Footnotes to New Mechanics...

1 Russell B., "The Problems of Philosophy", Hacket Publishing Company, Inc., Indianapolis, 1996; [p.63]

2 Historically, from the time of Aristotle, the Laws of Thought for formal logic were: The Law of identity: Whatever is, is. The Law of contradiction: Nothing can both be and not be. The Law of the excluded middle: Everything must either be or not be.

3 Russell, "My Philosophical Development", Ruskin House, George&Unwin Ltd, London, 1959; [p.54]

4 Russell, "Principlesof mathematics"; Bradford & Dickens, London, 1950, [p.141]

5 Aristotle, "A new Aristotle reader", Prinston University Press, Princenton, 1995[1004(,25]

6 Russell, "My Philosophical Development"; [p.61]

7 Plato, "Theatetus"; [160b-c])

8 I have appropriated this term in the tradition of early Plato, Nicholas of Cusa and early Hegel.

9 Wittgenstein L., "Tractatus Logico-philosophicus"; [6.4311]

10 Plato, "Cratylus", "Dialogues of Plato", Oxford at the Carendon Press, 1968, [440a]

11 Plato, "Parmenides", The Bobbs-Merrill Company, Inc, New York, 1957, [156c-157b]

12 Aristotle, "A new Aristotle reader", Prinston University Press, Princenton, 1995; [1005(,20]

13 "Because time is continuous, movement must be continuous, given that it is impossible there should be time without movement; time, then, is the number of a particular continuous movement, or circular movement therefore..." Aristotle, "A new Aristotle reader"; [337(,25]

14 According to my understanding of this dialogue: Diogenes: What, Your Majesty, is your greatest desire at present? Alexander: To subjugate Greece. Diogenes: And after you have subjugated Greece? Alexander: I will subjugate Asia Minor. Diogenes: And after that? Alexander: I plan to relax and enjoy myself. Diogenes: Why not save yourself all the trouble by relaxing and enjoying yourself right now? I can conclude that things aim to complete themselves and to rest -- "what is unlimited has no telos (end) and is a-telos, which means both 'endless' and 'incomplete'." Encyclopedia of Philossophy, Macmillian Publishing Corp., New York, 1972; ['Pythagoras and Pythogoreanism']

15 Aristotle, "A new Aristotle reader"; [194(,30]

16 The universe is declared by Idealism to be spiritual -- it is conscious: it is intelligent; it is purposeful. People do not possess a quality that makes them superior to things whhich seem to be inanimate -- human beings have equal rights among things.

17 Plato, "Phaedo", [107c-e]

18 Plato, "Parmenides'; [129c]. Bradley F.H. "Appeararnce and Reality", Oxford at the Clarendon Press, 1959; [p.124-127]

19 "...in cognition, too, restriction and defect are only determined as restriction and defect by comparison with the Idea that is present -- the Idea of universal, of something-whole and perfect." Hegel, "The Encyclopedia Logic", Hacket Publishing Company, Inc., Indianapolis, 1991, [p.106]

20 If two plus two is not equal to four, it means that all Whole-Natural numbers are universals and it must not be said that an empty set plus another empty set is equal to a third empty set, because there is only one empty set!

21 Hegel, "The Encyclopedia Logic"; [p.140-141]

22 Hegel, "On Art, Religion, Philosophy", Harper Tourchbooks, Harper&Row, Publishers, NY, 1980; [p.208]. The instantaneous rate of change of y =(x) with respect to x for a particular x is provided this Limit exists; where lim (y is Pure Knowledge; where f(x) is a constantly changing set(network) of opinions(Searle J.,"The Rediscovery of the Mind"); where (x is the constantly modifying difference between Pure Knowledge and one's set of opinions(the "Measure of Abstraction" -- "For we know in part and we prophesy in part. But when that which is perfect has come, then that which is in part will be ddone away." Bible, Paul, I to Corinthians, 9&10

23 Aristotle, "Physics", Book III, Ch.4-8 I think that "For My people have committed two evils. They have forsaken Me, the fountain of living waters, to hew for themselves cisterns, broken cisterns, that can hold no water" ( Bible, Jeremiah, Chapter 2&13) means that mind is the limitlessness that endeavors to fix itself and not to be limited by others("Do not stand between me and the sun!" Diogenes of Sinope); where universals are standards -- self-limitations: one 'is becoming' the center of this universe and everything around one exists as long as this world inteeracts with one, and it must be admitted that this totality of things exists as the inadequately reflected universe inside one's mind(the network of sense-data); the statement -- one 'is' the center of this universe -- is Pure Lie because there are no things which 'are' but only which 'are becoming': if one 'is' the center one 'is' a Form and possesses knowledge.

