Re: Philosophy Request Line: Why, "Plato was a jerk"
Posted: Tue Aug 15, 2023 11:08 am
(Continued from previous post.)
2. Value (quantity)
So, Hegel, by cunning and vague logical operations, passes to quantity. All categories of this transition are based on emphasizing the difference between directly qualitative certainty and that certainty that appears as quantitative.
Diamatics teaches that quantity is the coincidence of qualities at a certain level. That is, strictly speaking, there is no quantity as such in the universe. When we talk about quantity, we are always talking about the quantity of something.
The mystical fog of the Hegelian transition from quality to quantity is precisely connected with the non-recognition of this, although in its logical construction one can see the mediation of quantity by quality. But Hegel did not bring this element of logic to clarity, therefore he preferred the descriptive construction presented above. Almost certainly, this shortcoming is connected with conscious abstraction, the impoverishment of reasoning itself from pure being and nothingness, in which the transition of being-for-itself something to quantity can be represented only on the basis of the opposition of determinateness as a quality (boundary) and determinateness as quantity (boundary indifferent to quality), and when the latter has already gone beyond the limit to infinity. Therefore, Hegel has a monstrously incomprehensible formula for those who did not follow his derivation: quantity is "being-for-itself, which is unconditionally identical with being-for-other ” (NL 197).
Usually, the initial difficulty in understanding Hegelian quantity is due to the obvious presentation of quantity as several things. Naturally, when such an assumption from the sphere of being is applied to some examples from real life, where things not only mentally add up to each other, but also have internal quantitative parameters, this causes difficulty. Therefore, one must understand that being-for-itself, which is unconditionally identical with being-for-other , is an intermediate formulation, even in the system of Hegelian philosophy, suitable only for a certain level of reasoning.
According to Hegel, the quantitative certainty of something is its boundary, which is indifferent to itself and to which something itself is indifferent . We can say that quantity is one of the moments of certainty, along with quality. It arises, firstly, because the infinite prevails over the finite (which is missed by most interpreters of Hegel), and secondly, because qualitative certainty (boundary) exists only as a distinction between something from everything else, which means “existing-for- itself now it is posited in such a way as not to exclude the other, but, on the contrary, affirmatively continue oneself into the last .”
By the way, the fact that Hegel called both qualitative certainty and quantitative certainty a boundary (in the second case, a boundary indifferent to quality) shows that he at least guessed or assumed that quantity is also a quality, simply acting as some kind of sameness.
A simpler and clearer description of the transition to quantity according to Hegel can be represented approximately as follows.
So, we have reached the final something. Its determinateness is its boundary, which, on the positive side, limiting its definition (appointment), acts as an obligation, and on the negative side, linking something with another, acts as a limit. The interrelation of obligation and limit is the finite itself. Further logical movement is possible only in the form of overstepping the limit, because the inner picture of something is completely completed. Going beyond the limit leads us first to bad, and then to true infinity; and we discover that the finite is only a moment of the infinite (perhaps the most important Hegelian thought in the system of the sphere of being). It turns out that it is the infinite that is the true reality.
What can be said about the border in this connection? The boundary must be considered not only as an obligation and a limit, but also as something indifferent to quality in general . It seems to be drowning in infinity, infinity absorbs it, but at the same time, the outlines of something and its qualities remain. The boundary, taken indifferent to quality, is quantity . And now it is necessary to focus only on how quantity relates to quality. To do this, we should look at how many there are, what logical content we can find in it.
Hegel begins his consideration of quantity with PURE QUANTITY - this is such an intermediate category that serves as a guide to further ones. The point is that quantity must first be considered in terms of the indifference of the boundary to something. Such a view gives us the concept of continuity , for nothing else can be said here. Continuity is defined as
“a simple, self-equal relationship with itself, uninterrupted by any boundary and by no exception, but it is not an immediate unity, but a unity for-itself-existing alone” (NL 200).
Something like the continuity of flowing something into another something, and so on ad infinitum. But since the flow occurs from one to another and to many one, this must receive some kind of conceptual expression. Thus, along with continuity, we obtain discreteness. Therefore, in pure quantity one can see the difference between continuity and discreteness and nothing more.
Hegel was a great connoisseur of mathematics, and mathematics had an influence, first of all, on the consideration of the problems of the category of quantity, since quantitative definiteness and spatial forms are its immediate subject. In considering quantity, Hegel is primarily interested in deriving the meaning of mathematical operations.
The course of Hegel's thought is already familiar, the setting of the positive (being) and deepening into the negative as meaningful (nothing), so the assimilation of the category of quantity is much easier.
