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Dear Reader! I do Information Retrieval now and re-wrote the present Sketch as
that concerns Information Retrieval.
Russell B., "The Problems of Philosophy" 1
V. Mayakovsky, "Now Listen!"
It is interesting to note that more than two millennia ago Plato already said that "...nor can we reasonably say... that there is any knowing at all, if everything is in a state of transition and there is nothing abiding" 10 because there are no things in a moment of time right now 11 -- we must, if we use the deductive method of thinking, always study things in the past continuous/ present continuous but nevver in the simple present. It seems likely that even if "...we have just accepted that it is impossible to be and not be simultaneously, and we have shown by means of this that it is the firmest of all principles" 12 and if we have to admit that we must not say about the same coffee that it is hot and cold simultaneously, we may say that there exists this coffee -- the "scholastic" substance-essence of this coffee -- and that as for the terms 'hot' and 'cold', they mean nothinng positive in the substance of coffee considered in itself, nor are they anything other than the mode of thought, or notions, which we form from the mutual comparison of different conditions of the substance of coffee! By implying the preceding idea I see that if we do not exclude the notion of the change -- the hot coffee is becoming the cold coffee and vice versa -- from our thoughts and continue to follow the typical Aristotelian logic, we come to a dead end: we must either say that there is coffee that is cold or hot right now but we do not have the means to explain its modifications; or to formulate the new logic which will state that there is no moment of time right now and that everything is becoming: one can say that one does not see the hot coffee but the potential cold coffee -- the hot coffee must always change its condition as long as it is not in the condition of balance with its surroundings; one is capable of stating that one observes not the cold coffee that ' is ' but the former hot coffee that has become the cold coffee because it has changed its condition and, probably, has gained the condition that adequately reflects the condition of its environment; one cannot deny the existence of the substance of hot and/or cold coffee if it exists, but one must notice that it is not ' this ' coffee -- it is always becoming hot and/or cold. Accordingly, one's faculty of affirming and denying what is true or false concerns only the ability of the substance of coffee to become and/or of changes of its condition, but does not concern the possibility that coffee become or not become. It only looks like one is stating ' this ' and not ' this ' about the same thing at the same time. Now, I feel that I have every ground to suppose that infinity of time is the continuity of changes in the condition of substance, such that as soon as the hot coffee will become the cold one, continuity does not cease to be, nor infinity of time to exist 13 for substance: coffee will continue to transform its condition. And the question of my inquiry now is: does it strive to attain the condition of invariable 'simple' substance 14 ?
To remedy the situation I would like to propose the following foundation for my "new" logic: any process, which we have before our eyes, is not important -- only the result of an action has to be contemplated but not the process that preceded this result: this logic is the logic of absolute determinism! In view of this conjecture I think that "for the end should not be just any last thing, but the best" 15 , and that in the end everything will have the same quality -- the best 16 ! I state that 'the best' are universals which always exist in the simple present time, and that these universals are usually called Forms, Ideals, the Reality, Absolute, 'things-in-themselves', Monads, the 'simple' substance, Natural numbers, knowledge, etc. -- they are always given but are not and cannot be taken. A significant gap in the history of contemporary scientific thought can be filled if I risk postulating that there is only one best, and that the best cannot be disassociated from the best: the froggiest frog is the same as the doggiest dog and humanest human being; where all these abstractions or, in other words, universals are the result of the development (!) of these things and are the universal concepts of these things. My next step is that I would like of necessity to insist that 'the best' is not a plural but the only singular term which exists, and that there is only one universal even if there is a plurality of them: I plan to surprise Socrates' soul (which is held, as everybody knows, in a special underground storage 17 ) by trying to "prove that what is simply Unity itself is many or that Plurality itself is one... " 18 . I assume that for things to become the universal(s) means that they reach their Limit, and that there is only one Limit for all things, and that this Limit is existence without changes. In such an event, universals and the Limit are the same: they are the invariable standards of what all things strive to become 19 -- the 'simple' substance. A good example of this singularity of the plurality of universals is an empty set -- the cardinal number card A of all empty sets is equal to null and, therefore, they are the same, but there is a plurality of empty sets even if they are the same; and only the empty set(s) is/are the set(s) of universal(s) 20 .
Somebody must somehow begin to clean the Augean stable of physics. And with this honorable idèe fixe in my mind I am brought to a well known and much-debated question: does Ether exist? 9;Michelson pondered this problem and it led him to invent the Michelson interferometer, which was capable of measurements of the required sensitivity, and to plan the ether drift experiment which he carried to completion in collaboration with Edward W.Morley in Cleveland in 1887. This famous optical interference experiment was devised to measure the motion of the earth through the ether medium by means of an extremely sensitive comparison of the velocity of light traveling in two mutually perpendicular directions. The experiment, when completed in 1887, gave a most convincing null result and proved to be the culmination of the long nineteenth century search for the ether. In the theory which I have the pleasure of presenting, the null result of this experiment is the major evidence in favor of the existence of Ether. If I believe that universals constitute the Ether and that the Ether is composed of nothing , what is nothing ? And why did I claim that universals are in the simple present time and that they are nothing ?