24 Bradley F.H. "Appearance and Reality"; [p.9;p.120]

25 Plato, "Phaedo", [79a]

26 'to be is to be perceived'. Berkeley G., "A Treatise Concerning the Principles of Human Knowledge", The Library of Liberal Arts, The Bobbs-Merill Company Inc., London, 1957; [#3]

27 Hegel, "The Encyclopedia Logic"; [p.87-89].

28 "6.45 To view the world sub specie aeterni is to view it as a whole -- a limited whole." Wittgenstein L., "Tractatus Logico-philosophicus"

29 Hume D., "Dialogues Concerning Natural Religion", Hacket Publishing Conpany, Cambrige, 1984; [p.50]

30 Ibid; [p.73]

31 Ibid;[p.50]

32 Aristotle, "A new Aristotle reader"; [259(,20]

33 Hume D., "Dialogues Concerning Natural Religion"; [p.50]

34

35 see Newton's First Law: every body continues in its state of rest, or of uniform motion in a right[i.e., straight] line, unless it is compelled to change that state by forces impressed upon it -- if things-in-themselves/ Monads are nothing it means that they become the thing/ things as soon as they are impressed by thhings. 36 This is my reading of Plato's early position, which in the Theatetus is represented as Heraclitus'; since most Western scholars read Plato through the Republic (even though it was written by Academy but not by Plato himself; however, I read Plato through Apology and Phaedo) they (mis)read this as contradictory to his position. I find Plato position to have changed over time; therefore I took the dialectic from Plato and left the sophistic: "...dialectic probes where philosophy seeks understanding, and sophistic is imagined to be science but is not really." (Aristotle, "A new Aristotle reader"; [1004(,25]). Any dialectical method in general must be the manifestation of principle of all motion, of all life, and of the actual world existence( Hegel W., "The Encyclopedia Logic"; [p.128]) -- the manifestation of the permanent shifting of values; of the constant endeavor to find the Forms; of the world of probabillities.

37 Plato, "Theatetus", Hackett Publishing, 1995; [157b]

38 Aristotle, "A new Aristotle reader" [1007(,20-35] Nicolas Cusanus, "Of Learned Ignorance", New Haven Yale University Press, 1954; [p.13]

39 to make them material points, solid bodies, etc.

40 For this kind of metaphysics Pure Truth is becoming nothing -- the becoming 'is' is Pure Truth; where Pure Lie is the Reality of being nothing -- the being 'is' is Pure Lie; there is no gap in the continuity of interaction among particles in time and there is no such condition as 'the being a universal' for things -- when one has uttered 'this' about things and a universal they have already been modified: the paradox of Zeno -- "One says that one is lying. Is what one says true or false?" -- found its solution in the assertion that Pure Truth is always becoming Pure Lie.

41 Hegel, Preface to Philosophy of Law, p.XIX

42 I am arguing against the Vienna Circle, Whitehead, Russell, Wittgenstein and Co.

43 Hegel W., "The Encyclopedia Logic"; [p.129].

44 Ayer A., "Logical Positivism", The Free Press, Glencoe, Illinois, 1960; [Moritz Schlick, The Turning Point in Philosophy, p.57]

45 I insist that the individual judgment of truth can be the test of truth and that any truth is Pure Truth only if it is accepted by all other minds or, in other words, if these minds will not exist. Next, men seek rest, and the search for truth in practice is the search for apathy: if one's opinion is to reach absolute fixity and to become the only Pure Knowledge, one will rest -- "He who knows Brahman becomes Brahman". The Upanishads; [Mundaka, p.48].