The category of pure quantity is similar to the category of pure being, it does not give anything except the definition of continuity (analogous to being) and discreteness (analogous to nothing). Thus, everything is both continuous and discrete. Continuity expresses the moment of equality with itself , and discreteness - the moment of inequality with itself .
The unity of continuity and discreteness for us is still quantity. However, the primacy in this unity belongs to continuity, since quantity is derived from being-for-itself something that previously led us to infinity. Here the analogy with being and nothing no longer works, because there we could take nothing and it became being, but here there is already a link between continuity and infinity. This point should not be overlooked and fall into the schematics.
The pure quantity has not yet become a definite quantity, it has no boundary, since we are still looking from the point of view of the indifference of the boundary to something. The mathematical expression of a pure quantity is the abstraction "straight line" and "plane". They are both continuous and discrete at the same time. A straight line is a line of infinite points, and a plane is a surface of parallel lines. Generally speaking, a point in geometry has the same properties, it's just that mathematics artificially assigns it to be indivisible. True, the absolute simplicity, finiteness and compositionlessness of a point will express the next category - continuous and discrete VALUE, namely the unit.
The transition to the value occurs as follows. In pure quantity, the unity of continuity and discreteness is posited only "in the definition of continuity." But what if we consider this unity, “put it down” from the standpoint of discreteness, that is, consider the boundary, which is indifferent to quality, from the point of view of the still existing connection with something? We get a continuous value - it will be a direct quantity.
Let me explain. We have a continuity of pure quantity, which is indifferent to something. But nevertheless, in this continuity there is also a moment of negation - something passes into another something and so on ad infinitum, that is, discreteness is observed. Now we look at the same process from the "back side", from the point of view of discreteness, just as we revealed the certainty of existence, considering everything that follows from nothing. In this case, we get a chain of something continuously passing into each other, that is, some continuous quantity or direct quantity .
In this case, the pure quantity is not mediated, but the magnitude is not direct. The word "immediate" is used here to mean that consideration of a pure quantity has led us to some immediate result, a continuous quantity.
And now Hegel’s cunning and yet another ingenious logical move: since the discreteness we have taken does not lose continuity, that is, it is discontinuity, but uninterrupted , which means that the resulting value is a collection of many alone as equal , “ not many alone in general, but posited as many of some single UNIT ".
So, one more time. Quantity has two moments: continuity and discreteness. We take the quantity from the discrete side and get a continuous value . What at this moment in continuity does this boundary delimit? Units. As a result, we get some discrete value . However, neither continuous nor discrete quantities can be taken separately, they are posited as a single quantity , which has both continuity and discreteness.
Indeed, if you imagine a certain sum not just as a quantity - a term of its constituent parts - but as a unity of continuity and discreteness, then after reflection you will notice that, firstly, the quantity is made up of equal elements (units), and secondly, that this unit is infinitely decomposable into smaller units, thirdly, that beyond this magnitude there is nothing but the same units. Of course, the concept of quantity is still very abstract and not suitable for simple counting, although it covers its mechanics.
“Continuous and discrete quantities are not yet definite quantities; they are only quantity itself in each of its two forms” (NL 218).
Now we have, on the one hand, a pure quantity - a very strong logical category of being that goes to infinity, on the other hand, a direct quantity - a quantity that is not yet a definite quantity, but only an approach to it. We need to dig further into discreteness.
So, we remember that quantity is generally indifferent to quality, but it is still a limit. She is currently delimiting units. Thus, peering into discreteness, we see not only a unit, but also a certain set of units . From whatever side we approach this conclusion, in the end we will have to admit that we have before us a certainty of magnitude (direct quantity). That is, we have received the certainty of something, connected with another, many and infinity, but which is not a quality of something and is indifferent to it. A definite value differs from a pure quantity primarily in that it can be increased or decreased, that is, it has certainty and dynamics in this certainty.
By the way, Hegel correlates the category of pure quantity with the concepts of matter, space and time:
“The absolute is pure quantity—this understanding of the absolute coincides in general with the one according to which the absolute is given the definition of matter, in which the form, although present, is an indifferent determination. Quantity also constitutes the basic definition of the absolute, when the latter is understood in such a way that in it, as absolutely indifferent to difference, any difference is only quantitative. As examples of quantity, one can, in addition, take also pure space, time, etc., since the real is understood as their content, indifferent to space and time ”(EFN 170).
Of course, such a view is inherent in Hegel as an idealist, for he initially denied the axiom of the materiality of the universe.