Hegel said that "...pure being is the pure abstraction , and hence it is the absolutely negative , which when taken immediately, is equal nothing . From this... a definition of the Absolute followed, that it is nothing ... Hence, the truth of being and nothing alike is the unity of both of them; this unity is becoming ." 21 According to the general theory of Idealism everything aims to become unchangeable, eternal, and to find its end in truth 22 -- in 'the best'; where the only universals are the changeless ones. If I think that Ether is formed by universals I muust, in protecting the name of Idealism , identify prototypes of these universals in the real world: what do they look like, how is it possible or not possible to observe/detect them?
Do we have a universal constant that can be taken as the foundation of absolute calculation in physics? Do we have anything that is constant and invariable? Putting everything in its rightful place, I have to note that the 'Theory of Relativity' seems like it can offer this absolute uniform or -- as applied to the theory of Idealism , the universal -- the speed of light. The suggestion that in this universe -- where nothing is stable and invariable in the eternity of simple present time and can be taken as the standarrd -- a particle, which has the greatest possible speed, exists, means that we have a universal right before us. Certainly, the answer to the questions: does light have a mass at rest and why does it not have it? is that light does not have a mass at rest because light in the condition of rest is nothing ! I do not see any valid objection to the following supposition of mine: all things are sets of particles, each of which is constituted by the smallest particles; and the smallest particles(or, what is the same, apeirons 23 ) have the mass of light in rest. A new question is: how are universals able to avoid opposing themselves and others if "ultimate reality is such that it does not contradict itself; here is an absolute criterion" 24 ? They are able to do so only because they do not exist in interaction! What does it mean that 'they do not exist in interaction'? As everybody knows, Plato said: "Do you then want us to assume two kinds of existence, the visible and the invisible? /Let us assume this. /And the invisible always remains the same, whereas the visible never does? /Let us assume this too." 25
About which two kinds of existence could Plato speak? Berkeley believed that 'Esse est percipi' 26 but I imply that this formula must be transformed to " 'to be' is becoming 'to interact'" or, what is the same, " 'to be' is becoming 'to become'". If this conjecture of mine is accepted, I expect that I have power to infer that Plato's two kinds of existence are: 1)the existence with interaction and 2)the existence without interaction with others. If so, I think that light does not have mass at rest as long as it does not interact with other things: universals are universals inasmuch as they are abstract concepts of really existing things or, what is the same, they are the 'things-in-themselves' 27 . On that account, I have to say that the universals are something in the simple present time -- in non-existence ; and in the effect of their becoming things all other things must change themselves if there is thee Whole.
The theory of internal relations points out that, according to kindly cynic Ecclesiastes, nothing is always new under the Sun; and that any 'old' idea suddenly and always returns in a new form after a while. As for me, the idea of the Whole means that there is a finite number of the smallest parts of this universe 28 -- apeirons -- and there is the Supreme Monad that contains in itself the Whole world. Another reason why I begin to usse the idea of the Whole is that I suppose that it is not necessary to be as smart as, for example, the idol of all physicists, Einstein , to see that, according to my reading of Hume it may be inferred that the force of interaction between all things depends on a defect in the things; where there are reasons to expect that the force of interaction is the Measure of the Ether -- the doctrine of the Whole is the doctrine of the internal relations: "All parts of each form must have a relation to each other and to the whole; and the whole itself must have a relation to the other parts of the universe, to the element in which the form subsists, to the materials with which it repairs its waste and decay..." 29 "It must be acknowledged that there are few parts of the universe which seem not to serve some purpose, and whose removal would not produce a visible defect and disorder in the whole. The parts hang all together, nor can be one touched without affecting the rest, in a greater or less degree." 30 At the same time, Hume conjectured that: "There is not probably at present, in the whole universe, one particle of matter at an absolute rest" 31 , or, in Aristotle's words: "Now it is evident that among existing things there are some that are something in motion and something at rest." 32 Hume gave a definition of parts of the Whole -- of things -- as of something that moves, and has defects. Consequently, if universals are at rest things must not bee at rest. And now we may take a look for comments that occur in Hume's "Dialogues...", where Hume said: "A defect in any of these particulars destroys the form,...till it unites itself to some other regular form ...and, by its very nature, that order, when once established, supports itself for many ages if not for eternity." 33 Is this the Law that is immanent in the substance? Absolutely! It suggests that "this world, therefore, with all its events, even the most minute, has been produced and destroyed before, and will again be produced and destroyed, without any bounds and limitation...": parts of the Whole strive to unite themselves to universals. Among other things, I can make a conclusion that the appearance of a constant ' G ' in Newton's interpretation of Kepler's law of gravity 34 is an argument in favor of the existence the Whole and that Newton's three laws of physics are laws of interaction only between two abstract(!) solid things; which laws do not observe the changes in all other things during these two things' interaction. This explains why Newton's version of Kepler's law and Newton's three laws coexist in physics: Newton's three laws are good only for the world of universals, while Newton's version of Kepler's law is appropriate for things. All the above offers the means to see that a metaphysic of internal relations is the metaphysic which strives to explain the presence of the constant in Newton's redaction of Kepler's law of gravity: there is the Whole, and any change in a part of the Whole means a change in all other parts of the Whole. Simultaneously, it is presumed that the Whole is a universal which can be imagined as an empty set; where any not empty set strives to liquidate its defect and to become an empty set which does not have any defect. Summarizing, any modification of 'things-in-themselves'/ Monads into things can be found -- an empty set suddenly becomes a set that has an actually existing cardinal number 35 . What is more, there is no portion of Ether which may influence the path of the motion of things without becoming the interacting thing -- the 'ether medium' does not exist, and any attempt to find the drift of Ether will end with the question: how can the immovable move?
