two hazynesses. For there to be two hazynesses, there would have to be some independent Platonic version of the real. There is not and so the two hazynesses intersect. How can all this be? It is because we construct our world; there may be a world behind “our world” it is not clear that that is a logically consistent concept; non existence of that concept is not inconsistent with external realism; but, just as an electron is not a mere expression of the real and of laws but also contributes, even if minutely, so, also, mind – that is the trivial aspect; disentanglement, not entanglement, is the prison of unrealism. We are half-way between idealism and realism. [ Wittgenstein is clarifying here; but to take him as limiting is a mistake. ] What, then, is mind? What “is” mind? “ “ “. And, where and how is it located? As best we know from the above, these questions will not receive definite answers and not just because we fall short of answers; but because it is not clear that there is one crystal clear answer: this is real; insisting on such answers [ the religion of clarity and certainty ] is a step into non-being – a step into the realm of minutiae, of trivia in the form of seemingly erudite sophistry where ideas will not hang together even as beads on a necklace… where even creative ideas will be floating as if in ether The approach, then, will be one of reflection on both sides of world-as-we-know-it. The two sides are underlined. There is room for confusion for in this topic what is known is what knows. Deflate by reflection without dualism, by negotiating the world knowing that that world is the world-as-we-know-it Questioning “what is mind” begins with examples of what passes for the mental. Refinement – later. Remember, to begin, we are providing examples not intentionally characterizing – let alone answering “What is characterizing?” – though of course it is difficult and not desirable to exclude theory. Just be aware of the presence of theory. Heidegger played down theory. Theory can be viewed: what we bring; concepts – concepts are essential to being human. When someone says, everything is theory – they want, likely, to control and manipulate… to keep you in your place, i.e., the place they want you to be; and, in clever manipulation, manipulation since birth and enculturation, you will believe what you are manipulated into as reality and defend it with anger, emotion, hostility, ingenuity… your life: you will give up your real freedom in slavery to it Examples: sensing, seeing-perceiving, thinking, imagining, describing, desiring, willing, acting, feeling, emoting, talking, using language – thinking, understanding, communicating, explaining… thinking in pictures 1. Complete this list and classify it. This is not independent of other developments / problems. We are able to formulate and understand because we have experience with the issues. Not independent includes: informing, require mutual solution 2. What is mind? What are [is] its essential characteristics? Are there any? 3. What kinds of things have minds? How do the different aspects of mind gel together – describe and explain the gelling. Some thoughts: the individual, the ego – in the dimension of having mind 4. Problem 3 with “mind” replaced by “language” 5. How, where is mind located. How = what is the relation mind / matter? Note that matter includes, also, energy and force. Remembering that these do not name definite things or kinds – mind and matter as describing different aspects of being: how mind arises in matter is not a valid question because it does not arise; even if mind is a high level phenomenon relative to a low level real [matter] it does not arise in matter but it “arises” at a certain level of, say, complexity; but, more properly, mind does not arise in matter because mind and matter are not categorically distinct. We could ask – when does mind manifest? The answering has multiple approaches – the right kind of dynamic complexity, the structure of the brain, adaptation. Where is mind located? – This question has multiple approaches The problems are regarding mind-as-I-know-it, or …as-we-can-know-it, or …as-can-be-known Review this list and the lists in On Mind and Metaphysics, Problems of Mind and Consciousness, Metaphysics and the Problems of Consciousness. Integrate the lists and conceptualize THE FUNDAMENTAL PROBLEM OF METAPHYSICSSunday 9.16.01 The two sections on the fundamental problem have been absorbed to The Fundamental Problem of Metaphysics THE FUNDAMENTAL PROBLEM OF METAPHYSICS AND ITS RESOLUTIONSunday 10.7.01 PHILOSOPHY, SCIENCE AND LIFE. WITTGENSTEIN AND HUMESaturday 10.6.01 The concept of the empiricalThe empirical, empiricism has numerous meanings and shades. Look at two: EmpiricismExperience – sensation and perception rather than ideas, concepts and thought – is the source of knowledge Radical empiricismA theory of knowledge in which ideas are reducible to sensations Scientific empiricismAnother name for logical positivism Problems with empiricismThe possibility and the form of knowledge do not occur through the senses. Instinct, various kinds of non-intellectual knowledge do not occur or occur partially through the senses. Conceptual knowledge is knowledge; yet, its form does not occur through the senses. Perception is colored by mood and other factors; yet, mood is not sensory Think of the symmetry of existence. how is that symmetry, the possibility of life, perception / conception impressed upon the forms of thought, knowledge, grammar, logic, science, mathematics, philosophy, humanities, art, technology, religion, the disciplines… Think this out, especially: what is the whole? There is place for an evolutionary account What makes something [a claim, a study… ] empirical?Perception and sensation Experiment Controlled situations Repeatability The claim that philosophy is not empiricalThat philosophy is not empirical is one concept of it that, some argue, is logically necessary from the character of the philosophical enterprise Does that mean that philosophy does not refer to the world? That would be absurd. Usually, claims are not made in the dark. The person