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forward to Part TwoThis Essay, consisting of three consecutive parts (Part One, Part Two and Part Three), is rather long and complicated. I advise the reader to first consult the following Essays : On Being and Essence, On Substance and Accident, and especially the Essay on Dynamical Systems, and maybe also the Essay on The Principle of Individuation (See the table of contents on the homepage).
THE DETERMINATIONS OF A SUBSTANCE,
especially their relation with that substance and their ONTOLOGICAL status (i.e. their status of being, their way of being).
This Essay is motivated by the following considerations :
It is possible that the World consists of some sort of ultimate microscopical constituents. Those constituents could be subatomic particles, like protons, electrons and quarks (Those particles could be inseparably tied up with corresponding quantum-fields). So it could be the case that they (those particles and / or those quantum fields) are the only genuine uniform things. Everything else is just a more or less patterned aggregate of those ultimate constituents.
Such a consideration can be called a reductionistic approach.
But the actual existence of self-conscious beings suggests otherwise. These beings, like ourselves, seem to be genuine uniform beings, despite the fact that they appear to be some sort of machines consisting of parts, thus consisting of a multitude of (other) things, many of which in turn are consisting of parts. Nevertheless we cannot be totally sure that, say, a human being is indeed a strict unity, in the sense that it is ONE thing only, not a multitude of things. Our self-consciousness could deceive us. Our "individual unity" could be an illusion, useful for surviving but an illusion nonetheless. Isn't it so that our parts are often only loosely connected, or even more or less free, as is the case with our blood cells and also with many molecules and ions wandering freely in our body? All we can do is presuppose everyone of us to be such a genuine unity, assuming that self-consciousness points in that direction, and in presupposing so, the unity of all kinds of other things, like atoms, molecules and crystals, can also be presupposed, because in their case such an interpretation seems less problematic, because their ' parts ' are much stronger integrated into the relevant whole than the macroscopical parts of an organism are, and also (are they much stronger integrated) than the many atoms and molecules that freely exist inside the organism (performing certain biochemical functions) are integrated with each other within the organism. So we entertain the possibility that there does exist a certain class of things, things, that are, admittedly, composed of physical parts, without however any one of them being turned into a multitude (as their composed nature would suggest). All other 'things', not belonging to this class are aggregates that ultimately consist of genuine things.
And along these lines we could assume that there exist wholes that are ontologically presupposed by their parts.
This can be called a holistic approach.
So what we are going to do in this Essay is the following :
We presuppose (1) the ontological UNITY of every freely (meaning here : outside any organism and, generally, outside any whole) existing Atom and Molecule, (2) the ontological UNITY of every (pure) single Crystal, and (3) the ontological UNITY of every Organism. Within the context of this website these presuppositions are equivalent to the presupposition that each thing, to which such a UNITY is attributed, stands under ONE (ultimate) dynamical law, representing its ONE Essence, a law that generated, or could have generated that thing. We do not presuppose a UNITY for things that do not present themselves as a regular pattern which could be repeated. Such things we call Aggregates, they are each for themselves not one thing but many.
By presupposing such a UNITY for the things mentioned, we will -- in this Essay -- try to account for that, by setting up an adequate metaphysical description of such a uniform thing, i.e. a description in terms of principles of being, guaranteeing the UNITY of those things, guaranteeing their being First Substances. In such a metaphysical description the assessment of the status of all kinds of determinations is highly important. A first substance is an individual uniform thing (such a thing can be called a Totality ) consisting of elements (parts). These parts are intrinsically (intrinsically with respect to the thing) organized into a definite PATTERN. The ontological status of those parts must probably be interpreted as virtual (versus actual), i.e.: from a metaphysical point of view -- which means from the viewpoint of unity of the thing -- those parts as parts are existing in a virtual mode of being, whereas as properties of the uniform thing they exist actually. From a physical viewpoint on the other hand, those parts are actually existing in the thing as parts, i.e. as things. Said differently, from a metaphysical point of view the parts are not a distribution of things (particles) in the thing, but a distribution of properties of the thing, otherwise the uniform thing would not be ONE thing but many (See for this problem also the Essay on the Mixtum and its Elements).
Without elaborating this problem right now, we will just speak about the first substance and its properties. But instead of using this term " properties " it is more appropriate to speak about the determinations of a first substance, of a Totality.