46 "When it is said then that we 'localize' such an object at such and such a point of space, what does it mean? It simply mean that we represent to ourselves the movements it would be necessary to make to reach that object; and one may not say that to represent to oneself these movements, it is necessary to project the movements themselves in space and that the notion of space must, consequently, pre-exist. When I say that we represent to ourselves these movements, I mean only that we represent to ouselves the muscular these movements... None of our sensation, isolated, could have conducted us to the idea of space; we are led to it only in the studying of laws, according to which these sensations succeed each other." Poincare J., "The Foundations of Science", The Science Press, Lancaster, 1946; [p.70] In other words, if one strives to include things from one's neighborhood within the orisphere of one's influence according to the rule of Pragmatic Esthetic, one thinks about the muscular movements that are necessary for this purpose -- one endeavors to promote the being of everything that one can imagine conductive to pleasure; but what one finds repugnant to oneself or conductive to pain one endeavors to remove or destroy. Spinoza, "Ethics". (See Part 22 of this essay)

47 An orisphere is a sphere with a constantly changing radius, which strives to become infinitely big (Lobachevskii N., "Works", Moscow); where "big" does not mean a size in comparison with some arbitrarily chosen measure of space, but a measure of quantity of the smallest parts of the Whole, which are united in this open set of them, in comparison with their entire quantity; and the preceding conjecture should be read in the following way: instead of supposing the quantity of apeirons infinite, let us suppose that their number is finite and that the infinitum exists not in the number of apeirons but is in their endless changes -- "Instead of supposing matter infinite, ... let us suppose it is finite." Hume D., "Dialogues Concerning Natural Religion";; [p.49] So, I oppose to Descartes' agnosticism -- see "The Principles of Philosophy", Principles XXV-XXVIII.

48 Seeking the solution of Zeno's paradox I found that one could not attempt to measure the 'distance between' Achilles and the tortoise but only their changes of orispheres. For that reason, I can, through the comparison of both objects' orispheres find out the ultimate truth: will Achilles finally gain on the tortoise or not -- things with an equal condition within the given thing's orisphere are called shells of this orispherea. The shell is a spacce such that any path which joins any two things with the same condition is wholly within this space; there are several shells within any orisphere corresponding to the conditions of its things if there is more than one smallest apeiron within the given.

49 The terms "content" and "matter" are equal in their meaning: "by the matter I mean... the bronze, by the shape the plan of its form, and by the compound of these the statue." Aristotle, "A new Aristotle reader"; [1029(,5]

50 periodical table of the elements.

51 In order to make this concept quite unambiguous, it should be brought to the proposition that space is nothing but a relation of spaces. Bradley F.H. "Appearance and Reality"; [p.31] Therefore, Kant's 'things which are to be met with in space' means that all things have shapes -- and this is my response to the attempt by Moore to refute Idealism. Moore G.E., Selecting Writings, International Library of Philosophy, Edited by Thomas Baldwin, New York, 1993; [Proof of an External World]

52 "Clearly, then, all in some way agree that opposites are the principles." Aristotle, "A new Aristotle reader"; [188(,25] Therefore, it appears that for any universal and, therefore, unreal mass of the given thing there is only one the thing's abstract space; which the universal pair of mass and space exists only for the condition of the thing's rest such that: where m1 and m2 are the constant meanings of masses of any two different things, where l1 and l2 are the constant meanings of space of any two different things, where P is the constant Density of substance and is called 'the constant Density' of any Monad/the Supreme Monad, or the Density of the 'simple' substance: the experiments with the 'simple' substance are usually called nuclear explosions. I put forward the idea that we should consider both changes of things' matters and spaces with the same necessity: things with an increment dm are called 'White things' and they have magnetic properties -- they strive to restore their lack of mass and rest. Things with an increment d1 are called 'Black things', and have electriical properties -- they attempt to fix their shortage of space and rest.