making the claim will usually have some experience with the subject matter, the methods and so on… and with the world as-it-was-found but remember that all worlds have a “found” character but that is never – proximally – complete for all worlds are seen through the medium of the knower. Therefore, there is an element of the empirical [the senses] in all claims about he world. Experiment, control, repeatability: these function to control error and bias. I could even say: there is something empirical about dreams, fiction, fantasy. Logic, too, is empirical in that it is of the world; from experience although in some sense it also transcends experience. This is especially true, regarding dreams and fantasy, even logic, when I remember that the meaning of something is not always the ‘literal’ content but include what is evoked, the mythical – the meaning transcends the story… it is the meta-literal, and the content is meta-content. A story as a whole can point at something that is other than the individual meanings and pointings. Here we go somewhat beyond the ‘empirical’: the setting up of measurement, the search for evidence, continual contact with data sources, Ockham’s Razor, Dirac’s “Its in the mathematics”… but in the end its also and largely community practice maintained that defines empiricism [sense or reference]; its in the continuity and applicability of the tradition. But, applicability of the tradition is not [merely] its practical application but a function or perceived function So, what is it about that concept, largely associated with Wittgenstein, of philosophy that makes it non-empirical? If I say something about language, am I referring to something in the world – I think so. Is it not like [some kinds of] good art: although it comes, also if not primarily, from the heart and is in a realm too complex and too suffused with sentiment [in a positive way] to even want to be empirical in a narrow way – is it still not of our world, and in that, does not it come, also, from experience? If the philosopher talks of examples, are not the examples real? Is not that true even of an imagined example? True, the examples may not be repeatable – repeatability may not even be relevant if the example is sufficiently particular; but that means, simply, that the scientific / empirical means of eliminating bias and so on are not being used. But there is one thing that, in the end, stands above all else in terms of reality: the continuity of tradition and practice – and this implies that the endeavor remains in the loop: knowing ® acting. Despite blind paths and variety, this remains true. This was also one of the main concepts of Evolution and Design So what must Wittgenstein have been saying? Perhaps, in making the point, he exaggerated the claim into the absolute Wittgenstein argued the following case for philosophy: “Philosophy is above or below the sciences. It is not beside them.” Philosophy seeks the particular meanings of ideas that science uses generically Philosophy must study the special case – it cannot build theories of language [reasons below]. Science is contemptuous of the special case [as far as this is true it is so only of the metaphysics and metaphysicians of science – those who come from science.] Theorizing about science / philosophy violates Wittgenstein’s canons and points to the difficulty of thinking of them as objects [with simple, low dimensional essences and boundaries] and about our ability to view them from a high branch atop a tree, above the mist The errors of the old philosophy [dogmatic metaphysics of Plato, Leibniz, Hegel, and the neo-Hegelian idealists of the continent and 19th century Britain and America] arose from taking the meanings of words out of their context where use stabilized meaning-in-process… and meaning was, at bottom, stabilized use The nature of use has to be studied by special cases without generalization and the method of study was to be lateral – not depth / atomic analysis… for there is no foundation in an unfathomed and likely non-existent depth and the very “foundation” of use is in its context which is lateral Thus the “way back from the desert” was to study philosophy in ways which would make the study non-empirical and especially so since both the method and “object” of philosophy is in this world and not merely as an object but as an enmeshment and therefore not something to even want to get out of – if we knew the true nature of our world – not something logically or actually to stand outside of from the clear, rarefied vantage point of a tall peak “outside, we cannot breath.” So we could go on from science and philosophy to art, literature and drama, music, humanities, and all the institutions of society: religion, politics… and the institutions of nature: physical, biological, mental… and each one would be a fortress with its own moat. This would be philosophy1, science1…; and the argument has the result that there is no philosophy2, science2… That would be taking the needs of a phase of history, and because we are slaves in front of a superior imagination, saying that that phase is the world I want to argue that there is a philosophy2, science2… I have been doing this in action [since 1960] and thought [since 1970]. So, I do not need to do this now. What is needed is a necessary rather than merely empirical analysis Hume and science – or, Hume’s brilliant errorThe essence of this section has been absorbed to History of Western Philosophy This is a good place to take up Hume’s arguments. Almost every major philosopher since Hume has something to say about Hume. Popper is a main modern example and he is thought to have liberated science from “Hume’s curse” – as well as Bacon’s curse of linear induction – just as Kant so delivered philosophy. Yet I think I have something new to say A fundamental criticism of reason typical of and due to Hume, one that is foundational, is the criticism of induction – the generalization from a set of data to a law. This includes but is more general than Baconian induction. For, given a set of data and a law that fits or explains, there is always another law that also fits. So