Section 42 (last updated 2.12.2021)
Infinitesimal is not a mere general continuity but it is rather the infinite continuity within a discrete point of singularity. This means that on the one hand there are an infinite number of separate discrete points such that their amount is innumerable, cannot be counted as individually separate points, and so this constitutes their limitation, in other words, any number of different objects making up a group is finite. The infinite is therefore innumerable and so it is the shape or the number of forms that a single object may possess at any discrete point separable from another object occupying a discrete point.
These are all the complexes of an infinite shape that an event can assume to take disclosed within a discrete measure, the total number of which making up a group of individual events is itself finite, what happens within each individual event, that is infinite.
Infinity = finite
As Peirce points out the equation, the infinite itself is finite. What this means is that the finite by definition assumes uniqueness. But there is an infinite finites. The infinite is the collection of finites that are themselves the expression of the similarity they share, which is infinite. So each finite is at the same time an infinite. This contradictions means that when something is finite and unique, it exists externally from everything else that is finite and unique, but they relate in that all finites are infinitely unique. So each finite exists as something unique but share the infinite nature in that every finite is infinitely different. Numbers are this example.
1,2,3,4,5
Each number is unique but follows the next as the infinite form of addition.
3.4.Continuity
Pierce says that continuity according to Kant means infinite divisibility. For example, between any two variables in a series a third can be found. Division in this sense constitutes continuity. According to Pierce, although Kant recognizes an important feature of continuity, that it is divisible, he fails to deal with a problem that his definition of continuity creates. Kant’s definition of continuity is problematic when we compare a series of numbers with points on a line (The Law of Mind, 542). Both of which constitutes continuity in different forms.
The entire series of rational fractions arranged in the order of their magnitude is an infinite series that is numerals, but the points of a line are innumerable. Between any two numbers a third can be found, that is a point of divisibility in the whole series. Yet the points on a line are innumerable and so they cannot be divided without breaking up the line. The points on a line must be divided while maintaining the line intact, and so in what sense can the points in a line be something different than the line itself?
Kant’s definition of continuity creates a mathematical problem between numerable and innumerable series. The reason for this problem is that the rational fractions constituting an infinite series are seen as points of divisibility while the same points on a line are seen as continuous and indivisible. This does not explain how rational fractions are divisible from one another; it just recognizes that they are divisible.
Cantor defines a continuous series as “concatenated”, meaning that continuity is the linking together in a perfect chain. (The Law of Mind, 543) By concatenated Cantor means that any finite distance however small between two given points in a series allows for proceeding from the first point to the second through a succession of points each at a distance from the proceeding one less than the given distance. In other words, the finite distance between the first point and a second point includes an even shorter distance. Any finite distance between two points includes a shorter distance proceeding from one to the other point. Pierce argues that Cantor’s understanding is a “definition by negation” which does not indicate what the components making up continuity are (The Law of Mind, 543). It leaves a vague conception of continuity like Kant’s definition.
Figure: A……….B C……….D
Although Kant explains one important property of a continuum, it’s divisibility, this divisibility allows for gabs in the series. Each point in a series is divisible leaves a discontinuity in the series. A gap between variables in a series does not take into account their relation. Pierce demonstrates:
Let us suppose, then, a linear series of points extending from a point, A, to a point, B, having a gap from B to a third point, C, and thence extending to a final limit, D; and let us suppose this series conforms to Kant’s definition. Then, of the two points, B and C, one or both must be excluded from the series; for otherwise, by the definition, there would be points between them. That is, if the series contains C, though it contains all the points up to B, it cannot contain B (The Law of Mind, 543-544).
For instance if we look at the figure above and assume that B and C constitutes a gap in the series, according to Kant’s divisibility, either B or C, or both, must be excluded from the series. Otherwise there would be points between them or the continuity of the linear series is broken. If the series contains C, even though it contains all the points up to B, it cannot contain B because than B would just be one of the points leading to C which then makes B something having no distinct points. What is required is that, if a series of points leading up to a limit is included in a continuum, the limit is also included in that series (The Law of Mind, 544).
Figure: 0, 0.1, 0.11, 0.111,…1
According to Aristotle, because the series between 0 and 1 is continuous there must be a “least” real number greater than every number in the endless series. If we abstract one number from the endless series; say 0.111, that number would be the limit because it is the interval between 0 and 1. The limit in the infinite series is both greater than all numbers before it and less than all numbers after it, e.g. 0.111 is greater than 0,0.1,0.11 but less than 0.1111, 0.11111 etc. According to Pierce, the Aristotelicity principle indicates that a continuum contains the end point belonging to every endless series of points it contains. In other words, Aristotle implies that between any two points an innumerable series of points can be taken. This means that the limit itself is infinite, or that it is infinitely limiting. For Aristotle the limit is a quality because it is the standard between its two neighboring variables.
According to Pierce, continuity supposes infinitesimal quantities. Quantity in the infinitesimal presupposes an “Infinitieth” place of decimals. The term Infinitieth means infinity in a sequence. This means that each number supposes an infinite decimal points between it and every other number (1, 1.1,1.2,1.3…2, 2.1, 2.2, 2.3…3…). The concept of the infinitesimal aims to capture the magnitude of infinity in sequence ( The Law of Mind, 545).
The notion of the infinite is one of the most challenging concepts in mathematics and metaphysics. The Ancient Greek term for the infinite is “apeiron”, which according to Aristotle means; “a quantity is infinite if it is such that we can always take a part outside” (Physics.III.6.Gaye). This is a perfect example of what we always reference to as the definition of space, I.e., space is infinite. Space is a perfect example of a compact finitude of infinity. Nature uses space as a practical approach to infinity, using infinity for a finite purpose, e.g, I can move always outside the position I’m currently in, I can move always outside my self, forever and ever and anywhere I can reach, space is both this extension to anywhere, and a particular position here and there I am already in.
Having a basic grasp of the infinite is necessary to understanding the nature of development in terms of continuity.
The notion of the limit is generally used to solve the infinite. The common opinion is that the sum total of all finite numbers is considered the infinite. For Pierce this is “an irrational prejudice” because the infinite is not a collection of finite numbers it is instead the incommensurable relation that produces numerable results (The Law of Mind, 538). This means that infinity is not scattered or detached finite variables separate from each other. This understanding of infinity is derived from sense perception, which sees objects as separate from each other, and concludes that the sum collection of all these objects identifies infinity.
Finite numbers are distinguished from infinite numbers by what Pierce identifies as the “syllogism of transposed quantity” (The Law of Mind, 538). In short this syllogism presupposes a set of limitations set onto any series of numbers to see whether certain circumstances follow through as true. Pierce references the example that if every young Frenchman boasts of having seduced some Frenchwomen, and if a woman can only be seduced once, it follows that no Frenchwomen escapes seduction. This reasoning stands if these finite presuppositions are true, but because the population is always increasing, a women can be seduced more than once and the seduced is on average younger than the seducers, the conclusion that no Frenchwomen can escape seduction does not hold. This is the case because now there is an incommensurable set of circumstances where the Frenchwomen can in fact escape seduction.