If universals exist in the simple present time the Laws of Thought for things must be radically different from those for universals, because it is easy to see from Plato 36 that "the verb 'to be' must be totally abolished -- though indeed we have been led by habit and ignorance into using it ourselves more than once, even in what we have been jusst saying. That is wrong, these wise men tell us, nor should we allow the use of such words as 'something', "of something", or "mine", "this" or "that", or any other name that make things stand still. We ought, rather, to speak according to nature and refer to things as "becoming", "being produced", "passing away", "changing"; for if you speak in such a way as to make things stand still, you will easily be refuted" 37 : The Law of identity: 'Whatever is becoming, is coming to be universals.'The Law of contradiction: 'Universals can both be universals and become things.' 38 The Law of the excluded middle: 'Universals must either become things or be universals.' I must say, at this point, that all sciences work with particles in past tence and, it has to be underlined, they try to use both deductive and inductive methods of reasoning with the same certainty according to examinations of things that had been done by these sciences in the past: they endeavor not only to infer universals from the objects of their experiments but to make these objects the universals 39 . However, metaphysics deals with objects in the present continuous 40 and states, in spite of Hegel, that what seems reasonable may become actual, but what is actual is reasonable 41 . Furthermore, sciences have only changed the world in various ways but the metaphysical point is to consider it in its becoming without getting involved in the universe of things. It is also presupposed that:-- physics is the science of external relations and, accordingly, the science of internal relations is metaphysics: physics aiims to fix and to describe facts and metaphysics does not 42 ;-- philosophies are kinds of activity, inasmuch as their essence, even in their most abstract and otherworldly aspects, consissts precisely in making one-sided and abstract determinations valid in their isolation, in accord with the individual's interest of the moment and particular situation 43 ; in contrast, the effort of metaphysics is directed to the absurd end of expressing the content of substance by means of pure cognition, hence of uttering the unutterable; 44 -- philosophies interpret results of scientific researches; the metaphysic explains them; -- one may become the indisputable judge 45 of and for everything -- Pure Reason; thhe 'new' science after physics simply points to opposites and leaves the right to choose the way among them to a school of thought -- to a philosophy; a school of thought forces one to choose the exact path for one to operate with and under contradictions: "Enter ye in the strait gate: for wide is the gate, and broad is the way, that leadeth to destruction, and many there be which go in thereat: Because strait is the gate, and narrow is the way, which leadeth unto life, and few there be that find it."
Let us consider the next query: if things are continually interacting, what changes inside these things at the time of this interaction? If they can take place in a vacuum, how can they move to this place, where they had not been before; where is it now? For the answers to these questions, as can be readily appreciated, we must define the term 'distance between' any two points. Traditionally, all laws of physics, such as, for instance, Coulomb's and Newton's interpretation of Kepler's law, use this term. But I insist -- though it seems a ridiculous thing to say because the prevailing view today opposes this conjecture of mine -- that the forrce of interaction does not depend on a "distance between", which traditionally is the reverse proportion of the square of (I am not afraid to say this) the mysterious variable -- the distance between two things in Newton's Law of gravity. I am not even striving to look original. All I am attempting to do is to use Kant's Cosmogony as the basis for Lyapunov's theory of Celestial bodies, and both theories as the reason to totally abandon the necessity to employ of the term 'distance between' meaning in any study of nature and as a reason to begin using the term ' orisphere' . By the way, even Empedocles of Acragas a few millennia ago thought that divinity is spherical and that the two opposites, Love and Strife, rule this world. I admit, according to my understanding of Empedocles of Acragas, Kant, Lyapunov and Poincare 46 that this argument can be understood and interpreted, first, as a changing variable; in fact, secondly, it is connected to the radius of the orisphere 47 , but not to the mythical 'distance between' in the nowhere 48 of vacuum. This maneuver has shifted the emphasis of the problem of searching for centers of mass for all interacting things -- which are needed as the centers of and for Cartesian reference frames -- to the problem of examining what the term ' orissphere ' means. It is evident to me that all Laws of physics ought to be re-established and seen in the following way: any mass-matter-content has only one strictly determined volume-form-shape and vice versa 49 , for things. Naturally, the manner in which atoms, planetary systems etc. are arranged in connection with that order, which is determined by Mendeleev's table 50 , is evidence in favor of this supposition. I see and understand this order to mean that in the simple case of two similarly oriented Cartesian reference frames, moving along their common (x,x') axis, the transformation equations cannot anymore be put in the form:x'=x- v t y'=y z'=z t'=t, -- where x,y,z and x',y',z' are the space coordinates of a given thing, and v < is the speed of one system relative to the other: the internal concept of relations, turning the world of scientists upside down, states that there is no space between things but the spaces of things 51 .