suppose we perform more experiments, gather more data. Either the old law fits the data or we need a new law. In either case, there is another law that will fit the data equally well. An example would be one that agrees with the law on the data points but is different elsewhere. This criticism applies to all physical laws, concepts, theories… and it applies specifically to the concepts of cause or causality and space-time. I’m not sure why Hume did not apply his idea to determinism – perhaps because it would have made his point moot A simple answer to Hume is that his argument forgets that we are of this world. This is not a trivial answer because it includes the way when a theory is right it suddenly “clicks.” So, some irregular alternative, is not only artificial but, likely, excessively cumbersome. When a new law or theory becomes necessary by virtue of new data and inspiration – the law itself – the situation is different; thus Einstein’s theory of gravitation is not an artificial successor to Newton’s – and there is an history of inelegant and ad hoc alternatives to Newton’s theory that have been considered and abandoned. Hume’s argument ignores the place of intuition and aesthetics But this argument does not remove the logical force of Hume’s point. One argument that does remove the logical force of Hume’s point is Popper’s. Popper’s argument is that theories, laws and so on are always tentative and always carry their hypothetical nature: they can be disproved but not proven. The actual situation is complex for one data point that is unexplained by hitherto successful law casts doubt not only on the law but on the data itself; and, perhaps, the resolution lies in some kind of adjustment rather than abandoning either the data or the law. It is only when the weight of exceptional “data” is excessive and an alternative theory is available that transitions to new theories occur. The word “data” is in quotes because it is intended in a generalized sense. For example, the conflicts regarding Newtonian Mechanics were not merely data points; the foundations of Newtonian Mechanics were inconsistent with Maxwell’s Equations of Electromagnetism and, as it turned out, it was Newtonian Mechanics that had to “give.” What is Popper doing? He is taking science of its high perch as certain and absolute knowledge and saying that, within its own domain, it is the best explanation of what is thus far known and the best predictor within a similar domain of what is unknown. Here, though being plain and direct, Popper is being Wittgensteinian… and, just as Kuhn is ‘obvious’ so is Popper There is a way in which both Hume and Popper are right. Hume is right in insisting that science and its underlying metaphysics such as space, time and causation are not absolute. In fact this is one approach to a solution of some fundamental metaphysical problems – e.g. The Fundamental Problem Of Metaphysics and The Fundamental Problem Of Metaphysics And Its Resolution; see also On Mind and Metaphysics. At the same time Popper is right in accepting Hume’s point that science is not absolute and recognizing that this is the nature of science and, then, developing a philosophy about this point instead of wringing his hands like Hume [Popper had, of course, knowledge of two hundred additional years of history of science than did Hume] or trying to reclaim the absolute nature of science as did the Logical Positivists But there is a way in which Hume and, to some extent Popper, are wrong. The following is not fully contra-Popper but, also, complementary to Popper Hume’s mistake was that he did not fully understand the nature of scientific theories. But he was quite right in making that mistake for it was the conventional understanding of scientists and philosophers to that point and even today – despite Popper, Kuhn, Lakatos, Feyeraband – the four irrationalist 20th century philosophers of science. It is one thing to practice science and another to say what it is, what is its nature and what are its justifications – other than success. One of the, perhaps implicit, claims was that it was about certainty with regard to fact and concept – Kant invented a form of the transcendental analytic to allow this to remain true despite Hume – and that there was a logic of this truth: the logic of induction Hence Hume’s valid criticism of Baconian induction. Note: despite the evident validity of Hume and the emptiness of induction [this is quite different than mathematical induction which is a separate and distinct concept] I believe that the jury has not yet returned the final verdict, see Kinds of Knowledge But Hume, Bacon, and the rest including the British Empiricists from Locke to Russell and, to some extent Popper, miss the following point to science and knowledge. Science is not merely about explanation, validity, certainty, absoluteness. Science is also about finding and seeing patterns; the universe is patterned and the concept of a pattern is, in some ways, more fundamental than explanation, certainty, prediction. It is true, though, that a valid pattern is aesthetic precisely because it is a pattern of the world – even if an approximation it is not a mere numerical approximation but it is an approximation to the mechanism of the world – and, additionally a valid pattern is economic with regard to explanation, understanding and prediction. Surely Darwinian theory of evolution, Maxwell’s electromagnetic theory, Einstein’s theories of space-time-gravitation, Newton’s earlier theories, modern cosmology and the standard model of elementary particles reveal deep patterns of behavior and structure. And once these structures are revealed, power – both intellectual and practical – is released. The practical or instrumental covers politics, economics, technology and art; the intellectual includes the raw intellectual aspect – the ideas in themselves – and, also, art and spirit and religion… Now, it is not neurotic t be concerned about the reliability of science but it is rather neurotic, rather like the story of the goose that laid golden eggs, to set up certainty and absoluteness as absolute values To do that