The most important characteristic of a certain quantity is that it, as a set of units, excludes all other definitions (units), therefore it is a limited quantity (EFN 174).
Hegel liked to explain that a certain quantity is the actual existence of quantity, by analogy with the existence of existence from the chapter on quality. In this sense, pure quantity = pure being, repulsion = pure nothing, continuity (which can also be represented as attraction) = being, and discreteness (as a development of repulsion) = nothing. Therefore, a determinate quantity is a one-sided (in terms of discreteness) taken unity of continuity and discreteness, which appears as immediate and simple. In principle, this is how it turns out, a certain quantity is a completely direct and simple limited number of units. True, if you look closely at the unit itself, it can be decomposed to infinity. Qualitative certainty, however, was not represented by something so crystallized, so this analogy, in my opinion, is conditional.
Logical exercises about the magnitude can also be turned using the numerical axis.
A certain quantity (continuous and discrete quantity), in contrast to a pure quantity, already has a fixed limit in itself , a certainty that limits the units taken. Continuity here is no longer manifested in the endless transition of one something into other somethings, but directly in one, in the unit . Discreteness is manifested in the fact that a certain amount is a set (of one) . Consequently, the unity of continuity and discreteness, in addition to being a certain amount (value), also excludes everything else, limits. Thus, a certain quantity in its final form is a NUMBER.
“The complete positing [of a certain amount] lies in the existence of the boundary as a multitude and, therefore, in its difference from unity. A number is therefore represented as a discrete quantity, but it also has continuity in the form of a unit. Therefore, it is a definite quantity in perfect determinateness, since in number the boundary appears in the form of a definite multitude, which has as its principle one, i.e., something unreservedly determined. Continuity, in which the one is only in itself, as sublated (posited as a unit), is a form of indeterminacy.
Everything according to Hegel is logical: being (pure quantity and continuity) into nothingness (quantitative definiteness and discreteness) is contained in a removed form.
To be continued…
A. Redin
https://prorivists.org/sol/#p10
Google Translator
Don't think I'll post the Q&A, it is at the link, in Russian. As earlier stated, I dunno about the usefulness of this machine translation. I've found Hegel very tough sledding in English and honestly can't tell if the machine is causing problems or not. Goddamn philosophy... why couldn't this be easy like Epicurius?
2. Value (quantity)
So, Hegel, by cunning and vague logical operations, passes to quantity. All categories of this transition are based on emphasizing the difference between directly qualitative certainty and that certainty that appears as quantitative.
Diamatics teaches that quantity is the coincidence of qualities at a certain level. That is, strictly speaking, there is no quantity as such in the universe. When we talk about quantity, we are always talking about the quantity of something.
The mystical fog of the Hegelian transition from quality to quantity is precisely connected with the non-recognition of this, although in its logical construction one can see the mediation of quantity by quality. But Hegel did not bring this element of logic to clarity, therefore he preferred the descriptive construction presented above. Almost certainly, this shortcoming is connected with conscious abstraction, the impoverishment of reasoning itself from pure being and nothingness, in which the transition of being-for-itself something to quantity can be represented only on the basis of the opposition of determinateness as a quality (boundary) and determinateness as quantity (boundary indifferent to quality), and when the latter has already gone beyond the limit to infinity. Therefore, Hegel has a monstrously incomprehensible formula for those who did not follow his derivation: quantity is "being-for-itself, which is unconditionally identical with being-for-other ” (NL 197).
Usually, the initial difficulty in understanding Hegelian quantity is due to the obvious presentation of quantity as several things. Naturally, when such an assumption from the sphere of being is applied to some examples from real life, where things not only mentally add up to each other, but also have internal quantitative parameters, this causes difficulty. Therefore, one must understand that being-for-itself, which is unconditionally identical with being-for-other , is an intermediate formulation, even in the system of Hegelian philosophy, suitable only for a certain level of reasoning.
According to Hegel, the quantitative certainty of something is its boundary, which is indifferent to itself and to which something itself is indifferent . We can say that quantity is one of the moments of certainty, along with quality. It arises, firstly, because the infinite prevails over the finite (which is missed by most interpreters of Hegel), and secondly, because qualitative certainty (boundary) exists only as a distinction between something from everything else, which means “existing-for- itself now it is posited in such a way as not to exclude the other, but, on the contrary, affirmatively continue oneself into the last .”