53 This is my other answer to Moore -- "All bodies are heavy" means that they appear; that they have increments dm and/or dl. Moore G.E., Selecting Writings; [Thhe Nature of Judgment; The Refutation of Idealism]

54 which is presented as the constant G in Newton's interpretation of Kepler's Law and if something fixed exists it confirms that the Whole must exist. On the assumption that the Whole comes to be the plurality of its parts -- the totality of things -- and that it is not indifferent to whether it is observed or not ("Hegel. The Essential Writings",, Harper Torchbooks, Harper&Row, Publisher, NY; ['Lordship and Bondage'; p.72]) I built 'my' conjecture that "...all things stand in some sort of relation to one another; that, in virtue of this inter-relation, all the individuals constitute one universe and that in the one Absolute the multiplicity of beings is unity itself." Nicolas Cusanus, "Of Learned Ignorance"; [p.25]

55 The observation of an event from two different frames of reference moving with a relative velocity v along the z axis would be related by the Lorenz transformation: where the Lorenz transformations confirm that activities of things mean changes in their forms and/or matters.

56 "...clearly to say that something comes to be out of what is not, is to say that it does so out of what is not, as something which is not... We too say that nothing comes to be simply out of what is not; but that things do come to be in a way out of what is not, namely by virtue of concurrence" ("A new Aristotle reader"; [191(,5-15]); where the virtue of concurrence means that things oppose and compete in their attempt to become complete and harmonious -- to become the 'simple' substance -- and "...there must always be something underlying which is the coming-to-be thing, and this, even if it is one in number, is not one in form..."( "A new Aristotle reader"; [190(,15])

57 Plato, "Meno"; [86b-87c]

58 Ryle G., "Dilemmas"

59 Wittgenstein L., "Tractatus Logico-philosophicus", Routledge Humanites Press International, Inc., London, 1988; [6.522]

60 Nicolas Cusanus, "Of Learned Ignorance"; [p.14]

61 Ibid; [p.55]

62 Hegel W., "The Encyclopedia Logic"; [p.133]

63 Spinoza, "Ethics"

64 All things which are becoming, are becoming in themselves (they can be conceived as units of many) and always interact with others (they can be viewed as one among many) and all that can be conceived through another thing may also be detected through changes within a Given union -- through itself.

65 Kant I., "Critique of Pure Reason", St. Martin's Press, New York,1965; [A35-B52]

66 Bohr N., "Atomic Physics and Human Perception", Moscow, 1962

67 Aristotle; [1028(,35] Corollary I. Existence appertains to the nature of substance. Corollary II. In the nature of things, two or more substances may not be granted the same nature of attribute. Spinoza, "Ethics", J.M.Dent&Sons Ltd, London, 1970; [p.3-4, Theorem 5 and 7]

68 The ideal substance Li is primary while the material substance (predicatively defined) is secondary: "the secondary qualities, therefore, are appearance, coming from reality, which itself has no quality but extension". Bradley F.H. "Appeararnce and Reality"; [p.10]. The illusory substance Li is devoid of form and properties and is inaccessible to sense perception. Dictionary of Philosophy, International Publishers, New York, 1984; [Chu Hsi].

69 The Li condition of substance has the metrical topological space which satisfies both axioms (first and second) of countability and is perfectly separable, where an apeiron constitutes the countable base for all Monads' orispheres. The Yin condition satisfies only the first axiom of countability and Yang does not satisfy both axioms. Aleksandrov P., "An introduction in the theory of sets and general topology", Moscow, 1977

70 Death could be conceived as a Dedekind cut; where a cut AЅB is the cut between two closed loops of changes A and B, where they can be imagined as Cantor sets -- the subset of the real interval [0,1] consisting of all numbers of the form ((i=1 = (i/3i, where (i is 0 or 2. A and B are not related in the formal sense of this world: they are similar to one another from the functional point of view -- no predicate can follow from one to another. So, one is dead if one became the One/ a thing-in-itself and/or if this association of many stopped satisfying the requirement of many (which constitute one) to constantly overcome self-limitations; in all these three cases the One/ a thing-in-itself/ the association of many ceases to exist as a set of many -- one.

71 An accumulation point of a set of points is a point P such that there is at least one point of the set distinct from P in any neighborhood of the given point. Therefore, by accumulation points or, what is the same, invariant groups I understand those which are not finite and have a determined existence in interaction with others; if several things so concur in one action that they are all at the same time the cause of one effect, they are to be considered to be one individual thing. Spinoza, "Ethics"; [Def. VII,p.38]. All accumulation points are open systems that constantly change themselves and others' condition of substance.