is to set the pyramid upon its apex Ñ – which makes it rather easy to topple over. But, since the scientific-philosophical-academic community identified with that Ñ, its toppling sent waves emanating from Hume, through history and to the 21st century Hume’s mistake is that it detracts from the real nature of knowledge and is a misunderstanding of our place in the world. Imagine being in the 31st century and assume that time to have continuity with Western Civilization and the Modern World. From that perspective, the mistake is understandable. It is the exuberance of first discovery – the origin not of a scientific theory but of science itself; it is the confidence of first discovery. But the focus on pattern restores some confidence: even if we stumble, we are still of the universe and its patterns. We are of the universe even in that stumbling; for the path of history and evolution are not linear, progressive, inexorable or predetermined: those paths are halting and experimental – we could call them nature’s experiments in being. We learn from Hume’s “brilliant” error what is knowledge and what is our place in the tidal flow of being EVOLUTION OF BEINGWhat are the assumptions to making the obvious – common sense – claim that human being has limits? There is such an entity: human-being-as-it-is I know that entity enough to say it has limits The only way of evolution beyond its defining limits [I assume there are some] is “biological” – i.e., human being cannot take over its own evolution Put the previous statement in another way. Human being is of the universe. The universe contains its own creative principles. Despite the fact that human being is of the universe it cannot sufficiently participate in the creative principle to take over its own creation Let us consider the most basic limit: the physical limits. The fundamental forces of nature; the laws of physics. Human being is subject to these! Is that so? But the universe is not something other than the origin of its own laws… Evolution and the Boundaries of BeingBeing internalizes [represents, models, adapts to…] the world: § Internalizes? § This is a generalization of mind = the functioning of adaptability …not mere adaptation or the function or functioning of adaptation A teacup has a boundary and a certain minimal amount of being. And, though a teacup functions for certain purposes as an object, its “teacup-hood” is significantly dependent on the perception and assignment that nature. The same considerations are true for natural objects such as trees and atoms but the dependence on perception and assignment and even less so for the concept of being. There is no contradiction between that and the idea that trees, atoms, and teacups have the character of being. Is there a way of “seeing” being that does not depend on concept and assignment? It is not any putative boundary of a being that makes for its being-hood ON INFERENCE[written later but preliminary] Sunday 11.11.01 to Tuesday 11.27.01 Incorporate Knowledge, Logic, Existence. The Concept of Logic and Inference: preliminaryWe want to characterize logic. The following cautions are in order: § We do not expect finality § We do, however, want to find logic as fundamental, to characterize deeply and in relation to the elements of being and knowledge § Characterizing, specifying and analysis are in interaction – therefore it is not a one step process The Concept of Logic and InferenceConsider the two historically important kinds of logic, deduction and induction. Inductive logic is nowhere near as emphasized as deduction in the 19th, 20th and early 21st centuries but, to begin, let us consider both kinds. We want as many “data points” as possible; even the consideration of spurious data may be revealing In deduction, the process of deduction leads from premises to conclusions. If the premises are true, the conclusions are true. If the premises are known or agreed upon to be true, so must be the conclusions. Thus, we get new knowledge from given knowledge. Of course, the conclusions are in a sense contained in the premises – deductive logic is one big system of tautology. But, there is more to deduction than that. Even within a given system, although the conclusions are contained in the premises, that may be difficult or impossible to see and therefore deduction is necessary; and, deduction is not a linear process from premise to conclusion for not only are the conclusions not known in advance and must be initially guessed, the proof itself must be found by trial and error. Additionally, premises, too, may be called into question, are tentative and thus entire axiomatic systems are, to some extent, in evolution On rigorConclusions follow from premises. The first point to rigor is to make sure that conclusions do indeed follow from premises. The history of logic from before Euclid, to Aristotle and to today is this: [1] expanding the scope of the kinds of assertion permitted as premise or conclusion – from simple to compound to function [predicate] statements, modal statements, an apparent incompleteness of truth and falsity as encompassing the range of truth values; and, [2] enhancing rigor. There is, however, no absolute rigor – the story begins with the logical paradoxes starting from Bertrand Russell, the doubts cast on the classical forms by LEJ Brouwer, and the completeness theorems of Gödel and continues to today; and, today, mathematicians are willing to accept paradox so as to enrich content It is important to know that error is eliminated from each step. Therefore, rigor is important even when the overall validity is of a lower grade. But, conclusions do not simply follow from premises. Where do premises come from, what is their source of power – obviousness and common agreement… and, hidden, from success. The last point is a hint. An entire system of premises, deduction and conclusions is tentative; it is empirical and when no longer valid across the domain of application, premises must be inductively modified “Rigor” is incomplete. Further, practice has it that we focus on the domain of success – this is the institutional blindness to the domain of