Now everything falls into place. Paving the way for the 'new' science after physics, I can formulate the rule of Nonpredicative Definition: Any parts of the Whole Definition are Nonpredicatively defined: it is impossible to define one part of the Whole Definition without using in it all the remaining parts of the Whole Definition; modification of one part of the Whole Definition is a modification of all the remaining parts of the Whole Definition; All things are Nonpredicatively Defined: it is impossible to give the Whole Definition to any thing without defining its interaction with all the other things; any modification of one thing is a modification of all the remaining things. This Whole Definition emanates from the supposition that if all things have form and matter all changes in the conditions of things should be detected only as modifications of the forms and contents of these things:
where m1 is one interacting thing's matter and l1 is its space -- orispher ; where m2 is another interacting thing's matter and l2 is its space 52 -- orispher ; where tr and tr' are trigonometrical functions: sec, sin, cosec and cos ;where 0 is nothing : the condition of rest; where d l and d m are the increments of the matters and spaces of things; they are called 'appearances' 53 : if d m and d l do not exist then (l/(m + d m))*tr( d l/ d t) and (m/(l + d l))*tr( d l/ d t) is equal to null -- these things are nothing ;where F is the continuously modifying Measure of Ether or, what is the same, the force of interaction between things;where d t is an interval of time less than an interval of time between two extremums ; where an extremum is a moment of time, when the given things rest; where L/M or M/L is the Factor of the Event Associativity of substance, called Zolt Factor 54 ;where there is the Lomonosov - Lavoisier Law of Preservation of substance: m1 + m2 + 2dm + dM + M' = Mon, l1 + l2 + 2d1 + dL + L' = Lon, where Mon and Lon are the theoretical mass and space of the Supreme Monad; where M' and L' are the sum of abstract masses and spaces of all smallest apeirons , which constitute Ether. The Density of substance such that:
is called the continuously modifying Density of substance. If the continuously modifying Density of substance is constant:
the continuously modifying Density of substance is called the Density of "things-in- themselves": if the hot/cold coffee has gained the condition that adequately reflects the condition of its environment, it has the condition of a 'thing-in-itself' 55 . The definition of Inertia emanates from the preceded equations:In = P'- P where 'In' is called the continuously modifying Meaning of Inertia.
However, the story is not completed as long as it is not apparent that according to my generalization of Aristotle's idea 56 the virtue of concurrence is different from knowledge: it is neither teachable nor recollectable -- it is the immanent in substance striving to concur with the better and to become better 57 . It means that that any definition of any language 58 should become 'the best' due to the virtue of concurrence -- thoughts, which cannot be expressed laconically are not correct and any obscurity of understanding ends in the simpllicity of the clarified pure knowledge. This is of prime importance to see that the diversity of things in their qualities resides in their predicates, and that it is to be found only in the appearances of this 'simple' substance -- things are what they are by virtue of their qualities, and if they are to lose their qualities they become what they are not: nothingness of the 'simple' substance. The 'simple' substance must appear: the composite substance is what interacts; Nonpredicative definition shows that the 'simple' substance without its appearances does not consist of parts-things and cannot be pictured: there exists, indeed, only the 'simple' substance that cannot be touched and put into words -- Absolute. It makes itself manifest: it is that which is traditionally thought to be mystical 59 because "the absolute maximum is beyond our comprehension yet intelligible, able to be named whilst remaining ineffable 60 ... Every affirmation puts, so to speak, in God something of the thing it signifies; but He is as much all things as He is something; therefore, all affirmations are inappropriate. If, therefore, affirmative names are used, they can only apply to Him in relation to creatures..." 61 In this regard, "...the mystical is the concrete unity of just those determinations that count as true for the understanding only in their separation and opposition. ...everything rational can equally be called "mystical"; but this only amounts to saying that it transcends the understanding. It does not at all imply that what is so spoken of must be considered inaccessible to thinking and incomprehensible..." 62 Summarizing, I conclude that the notion of the mystical-transcendent nothing is already used by scientists as the notion of abstract ideas although they have not realized this yet: universals in our minds are meant to explain how it is possible to think generally about things of one kind and how it becomes possible to attach a meaning to common names.
