Intensive Magnitude and Moment of Gravity

At B210 of the 1st Critique, and then again at B211, the expression "moment of gravity" is included in Kant's explanation of his concept of Intensive Magnitude.  He uses it to refer to a cause that occurs in an instant, within which the cause can be conceived as always being diminished to a lesser degree, the range of which is 'intensive magnitude'.  However, whatever 'gravity' connotes in the expression, it is, at minimum, unhelpful in this context.  For, in its meaning that is most closely associated with causality, 'gravity' is a constant, and, therefore, is inconceivable as an intensive magnitude.

Intensive Magnitude and Magnitude of Intensity

Kant's concept of 'Intensive Magnitude' connotes 'degree of fulfillment'.  Hence, it is a concept that is appropriate to 'matter filling a space'.  Now, as has been previously discussed, Capacity, but not Volume, entails a separation of contour from content.  Hence, Intensive Magnitude is applicable to Capacity, but not to Volume.  Furthermore, 'intensity' usually entails 'pressure', directed either inwardly or outwardly.  But, in either case, pressure is independent of Capacity--inwardly, it is the product of the interplay of Attraction and Repulsion within a quantum of space, while outwardly, it is exerted on an external body, and, hence, exceeds its given quantum of space.  Thus, a concept that can be characterized as 'Magnitude of Intensity' applies to a Volume of forces, i. e. to a Force Field, and, so, is not to be confused with Kant's concept.

Repulsion, Attraction, Intensive Magnitude

As previously discussed, Kant vacillates between characterizing Repulsion as 'filling a space', and as 'extending infinitely'.  Now, his characterizations of Attraction are also inconsistent--on the one hand it 'empties space', while on the other, it 'reduces matter to a point', which is still an occupation of space.  The two discrepancies reflect a significant shortcoming in his effort to derive those dynamic forces from the concept of Intensive Magnitude.  At the source of that shortcoming is an attempted application of a pure Concept to a non-sensible manifold--e. g. to the interior constitution of matter--which violates his own principle governing the application of any such Concept to Experience.

Volume, Capacity, Density

Since the limit of the extensity of a body can be internally pre-inscribed in its matter, the previously proposed criterion for distinguishing 'Volume' from 'Capacity'--source of delimitation as internal vs. external--is inadequate, though it still follows that any externally imposed circumscription is a capacity.  So, an alternative characterization of that contrast is that Capacity, but not Volume, connotes a heterogeneity of contour and content, such that content is conceivable as variable with respect to contour.  Thus, the standard definition of 'density', which conceives the 'mass' of a body as variable with respect to a cubic unit, entails Capacity, properly, not Volume.  In contrast, 'density', as conceived as how 'tightly packed' the parts of a body are, i. e. conceived in terms of its internal relation of Repulsion to Attraction, maintains the actual integrity of Volume.  Now, clearly illustrating the distinction between Volume and Capacity is the contrast between solids, on the one hand, and liquids and gases, on the other, respectively.  Hence, the standard definition of 'density' is more appropriate to liquids and gases than to solids.

Volume and Capacity

There are two main ways that a repulsive force can be counteracted--by an attractive force acting on the same matter that is being repelled, or, by an external, e. g.  compressive force.  Hence, the quantum of space in which some matter exists can be either internally constituted, or, externally imposed.  Thus, the Kantian pure space, as given a priori to any matter that fills it a posteriori, is externally imposed on that matter.  Accordingly, a volume of matter can be determined either intrinsically or extrinsically.  So, to distinguish the former from the latter, 'Volume' can be contrasted with 'Capacity', respectively.  Now, the standard concept of spatial 'dimensionality' entails elements of pure space--points, lines, and angles, primarily.  Thus, the cubic meter, as representing three-'dimensionality', is a construction of pure space.  Hence, the cubic meter represents, more properly, Capacity, rather than Volume.

Space, Quantum, Repulsion

As has been previously argued here, the fundamental quantum of Space is Volume, rather than Point, as is prevalently held, or even Whitehead's Region.  However, it does not follow that Space is essentially quantized, as Kant shows, perhaps unwittingly.  For, in one place he asserts that "matter fills its space by the repulsive forces of all its parts" (Metaphysical Foundations of the Natural Sciences, ch. 2, prop. 2), while he elsewhere observes that "if no other moving force counteracted this repulsive one, would be held within no limits of extension, i. e. would disperse itself to infinity" (MFNS, ch. 2, prop. 5, proof).  In other words, Repulsion, when not counteracted, exceeds any quantum, entailing a more fundamental Spatiality--a process of indefinite extending, the sole 'dimension' of which is, therefore, 'outside of'.  Thus, it is only as a product of the counteracting of Repulsion that Space first becomes quantized.