failure. This is also true of biology, of biological constitution. In the end, we still die for our ideas – even though Popper popularized the idea that our ideas now die for us… he was talking of science; he also talked of the searchlight metaphor for science InductionInduction is, typically, a process of generalization. From a number of data points we “induce” a pattern. Or, from a set of scientific data, we conclude a law or a theory; the reality is more complex than just that. An example is Newton’s system of mechanics; it involved, at least, three main components: the idea that constant momentum is the natural state of a body so that force equals rate of change of momentum, the idea of force as mutual interaction between bodies – the concept of action and reaction… and the important special case of gravitation being given by the inverse square law, and the development of a calculus that permitted the analysis of complex forces and motions. Clearly, this was not a one step process and Newton’s efforts were continuous with those his predecessors and successors. Finally Newton’s theories, after centuries during which its conceptual and empirical domain expanded, met against some of its limits and gave way to the radical new theories of the 20th century: the new theories of space, time, gravitation and quantum mechanics. Thus, induction, is more like a conversation between data and law or between world and theory than an instruction from world to theory. But, we saw that deduction is also a “dialog”. There was a concept of the necessity of induction which exalted its status; but, the reality is less exalted but more real. Let us consider a simple example of induction to make some points. Consider the sequence 1, 2, 4 – what is the next number? That requires to discover the pattern that the sequence follows. It is easy to see that each number is double the previous and so the next number is eight. But that is just one possibility. For each number is 2 raised to the power of the previous number and, according to this pattern, the next number is 16. In this example, we found two simple patterns:
However, generally, it is not necessary to find two patterns or two simple formulas. If a law covers a set of data points, then clearly a second law that is identical to the first only at the data points also covers the data points. In practice, it should count as something that one pattern makes understanding clearer, prediction simpler just as the Copernican system was simpler than the Ptolemaic. This would figure into a “logic of deduction” and does but as an intuitive and practical point and not in any formally necessary way What is being done in induction? Generalization allows us to come up with a pattern or theory; then, we think, the theory tells us, at least approximately, about the nature of the universe. Practically, it permits prediction. In either case, we get new knowledge from old Logic as the Process of Knowledge Acquisition and “Verification”Verification in quotes because it is meant in the sense of justification; not in the sense of positive verification As a simplification, we saw that both deduction and induction involved coming up with new knowledge from given knowledge. Deduction as a straightforward process was rather lateral – premises and conclusions were rather on the same level and therefore deductive conclusions were “certain” but that was only within a given system and the certainty was no more secure than the system itself. On, the other hand, induction as generalization was not certain but that is the price to pay for generalization. However, when generalization lead to simplicity, greater predictive power; and when we find theories to transcend origins into a degree of universality we then think that the theory has captured something of the nature of things – even if approximately and in a limited domain But, is all logic acquisition / “verification” / the process of knowledge? I see a cow in the field, I then know that there is a cow in the field. Is that logic? Not in the traditional view; traditionally that is perception. What if I wanted to be really sure? Or, what if I saw a cow in my bedroom when I woke and I doubted its presence. Or, I had a dream of a cow in my bedroom and on waking I felt confused and wanted to ascertain whether there really was a cow? I could do various things. If I wanted to be sure that there were a cow in the field I could touch it, I could prod it and see if it mooed like a cow, I could look for other cows, I could look for manure and see if were like the cow manure I have seen so many times before, I could ask others for corroboration. In the case of the cow in my bedroom or in a dream, I would probably search for evidence to invalidate rather than corroborate my first impression. But, there is a process of testing in all cases. In everyday situations, I bypass corroboration; or, rather, I assume the context is adequate corroboration. Thus, there is a kind of logic that, in the contextual case, is “null” logic. Logic is the process of knowledge Then note: Logos is the process of being But: There is a dual between
being and process; and, therefore: Logos is the form of being And, Logic is the form of knowledge. There is no absolute reason that everything ever called “logic” needs to fit into this framework. That is, if for example we use “family resemblance” as the mark of all things of a kind, not everything thus far called “logic” need fall under the kind that we call “logic”. Some of the things called “logic” may fall under some other kind, others may fall under some other thing, others may be discarded as “error”. This discounts the possibility that there may be two kinds called “logic”. All this is not the result, only, of divergent / convergent / erroneous / metaphorical / analogical thinking; there is also historical accident. We can rid ourselves of the delusion that the system into which we are enculturated / educated is absolute, infallible, completely consistent, complete, perfect…