By the way, the fact that Hegel called both qualitative certainty and quantitative certainty a boundary (in the second case, a boundary indifferent to quality) shows that he at least guessed or assumed that quantity is also a quality, simply acting as some kind of sameness.
A simpler and clearer description of the transition to quantity according to Hegel can be represented approximately as follows.
So, we have reached the final something. Its determinateness is its boundary, which, on the positive side, limiting its definition (appointment), acts as an obligation, and on the negative side, linking something with another, acts as a limit. The interrelation of obligation and limit is the finite itself. Further logical movement is possible only in the form of overstepping the limit, because the inner picture of something is completely completed. Going beyond the limit leads us first to bad, and then to true infinity; and we discover that the finite is only a moment of the infinite (perhaps the most important Hegelian thought in the system of the sphere of being). It turns out that it is the infinite that is the true reality.
What can be said about the border in this connection? The boundary must be considered not only as an obligation and a limit, but also as something indifferent to quality in general . It seems to be drowning in infinity, infinity absorbs it, but at the same time, the outlines of something and its qualities remain. The boundary, taken indifferent to quality, is quantity . And now it is necessary to focus only on how quantity relates to quality. To do this, we should look at how many there are, what logical content we can find in it.
Hegel begins his consideration of quantity with PURE QUANTITY - this is such an intermediate category that serves as a guide to further ones. The point is that quantity must first be considered in terms of the indifference of the boundary to something. Such a view gives us the concept of continuity , for nothing else can be said here. Continuity is defined as
“a simple, self-equal relationship with itself, uninterrupted by any boundary and by no exception, but it is not an immediate unity, but a unity for-itself-existing alone” (NL 200).
Something like the continuity of flowing something into another something, and so on ad infinitum. But since the flow occurs from one to another and to many one, this must receive some kind of conceptual expression. Thus, along with continuity, we obtain discreteness. Therefore, in pure quantity one can see the difference between continuity and discreteness and nothing more.
Hegel was a great connoisseur of mathematics, and mathematics had an influence, first of all, on the consideration of the problems of the category of quantity, since quantitative definiteness and spatial forms are its immediate subject. In considering quantity, Hegel is primarily interested in deriving the meaning of mathematical operations.
The course of Hegel's thought is already familiar, the setting of the positive (being) and deepening into the negative as meaningful (nothing), so the assimilation of the category of quantity is much easier.
The category of pure quantity is similar to the category of pure being, it does not give anything except the definition of continuity (analogous to being) and discreteness (analogous to nothing). Thus, everything is both continuous and discrete. Continuity expresses the moment of equality with itself , and discreteness - the moment of inequality with itself .
The unity of continuity and discreteness for us is still quantity. However, the primacy in this unity belongs to continuity, since quantity is derived from being-for-itself something that previously led us to infinity. Here the analogy with being and nothing no longer works, because there we could take nothing and it became being, but here there is already a link between continuity and infinity. This point should not be overlooked and fall into the schematics.
The pure quantity has not yet become a definite quantity, it has no boundary, since we are still looking from the point of view of the indifference of the boundary to something. The mathematical expression of a pure quantity is the abstraction "straight line" and "plane". They are both continuous and discrete at the same time. A straight line is a line of infinite points, and a plane is a surface of parallel lines. Generally speaking, a point in geometry has the same properties, it's just that mathematics artificially assigns it to be indivisible. True, the absolute simplicity, finiteness and compositionlessness of a point will express the next category - continuous and discrete VALUE, namely the unit.
The transition to the value occurs as follows. In pure quantity, the unity of continuity and discreteness is posited only "in the definition of continuity." But what if we consider this unity, “put it down” from the standpoint of discreteness, that is, consider the boundary, which is indifferent to quality, from the point of view of the still existing connection with something? We get a continuous value - it will be a direct quantity.
Let me explain. We have a continuity of pure quantity, which is indifferent to something. But nevertheless, in this continuity there is also a moment of negation - something passes into another something and so on ad infinitum, that is, discreteness is observed. Now we look at the same process from the "back side", from the point of view of discreteness, just as we revealed the certainty of existence, considering everything that follows from nothing. In this case, we get a chain of something continuously passing into each other, that is, some continuous quantity or direct quantity .
In this case, the pure quantity is not mediated, but the magnitude is not direct. The word "immediate" is used here to mean that consideration of a pure quantity has led us to some immediate result, a continuous quantity.
And now Hegel’s cunning and yet another ingenious logical move: since the discreteness we have taken does not lose continuity, that is, it is discontinuity, but uninterrupted , which means that the resulting value is a collection of many alone as equal , “ not many alone in general, but posited as many of some single UNIT ".