A Totality is a patterned whole, generated by a dynamical system (See for dynamical systems and their ability to generate patterns the Essays On Being and Essence and on Dynamical Systems).
The DYNAMICAL LAW of that dynamical system is the ESSENCE or (the specific) IDENTITY of the Totality (the uniform patterned thing) generated by that dynamical system. And a principle of individuation individuates this specific identity, and so accounts for the individual identity.
We shall call the domain-of-existence of the Dynamical Law the GENOTYPICAL DOMAIN .
We shall call the domain-of-existence of Things and their Properties or Determinations the PHENOTYPICAL DOMAIN .
( I borrow these terms from Genetics, and generalize them. And this makes sense because I interpret an organism as a Totality generated by a dynamical system. It is a highly dynamical Totality because the dynamical process keeps on running and produces one Totality state after another. The (penultimate) dynamical law of such an organic Totality must be located in and around the instruction set of the DNA, while the ultimate dynamical law is contained in the initial set of atoms. In both cases the law itself is not an entity but represents as such the genotypic domain, i.e. it enjoys a genotypical existence. See for the meaning of penultimate and ultimate dynamical law the Essay on Organisms, Part One, the relevant Section. )
All entities that are generated by a dynamical system belong to the phenotypical domain. Only the dynamical law belongs to the genotypical domain.
This interpretation solves a problem in Classical Substance-Accident Metaphysics, because there it was not clear where to draw the boundary between the quantitative and qualitative determinations of a thing on the one hand, and the Essence (Whatness) of that thing on the other. In my new interpretation it is easy to draw the line : The Essence belongs to the genotypic domain and the quantitative and qualitative determinations belong to the phenotypic domain. Or in other words : The Essence (of the thing) is the dynamical law and the quantitative and qualitative determinations (of the thing) are generated by the dynamical system governed by that law.
In the next two sections we will introduce some relevant terms from Classical Metaphysics, as we see it in the works of Aristotle and St.Thomas Aquinas. Later we shall elaborate on them still further. For the concept of prime matter the reader should consult the beginning of the Essay on Substance and Accident and the beginning of the Essay on The Principle of Individuation. The same prime matter, as understood in Classical Metaphysics, can be considered either as non-delimited (non-terminated), or as delimited, terminated. The mentioned sections will establish the substrate, as such containing matter, that can be informed by (further) determinations.
Remark : The just mentioned prime matter is -- as a potentially existing ultimate substrate -- a principle of the possibility of radical change and (a principle) of individuation.
This, however, needs some further qualification :
Elsewhere in the present Series of Essays (See the Essay on Mereotopology of Reality) we discussed Substance within a more or less formal, mereotopological, approach (based on an article by SMITH, B. 1997). There we spoke about the CARRIER-ONLY, which is supposed to be the SUBJECT of the determinations, and we tried to assess that carrier-only, i.e. we attempted to determine the exact content of the concept CARRIER-ONLY, and obtained a somewhat different result, different from that what is stated above about the SUBJECT :
The carrier-only does not involve entities that are one-sidedly specifically dependent on it. Such entities (Accidents) are conceptually removed (from a full-fledged Mereo-totality - a Substance in the broadest sense, including non-scattered aggregates) resulting in the carrier-only. But we found out that not all such entities can be removed without destroying the specific identity of the Mereo-totality. The only entities that can be so removed are the occurrent entities, i.e. the replaceable determinations (Accidents) like being tanned by the summer sun.
In the present context these removable entities are the extrinsic determinations as well as the intrinsic per accidens determinations. The determinations that should remain, i.e. that should not be removed, are completely specified individual determinations that are necessary for the (content of the) Mereo-totality's specific identity, but also every necessary sequence of determinations : although the particular determinations, composing such a necessary sequence, are replaced by others (successively belonging to such a sequence) they cannot be removed, because the sequence as a whole is, ex hypothesi, necessary in constituting the Mereo-totality's phenotypical specific identity.
For the full-fledged Mereo-totality to actually be able to exist it must involve a complete set of types of determinations, intrinsic and extrinsic. After removal of the replaceable determinations, but not of those that belong to a necessary sequence, we are left with the CARRIER-ONLY. So this carrier-only is still determined. It is determined by the "ESSENTIAL PARTS" (of the Mereo-totality), and, moreover, these 'parts' represent the only determinations of that carrier-only.