So, what I want to do is to focus on logic as the process of acquiring knowledge. I will not require that there be an algorithmic formulation. I will allow intuition and so on; but we will distinguish between formal and informal approaches and not confuse one for the other. First, I want to enquire: have we covered the modes of knowledge acquisition? Seeing a cow in a field is knowledge by acquaintance: perception. For the usual inductive and deductive process, we use language and therefore require knowledge by description. However, we saw in Kinds of Knowledge, that we can think or infer in pictures. Thus, logic is used for both kinds. But, are there other kinds? We also saw another kind in Kinds of Knowledge – knowledge by immersion. A model is tacit knowledge. But, to be able to have knowledge, the being must have the capability for knowledge – this is contained in part in the genetic code which gives the individual capacities. Now, the genetic code contains information – does it not? Is that a form of knowledge? Not in the usual anthropic or biotropic way. But, as I noted in Evolution and Design, it may be regarded as phylogenetic knowledge: picked up, without intention, during evolution; this is in contrast to the usual ontogenetic knowledge. Of course, phylogenetic knowledge is not knowledge under the acquisitive process of individuals or societies. The observation is useful because it rounds out a conception of knowledge. Can we go further? The furthest is that the possibility of universal structure, as in the formation or beginning of a universe, is the Platonic form. The Platonic forms are the possibilities of structures of all universes. Thus, there is not a separate Platonic universe; there is not a Platonic universe at all except as a metaphor. The Analysis of LogicThis is done preliminarily in Knowledge, Logic, Existence, in Kinds of Knowledge, and in as yet un-typed notes “On Inference”, and “Mathematics and its Foundations” from Journey 2001. This needs to be refined and elaborated I will also use the following ideas. The idea of knowledge as a picture of the world as a picture; this implies, among other things, a regress without external foundation. Rather than being a criticism which it is from the “justified true belief” point of view, it is a freeing and a true anchoring or centering. We are in and of the real rather than alien critics; and, but for our neuroses, we need no alien concept of certainty or alien foundation; experiment is the nature of temporal being; we can go beyond the temporal by being ever in the moment or by knowing our true nature; and, our putative limits are just that – for if the certainty of knowledge is an illusion so must be the absolute and final nature of limits no matter how real and smack-in-the-face they seem from the immediate and pragmatic view Note the following point: the analysis of logic is the analysis of knowledge [and being.] Knowledge and logic are inseparably tied together. And therefore we need Knowledge / process-logic / truth / cognition / language. What is the full field of analysis? When the system is compromised, the entire field of concepts may need simultaneous revision. The Analysis of KnowledgePresentation vs. representation. Representationalism: the mind perceives only mental images [representations] of material objects outside the mind, not the objects themselves Picture theory. How does picture theory fit in? Picture as presentation, representation, immersion in. Language as picture Immersion theory. Immersion and adaptation Phylogenetic vs. ontogenetic. Ontogenetic / acquired: dual interpretation as picture and as immersion. Phylogenetic as: body structure as adapted, as evolution incarnate, as the possibility of ontogenetic knowledge. The Analysis of TruthTruth and knowledge. Truth and logic. The concept of logic requires the concepts of truth and of inference. But if truth is compromised, so is logic. However, when the concept of truth seems compromised, it may simply be that we are using an incorrect or limited concept of truth “Definition” vs. criteriaThe meaning of this is clear. It is something like “sense and reference.” Concepts or theories of truth:Aristotle: “to say of what is that it is not, or what is not that it is, is false; to say of what is that it is, or of what is not, that it is not, is true Aristotle directly influences the semantic view and has affinities with the redundancy and correspondence views Redundancy [Ramsey] This theory says that “true” is redundant because to say that “it is true that it is raining” is equivalent to saying that “it is raining” Variations are simple [Prior, Mackie, Williams], prosentential [Belnap, Camp, Grover], and performative [Strawson] Semantic [Tarski who influenced Davidson, Kripke and Popper] Correspondence [Russell, Wittgenstein who influenced Austin and Popper] Pragmatist [Peirce, James, Dewey who influenced Wittgenstein and Dummett] Coherence [Bradley who influenced Rescher]. Notice that coherence theory is close to the idea that knowledge is the knowledge of patterns. But that makes it merge with the correspondence theory Relationship among and status of the theoriesIndependently complete and competing… or complementary? There is an element of independence and competition but that is and should not be the whole picture. Pragmatism with its selectionist account may underlie other theories so that, for example, correspondence may explain selectional advantage. That is a “vertical” relation. There may also be horizontal relations: e.g. coherence being about internal or logical relations and correspondence about external or empirical relations. The redundancy theory can be seen as a clarification of Aristotle’s position; the semantic theory can be seen as providing a more precise version of the correspondence theories To see the various theories is a gross simplification; and ignores the multifaceted nature of knowledge and truth An example: the pragmatist theoryRoughly, the pragmatist theory is “what works.” Nothing works; all we know is that something has worked in certain cases. This is Hume’s problem revisited and the answer must be the same “What works,” is refined as the practical or experimental consequences. But, the correspondence theory is one