Space and Volume

As has been previously discussed, while Kant characterizes the interplay of the two fundamental forces, Attraction and Repulsion, e. g. a particle, as 'filling' a space, here that characterization is, alternatively, 'creating' a space.  So, there is no disagreement that the fundamental quantum of space is Volume, a fundamentality that is reflected neither in geometries in which a 'point' is the basic quantum, nor in anti-Atomistic ones, such as Whitehead's, in which a 'region', i. e. a surface, is basic.  Furthermore, the standard concept of spatial 'dimensionality' is constructed in terms of lines and angles, which are derived ultimately derived from points, in both those types of geometry.  Hence, Volume can be distinguished from the measure of Volume, the standard of which is a cubic unit, i. e. is derived from lines, and, thus, from points.

Dynamics, Mechanics, Locomotion

While Mechanics studies Locomotion, i. e. movement between locations, Dynamics studies, primarily, localized motion, i. e. Repulsion and Attraction, at a single location.  Hence, insofar as Locomotion is independent of localized Repulsion and Attraction, Mechanics is independent of Dynamics.  However, the simplest human locomotion originates with a step, and a step begins as a pushing against a surface, i. e. as a localized repulsive force, and likewise for other modes of locomotion.  In other words, motion between locations is a special case of extending from a location.  Thus, Locomotion is a a mode of Repulsion, and, so, presents no exception to the classification of Mechanics as a branch of Dynamics.

Dynamics, Mechanics, Experience

According to Dynamics, Nature is constituted by Force Fields, of varying densities.  In contrast, according to Mechanics, Nature is constituted by discrete solid bodies, separated by nothingness.  Now, this distinction between Dynamics and Mechanics is not merely of interest to theoretical Physics--it is implicated in everyday experience, as well.  For, ordinary activity is often conceived mechanistically, e. g. as the motion of a solid body, from point A, through empty space, to point B.  However, Dynamics instructs about what is easily forgotten in that concept until, e. g. the wind picks up, or breathing at a high altitude becomes labored--that the human body is surrounded by, not nothingness, but at least one Force Field, that happens to be of lesser density than the body, and which the body penetrates en route to point B.  In this way, Dynamics presents a reminder of what is commonly abstracted from in everyday experience, without resorting to the potential mystification of Bergsonian 'Metaphysics', or of Heideggerian 'Fundamental Ontology'.

Density, Dynamics, Mechanics

As Kant shows, the dynamic forces Repulsion and Attraction combine as bodies of infinite possible degrees of density, ranging from absolutely solid, to absolutely empty.  In contrast, the bodies that populate fields of mechanical causality are all absolutely solid, separated by absolutely empty spaces.  Furthermore, Newton's 2nd Law of Motion, holds only for absolutely solid bodies, for, e. g., when impacted upon, a body of lesser density might get smashed and remain where it is, thereby violating the Force-Acceleration correspondence entailed by that Law.  Thus, Mechanics is derived from Dynamics, as a special case of the latter, a relation that is implicit, but remains underdeveloped, in Kant's classifications of the natural sciences.

Force Field, Unified Field Theory, Human Sciences

Entailed in some ambitions of a 'Unified Field Theory' is the reduction of the 'human sciences' to the 'physical sciences', e. g. of the study of 'conscious' activity to that of electrochemical events.  Now, while the success of the most prominent version of such a project remains debatable, previously presented here has been an alternative version, in which the concept of Force Field has been shown to be derived from Physics, and to be applicable to Biology, Psychology, and Morality.  What distinguishes this attempt from the standard effort is its fundamental principles--Repulsion and Attraction, the fruitfulness of which is entailed in Kant's classification of them, though he does not pursue the elaboration that has been developed here.  In that classification, whereas the ground of the standard model of Physics is mechanical external causality, Repulsion and Attraction are dynamic internal forces.  Thus, the concept of Force Field, i. e. of the interplay of Repulsion and Attraction, can be applied to an activity without reducing it to a dehumanized mechanical event.

Force Field and Morality

As has been previously discussed here, a species can be conceived as a Force Field.  So, insofar as Morality, as is typically the case, serves as a corrective to social dissolution or antagonisms, i. e. to repulsive social forces, it functions as an attractive force in such a field.  On the other hand, insofar as it serves as a corrective to conformism or totalitarianism, as it does for Existentialists, it functions as a repulsive force.  Thus, in general, Morality can itself be conceived as a Force Field, i. e. as an interplay of Attraction and Repulsion, in which the human species seeks a balance between homogeneous and heterogeneous tendencies.