So, one more time. Quantity has two moments: continuity and discreteness. We take the quantity from the discrete side and get a continuous value . What at this moment in continuity does this boundary delimit? Units. As a result, we get some discrete value . However, neither continuous nor discrete quantities can be taken separately, they are posited as a single quantity , which has both continuity and discreteness.
Indeed, if you imagine a certain sum not just as a quantity - a term of its constituent parts - but as a unity of continuity and discreteness, then after reflection you will notice that, firstly, the quantity is made up of equal elements (units), and secondly, that this unit is infinitely decomposable into smaller units, thirdly, that beyond this magnitude there is nothing but the same units. Of course, the concept of quantity is still very abstract and not suitable for simple counting, although it covers its mechanics.
“Continuous and discrete quantities are not yet definite quantities; they are only quantity itself in each of its two forms” (NL 218).
Now we have, on the one hand, a pure quantity - a very strong logical category of being that goes to infinity, on the other hand, a direct quantity - a quantity that is not yet a definite quantity, but only an approach to it. We need to dig further into discreteness.
So, we remember that quantity is generally indifferent to quality, but it is still a limit. She is currently delimiting units. Thus, peering into discreteness, we see not only a unit, but also a certain set of units . From whatever side we approach this conclusion, in the end we will have to admit that we have before us a certainty of magnitude (direct quantity). That is, we have received the certainty of something, connected with another, many and infinity, but which is not a quality of something and is indifferent to it. A definite value differs from a pure quantity primarily in that it can be increased or decreased, that is, it has certainty and dynamics in this certainty.
By the way, Hegel correlates the category of pure quantity with the concepts of matter, space and time:
“The absolute is pure quantity—this understanding of the absolute coincides in general with the one according to which the absolute is given the definition of matter, in which the form, although present, is an indifferent determination. Quantity also constitutes the basic definition of the absolute, when the latter is understood in such a way that in it, as absolutely indifferent to difference, any difference is only quantitative. As examples of quantity, one can, in addition, take also pure space, time, etc., since the real is understood as their content, indifferent to space and time ”(EFN 170).
Of course, such a view is inherent in Hegel as an idealist, for he initially denied the axiom of the materiality of the universe.
The most important characteristic of a certain quantity is that it, as a set of units, excludes all other definitions (units), therefore it is a limited quantity (EFN 174).
Hegel liked to explain that a certain quantity is the actual existence of quantity, by analogy with the existence of existence from the chapter on quality. In this sense, pure quantity = pure being, repulsion = pure nothing, continuity (which can also be represented as attraction) = being, and discreteness (as a development of repulsion) = nothing. Therefore, a determinate quantity is a one-sided (in terms of discreteness) taken unity of continuity and discreteness, which appears as immediate and simple. In principle, this is how it turns out, a certain quantity is a completely direct and simple limited number of units. True, if you look closely at the unit itself, it can be decomposed to infinity. Qualitative certainty, however, was not represented by something so crystallized, so this analogy, in my opinion, is conditional.
Logical exercises about the magnitude can also be turned using the numerical axis.
A certain quantity (continuous and discrete quantity), in contrast to a pure quantity, already has a fixed limit in itself , a certainty that limits the units taken. Continuity here is no longer manifested in the endless transition of one something into other somethings, but directly in one, in the unit . Discreteness is manifested in the fact that a certain amount is a set (of one) . Consequently, the unity of continuity and discreteness, in addition to being a certain amount (value), also excludes everything else, limits. Thus, a certain quantity in its final form is a NUMBER.
“The complete positing [of a certain amount] lies in the existence of the boundary as a multitude and, therefore, in its difference from unity. A number is therefore represented as a discrete quantity, but it also has continuity in the form of a unit. Therefore, it is a definite quantity in perfect determinateness, since in number the boundary appears in the form of a definite multitude, which has as its principle one, i.e., something unreservedly determined. Continuity, in which the one is only in itself, as sublated (posited as a unit), is a form of indeterminacy.
Everything according to Hegel is logical: being (pure quantity and continuity) into nothingness (quantitative definiteness and discreteness) is contained in a removed form.
To be continued…
A. Redin
https://prorivists.org/sol/#p10
Google Translator
Don't think I'll post the Q&A, it is at the link, in Russian. As earlier stated, I dunno about the usefulness of this machine translation. I've found Hegel very tough sledding in English and honestly can't tell if the machine is causing problems or not. Goddamn philosophy... why couldn't this be easy like Epicurius?