"To every action there is always opposed an equal reaction...", "if you press a stone with your finger, the finger is also pressed by stone...": Newton's Law is a Nonpredicative definition in itself. However, what I am interested in rather is the suggestion that as long as things are open sets of things 63 , the bigger the quantity of apeirons that are 'defective' because of their interaction/interacting as result of of their defects concurred into the given open set, the smaller the changes of mass and space of each particle of the given open set of these things during the mutual modification with others, and vice versa 64 . For example, parts of a man who is falling to the Earth change their condition much quicker than the condition of any part of the Earth because the quantity of apeirons within the man is much less than the quantity of apeirons within the Earth, but to an observer it seems like time for the Earth changes much more slowly than for the man, if the man travels with great velocity. This is not true: "time is therefore a purely subjective condition of our(human) intuition (which is always sensible, that is, so far as we are affected by objects), and in itself, apart from the subject, is nothing. We cannot say that all things are in time, because in this concept of things in general we are abstracting from every mode of their intuition and therefore from that condition under which alone objects can be represented as being in time. 65 " An observer (according to the Lomonosov - Lavoisier Law of Preservation of substance) cannot be freed from the interaction between objects of observation -- all changes in objects must be seen through changes in a subject; also, if two components of the only Whole Definition are changing, the third component -- the Factor of the Event Associativity of substance -- may change if nothing becomes the thing(s)-apeiron(s) 66 . It means that the appearance of the attribute of existence in interaction -- of Time -- is not something to changes, but an observer is.
There are some axioms of the theory of Absolute Positivism for the irrational world of absurdity: Axiom 1 . There is the ultimate Reality -- the 'simple substance'; where this substance is that upon which all predicates exist, while it is itself not predicated on anything else 67 . The 'simple' substance is the universal nothing ; the 'simple' substance, as the Whole, is things which became nothing ; things and the 'simple' substance are parts of the only Whole Definition. Any qualitative description of things, which have an opposite, is called a 'predicate'. In fact, such parts of any language as verbs, adjectives, participles and gerunds are qualitative descriptions -- they contain (sometimes covertly) a metrica (a "distance between" two things which interact) within themselvves. There are three conditions of substance:- Yang ; substance has three measures for any point: form, matter and time;- Yin ; substance has two measures for any point: form and matter;- Li 68 ; substance has only one measure for any point: Existence in the eternity of immovability; 9;where words exist only for Yang condition; where all Irrational numbers are the immanent quality of the Yang condition of substance: if there are the given geodesic path a and a point A not on a , there is no geodesic line (path) through A , which lies in the plane containing both a and A, and which does not intersect; where all Rational numbers are the immanent quality of the Yin condition of substance: if there are the given geodesic path a and a point A not on a , there is only one geodesic line (path) through A , which lies in the plane containing both a and A , and which does not intersect; where all Natural numbers are the immanent quality of the Li condition of substance: if there are the given geodesic path(line) a and a point A not on a , there is more than one geodesic line (path) through A which lies in the plane containing both a and A, which lines do not intersect; there is no path that can be drawn through the point A .
On my account of this theory, is the space of things the measurable by the constant metrica topological space -- the metrical space? Yes, it is! But only for the Li and Yin conditions of substance can the unaalterable metrica -- an apeiron in rest -- be determined 69 ! All Axioms of Separation can be useful for only these two conditions of substance, but not for the Yang condition. In the Yang condition of substance there are no things that can be separated from others, and, after all, in time all three conditions cannot exist independently but simultaneously: a change of one must be reflected as a change of others. And this is the general conclusion to which I am driven with regard to the existence of the 'simple' substance: three different kinds of points exist, two of which exist as nothing ; where I assume that making a cut 70 in the infinitum of changes of things does not mean making a cut in the eternity of Existence . All things, with the exception of apeirons , are open sets of continuously interacting things and they are called Accumulation Points 71 , or simply -- Points. Universals in the Yin c ondition of substance are called "things-in-themselves", or points of the Whole Accumulation 72 , which points contain all things from their neighborhoods in themselves or, simply -- a Point. 9;The Supreme Monad/Monads is/are the point(s) of Absolute Accumulation, which does(do) not have things in its/their neighborhoods, or the 'simple' substance 73 , or simply -- the Point(s).
In a broad sense the absence of any kind of substance -- vacuum -- is not nothing : for in the nature of things nothing is given besides substance -- a vacuum does nott cut the chain of interaction between things. One more time: there are no things which change into the space of this universe, but spaces of things change because they do: space exists only for and within particles. This assumption gives me all the necessary power to insist that vacuum is neither space nor nothing nor something 74 : it is nowhere 75 .