According to Pierce, the syllogism of transposed quantity is not required for infinite numbers. The Ancient Greek mathematician Euclid is mistaken to formulate the proposition ‘that the whole is greater than its part‘ as an absolute axiom (The Law of Mind, 539). It is instead a theorem made to be proven by the syllogism of transposed quantity. According to Pierce the whole being greater than the part is not universally applicable to all numbers, and especially not applicable for infinite numbers. Any limitation set onto a series of numbers involves innumerable possibilities where the limit itself can be limited in the series. For example, the relation between whole and part as discussed above in terms of motion proves to be an indivisible relation where part and whole are not separate properties. Their separation is a condition set by the syllogism of transposed quantity that makes an abstraction from the whole and qualifies that as a part. In truth any part of substance is not anything without whole of substance. For example the function of the heart ceases without the totality of the body as a whole. The part is just an abstraction taken from the whole.
The infinite when defined in terms of scale is said to be unlimitedly large. The mathematical understanding of the “limit”, especially it’s practical application in differential calculus, is introduced to deal with the infinite. The limit is used to make the infinite into a divisible sequence. This however faces the same problems Kant’s definition of continuity creates. Pierce does not like using the term “limit” because it has an underlining suggestion that variables are separate from each other by a borderline and their separation suggests some kind of gap, hence continuity has no place in this understanding.
To demonstrate the arbitrary nature of the limit understood as a kind of boundary between variables, Pierce explains the “Aristotelical principle which is particularly important in philosophy”. Imagine a surface that is part red and part blue; so that every point on it is either red or blue with no part being both red and blue. Pierce asks: what then is the color of the boundary line between the red and the blue? The answer is that in order for red or blue to exist at all, they must be spread over a surface and the color of the surface is that of the immediate neighborhood of the point (The Law of Mind, 545).
It follows then that the boundary is half red and half blue, or in other words, it is both red and blue respectively. This means that the limit between any two variables, red or blue, is not something altogether different than the variables. The limit for each color is that they are together with each other. This does not mean that each color individually is the limit for the other color. For example red is not the limit of blue or blue the limit of red. Instead, the relation of both colors together is the limit for each respectively which makes one side blue and the other red. Pierce explains: “the color of the parts of a surface at any finite distance from a point has nothing to do with its color just at that point” (The Law of Mind, 546) This means that not each color on its own serves as the limit for the other it is rather the continuity between the two in relation that is the limit for each.
The value that serves as the limit in the sequence means at the same time the sequence is the limit of the value that is the limit of the sequence. This means that whenever something is the limit of everything else, everything else is the limit of that something that is the limit of everything. In this way the limit is self-limiting, meaning that whenever a limit is set, there is a limit to that very limit. The limit is therefore the point beyond the limit of itself. The limit is inherently continuous because it is always chasing the further limit of itself that is to be limited. For example,
Figure:
1,2,3,4,5,6,7,8,9,10 etc.
2,4,6,8,10,12,14,16,18,20 etc.
Looking at the two above series, if the first endless series is doubled by separating each unit into two parts, and the first part and the second part taken in the same order as the units from which they are derived, the double endless series will appear as twice as large as the original series. The second series appears larger than the first even though the second series is derived from the first.
If we look at these finite numbers alone with out understanding how they form an infinite series, we will be met with a dead-end. How is it that the series of even numbers is larger from the series of whole numbers even though the former is derived from the latter? When looking at the whole numbers we see that every number presupposes a distinct even number. There are as many distinct doubles of numbers as there are of odd numbers, but the doubles of numbers are all even numbers(the Law of Mind, 539)
What this means is that each number captures the relation between the previous numbers before it. The relations between the previous numbers serve as the limit for the number that is their proceeding limit. For example, if we abstract 5 as the interval limit in the series, we have that the relations between 1,2,3,4, serve as the limit for 5. Possible configuration such as: 1+1+1+1+1=5, or 2+3=5, 1+1+1+2=5, 4+1=5 etc. All such possibilities added up to 5. Also all numbers after 5 are also the limit of 5 since when subtracted equals to 5, such as possible configurations 12-7=5, or 14-9=5, etc. This means that when the limit is the interval in a series, the limit captures both the greatest and the least of possible relations in the sequence. The limit is the culmination of all possible relations that under that limit. And each particular relation is restricted by the total of all possible relations leading to the limit.
For Pierce the term infinitesimal is better suited to deal with the notion of the infinite because it solves the self-contradictory nature of the limit as endlessly self-limiting. In this way the infinitesimal actually measures the magnitude of the infinite. For example, Pierce points to this equation of the infinitesimal;
Figure: A+i=A
Pierce classifies A as a finite quantity and i is the infinite one (The Law of Mind, 545). The above equation shows that the finite + infinity is equal to finitude. This conclusion is logically derived, meaning that anything beyond the infinite is just the infinite itself, and so the infinite taken in its totality is just a finite point that is infinitely going.
In mathematics, specifically calculus, the limit is used to understand the infinite, yet at the same time the infinite is taken to define the limit. This means that the limit in calculus is a value that the function or sequences approaches but never fully attains. The limit in mathematics is just the abstract function for the next value, devoid of any real value; it is the place where the value ought to be. In this way the mathematical limit exhibits itself as a continuous infinite regress for the next finite point. This infinite regress is however a necessary function for derivatives, integrals, and so on. It captures the quantitative measure of finite variables.
In logic the relationship between the limit and the infinite is inverted in comparison to mathematics. In logic the infinite and the limit are understood to be the same, that is, the infinite is the limit. This means that when the infinite is reached that it is the limit. According to Aristotle, the infinite as a totality is still a finitude. This simply states that no matter how large or small the magnitude of something is, it is still measurable as a whole, and this whole is finite.
The only difference between the finite as finitude and the infinite as finitude is that whereas the former is a finite restricted to whatever it is as a finite, the latter is a finitude because it is the infinite possibility of all finites. For Aristotle, the infinite is the activity that takes on finite forms. Concerning thought as substance, reason is the infinite substance consisting of finite forms. And each finite form is an abstraction taken from the infinite activity that bears structure. Each finite form in turn is the interval limit of thought as the infinite activity. The infinite goes through every finite possibility of itself and perceives its infinity from each finite point.
Infinitesimal
The concept of the infinitesimal describes the magnitude of existence. Magnitude usually means size and scale but both of those are essentially defined by the concept of the infinite. Magnitude describes the nature of matter. Matter for Kant is divisibility. For cantor its… (Unused parts of thesis) the infinitesimal resolves the infinite by making it a particular.