72 or, the same, points which are the Limit and which do not interact with things. "Things-in-themselves" are isolated systems that makes no exchange with their surroundings.

73 This(these) point(s) does(do) not exist/ does(do) not interact with others: "...for a Thing without qualities is clearly not real. It is mere Being, or mere Nothing, according as you take it simply for what it is, or consider also that which it means to be. Such an abstraction is palpably of no use to us." Bradley F.H. "Appeararnce and Reality"; [p.112]

74 It must be said that the result of one's becoming nothing is not empty, abstract nothing, "...but the negation of certain determinations, which are contained in the result precisely because it is not an immediate nothing, but a result." This result "...is not simple, formal unity, but a unity of distinct determinations." Hegel W., "The Encyclopedia Logic"; [p.131]

75 Since nature abhors a vacuum, and all things must so concur as to prevent the formation of a vacuum, it follows that things cannot be distinguished one from the other; that is, substance cannot be divided into parts which are stable and have an edge: the idea of vacuum exists only insofar as we try to measure a metrica -- 'distance between' -- two things. Spinoza, "Ethics"

76 Hume, "Enquiries concerning the human understanding and concerning the principles of morals"; Oxford, Clarendon P., 1969

77 The world of internal relations is the world of probabilities.

78 Otherwise, Leibniz's idea about "...the roaring of the sea with which one is assailed when near the shore" should be considered sufficient, and the continuity of interaction must consist of many smaller interactions. Indeed, according to Leibniz to hear the seas' noise "...as one does, one must hear the parts which compose its totality, that is, the noise of each wave, ...although this noise would not be noticed if its were alone." I think that any action is continuous and that Irrational numbers convert one to another. The case of the spectrum of radiation of things, which I plan to examine later, gives proofs in favor of this assertion.

79 Poincare J., "The Foundations of Science"

80 Plato, "Phaedo"; [103b] This is the initial idea, which forced me to formulate "Nonpredicative definition".

81 All correct propositions of mathematics are tautologies. They are proper ones only if things and Irrational numbers, which can be substituted to things in correct propositions, are becoming the 'simple' substance -- Rational-Natural numbers -- and, in effect, all correct statements are meaningless -- they are becoming Pure Lie: "tautologgy and contradictions are the limiting cases -- indeed the disintegration of the combination of signs" Wittgenstein L., "Tractatus Logico-philosophicus"; [4.461-4.661]: a - b = 0 or, what is the same 1 = 0 Accordingly, all actual equations/ correct sentences and even texts, which they can compose, are senseless-nonsensical: they create the complete, and because of that, useless pictures of the Reality -- nothing.

82 Due to the fact that there is no theory which can offer a more or less satisfactory explanation for the nature of negative numbers: how they are different from, and how they can annihilate positive numbers, I will risk putting forward my own theory. If we have the row of cardinal whole-Natural numbers, what can be counted by use of negative Natural numbers? I guess that if we always have two opposites we can infer that the negative cardinal numbers count things that positives do not: the presence of opposites is the firmest principle for the universe of things and negative numbers count the opposites for positive numbers: negative numbers count 'Black things' things and positive numbers count 'White things'. This is easy, isn't it? Next, I think that it is evident, then, that any experiment must establish the right connections among the general principles for things and the absence of principles of the 'simple' substance: connection between the principledness of things and the unprincipledness of the 'simple' substance.

83 In this sense it can be concluded that all a priori opinions (which are required by one only for practical purposes) deal exclusively with the relations of universals -- with the hierarchy of numbers; where universals are the Limit(s) and insofar as knowledge, in spite to Hegel, stands on thee same side as Absolute does, 'a priori knowledge' is not accessible -- any attempt to operate with Irrational numbers makes them Rational-Natural and vice versa. Russell, "The Problems of Philosophy"; [On Our Knowledge of Universals]

84 Aristotle, "A new Aristotle reader"; [1072(,35]

85 Ibid.;[1004(,5-20]

86 Russell, "Principles of Mathematics"; Bradford & Dickens, London, 1950

87 Plato, "Theatetus"; [157a]

88 Plato, "Theatetus", Hackett Publishing, 1995; [152e]

89 Nicolas Cusanus, "Of Learned Ignorance", New Haven Yale University Press, 1954; [p.111]

90 Aristotle, "A new Aristotle reader"; [1074(,25]

91 I use Nicholas of Cusa's concept of 'absolute maximum' and 'absolute minimum'.

92 Thus, if there is to be any diversity between things, there must be the diversity reducible to thing's meanings of Inertia and these things' numbers of pairs of mass and space in the set T.