Force Field and Psychology

Psychology is the study of behavior, which is primarily constituted by the interplay of sensory functions and motor functions, i. e. the interplay of the intake of information and physiological output.  In other words, it is constituted by an interplay of afferential and efferential processes.  But afferential processes and efferential processes are types of Attraction and Repulsion, respectively, and, as has been previously discussed, the interplay of Attraction and Repulsion constitutes a Force Field.  Thus, Psychology is the study of a kind of Force Field.

Force Field and Species

The applicability, as has been previously discussed here, of the concept of Force Field to Biology, i. e. to an individual organism, opens the possibility of its applicability to pluralities of organisms, i. e. to a species, as well.  For example, the species instinct that is often attributed to the patterned motions of insects and birds can be classified as an 'attractive' force, and, therefore, as an indication of the presence of a Force Field.  Likewise, any 'survival' instinct of a species that governs the behavior of its members is an attractive force in a Force Field.  Thus, the interplay of a 'war of all against all' and a Leviathan exemplifies the Repulsion-Attraction constitution of a Force Field, as do post-Hobbesian models of the human species in which the repulsive component happens to be less emphatic.  Also, that the interplay involved in such concepts is between a 'natural' repulsive force and an 'artifactual' attractive force, is no argument against their constituting a Force Field--any effort to construct political institutions can be just as instinctive as is individual anti-sociality.  In other words, a tendency to socialize is as much an attractive force in a species as is the actualized sociality that is usually ascribed to insects.

Force Field and Organism

Since, as Kant briefly suggests, 'body' is a type of space-filling force, then, it, too, constitutes a Force Field.  Furthermore, an organism is a type of body.  So, for example, the annual addition and retention of a tree ring can be conceived as an interplay of Repulsion and Attraction, and, hence, as constituting a Force Field.  In other words, growth is a combination of repulsion and attraction, i. e. an extending in which cohesion with the antecedent condition is preserved.  Thus, the concept of Force Field is applicable beyond, as usual, Physics and Chemistry, to Biology, as well.

Gravity and Repulsion

When an object falls to the Earth, it will often smash, leaving an imprint on the ground.  On the other hand, when two liquids are placed in the same location, e. g. a beaker, they will sometimes combine to form a different liquid.  The contrast demonstrates that a gravitational field is only relatively attractive, and involves relative impenetrability.  In other words, a gravitational field involves repulsive forces.  Hence, the widely-held thesis that 'Gravity involves no Repulsion, and only Attraction' is inaccurate, at best.  Accordingly, any denial of the universality of Repulsion, on the basis of the absence of repulsive forces in a gravitational field, is ungrounded.

Unified Field Theory and Heterogeneity

Attraction and Repulsion can combine in an infinite variety of ways, i. e. resulting in a range from predominantly contractive, to predominantly expansive, interactions.  Thus, since any combination of the two constitutes a Force Field, there are an infinite variety of  Force Fields possible.  Furthermore, since different combinations produce differently constituted Fields, any two differently constituted Fields are mutually heterogeneous.  Thus, for example, a Force Field and one that it is part of are mutually heterogeneous, which is why the internal integrity of the former, e. g. a particle, can remain unaffected by its external interactions in the latter.  Now, three such mutually heterogeneous types of Force Field are nuclear, electromagnetic, and gravitational fields.  Thus, the efforts of contemporary Physics to formulate a 'Unified Field Theory', by homogenizing fields that they erroneously call 'forces'--Strong and Weak Interaction, Electromagnetism, and Gravity--are misguided, beginning with the assumption that a 'unified field theory' precludes the possibility of heterogeneous fields.

Force, Big Bang, Black Hole

Kant suggests that in the absence of a counter-force, Repulsion would effect infinite expansion, and that Attraction would effect contraction to a point. What seems erroneous in the latter is that since matter is infinitely divisible, the contraction that Attraction would effect would, likewise, be infinite.  Furthermore, what he misses in both possibilities is that each would occur instantaneously, since any time-lapse would imply the presence of a counteractive force.  So, a 'big bang' and a 'black hole' are not so much actual events but imaginative approximations of the two theoretical extremes, i. e. of Repulsion and Attraction, respective, taken in isolation.