In the present discussion, on the other hand, we found out that the SUBJECT is subject with respect to one or several determinations for which it is the subject. It is identical to the whole Mereo-totality minus those particular determinations, and thus still containing, in addition to the non-replaceable determinations, some replaceable determinations.
But it is also possible to assess the SUBJECT (the carrier-only) in an absolute way, as we did in the mereotopological discussion :
When we consider all replaceable determinations (Accidents) 'simultaneously' to be involved in a dynamics of replacement, we finally will obtain the (genuine) CARRIER-ONLY (subject) just like that, i.e. in an absolute sense, after we have removed those determinations.
And this genuine carrier-only, the genuine subject in an absolute sense, is - as we found out in the mereotopological discussion - identical to the HISTORICAL individual : The individual, taken in its whole time span of existence, contains, in addition to its essential determinations, other determinations that are not fully specified (because they vary during the individual's existence), and that is equivalent to their being removed. What is left is indeed the carrier-only.
The complete set of types of determinations, mentioned earlier, is, as we found out in the mereotopological discussion, not the carrier-only (or subject) in an absolute sense, but only in a relative sense, namely with respect to one or another single determination (or a few such determinations), when viewed without these particular determinations. It (i.e. the mentioned set) is just a general precondition for the Mereo-totality to exist.
Determinations are always determinations of something (else). Parts of a subsistent being can also be interpreted as determinations. Everything that (ontologically) comes after the prime matter of such a being can be seen as a determination, including the essential parts. They are determinations of the prime matter. The latter is the ultimate substrate, the ultimate subject. But as such the substrate for any possible content.
Further down we will discuss how to interpret parts as determinations.
Intrinsic Determinations show two types :
An intrinsic (but in spite of that) per accidens determination can alternate with the alterations of environmental factors (external agents), or can alternate with the alternation of the states (stadia) of the Totality, or with both.
Such a determination is partly generated by the Essence, partly by external agents.
Examples : The outer form (figure) of a crystal is dependent on the environment in which the crystal grows, as well as on the growing state (stadium of development) of the crystal, and (with it) on the crystal's Essence.
The term " (outer) form " is in fact an abstract term (i.e. it does not signify a concrete item). In the present context we must always have in mind one or another of its concretizations, for example " tetrahedral ". The predication expressing this outer form then goes like this : " This crystal IS tetrahedrical " (is tetrahedrically formed).
The outer form (figure, shape) of an organism generally is almost entirely dependent on the growing state (stadium of development) of that organism. This is very clear in the case of those organisms which, during their individual development, undergo a metamorphosis, as is the case for some Insects and the Amphibians. Insofar as a determination is dependent on the growing state (system state, Totality state), it is, to be sure, related to the point in time of observation, which is per accidens, but because the growing states succeed each other according to the dynamical law, the per accidens status of such a determination is not absolute. Each form (figure) in the developmental succession is as such dependent on the organism's Essence anyway. But also in organisms (like in crystals) the form can undergo changes because of environmental factors, like we see for example in Diatoms (siliceous unicellular algae) : In fresh water species the form (figure, shape) can undergo definite changes when the salinity of the water increases. The nature of such changes is, however, often species specific.
Still stronger per accidens , because less specific, is a determination like " tanned " (caused by the sun), as a determination of, say, Socrates. Here we have to do with a stadium-independent, but environmentally dependent, intrinsic per accidens determination (intrinsic, because it is HIS (i.e. Socrates') reaction with sunlight, per accidens because he is not tanned during all of his life, and moreover because tanning is not specific for Socrates (as representing a certain species of Substance).
Concerning " because it is HIS reaction with sunlight " the following remark could be useful : Socrates' body possesses certain chemical configurations, which react with sunlight in a specific way. These constant chemical configurations -- making the tanning of the skin possible -- are themselves per se determinations of Socrates, although they are not unique for Socrates.
Extrinsic determinations like Point in time, or Place, always are, with respect to the Essence (of a Totality), per accidens, and, moreover in an absolute sense.
Every determination which varies in time, is a per accidens determination, because such a determination is a function of time, and varies with the point in time of observation (or contemplation) of the Totality (by an observer). And a point in time is itself a per accidens determination because it is an extrinsic determination.