prescription of “what works,” or “what would work in all situations.” It is only in certain environments that we may determine what would work in a variety of situations. Consistency is one test; experiment is another. Thus pragmatism reduces to coherence and correspondence. What when determination of what would work is not possible, or not conceivable? We then have a broader concept of knowledge and truth: what has worked. But it remains necessary to find ways of identifying the bearer of knowledge and the criterion for knowledge. The Analysis of Thinking… Cognition…Thinking vs. imagination. Thinking as connected images for which the connection and the images correspond to the [structure and process of the] real. The Analysis of LanguageElsewhere. Sunday 10.7.01 I think this is what I wanted to say There has long been concern [since before Euclid in the realm of History, but implicitly whenever any being wanted to transcend contingency] about the fundamental nature of axioms For, if the axioms are true, and if inference is that which from true inputs [premises] results in true results [conclusions] then the theorems would be true There are two strikes against this First, therefore logic or inference is one large system of tautology in that the theorems are contained in the axioms. But the “argument” against this is trivial: that if we could see the tautology we would not need the labor of proof. But we cannot see the tautology [although we know it is so]. And, so, much of the depth of the search for theorems and proofs – including search for contradiction. Since we cannot see the consistency of the axioms, proof is one way of establishing inconsistency. However, lack of proof of inconsistency does not establish consistency. [Consistency and inconsistency may sometimes be established by meta-logical and model-theoretic means.] An example of meta-logical proof is Gödel’s proof of the incompleteness of arithmetic Second, what we would like is some method of establishing / seeing the truth of the axioms. But if we could see this truth, we could also see the truth of the axioms and would so need neither axioms nor proofs. This is why God does not need philosophy or mathematics. Schopenhauer noted this. Actually, something like this is the case although we do not see directly. Rather, proof is an aid in seeing Here is how proof is an aid in seeing. To finite minds, some things are easier to see – even if seeing, in this sense, does not guarantee truth [In this and other ways, in the realm of the finite mind, truth-as-known must take on a relative character. Regardless of whether there is a Platonic mathematics and whether we can see that in some cases, our mathematics is the mathematics of humans.] For example, it is much easier to see that 1 + 0 = 1 than it is to see the non-esoteric “Fermat’s last theorem” which proved so difficult; and it is much easier to “see” the axiom of parallels than the relatively easy theorem of Pythagoras. The interconnections between propositions can also be “seen” though imperfectly. Proof enhances seeing and confidence in seeing This discussion starts from the premise that axiomatic systems are cast in stone But they are not and this is one place where fact = value. As long as we do not know the systems to be cast in stone there is no reason that they should be; and if we did know them to be cast in stone, then that they should be so cast becomes trivial. An essence of value is that outcomes be contingent. One reason we regard axiom systems as given is the way they are written and taught Axiom systems – axiomatic formulations of, say, mathematical truth – are not fixed. Somehow, the system begins by matching reality. Early geometry tries to model space and results in the [euclidean] geometry of space. As the system becomes vast, an enterprise of its own it becomes, not the geometry of anything, but Euclidean Geometry standing on its own. It is regarded as a Platonic Edifice and also the model of Platonism. But, after, about 2000 years – of course doubts always lingered about E5, the axiom of parallels so called because it is equivalent to the assertion that through any point not on a straight line there is only one line parallel to it – it was realized [shown] that [1] both E5 and ~ E5 are consistent with E1 through E4, [2] therefore, the axiom of parallels is neither true nor false [of course, standing by itself, it would not be a candidate for truth], [3] E1 through E4 and E5 – called Euclidean geometry and E1 through E4 and ~E5 – called non-Euclidean geometry are, both of them, consistent bases of axiom systems and realizable geometries, and [4] some non-Euclidean geometries can be embedded in Euclidean spaces This is one way in which axiom systems are relative This is one reason that we do not want axiom systems to be fixed: Intuition is finite We want to remain in contact with the real – regardless of whether there is one world or there is our world and a world of Platonic forms In these ways axiomatic systems are relative, experimental and necessarily and desirably so The investment in certainty here is like the investment in the certainty of induction. We would want an axiomatic system to be final and true. Schopenhauer’s argument is like Hume’s. And, the response is similar This kind of certainty would be another example of school thought being taken for real thought. Hume, Schopenhauer, Kuhn are “bedfellows” Thus, we can and want to live with lurking and actual paradox; intuition and experience will be our first guides and the final guide will be selection On the obviousWhat is obvious to some – groups, cultures – or during some periods of history is not obvious at others § It is important to state the obvious, to see what agreement there may be. We then start with what is obvious to all – in the group – or we can regard the “common” as tentative if there is nothing tentative to all. That there will be sub-groups is not merely due to patience – for action, judgment is necessary. But, taking the common as tentative may lead to consensus. We then see what follows: consistency or internal / external inconsistency; in the latter