The term infinitesimal presupposes a meaning of a culmination derived from the smallest possible point. Now the term culmination is not wrong in describing the infinitesimal per say but rather is misplaced because it only explains the quantitive measure of being, that is, it assumes that the last point in the series takes on equally all previous points before. If this were true then any greatest number in the series would always be greater than what it is, surly a claim breaking the law of non contradiction, I.e the same number would be greater and least at the same time which makes it impossible for the number to be divisible. For example, the series 1,2,3,4… Is an ordinary series of rational (Cardinal?) numbers. The number 4 is simply the result of all previous number, by result, it characterizes all the possible relations, I.e. 1+1=2+1=3+1=4.
If the notion of culmination is understood as only being the quantitive addition of all before, 4 would not be the greatest number in the series. I.e, 1+2+3=6. How is it that 4 follows 1,2,3? The answer is that 4 is the quality in of all previous not just a quantity, which means that it encompasses the set of real relations necessary for its expression. This literally means that every number in an infinite series is both a quality and a quantity. A quantity because it belongs as an integral part to a number else, quality because it captures the sum of all possible relations before it that are expressive of itself.
Being however is a quality, which means that it is a determination with an essential character. In Aristotle’s terms, it is an activity taking on a form. And that form brings with it an efficient cause that sustains it. This is the level of insistency according to Pierce, which is general. But before being achieves this general state; we have to ask what it is and what is its importance? The general state is the relation which consists of two inverse determinations, each of which derives its own particular character by being different from the other, and their very difference is the similarity they share, a similarity that itself has its own nature, a nature more fundamental than each particular, which is to say, the relation is the being whereby the particular parts are attributes of.
The general state is important because it is that which the other is correlated to, the other from the general is the particular, from the particular the general, an equal correlation where non is prior to the other, but both equally play a different role. And so the general or the universal is important because it portrays the parts by disclosing their relation, the particular is important because it expresses the universal by encompassing it as a definite thing. So back to the question of what exactly is the infinitesimal as the culmination of being? The answer is that culmination assumes that that the sum total of all parts constitute the whole, or rather the particulars against each other make the relation. Logically however the parts are each an expression of the whole, and that the particulars are themselves an expression of the relations. The latter describes being because each particular part is an expression of some being, which is to say, that being is a substance, that which has an essential nature for its activity.
–Difference between infinitesimal and infinite.
The infinitesimal is different than the infinite thusly; the infinitesimal is said to be an endlessly small point whereas the infinite is endlessly large. There is a difference in scale. In each concept, there is an innumerable series of finite points that we can arbitrarily pick from. In the series, 1, 2,3,4,5 we can pick any number and make that the limit. For example, with the Infinite we can stop at 5 and go up to 5000000. The infinitesimal is different then the infinite because it allows us to pick an arbitrary finite point and have that be the general point to a series. Meaning that we can talk about all the numbers before the chosen point. Whereas in the infinite, because it is endlessly large any randomly chosen point in a series supposes the points after and before.
1,2,3,4,5,6,7,8,9,0
The infinitesimal allows us to pick any number and have that number be the general limit for all previous numbers forming a series. For example, number 5 is the general number to all previous numbers: 1,2,3,4, but more specifically it is also general for every other possible configuration such as: 1+1+1+1+1=5, or 2+3=5, or 1+1+1+2=5 etc. All those possibilities added up to 5.
In each series each number is both a quantity because it is the double of the number before, but also a quality because it is greater than all previous numbers and smaller than all after numbers. What this means is that each number has a special relation to the number before and the number after than another number having its own special relation to the numbers before and after it, but the number in between any two number is also the previous number for one number after it and the number after for the number before it.
1,2,3,4,5
2 has a special relation to 1 and 3, but 3 has a special relation with 2 and 4. But 3 is also the number after 2 because it is the number before 4, and in that relation they are the same because 2 is the number that is after 1, so 3 is the same as 1 and 2.
In this same way, time, the past needs the future not in the same way the future needs the past, because the future needs the past as basis it goes off of, whereas the past needs the future as an aim it is going towards. the present needs both as a link of leaving something behind and entering into something new. From the past you can only speak of what is before, whereas in the future, you only speak of what is before, in both cases, the similarity is that the thing in question is not present, while in the present both potentials or lack of, are both not.
Reason is the quanta, the smallest amount that cannot be quantified. So reason is a quantity that is not a particular kind of thing but every infinite kind of thing.
Peirce asserts that the infinitesimal exists as a continuity. This notion can be understood in two related ways: first, the infinitesimal emerges as a continuity of time. This is an emergence of ideas where at the very smallest unit of space and time ideas operate with intensity. This intensive relation between ideas result in the generalization of ideas. In this way the infinitesimal emerges as a spectrum of a general state and a particular state. In the particular state ideas are continuously relating in an intense manner because each idea in its unique form is infringing on the other idea. For example, if one idea is a circle and another is a square they automatically formulate a contradiction. This is the level of pure process. The contradiction between ideas generalizes into a distinct form different then each variable would have on its own. This is the general level.
The other way of understanding the infinitesimal is deducing backwards from the general level to the particular. This means that between ideas that generalize there is an infinitesimal continuity. This means that between any two distinct objects, there is an infinitesimally small quantitative continuity. For example, when you yourself as an object looks at a chair, there is a physical continuity between your eyes and the chair. This has to be true for the chair to be registered by your eyes and then perceived into the mind as an idea. The colour from the chair for instance is one physical continuity being received by the eyes.
From this understanding of the infinitesimal as continuity we can make a startling conclusion. Mainly that if we stated earlier that mind constitutes the nature of matter as the unquantifiable quantity, then mind is the continuity in two ways related as the infinitesimal. First, the infinitesimal emergence of matter on time from the smallest possible unite to the largest space, is just abstract. Or that the continuity between any two general objects is also abstract.
Unquantifiable quantity does not mean quantity that is not measurable, it just means that it is an infinite quantity. So that we can only take a finite segment of the infinite quantity and measure it, it just cannot be defined as an infinite quantity. It is indivisible and cannot be separated into distinct parts. This however does not mean that what is indivisible cannot produce parts that are divisible. In fact an indivisibility is necessary to exist before parts that are divisible. How? Because if every part is divisible then nothing would ever be together, everything would be separated bearing no relation. So things that are separated must necessarily be contained in something that is indivisible. This indivisibility is thought or reason.
Continuity
The infinitesimal is defined by continuity, and continuity is defined by time, and time is defined by consciousness, and consciousness is defined by ideas, and ideas is exrepssed by feeling. This entire process is demonstrated by mathematics and logical understanding of infinite numbers in relation to finite. This describes how the infinitesimal is continuity, how that continuity is consciousness in time, and what is consciousness in time is the spreading of ideas. The law of mind is the infinitesimal.
(Find logic and math)
The idea of infinity in mathematics is generally understood by finite numbers, that is, the sum total of all finite numbers is considered the infinite. (Talk about the gublars incomplete theorem)
Pierce made the abstract concept of infinity concrete by associating it as the infinitesimal.