Force Field and Unified Field Theory

As has been previously developed here, on the basis of Kant's premises--Attraction and Repulsion are the two fundamental, complementary forces, any combination of which constitutes a 'Field', a special case of which is a 'particle'.  Together, these propositions comprise the basis of what could be called a 'Unified Field Theory'.  Of course, though, that rubric is better known as referring to four so-called 'forces'--Gravity, Strong Interaction, Weak Interaction, and Electromagnetism--most of which involve, arguably, attraction, while some of which involve, arguably, repulsion, with various particles as their independent substrata.  So, the standard version of the theory is plainly more incoherent that the proposed alternative, beginning with a confusion of 'force' and 'field', i. e. if it is granted that Attraction and Repulsion are fundamental 'forces', then Gravity, etc. are distinguished as 'fields', not as 'forces'.  Furthermore, the alternative already surpasses the standard by accounting for the existence of Matter, without recourse to conceptual gimmickry such as 'anti-matter' or 'dark matter'.  Thus, given that it is generally acknowledged that the standard theory remains stalled in achieving its ambition, perhaps a more systematic approach, such as the one proposed here, might be an improvement.

Force Field, Space, Contour

A Force Field is constituted by an interplay of Repulsion and Attraction--the former opens it up, while the latter delimits the opening.  That interplay thus defines, a posteriori, the 'space' of a Force Field, independently of any a priori division of 'Space', qua form of outer appearances, as Kant's theory has it.  That independence is clear from his own example of a 'body' as a space-filling force, for, plainly a body 'fills a space' only by virtue of being a Force Field the contour of which is a product of its internal interplay of Repulsion and Attraction.

Repulsion and Space

According to Kant, in the Metaphysical Foundations of Natural Science, "matter fills its space by the repulsive forces of all its parts."  That matter "fills its space" follows from his doctrine that infinitely divisible Space is given a priori to any such phenomenon.  However, Repulsion effects a process of separation, and a process of separation opens up a gap between what it separates.  Hence, Repulsion fills a presumed a priori given space by creating a space a posteriori.  Thus, Kant's concept of Repulsion seems to present a formidable challenge to his theory of Space.

Force Field

Kant, in the Metaphysical Foundations of Natural Science, defines Force, i. e. Attraction or Repulsion, as fundamentally occupying a single space.  Though, since his primary focus in the work is motion in multiple spaces, his examination of chemical penetration, as an example of a space-filling force, amounts to a minor digression.  However, substitute 'space' with 'field', and the broader implications of the seemingly minor notion become more apparent--it plainly pioneers the concept of Force Field that has subsequently become significant in the representation of not only chemical events, but of gravitational and electromagnetic ones. as well.  Furthermore, another example of a space-filling force that he briefly discusses is 'body'.  So, since an organism is a special type of body, Force Field is also a structure with potential application to Biology.

Matter, Force, Particle

In the Metaphysical Foundations of Natural Science, Kant first defines 'matter' as that which is "movable in space".  Furthermore, it is "movable insofar as it fills a space".  Now, it fills a space by virtue of a "special moving force", namely, Repulsion.  More precisely, it "fills its space by the repulsive forces of all its parts."  However, by virtue of Repulsion alone, matter would "disperse itself to infinity".  Hence, it fills a determinate space only by virtue of Repulsion in coordination with a counter-force, namely, Attraction.  So, likewise, any determinate part of matter, i. e. any particle, is the product of a combination of Repulsion and Attraction.  If so, then it follows that particulate matter is not the substratum of motion, which, in the absence of any other concept of matter, contradicts the initial premise, a contradiction which the thesis of the infinite divisibility of matter does not circumvent.

Chemistry, Physics, Cause, Force

Kant's analysis of chemical penetration appears in the context of his study of 'Dynamics', in the Metaphysical Foundations of Natural Science, suggesting that he conceives it as a special case of Attraction, one of the two fundamental 'Forces' that he studies in the chapter.  In contrast, 'Causality' is not introduced until the subsequent chapter, on 'Mechanics', thereby suggesting both that Force is more fundamental than Causality, and that the lack, in the work, of a Causal classification for Chemical events, reflects that priority, rather than expresses a neglect of, or a befuddlement over, such classification.  Likewise, what is widely interpreted as a supplanting, by Newtonian Physics, of Aristotelian Teleological Causality by Efficient Causality, is, more accurately, a replacement of the concept of Cause with that of Force, a replacement generalizable to all Sciences, including Chemistry.