93 "I shall point out that the world, as so understood, contradicts itself; and is therefore, appearance, and not reality... Ultimate reality is such that it does not contradict itself; here is an absolute criterion." Bradley F.H. "Appearance and Reality"; [p.9;p.120]

94 There is not an apple that 'is' red but the apple that is becoming/ had become/ became/ was becoming/ will become red.

95 Things-in-themselves are that which are indeterminate, but with form and, therefore, with content.

96 Poincare J., "The Foundations of Science"; [p.29;p.125]

97 Hume D., "Dialogues Concerning Natural Religion"; [p.18]

98 Poincare J., "The Foundations of Science"; [p.120]

99 Ryle G., "Dilemmas", Cambridge at the University Press, 1954; [p.79-80]

100 "Quality is, to being with, the determinacy that is identical with being, in such a way that something ceases to be what it is if it loses its quality." Hegel W., "The Encyclopedia Logic"; [p.136]. Bradley F.H. "Appearance and Reality"

101 Descartes R., "Rules for the Direction of the Mind"

102 Armstrong D.M."A Materialist Theory of the Mind", London, Routledge and Kegan Paul, 1968.; [p.10].

103 Plato, "Gorgias", Hackett Publishing, 1995; [506d]

104 For instance, the use of drugs can make one a pseudo-universal -- can give rest -- but will destroy the given living being finally even if one has not reached the condition of the 'simple' substance because "the good is one thing; the pleasant is another. These two, differing in their ends, both prompt to action." The Upanishads; [Katha, p.16]

105 Encyclopedia of Philosophy, Macmillian Publishing Corp., New York, 1972; ['Pragmatism,' W.James, 'Value']

106 Other minds exist as long as they resist the striving of one to become the One -- the essence of one is not contained in the community and unity of one with others; it is the singularity, however, which brrings rest. Feuerbach L., "Principles of the Philosophy of the Future", The Bobbs-Merrill Company, Inc., 1966; [#59]

107 Kierkegard, Fear and Trembling

108 "...when he approaches what is great it can nether escape his mind that from creation of the world it has been customary for the result to come last, and that, if one would truly learn anything from great actions, one must pay attention precisely to the beginning. in case he who should act were to judge himself according to the result, he would never get to the point of beginning."

109 part XI

110 The Forth Law of Thought emanates from this contemplation: The Law of unprincipledness: the One always begins to contradict the Oneself. The Law of principledness for Formal Logic: one should not contradict oneself.

111 Hegel was not just an Idealist but a German Idealist: he advocated the doctrine of French Enlightenment that it was possible for many to coexist in the world of things and to have knowledge at the same time even if he saw that "freedom is only present where there is no other for me that is not myself[p.58]... So, insofar as man wills this state of nature, he wills singularity[p.63]." (Hegel W., "The Encyclopedia Logic".) I am, however, an anti-Communist: I speculate that only the One has knowledge; I reject the communitarian or, what is the same, the communistic worldview (I imply here Feuerbach's primary definition of communism -- 'The highest and last principle of philosophy is, therefore, the unity of man with man' (Principles of the Philosophy of thhe Future; [#63]) -- as well as Engels' development of it -- see Socialism: Utopian and Scientific); I think that "to this war of every man, against every man, this also is consequent: that nothing can be just. The notion of right and wrong, justice and injustice have there no place" ( Hobbes Th., Leviathan) insofar as all abstract notions are nothing and the natural condition of men is the state of war. Therefore, I am a disciple of the dialectical method of reasoning -- I think that human beings can have only opinions!

112 Russell B., "Why I am not a Christian"

113 Spencer H., "An Epitome of the Synthetic Philosophy", D.Appleton and Company, NY, 1989; [p.35]

114 Hamlet, W.Shakespeare

115 Paul,"To the Romans", 8&24

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