Infinitesimal indivisible
The idea of infinitesimal aims to explain how we can divide an indivisible substance. What it means for a substance to be indivisible just means that the substance is abstract, in other words, the physical representation of it does not comply with ordinary matter of classical physics, analogously it’s physical make up is Lorre holographic. This substance is the infinite complexity of mind bundled up into a warped undiscerned and undetermined slab of nature. Plato’s calls it the Forms, Aristotle describe it as thought, Hegel as reason, Whitehead describes it as a relatum, psychologist like Jung describe it as a complexity and the unconscious , Einstein calls it spacetime, all these are different perspectives of the same infinite fundamental nature.
The infinitesimal concerns how this is divided,that from a certain perspective it appears to be a two dimensional objects in space, but as the observer develops momentum in motion and therefore acceleration towards it, it becomes a 3 dimensional object, it begins to transform into particular and specific finite objects that is compost. Consciousness goes at the speed of light in respect to this object, and therefore becomes a particle state, becomes a finite and specific thing within it.
Let us apply our general ontological scheme to this more definite conception of substance. If we start let’s say at the beginning, as furthest back, or the state that is furthest unlike the state we are in at this moment right now. In this state we have an indiscernible state of nature, an infinity, which is the indeterminacy of everything. This fills in the content of the notion that if we begin with nothing, that itself is a something. If we have an infinity that is everything, that itself is still a single thing, or rather an identical conception. However it is not a single thing in being one thing distinct from another, because in this case we have a multiplicity of separate things the collection of which constitutes their whole.
When Aristotle proposes the claim that the “whole is greater than the sum of its parts”, this means that the efforts generated by all the parts working together out weighs the maximum effort any single part may have on its own. However this so called collective energy is not a result of the parts merely coming together to make it happen, it is rather according to Aristotle a potential energy that is at the base to which the parts tap into and access and therefore actualize, or they are the products of which they realize. It is this latter claim that is confusing because we ask where does a potential energy exist? However as to where it exists is a wrong question in the first place. The conception of infinity as a distinct self identical thing is non of these. So how is the conception of infinity of everything a distinct thing while not being any single and specific kind of thing? This can be answered by the next ontological claim following the proposition that if nothing is itself a being, then being is technically nothing, or rather no thing, not a single thing, that is the feature not a negation. but as we stated it cannot be the sum total of all single things since we cannot propose what we are trying to prove. So how can the characteristic of being be nothing define fundamentally what a thing is? From a purely spatial domain this cannot be true because when a thing is being it cannot be at the same time nothing, but rather nothing stands relative to it as what it is not, or rather an other, whether that be the space it maneuvers within, or some other object occupying another location, the point is an object cannot occupy the same position at the same time as some other object within the same space, however both nothing and being can occupy the same space at the same time as they are opposite substances and are within each other because one fills in where the other is not.
If we add the element of time, then it becomes clear how nothing can be the characteristic of a thing because the characteristic of any particular kind of thing is that it is potentially itself. This means that before even coming to be the kind of thing that it is, it must have been not that, and must have been potentially that, so that coming to be what it is, is the acting on its potential, it just simply conceived it’s potential into being from nothing. Moreover in time it is the case that an innumerable number of different things can occupy the same point in time, they share the same year, or moment, in other words they share the same space in which events common to all happen simultaneously. So if there is an infinity before us, and it is indiscernibly everything, and that is equal with no single thing, nor is it all things at once, then it must be the coming to be of one thing at one point in time. In order for everything to exist at once, it must have came to exist at one point in time, even if it was never created or destroyed but that it occupies the point of time we know as eternity, which is the temporal equivalence of entirety. It is the full content of the point of time. But the partial point of time, the finite duration of time, is not a piece of this full point of time, because the eternal point of time is infinitely dense in space, it is indivisible, therefore the finite point in time becomes distinct and separated from that in space, that which revolves around it, as we see galaxies revolving around the black hole singularity.
The nature of the universe has a very weird and strange physical layout, where things we take be to real things are literally on one side, and things we take to be indiscernible and only abstractly conceivable like black holes or dark matter, are on the other side, in other words, light may only enter the black hole but cannot escape, in space these two sides are rather separated from each other but maintained gravitationally by their separation, while in time,
How can a thing be nothing so that it can be any single thing at all? This is the only way everything can be any one thing at all because everything is in a state of nothing, or rather an abstract state. This means that it can penetrate through things, navigate through them, it is as Hegel calls it spirit, which goes through things, and it’s going through them is at the same time the very becoming of them, it’s penetration through them is their very creation.
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#44- (Whitehead in “concept of nature” talks about the senses and moments) A moment is a state it is not a passing incident. This means that moments are the experience of itself for its own development. And moments in time become structures, they become concrete. The moment in relation to time take on density. And it is this state what we call existence qua existence. Our subjective existence conceives this process as a flowing stream of events constituted by a set of unrelated passing periods, that once an event happens, it no longer exists. Equally the past is but just a memory of the present and the future has no yet reality. And so if you ask what is past and future, usually they are reduced to mere hypothesis. But potentiality is future which is the ability for the present to continue.
What we see as moments external from each other is but in fact the experience of existence itself. This is what Einstein sought out in the idea of space-time contuum, he however failed to make the connection of this fact about space and time and connect that with the fact Reason is the experience of itself. The latter is where spacetime exists as concrete density. What he also did not further develop, which was a truth beyond the subject matter of physics, and so he was not at fault, is the fact that the idea that spacetime are not just contingency of one another. It is rather the fact that spacetime bear a qualitative relation between each other, that is, the object. Space and time are different experiences of Reason and so they are the are the same thing in different states. The object in this sense bears anew external reality pressing against space and time. The object becomes the particular in tension with the universal. And this tension determines the qualitative process in nature, one that results in the process of evolution- the development of self-realization. But before we consider this we must understand how Reason plays a role as the entity of spacetime.
Planck length describes the density of Reason.
Nature is where such experience takes place. In nature the idea takes on a concrete form- the object in nature is the manifestation of Reason as the idea- the idea is the set of logical relations that constitute Reason. But if we assume that Reason is but the sum set of such logical relations our immediate intuition is that such ideas somehow exists in an abstract realm where ideas are scattered from each other, and only in this scattering we have the influx random association of logical propositions with one another;
Or in the materialist sense- the random process of external relations. But such a view conceives Reason in the abstract belonging to nothing but itself. And this abstract understanding of reason does not indicate to the very ground to which it lies, mainly it’s organic development- that Reason is organism. The organic in the ontological sense predicates the inorganic- the inorganic is the antithesis of the organic. With this in mind, any kind of organic existence presupposes a whole to which it can operate as a living system. Reason as such is only understood inseparable from the living entity. With this realization the idea that Reason is the scattering of every idea in the abstract realm does not hold.