In the search for certainty, it is natural to begin with my own experience, and, no doubt, my opinions are derived from it; where the authenticity of experiments, which form my experience, is determined by the probability of their repetition 76 . Looking for some general Law to which there are no exceptions I ought to note that: Axiom 2. The probability of repetition of any experiment exists 77 . This Axiom signifies that the Yang condition of substance is in the condition of transcendental and algebraic Irrational numbers which transforms one to others 78 . Citing Poincare I claim that "...it is clear that the causes which produced a certain effect will never be reproduced except approximately. Then we should modify our postulate and our definition. Instead of saying: 'The same causes take the same time to produce the same effects,' we should say: 'Causes almost identical take almost the same time to produce almost the same effects(p.227}. ...The observed action then will never recur; the only thing that can be affirmed is that under analogous circumstances an analogous action will be produced(p.128)" 79 . This speculation proves that blind faith in the absolute perfection of thinking, like blind faith in anything else, is an unsophisticated use of universals -- scientists use what I call the "Measure of Abstraction": they calculate probabilities -- they round Irrationall numbers -- and infer nothing .
According to my supposition that there exist both things and the 'simple' substance, I can assume that null is the 'simple' substance and, therefore, can the Whole numbers be things? Idealism studies not objects, but the qualitative relations between objects in their becoming; the replacement of these objects by numbers is therefore indifferent to it: things exist in the Yang condition of substance exclusively and the Whole numbers are not things. But what are they? 9;Is zero opposed to the number one of both signs? If we take a look at Plato we can see that he asserted that an "opposite thing came from its opposite thing" and "the opposite itself could never become its opposite, never that in us or that in nature" 80 . Based upon these assertions may I say that in all judgments in which the relation of zero to one is thought this relation is possible only in two different and similar ways: one is equal to or, what is the same, is becoming zero, as the notion of things which is(covertly) contained in this notion of nothing ; and one lies outside the concept of zero, although it does indeed stand in connection with it? May I admit that the number null and number one of both signs are the ultimate frontier numbers of and for all continuums -- the universals? In other words, I strive to prove that these two numbers are a pair of opposites 81 ! By these two numbers, I mean minus and plus one and zero; where I think there is not a difference between the number One of both signs: any closed set has a cardinal number equal to the cardinal number of the empty set and, consequently, we have two equal closed-empty sets of different signs 82 . I assume that the row of Natural numbers is the row of whole numbers, which means that they are apeirons in rest, but the row of cardinal Natural numbers is the row of numbers which count apeirons . Put another way, if one counts things, this one counts 'things-in-themselves'/Monads which are imagined as unchangeable things that do not have any qualitative characteristics in themselves and are not these things but only their abstract concepts -- Natural and Rational numbers 83 by virtue of cardinal Natural numbers. I think thhat: 1) 'things' mean qualitative measures- descriptions of the 'composite' substance -- things are sets of apeirons ; 2) 'a universal' means that the former thing does not have any nature and are the 'simple' substance -- a universal ' is ' an apeiron 84 . It is reasonable to expect that the 'simple substance' as the One is opposed to the plurality of things and that the process of converting the One to the plurality of things is that mysterious prime move for the substance as the Whole 85 -- the death of the One (the Supreme Monad most probably was not and will not be formed and the notion of the prime movvement may not be required: common logic loses its foundation). Anyway, the geometry of the Li condition of substance determines the interaction of apeirons following the death of the One. One may ask: what does two, three, and etc. mean? If there are apeirons , I can say that two means that one must consider two as the notion of some apeirons , which the notion -- as a class notion 86 -- is imagined to contain two apeirons in it; howeveer, there is no diversity of qualities within the Whole: the One' and 'one' are the only proper names for apeirons -- not two, three, etc. and the row of Natural numbers contains only one member -- the number One.
Axiom 3 . Any cause is consequence, any consequence is cause; the continuous interaction of things is both cause and consequence, within the time of the infinite changes of things; where this Axiom shows that if we use the deductive method of reasoning we should examine things only in the past continuous but not in the simple past/ past perfect time;where it also means that if sciences work in perfect times -- they consider limited quantity of final causes and consequences in finite intervals of time D t -- they stay out of ethics answering questions 'What?, Where? and When?'; where ethics is actualy only in continuous (!)) times and metaphysics cannot be thought without the ethical question "Why?" for this imperfect (!) world of things. And this is the primary difference between the science after physics and physics! (Philosophies are kinds of activity and they strive to answer the question "How?") Axiom 4. What appears as active in certain respects, consequently appears as passive from another point of view -- what comes into view as real in certain respects, becomes illusive from another point of view 87 .
If "we are wrong when we say they 'are', since nothing ever is, but everything is coming to be" 88 because "...the movement of any part is for the perfection of the whole..." 89 but the first change "would be change for worse, and this would be already a movement" 90 does it have to be correct that things must come into being out of the conditon of rest?