case – “back to the drawing board.” In this way axiom systems are experimental; and the equivalence of alternative axiom systems or models may be established. In this way, thought moves forward. In this way, mathematics and logic are experimental. This is a unified logic of logic and of science How do these considerations and the timeless philosophy intersect and relate? Where lies the metaphysics of presence? Is there a Logos? Can it be known? The world or universe that includes our thoughts = Logos? Details vs. abstraction Do we know Logos? Do infants? Animals, plants… § From what is obvious may follow what is not obvious. Therefore, it is necessary to state the obvious § What may seem or be obvious when stated may not have even been thought before On abstraction and generalityAbstraction lays bare what is essential, ignores the hair. It makes for easy agreement on what is common. Good abstraction, as part of the axiomatic process, is not one-off but us part if an experimental loop. So, good abstraction is not mere abstraction Abstraction enhances generality: applying the basic concepts to systems of wider scope and applicability. For example E2 ® … 2500 years … ® RN … Details and particulars can be studied independently or within a framework of abstraction and generality. But, again, this is not one-off or a simple case of details to generality or the reverse but is part of an experimental loop An example: independent universesThink of a line E1 in a plane E2, and a line parallel to E2. If the two lines move steadily toward one another, they must touch at some time. But if we lift one of the lines out of E2 into E3 then, the two lines can pass without touching Now think of our universe as all that was, is and will be. But there could be another embedded in R5 that did not touch our universe. What does this mean? These seem like ghost universes: each is a ghost to the other. But there is a scenario when, together, they both = F. Although causally separate, they are still “one.” ON INFERENCE IISunday 10.7.01 In the following “Þ“ means “implies” The law of inference “if A Þ B, then, whenever A is true B is also true” says very little – it is a definition. It is the definition of implication. This should be part of the concept of implication rather than an axiom 1. A Þ B does not mean that A causes or caused B. Review examples to show implication without causation and causation without implication. Examples are not necessary because without further specification, causation is a vague concept 2. A Þ B does seem to mean: If A Þ B and B Þ C, then A Þ C But that, too, is not saying much. But it is a law of logic and is the principle of proof – in steps But, what if Ai Þ Ai+1 for all integer i. Then, if A1 is true are all Ai true? And, if A¥ exists [how, in what sense?] does A1 imply A¥ 3. However, the following law of logic: [A Þ B] Þ [~B Þ ~A] unless the law of the excluded middle holds, i.e., unless propositions are either true or false. But, [2] does not need the law of the excluded middle Where does the variety of logics – predicate logic, modal logics… – fit in? The last fortressSo many institutions of human security and certainty are supposedly gone. Copernicus, Darwin, Nietzsche, Darwin, Einstein, Bohr, Freud, Existence and Causation… and, now, even analytic certainty – that shadowy symbolic certainty: the Last Fortress, the final refuge Even that begins to crumble. It depends on the contingencies of language and thought: that, regardless of correspondence or coherence or pragmatism or pictures or picture-less symbols, of presentation or representation: truth is not crisp even though the concept of truth may be presented as so But, what kind of man or woman seeks refuge in these things – one already indentured into bondage Without fortresses, being is infinite MATHEMATICS AND ITS FOUNDATIONSThursday 10.11.01 Mathematics and its Foundations ON YOGA: A TALK DELIVERED TO THE SKY AND THE WIND AT ENNI CAMPThursday 10.11.01 Combine with the earlier version of yoga Combine vision, meditation, dynamics of reality and being[?],yoga… I should not be talking to you or the people because you know much and have practiced yoga much more than have I Some of you know yoga as a series of exercises – Hatha Yoga. Hatha Yoga is good for health and as preparation for meditation In Sanskrit, Yoga means “yoke” meaning union – the positive union with the real, not a yoke of burden or the yoga of ignorance. There is a philosophical system Samkhya which is the foundation of yoga. Yoga is also outlined in the Bhagavad Gita in the metaphor of Arjuna faced with a terrible choice on the battlefield of Kurukshetra where to do battle is to kill his kin. But Sri Krishna, “the Lord”, is there, telling him that to not fight is mean, dishonorable. The battlefield is a metaphor for life and the voice of Sri Krishna is the voice of the self, of conscience, telling us to go not disengage from life and action, to act – in full awareness of but without attachment to the outcome. The Gita goes on to outline the ways of yoga: action, devotion, knowledge and meditation There is another message from another system – Vedanta. Brahman, the ultimate real known as external reality is identical to Atman, the self, the ultimate real known as inner reality through meditation. The metaphysics of presence… the presence of presence Yoga is union with self. Knowledge, real acceptance Everything else is a way or method. The ways listed above. Or, in their original names: karma, bhakti, gñana and raja Union is process Life combines these elements without naming them MAP OF MINDThursday 10.11.01 IntroductionI have approached this topic many times – giving lists and logic but never completing the “map”. My thought has reached sufficient maturity; I can now give the map a completed form THE ORIGINS OF LANGUAGEThursday 10.11.01 A MAP OF MY WORLD / A MAP OF THE WORLDA Map of my World / a Map of the World DESIGN: HORIZONS ENTERPRISESFriday 10.12.01 Absorbed to Design for a Journey in Being DESIGN: A JOURNEY IN NATUREFriday 10.12.01 Absorbed to Experiments in Transformation of Being SURFACE AND DEPTHTHE TRUTH CAN BE KNOWN |