What we must now consider what does this realization mean? This means that there is an entity into which Reason lies as a whole. Such an entity we may identify as God. The term God is so misleading at this point in history that asserting it is an empty indication to such a concrete truth. But aside from the semantics of the term, which plays a greater importance in the mind of most then the truth at hand, it is a fact that there exists some Being in which the whole lies- being that is the operates of Reason. This must also be organic, by this meaning that it is alive and not just merely a mathematical algorithm. The latter would bear no necessity to self-actualize itself as it is already the very definition as actuality independent from potentiality. This is what whitehead means by fatigue in contrast to Reason- fatigue being the contentment… But the very existence of space and time presupposes the immediacy to become what it is potentially. It’s mathematical nature is merely the skeleton for the process, and only one fundamental variable in the organism.
Scientific materliasm understands the expansion of the universe to be the infinite set of external relations between objects; that each object is multiplied forming a surplus of addition. The understanding into the universe in this sense indicates an infinite regress of material objects each relative in relation to each other. The ontological understanding of the universe, properly understanding the quantum states, indicates that the process of the universe operates as internal relations. The universe operates as the inner self reflection of itself. It’s expansion is the inward addition of multiplication of itself. It is the process of self- activity the actualization of self- movement. Such terms are ordinarily understood to be associated with the notion of God; that only a being capable of free will is able to set nature according to its self movement.
The word “God”
According to Hegel, the notion of God is semantics besides its meaning, he explaines;
“In a proposition of that kind we begin with the word God. By itself this is a meaningless sound, a mere name; the predicate says afterwards what it is, gives it content and meaning: the empty beginning becomes real knowledge only when we thus get to the end of the statement. So far as that goes, why not speak alone of the eternal, of the moral order of the world, etc., or, like the ancients, of pure conceptions such as being, the one, etc., i.e. of what gives the meaning without adding the meaningless sound at all?”
The understanding that nature is the product of Gods free will does not indicate what is truly meant by the universe as self activity. the universe operates according to the laws of Reason and is only identified as self activity according to such laws; but do not let the term “law” confuse the process as being fixed and static. It is merely meant to identify that the self movement, self activity or whatever other semantics meant to elaborate its meaning, is not an arbitrary process nor a process that is not aligned with Logic. The inquiry into how the universe operates as self movement is precisely the task of “quantum mechanics”; it is there where each moment in the process of self movement is made into a systematic predisposition. Stage by stage quantum mechanics will identify the whole to what is now only fragments of Reason in the world.
#56- (Sep.15.2015) In the timaeus, the attempt at describing the formulation of the universe is a more metaphysical account rather then a mere cosmological one. It is metaphysical in that it outlines the essential coming-to-being of the universe rather then it’s natural order. Although the latter is implicated with the demonstration of the former. The concept of “God” is elucidated as the cause of the universe. There are two possible interpretation to the term “God” invoked in the timieus; first, God can be taken in the traditional sense as ordinarily understood by monotheistic religions today. With this interpretation one can trace back the origin of monotheistic religions to Plato. In this interpretation the universe is understood to be created in accord with the will of God, that God is the consciouses entity guiding the world according to its determination. (Put the quote from the universe is one and there is not many one universes)
The second possible interpretation to the idea of God in the timieues is to conceive God as the universal force directing the universe with the laws of Reason. The universe is Reason because God actualizes the Good in the world. The difference between the first and the second interpretation follows in this sense; the first interpretation associates the idea of the Good in the universe to chance, in that whether God wills the good or not is a matter of free determination, the good is only good because God said it to be good. Whereas the second interpretation necessarily presupposes the good as the will of God because it is good. God is the good only because it is the Reason in the world; the good is because it is rational. The second interpretation characterizes the notion of God in the timieues in that nature is perfectly produced in the universal sense, as the whole, whereas it’s particular parts are accustomed to degeneration or death as willed by the universal. The good in the universe characterizes the nature of corporeality. The kind of form taken by each natural phenomenon assumes the kind of virtue so as to be itself, the material structure of objects portray virtue in that they are mathematical by nature.
The potential critique for the second interpretation is argued that the God is the Reason in the world, or that the world is rational because of God, is due to the simple fact that timieus projects his rational capabilities in understanding the world to be the actual order of the world. For example, timieus explains the division of the world “he took away one part of the whole, and then separated a second part…”. The critique is that timieus is applying his own mathematical capability to understand the nature of corporeality, but in doing so asserts that to be the actual nature of corporeality. This critique fails with the following question; where does timieues reason come from if not from the world, what is it based on, does it matter that reason belongs to him and that means it is divorced from the word? In this case, whether timieues is either wrong or right in expressing the nature it presupposes that his Reason is derived from the world, as such, the second interpretation stands that God is understood to be the Reason in the world. Where timieus does truly project his own human qualities onto the notion of God is with his language, that God is “the father…he rejoiced, and in his joy determined to make copy”. Such projections is however that of the irrational qualities of timieues and this cannot be stated to be the Reason in the world.
In the field of particle physics, the concept of the particle is mainly understood from classical physics. However the particle reflects the deeper meaning with the modern understanding that in the quantum state, matter and energy behave differently than what much of experience leads us to believe. Implicit in everyday particular objects is the universal process, meaning capacity for anything and everything, implicit in the objects we perceive are the ideas conceived in the mind, both these distinctions are part of the same underlying reality .
Classical physics is the observable inquiry into general objects; meaning that it is the understanding into usual objects conceived by experience. The observable inquiry into the universal state of the object indicates an otherwise nature from the general relativity between objects. The subatomic inquiry into the concept of the particle indicates that their is no distinction between the state of the particle in the universal form and in the quantum form. That the quantum form is proved precisely to be the universal state of the object.
Whether zooming into the subatomic nature of the particle or scaling out into the universal state of every general object, it proves to be governed by the same laws of quantum. Direction is trivial for the observation into the quantum state of the object. Whether the reflection is inner or outer, the quantum state operates as the universal nature to all objects. Every object is in fact the particular moderation of the universal. General objects are merely the universal in its moderate nature; they are the self actualization of the universal self movement. Light in its universal form operates both as particle and wave; wave-particle duality explains the universal process of matter. The uncertainty principles also elaborates the infinite nature of particles. The universal nature operates in a particular manner; a manner such that of reason. Each concept derived from the quantum state of the particle indicates an instance of the working of Reason.
The latter is an atomic unite of space in time. That space takes on the form of an idea. The notion of the infinitesimal is the concrete proposition to the concept of the infinite; (1) because in the infinitesimal the infinite takes on a specialized form, a particular and finite form- a form having bounds and limits. This at first indication seems to contradict the idea of the infinite- how can something be infinite if it’s bound? Then it becomes finite. This thinking however presupposes that the infinite bears no form. What if the form associated with the infinite is the form which can take on every form? It is however often claimed that the infinite bears no form because it is that which cannot exists in one direction in space but rather it must exist in every direction.