Let me take a brief look at the arithmetic and dialectic of language and at the language of arithmetic and dialectic: the claim a = a must be explicated: If the term ' equal ' means that a 'is' a it follows that a ' is ' a if, and only if, a ' is ' the 'simple' substance; otherwise these two things with the same combination of qualities and, therefore, with the same name ' a ', should oppose each other in their becoming, because a ' is ' either unique or ' is becoming ' probable -- universals must either become the plurality of things or be the singularity of the One: there may be two idenntical tables but the 'simple' substance is absolutely unique several identical things are to be imagined as the same Irrational number, and only in this sense are they indistinguishable. Nevertheless, these several alike things are subjects for the virtue of concurrence and they can be distinguished because they change. It means that there is the the closed set T that is bounded from below and above, the set of whole and positive cardinal numbers:l <=k <=N, where N is the greatest (frontier) number of the pair of constant meanings of mass and space of the Supreme Monad 91 ; where k is the number of a pair of constant meanings of any given thing's mass and space in this set T 92 . If all operations of summing and subtracting (' + ' and ' - '), mean that two opposite things with the same name ' a ' are interacting and that these things mutually compensate for their Meanings of Inertia and, in practical terms, they are becoming the 'simple' substance (they should get the form 'one = null' or, what is the same 'one = the One') the only correct expression is: a - a = 0 Therefore, if the sign ' = ' means that contraries are becoming nothing any correct assertion should contain the notion of antipodes 93 and, simultaneously, the notion of all conditions of substance should be presented in any actual statement: Pure Truth - Pure Lie = 0 (the becoming 'simple' substance is becoming the being 'simple' substance and this is the Whole definition of the "continuous movement, or circular movement therefore");where this assumption expresses the ultra -relativistic nature of Idealism -- substance must always change.
It is easy to see that the Yin condition of substance is the condition of the first derivative of the 'simple' substance; the Yang condition is the condition of the second derivative of the 'simple' substance:the 'simple' substance ' = a thing-in-itself; the 'simple' substance '' = things 94 . It follows that any proper name, any opinion about things that can be used by one without any supplementary description has a meaning of the first derivative from the 'simple' substance -- of an abstract idea: for instance, the meaning of the term 'house' without the notion of changes does not need predicates; this term has in itself only a general idea of form and content 95 . The condition of the second derivative affixes predicates to things; which predicates are able to describe and to distinguish one from all others in their diversity. As a rule, verbs, adjectives, participles and gerunds serve this purpose: they signify the presence of the Force of Interaction or, in the traditional terms, the presence of acceleration. Moreover, insofar as predicates manifest changes of things they are also to be imagined as Irrational numbers: there are no certain colors without shades, there are no sounds without nuances, etc. Furthermore, the existence of synonyms -- words with almost the same meaning -- is caused by differences in the minds of human beings and by the impossibility in thee Yang condition of substance to define-stop-grasp the moment of certainty. For, when one says whatever it might be and when another simply prefers to say something else, they will not be arguing about words, about what terminology is to be preferred, but of their pragmatic interests -- of their philosophies. Nature does not impose proper words upon one, but one imposes them upon nature, for one finds them convenient for the reason that the only true objective reality is the internal harmony of the world 96 ; I deduce that the ideas in human minds follow the rule of the 'inexplicable economy' 97 : all thoughts strive to become the singular one and to cease to become -- to be the ultimate antiderivative. In keeping with the usual practice of Idealism , in formulating a general, simple and precise picture of this universe on the basis of experiments one has only obeyed a necessity from which human minds cannot free themselves 98 : There is the T'ai Chi Law of the Supreme and Infinite Ultimate immanent in substance: all things which have continuously modifying Meanings of Inertia interact with all other things in their striving to become the 'simple' substance and to rest; There are three Laws of dialectic : The Law of the Unity and Struggle of Opposites: All things interact (all specific scientific theories try to describe the same things by means of their own languages) 99 . The Law of the Transformation of Quality 100 to Quantity: All things are open sets of smaller things and the given set of things is closer to the condition of the rest than that which any thing from this open set had before association in the open set of the given thing (all specific scientific theories try to compose a general theory that is closer to knowledge than that which any particular science was before the association in this general theory -- all languages of all specific scientific theories should compose a general language that is more correct than that which anny language of any particular science was before the association in this general language) 101 . The Law of the Negation of Negation: Interaction between things is continuous in infinitum of time (there is no general scientific theory that is perfect -- there is no language that can picture Absolute).