Chemical Penetration, Causality, Intussusception

In the Metaphysical Foundations of Natural Science, Kant distinguishes between 'mechanical' and 'chemical' penetration, observing that the former "does not act by its own force", thereby implying that the latter does.  However, since he proceeds to develop a theory of Causality for mechanical events only, he leaves undetermined the status of chemical penetration in that regard.  Perhaps he anticipates that Newton's Third Law of Motion, which he grounds in the concept of reciprocal causality, cannot account for chemical penetration.  For, perhaps he recognizes that reciprocal causality entails distance between its factors, whereas chemical penetration consists in 'intussusception", as he terms it, i. e. in no distance between its factors.  So, in segregating Chemistry from what is generally known as 'Physics', he leaves it without a concept of Causality.

Chemistry, Physics, Locomotion

'Chemistry', as a condition of simultaneity obtaining between several components, would seem to be distinct from 'Physics', the components of which, i. e. Cause and Effect, are successive.  However, some Chemic events, e. g. the melting of ice by the application of hear, involve causal successiveness, while Kant's Category of Community, from which he derives Newton's Third Law of Motion, entails the simultaneity of causal relations, so the fundamental distinction between Chemistry and Physics is not a temporal one.  Rather, among their modern versions, at least, the difference is a spatial one--while the primary theme of Newtonian Physics is Locomotion, Chemic events are not essentially constituted by such change of location, i. e. even insofar as they involve microscopic motions, distance is not a germane factor in them.  So, on the basis of that spatial feature, the two Sciences are mutually independent.

Chemistry, Physics, Combination

Aristotle is generally interpreted as having devoted little attention to Chemistry. However, though the relevant passages are not nearly as prominent as are his works on Physics, Psychology, Astronomy, and Biology, in On Generation and Corruption, he does examine a pattern that is characteristic of Chemistic events--combination, which entails simultaneous reciprocity.  In other words, on that analysis, if A and B 'combine', they simultaneously act upon one another.  But, then, what remains unclear is as which of the four Causes of Physics such combination can be classified, i. e. simultaneous reciprocity seems to be a characteristic of none of them.  In the absence of further clarification, Chemistry seems to elude a reduction to his Physics.

Philosophy and Chemistry

Modern Philosophy seems to accept the popular genealogy of Chemistry as a refinement of Alchemy.  Even after its stoichiometric systematization by Lavoisier, Kant's characterization of Chemistry as a haphazard "art"  remains seemingly unchallenged, e. g. Whitehead's studies of 'Science' barely acknowledge it.  Perhaps the philosophical status of Chemistry is epitomized by how its most significant contribution to Modern Philosophy--Locke's Boyle-inspired Primary Qualities--becomes a mere footnote to the rising dominance of Secondary Qualities, i. e. of Phenomenalism.  Nevertheless, Philosophy is born as Chemistry, i. e. in the notion that perceivable reality is constituted by permutations of often hidden substrata, e. g. of Water, Fire, Air, Atoms, etc., an ancestry that becomes obscured by the non-'materialist' doctrines of, notably, Pythagoras and Parmenides.  Even the neo-pre-Socratisms of Nietzsche and Heidegger fail to appreciate that lineage.

Causality, Chemistry, Catalyst

Kant's main variation on Hume's concept of Causality--that 'constant conjunction' is, more accurately, 'ordered succession'--accepts the Atomism of the latter, i. e. that such a succession, too, is a relation between two representations.  Now, while that Atomism might be suitable to Newtonian Mechanistic Physics, it seems inadequate to another Natural Science, namely Chemistry, which studies changes that ensue from the compresence  of several factors, e. g. of two elements and heat.  Accordingly, non-Atomistic patterns, such as Concrescence or Emergence, seem to better interpret 'chemical changes' than does Atomistic Causality.  Indeed, the event usually characterized as 'Gravity causing an apple to fall on Newton', can also be interpreted as the compresence of an apple-bearing tree, Newton, and gravitational pull, into which a gust of wind enters.  In those terms, the decisive factor is the gust of wind functioning as a 'catalyst'.

Acceleration and Quantification

As is clearly expressed in 'go faster than', and in 'increase speed', the concept of Acceleration is essentially indefinite, i. e. once initiated, acceleration is, in itself, undelimited.  In contrast, to quantify is to delimit.  Hence, 'd/t-squared', in which both d and t are finite, is an inadequate definition of A.  No exception to that judgment is either when t is instantaneous, or when it 'approaches Infinity'--in the former, an instant is a special case of an interval, while in the latter, 'Infinity' is the product of an hypostatization of the modifier 'indefinite', and, thus, entails a surreptitious introduction of delimitation into the definition.