If the infinite is that which exists in every direction does that activity itself not presuppose some ground in which it can exists in every direction? What about the nature of a circle- does that not expand into every direction- including the direction of into itself. Our understanding that the infinite is not bound limited the infinite to locomotion. Locomotion is only a general determination whereby the infinite assumes external from itself. The correct understanding of the infinite must see infinity in determination in every kind including the self determination of becoming- or coming to being. That which has the way of determining into infinity is what we can identify as the infinite (2) Yet that particular form still bears the nature of the infinite in that it is a universal form.
At the infinitesimal the universal is specialized as a particular that particular having within itself the means for applying itself generally- and so that particular form is able to take on every form. It is the general nature for anything specific. When we associate the idea at the infinitesimal level- we see A) that the idea takes on a particular material form but B) that material form takes the shape of whatever the idea perpetuates- the idea bears an infinite relation with itself. The infinite is a contradiction between itself as universal and yet manifesting that into a particular. Squaring the circle… This contradiction itself is concrete and it isn’t solved for a reason.
The notion of the “idea” in this sense is not only limited to the understanding that sees ideas in relation between individual minds, it rather sees an infinitesimal relation implicit between each Individual mind- implicit means that the relation between two separate minds is in such a way where they are materially intact with each other at the infinitesimal level. What links each idea in separate minds is FEELINGS. These we do not see but they take on a quantitive form- a material form, eg, protoplasm (law of mind). FEELING here is understood as a kind of affect triggering a reaction- like the laws of attraction and repulsion.
This continuity is Consciousness which is the continuity of ideas at the infinitesimal level. In this level the ideas bear an immediate relation that is constituted by intensity- the idea perpetuates such a relation where the contradiction is concrete. This means that the idea bears a logical relation where it takes opposing elements to bear a harmony and between opposing propositions to which constitutes a uniform whole. That uniform whole takes on the abstract notion of the infinite and propagates it as distinct energy states- each of which emphasize a kind of idea associated with Reason. The idea bears the abstract nature of the infinite which takes on an infinitesimal manifestation where the idea becomes an object- that object being the reality of the idea- and the idea being the actuality of the object- the object necessary for the idea to be the determinacy of thinking.
Demonstrating this mathematically will help clear how the infinite manifest as the infinitesimal. Perice outlines that each whole number presupposes a distinct even number. The doubling of numbers are all even numbers and this constitutes a distinct series of even numbers. For example (539):
1,2,3,4, 5, 6, 7, 8,-
2,4,6,8,10,12,14,16-
If we take for instance 1 as the whole number and 2 as the even number- we have that 2 is just but 1 + 1 together. But in order for 1 to be added with 1 it must first be equal with itself as 1 and so ; 1=1 must be true at the same time 1+1 is true (the law of identity). In this sense, 2 distinctively presupposes first; 1=1 and second; 1+1. But because 1+1 presupposes 1=1, 1=1 presupposes 2 because 1 and the identity with itself are two actions. Numbers do not characterize static objects only but also quantify changes discerned in a dynamic activity. And so 1=1 is 2 because 1 presupposing itself is an addition of itself (1=1 is 1+1).
When we say 1=1 we are talking about the same odd number (whole number)- every odd number is able to presuppose itself an infinite times but in presupposing itself it also presupposes a distinct even number, but that distinct even number presupposes the whole number. e.g, 1,3,5,7,9 presuppose 2,4,6,8,10, “presuppose” here means it must assume the other to be itself.
So when we subtract 1 from 2 we are left with 1. When 3 is subtracted by 4 we get 1. When 5 is subtracted by 6 we get 1. Each odd number in relation with the even number presuppose itself as a whole number.
Proposition #2:
once 1=1 presuppose 2, the 2 is now a distinct even number in relation to 1. – The very presupposition that 1 being equal with itself is 2 also presupposes that 1 being equal with 2 is 3. And this relation goes on into infinity. What this means is that the idea itself has within it the means to produce its own contradiction- that contradiction merely being the element to which it can relate with itself again as its own self. This is the dialectic- which is the logic predicting the mathematical application of infinite numbers. To understand the logic of the dialectic: take the odd number of 1 as equal to Being, the even number 2 as equal to Nothing, and 3 – the addition of 1 with 2- as equal to Becoming. Here we attributed a quality to our quantitive measure because numbers are meant to measure the quantitive consequence associated with a certain quality.
Being, Nothing and Becoming are essential logical propositions indicating a qualitative measure. Being = law of identity, Nothing= law of non-contradiction, Becoming= law of excluded middle. If Being is on its own relative to Nothing, it presupposes Nothing as something. In this sense Nothing itself is something and by presupposing something, which is in this case Being, Nothing is in fact that which is not being- the inverse of what being is- which on its own takes a form. But because this non-being is the 2 to the power of 1- it is the the multiplicity of what Being is not. This 2 times of what 1-is-not (-1) nevertheless presuppose 1 and therefore is in addition with 1 to assume 3. Now this 3 is constituted by 2 that is not-1 (-1–1=2) and the 1 (1+1=2) that is equal with itself as 2. The 3 itself is made up of 1 odd number presupposing 2 as its distinct even number. So when the even number 2 is equal with itself it becomes 4 while that 4 still presupposes the 1 as it is the division of it- and so when 4 is multiplied by 1 it is 4 again. The 3 we call the Becoming because it is that which is every possibility of the 1 that is, Being. What this is meant to show in relation to the idea- is that the idea itself is every idea as it has within it its own means to contradict itself and have that contradiction as a result.
The idea in the notion of continuity reaches the level of generality. In this level the idea is established and is no longer active- this does not mean it ceases to be activity because in continuity the idea is active at the infinitesimal level and that level culminates in the generality of itself. The notion of continuity does not only describe how ideas externally are related at the infinitesimal level; it also shows that there is continuity between the idea itself as intensity and generality. Continuity is not just horizontal but also vertical. –|–
These ideas at that level develop generality by establishing some truth- that truth being the object. And they exist as general as the implicit process is still intense. The idea of infinitesimal solves many pro élan associated with the infinite. The first problem it solves is that the infinite is no longer seen as an infinite duality between objects, it is rather an inner multiplicity from itself.
Explain how his math reinforces the idea that each number itself presupposes within itself a distinct even number. This means that each idea has within itself the means of multiplying itself as two even forms- from which both of these even forms carry their own distinct nature- and by virtue of their distinct nature they bear a contradiction in relation each other. But this contradiction is not antithetical insofar as being anoganstic for that negative relation is already constituting the relation whereby to allow each form to be distinct- that is always there for any each object to be itself and not the other. But this alone only means that these distinct ideas branch out from some common source that must exists so as to allow for ideas to be different. And because ideas have at least this minimum unity, they too must also be determined to unite further into the same idea- that same idea is a conception of the self- the idea is the consciousness of itself. predicates logic predicates math.