Ego sum, ergo cogito -- I am and, therefore, I must think! I argue that human beings are subjected to the T'ai Chi Law -- they enjoy no privileged status and, therefore, their uniqueness may be identified in almost certain terms: "the diffeerence between a living man with a mind, on one hand, and a corpse or a stone, on the other, is simply that the living man behaves, or has tendencies to behave, in a different way from the corpse or the stone." 102 There seems no escaping the conclusion that human bodies should be considered as associations of apeirons that are built on the basis of Pragmatical Esthetics: "and pleasant is that by which, when it's come to be present in us, we feel pleasure, and the good that by which, when it's present in us, we are good" 103 ; where 'pleasure' and 'good' have two different meanings: 'to feel pleasure' means that a beauty may not be the necessity 104 and 'we are good' only if the necessity is the beauty which is able to decrease our Meanings of Inertia: the necessity is the beauty but a beauty may not be the necessity. It means that our logic is determined by our substance or, in other words, by our essence, but not otherwise! So, I am positive that one's ideas are one's plan of action or, what is the same, the meaning of this operation -- they are an attempt to answer the question: how can I become Absolute? ; where the success of one's becoming Absolutee is the measure of one's judgment -- to determine the meaning of truth of ideas one must evaluate their 'practical consequences,' 'usefulness,' 'workability' 105 .
One, who is now ' dead and turn'd to clay', who 'might stop a hole to keep the wind away' , said impulsively that a dead lion is better than a live cynic . Studying the problem of principledness of things, I figure out that if a cynic and a lion look unlike, I have to discuss either two incomparable creatures of different species or two beings of the same human kind if one, who ' should patch a wall t' expel the [winter's] flaw' , used the previous expression metaphorically. And the questions arise for me: Is the 'dead lion' the former principled one that ends in the unprincipledness-nothingness of the 'simple' substance? Further, as long as contraries are always becoming one another and things are becoming the 'simple' substance: Was the 'dead lion' the live cynic who came from the nothingness of the 'simple' substance and should become the principled lion? And if one would like to repeat "Et tu, Brute!" 106 , has this one become the principled one at the right time and place (where I am certain that the principled one is one who has a character: an ability and desire to act, a definite purpose in mind)? As Goethe says, one who wants to do great things must know how to restrict oneself -- how to find one's own self-limitation(s) and how to evaluate the practical consequences of one's deeds according to one's wwish to become better as long as "in the beginning was the deed" (Goethe, ' Faust ') -- I am and, therefore, I must think how to overcome all limitations and how to create self- limitations of my own. In contrast, the unprincipled One , who is to become the plurality of the becoming principled cynics , is the One who wants to do everything but really wants to do nothing , and brings nothing off. It might be well to point out that the absence of character of the One is caused to be converted into the rigidness of character of former cynics -- lions not yet dead -- by the actuality of their dogmas' existence, in which dogmas the Limit is becoming the faith of formeer cynics because "faith is a miracle, and yet no man is excluded from it; for that in which all human life is unified is passion, and faith is a passion." 107 This conception is in general agreement with my theory of the principledness of things: the cynic, who is becoming the passionate lion, should make use of the deductive and inductive methods of reasoning with the same certainty -- if the cynic thinks that the cynic is able to use these methods with the same confidence, the cynic believes that one knows Absolute -- possesses Pure Knowledge -- or, at least, communicates with Absolute (see Fear and Trembling of Kierkegard in which he discussed the phenomenon of principledness 108 ). Following his own path, Fyodor Dostoyevsky in the Notes from the Underground examined the miserable quality of unprincipledness: "...we have reached the conclusion that the best thing for us to do is to do nothing at all, but to sink into a state of contemplative inertia." 109 Nevertheless, inasmuch as everyone must either interact with others or be nothing , the hero of the Notes... is compelled to ask himself: "Why should such desires occur to me at all? Merely in order that, eventually, I may come to the conclusion that my whole organization is a fraud? Is that the object of it all? I do not believe it." Dostoyevsky found that even love could not save his character, because love is a kind of activity in the world where the actuality of principles is the firmest of all principles; where the striving to be the unprincipled One -- the endeavor not to act -- is the virtue immanent in substance 110 . Laying the foundation for the coalition between Idealism and Existentialism 111 I state that if God is dead because He is nothing and, therefore, all Ideals are nothing, cynics strive toward their death searching for Ideals through the process of becoming dead lions or, what is the same, the constant repetition the Sisyphean work. In this respect, if one says in one's heart that 'There is no God' this one states that there is the norm and, therefore, everyone is departed and every deed vile and no one does good -- one thus gets the world of many things, with relations which are not to be deduced from a supposed 'nature' of the only subbstance of the related things 112 ; but 'God is dead' means that "the entire series of changes is comprehended in this: Loss of motion and consequent integration, eventually followed by gain of motion and consequent disintegration" 113 -- norm ceased to be and it shall be restored.
Can death be the aim of one's life? If at the end there should not be just any last thing, but the best does the theory of evolution look like this: the Strongest will die last? Does this end justify the means? Would enterprises of great pitch and moment with this regard turn awry their currents and loose the name of action 114 ? If 'hope that is seen is not hope: for what a man seeth, why doth he yet hope for' 115 or, what is the same, if one has found Absolute, does this one have any reason and, simply, a chance to continue the chase for it? Is this not a paradox : a limitlessness that has limited itself repeatedly finds that all previously found self-limitations cannot resist the examination by infinitum of time and that the hope is of eternity?..
Stars will shine!
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