Explain how the atom itself is a logical relation. String theory- each qourk is a proposition of itself. This is similar to saying that in discourse each proposition is an assertion- to claim something as if it were true. An argument aims to prove what is true by dividing truth into premises in support of a conclusion- the conclusion being just the reassurance of the premises- a valid argument is that if the premises are true there is no way the conclusion can be false. What is true in discourse is a fact about some external object. What is true for Reason is the fact about itself made into an idea- that idea is the reflection of what it is- but because itself is actuality- meaning that it is everything that can be potentially true- it takes its actuality and reverses it into something that is potentially all of actuality. This inversion is the transference of the idea into an atom- and then the atom into the idea. This is a fact about any complete object which renders its concrete- by this I mean what the perception sees to be an object that is whole. When we analysis any object that is whole and divide it into its essential nature- we are really only doing half the job of we divide it into a countable infinite set of atoms. This division itself is the first division of its quality- that is, the first essential quality, the first only to our understanding, of the object is that it consists of an infinite set of atoms- the second essential quality, which is in fact the first in the organic formulation of the object outside the understanding, is that each of these atoms are are the quantitive proposition of logic. Each atom is an idea of logic- the atom being the quantity of the idea, and quantity itself is the quality of logic. The quantity is the quality of Reason and Reason is the quality of quantity.
#34- light is the physical infinitesimal
The elements in the world follow a qualitative intervals of time, each interval being the sublation of the past. 1,2,3,4… With each interval in time, the idea develops quantitive momentum which is a signification that its idea has developed a further infinite series of ideas, each of which are an expression of the predicate limit. In Deduction, the relation between Being and non-being operates as the creation of particular instance from a general notion. The general notion is that being uncovers itself as possessing an element that is not of itself- because it already exists as the infinite- it has no where else beyond it self to see but inwards into itself since the infinite does now portray a finite element- that finite element simply is that when the infinite reaches itself as the limit- what is it left to do? It is now left with the task of sublating its infinite nature into a finite variable that is expressive of the infinite- it makes itself into a finite that is able to take the form of the infinite- able to take every form. This allows for its idea to take the form of an object, from which it can develop self-externality from that object to perceive its idea as the object- but this self externality cannot be something abstract but from this logic be another sequence of an object. This self externality is space, but this on its own cannot exists but presupposes a variables that self-identity- and that object must be activity. But any activity presupposes something that undergoes an activity. And so now we are left with space as self-externality to enable the idea be an object able to be perceived from another externality, and we are left with an activity that is pressing on the idea to be an object- the idea must have duration to be in time. What is then the very basic object that captures the idea mediating self-externality with self-identity? This very first object is light (definition)– “The indivisibility of light in its infinite expansion, a reality outside of itself that remains self-identical, can least of all be treated as incomprehensible by the understanding, for its own principle is rather this abstract identity.” (Hegel 220 nature)
Light is that externality that remains self identity and it this unity that remains it as indivisible and able to take every form. Light is the first finite idea that is able to be the infinite ideas.
Power
what the law of identity identified as the I or the Self- is the principle of difference- is not-the-self. That is the principle whereby the I recognizes that what it is essentially involves an element that is concealed from itself- or it does not exists as itself- otherwise it would just be. It is this element that it has to come in terms with and makes of itself so as to remain in identity with itself.
When an individual control others it’s mind grasping control over its self. It’s taking a hold of itself when it wonders into infinity and sets itself rightly back towards its logical direction. Or rather it takes a hold of itself and sets itself astray, as we saw in the case of Hitler in WW2. When certain individuals possess power over others it is a matter of consciousness aiming to cohere itself as a whole because from the beginning it has set itself astray into infinite unites. But this is no accident because it is a necessary step it takes upon itself to simulate every idea belonging to it. When one individual has power over another it is an initial step taking to understand an external part foreign from itself as that aspect of itself.
The idea of external relations defines the notion of power in the social relations between individual. Once one individual achieves recognition of another, they begin to attribute qualities belonging to the self into the other. Such qualities can vary to whatever purpose the the individual associates themselves. That purpose however is not so indifferent to other individuals.
Reality is the algorithm of infinite potentiality that insist on its actuality at a finite instance. The process itself is the infinite replaying of potential realities- all of that is mediated by freedom- the decisive element of actuality. Freedom began as a germ of consciousness each time choosing its place in a potential reality and therefore turning it into an actuality. In this it becomes reality whereby it is allowed to make another decision. Science is the phenomena in nature where consciousness is achieved about what consists of itself. Reason deploys its abilities at work to formulate every potential possibility of itself as an object- and that object is itself at the same time the working of its potentiality out as an actuality.
what is “power” both as an element in the world and how that element takes the actual form of the object. Power ontologically understood is intent- or in other words- determination. This determination in terms of being some kind of particular force as opposed to any and all potential forces, takes on identity of an “I” or a sense of Self, is the first moment of a Will. Power is the generation for a will. The will bears an ethical underpinning because it deals with operations of a kind of relations in the world. Fundamentally ethics is the science of relations in the world, and so the Will is something fundamental in ethics because it is that initiative action whereby relations are at work, whereby the component part of the relation maintain themselves as distinct parts of the same whole.
A moment
The Will is the drive for Reason to produce the infinite set of relations derived from the very first relation- that between the Self and the Not- between Being and non-being. This is captured by the following equation: I=i (hegel logic). The uppercase “I” captures the identity that Being exists as something relative to the Non, this must be objectively true otherwise their would be no being and therefore only Nothing. The lowercase “i” explains how Being sublates a potentiality of itself derived from Nothing, and makes that into something- a Being. In other words, the lower case “i” makes that ultimate distinction between nothing and being abbreviated capital case “I” into a particular instance, a moment in the time duration of existence. The usage of the term “moment” here does not imply an insignificant instance that passes within a short span of time.
This understanding of a “fleeting moment” is one we are accustomed with because our normal day to day experience consists of these short burst of different moments that come and go, and so we develop the implication that a single moment is insignificant. But reality in fact consists of nothing else but moments, there are however fundamental moments that do not occupy a short time span but extend on for eternity, like the moments of being and nothing. These two fundamental moments can be looked at in two ways; first, there is either being for an extended period of time or there is nothing for an extended period of time, and when one moment is present the other is not. Second, we can see being and nothing alternating in a rapid burst fire between each other happening right after each other at the fastest and shortest periods of time. These are the two extremes of the duration of time as in the first case characterizes infinity, or the longest span periods of time, or as in the second case characterizes infinitesimal, the shortest periods and most instantaneous time span divisible into the quickest moments.
The reality is somewhere in the middle of these two extremes, such that we experience a lifetime as the longest extent of our own individual consciousness, and within that we experience fast fleeting moments. The relation between Being and Non is merely an abstraction meant to display the very first dialectic derived from existence- more specifically- immediate consciousness. Immediate consciousness (explain more) shares an infinitesimal relation with consciousness generally. Their synthesis is self-consciousness- the identification of Being with non-being- the I=I. Every time there is a principle of identity that itself is an immediate consciousness which takes the form of an object- or that it is reflected into a representation of itself, and that representation is the object in nature. Light for example.
The question of in what sense do people have power over another is where the Will and its power reaches a limit in its infinitesimal process in time. The present always characterizes the limit of the infinite in time. It is here whereby its transitioning into the future and this transition is an energy state- a motion forward in space involves an element of entropy, where it can be repulsed against, changes direction or determination, looses track of the aim etc., , . When we are referring to human history we are indicating a particular interval in the infinite series constituting the infinitesimal process. If we recall the mathematical understanding of infinite numbers bearing two magnitudes of infinite association: endless series and innumerable. In this understanding, the Aristotle principle: that each continuum has its own limit- it must be least than the next but greater than all previous. And how the moment is that instant constituting all instants. Human history then characterizes world history because it is the present, and as such it is the interval that holds all previous ones.
The way power took place in human history leading to the present is of control and tyranny. Hegel says history is a slaughter bench. This is the case because in this time of the present the ideas of consciousness is operating intensely and this has not yet generalized. Whereas in contrast to nature at large- we see more of a infinite cycle of regress- the idea has already generalized. The universe is the past that remains infinitesimally attached to the present. The infinitesimal is not just smallest microscopic unit of time and space but it is also the most macroscopic. The working of dimensions is extended in every direction- looking at the basic geometric shape shows that each angel is equilateral with the rest.
We see this tridimensional process as a spectrum extended macroscopically and microscopically, and in the median we have the present state of time- taking a metamorphosis of its idea with the insistency of future generalization. In this generalization the idea becomes established as an object for consciousness. When individuals hold powers over others it is not a battle of survival or rather competition- these ideas we created to resolve the disparity of equality that power presupposes with it. And so if we are in competition we all are equally potentially tyrants and it is a matter of the luck of the draw that some are whereas the rest is not. And power is only done for survival- this idea derived from the Darwinian understanding of adaptation, we can now say that “we are all trying to make it and in doing so- some make it more than the others”. Both of these attempts to understand power fail a very important consideration when understanding power. Power presupposes both a qualitative and quantitive measure both of which bear a kind of mathematical relation to one another.
Power presupposes a quantitive measure insofar as there is a series of variables set in a particular sequence. The setting of particulars in a specific kind of sequence is caused by a variable bearing a quantitive measure in the quantitive chain. In fact, the qualitative measure is first true before any quantitive sequence because the sequence follows the integral value of a variable, then it’s place, and not the other way around- its place cannot be its integral value it is instead the integral value that assumes the place ( Perice law of mind series (f)…).
The following question arises concerning the quantitive relation between the tyrant and the followers. Quantitively speaking the tyrant is one equal variable among others and so what about the ruler that enables them to be the integral value of the sequence? There is some quality that the ruler must presuppose to direct the quantitive chain. The real relation between ruler and followers is that the followers are the quantitive chain that recognizes some quality in the ruler as one variable that they lack in themselves . It is not that the followers lack the quality the ruler has, it is instead they do not possess it to the same degree. This difference in degree is the difference of being conscious and unconscious. The tyrant only bears the quality of acting on the variable. The tyrant is not afraid to embrace his nature and act on that with emphasis. Whereas the followers act on their nature more implicitly and as such are not acting on their nature as variables they are rather just the necessity so as to be the variable. When the ruler is the variable that acts as itself the variable, the followers derive consciousness of their own nature as variables, but still they are unable to act, otherwise they would of and there would be no need for ruler. The followers then submit to the ruler, this submission is itself an action of the variable as it’s necessary self. The followers on this case are not reactive they are rather proactive. This of course is an unconsciousness process which results in consequences against the interest of the followers, but what they might take to be against their interest is in fact the development towards their interest, as they have the interest that is portrayed by the tyrant- submitting themselves to what ever they are helps them becomes what they want to be. It is then the case that the ruler bears the qualities that characterizes the entire series.
The quantitive measure is not equal- there is one leader and many followers- that’s because the followers submit themselves to the one because they lack the quality of the one. What does this mean for consciousness as a power in the world. When this happens- consciousness is taking a hold of itself- when it wonders of into infinity.
Law of mind intensive general
This far we understood that there is an implicit process of consciousness governing the species- religion calls that God, psychology calls it the unconscious, philosophy calls it Reason etc., that the human being is in fact a particular way of consciousness deriving knowledge of itself.
Generalized vs intensive stage
However what is the mechanics of this process, how does it play out at a fundamental level? Peirce answers this question with the notion of the infinitesimal. The idea of the infinitesimal defines the infinite and it is the home for the quantum realm. The infinitesimal realm is defined by time in such a manner whereby in the past the idea generalize and thus become objects in existence; while in the present they involve the insistency of the past and thus operate at an intensive level. Pierce outlines two stages of the infinitesimal which are magnitudes of time, the generalized and the intensive state. The generalized state is simply the condition of time and high has gone through an extended length of time such that it is established as a form or an element in nature. The reason why a longer length of time denotes the establishment of a form in nature is because something that maintains itself a longer place in time – “stand the test of time” – is still relevant for a future possibility, a potential of the event not present. It is this latter point that transitions the discussion to the intensive stage which describes the present moment in time as the intense and insistent point in time where events are aiming to generalize.
this stage the generalized ideas are relating with intensity with one another as they are leading into the future. The human being in this sense is that general idea that holds the process of insistency where ideas relate intensely with one another at an infinitesimal level between mind. The very present moment is an axiom for the idea in its intensive form. Behind the present, consciousness has not yet derived an actual understanding of its ideas as it has not yet generalized it has an object. The future is where consciousness possess a potentiality of its ideas. This potentiality is not something abstract existing somewhere out there who knows where, it is rather a concrete process whereby ideas are integrating together to simulate every possible notion of itself and produces that as a uniform whole- that uniform whole is the truth it finds that characterizes every possibility of itself.
Human history is a peculiar stage of this infinitesimal process. Human history is where consciousness derives knowledge of the self- and therefore we have the transitioning of consciousness to self-consciousness. If you have been following our logic thus far it is clear that consciousness is not something excluded when it develops into self consciousness, it rather now turns inwards into examining its own operations. What we mean exactly by this is that the entire process of consciousness has been the development of outlining its thought logically outwards making it into a generalized whole.
The process of consciousness proceeded by taking its idea and making that an object for itself. Nature at large we can say is the result beginning with the logical beginning of space and time- transitioning into energy states like light and all the element- and finally into the process of life which is predicated by the laying out of the gene pool- which is but just the recording of its entire working thus far- a documentation of the information it logically achieved from deriving nature and outlining that- spreading it out- and seeing how that information interacts in an environment. The result is the biological organism. The evidence for this is that the human being only uses about 5% of there genetic information pertaining to their subjective ends. The rest 95 is the historical documentation of the universe at large (explain more).