All these (types of) determinations together form the Totality. Each determination for itself, i.e. on its own accord, is not a complete being, but taken together they ARE the Totality, and this Totality has an Essence, which is inherent and implicit in that Totality. But this described composition is not to be understood as a physical construction, but as an ontological state of affairs, which means the establishment of the intrinsic principles of being, which cause something to be a Totality, and (the establishment) of extrinsic general preconditions for it to exist at all. It is a metaphysical ' construction ', a metaphysical constitution.
Each determination for itself is accordingly a determination of the Totality. The Totality, and thus implying all its determinations, can be interpreted as a phenotypical explicitation or manifestation of the Essence, i.e. of the dynamical law -- which itself is only genotypical, or implicit.
In a physical approach the emphasis is on concrete parts and their interactions. In such an approach the Totality i.e. the individual being, does not claim a central position in the considerations. In physical considerations the emphasis is on lawful processes, at the macroscopic, microscopic and submicroscopical levels, between the elements (parts) of whatever Totality, but also between those elements and external agents (factors), whereby one does not explicitly discriminate between internal interactions and interactions with the environment (to be sure, one does dicriminate between those interactions, but the main reason for doing so is just to identify the interactions concerned). The World is conceived as a historically evolved and continually evolving (including inorganic or cosmic evolution, as well as organic) NETWORK OF INTERACTIONS : interactions between matter and radiation, transformations of one energy type into another, chemical interactions between molecules, and, on a larger scale, the processes governed by gravitational forces (which only become significant with respect to large masses),which lead to the formation of galaxies, stars and planets.
In Biology, one is, it is true, more explicitly concerned with Totalities, but these are always understood in an evolutionary and ecological context, in which all possible processes take place in organisms, between organisms (among themselves), and between organisms and their abiotic environment. In such a context the organism is inseparable from its evolutionary past and from its ecological entanglement and integration with biotic and abiotic factors. And this in such a way that there is no sharp boundary between an organism and its environment, because, in the form of strong metabolic interactions, energy and matter continuously flow in and out of the organism, forcing the organism continuously to be a process state, and so causing it sometimes to show more resemblance with an organ, functioning in the ecosystem.
In a metaphysical approach (an approach from a theory of Being) individual Beings insofar as (they are) beings, occupy a central position, specifically real ' full-fledged ' beings, and thus individuals . Such a real being is an individual intrinsic Totality (of elements). This in contradistinction to an Aggregate of elements. An Aggregate is a collection of concrete actual existing elements, elements which are put together mainly by extrinsic agents, extrinsic with respect to that collection. They do not form repeatable PATTERNS. Aggregates are fragments of large(r) dynamical systems. The collection of elements, present in an Aggregate does not form a dynamical system, but only a fragment of such a system, and so does not imply an actual dynamical law. Hence an Aggregate has no Essence ( NOTE 1 ).
A real, individual, intrinsic, complete being, on the other hand, that is the subject of metaphysics, has an Essence, and particularly, it has ONE Essence, and therefore it is ONE being. This aspect of one-ness is the focus of a metaphysical approach.
So in what way must DETERMINATIONS be interpreted in a physical context, and in what way in a metaphysical context?
Some determinations can be interpreted as an interaction of the Totality, or parts of it, with agents outside that Totality. Other determinations can be interpreted as one or another interaction between the parts of the Totality among each other.
A color, say, RED, is -- considered from the position of (the) observing (human) subject -- a quale , generated by our visual-neurological apparatus, normally as a result of the action emanating from some object outside the mind. Considered from the position of the Totality (which is observed), RED must be taken as a lawful (i.e. regular) interaction of the Totality, or parts thereof, with light (We then observe that the Totality in question is red ). We can also say that RED (considered from the position of the Totality) is a reaction of the Totality, when it is subjected to light (that strikes that Totality). (Light is electromagnetic radiation comprising a certain range of wavelengths ). In this reaction, this process, absorption, emission, scattering and interference of light play a role. The determination RED thus is an interaction, attributed to the Totality, an interaction with light. With it -- as far as the Totality itself is concerned -- special concrete elements of structure, belonging to the overall structure of the Totality, play a role. Thus in a physical context it is said -- with respect to the attribution of RED to the Totality -- that the Totality HAS those elements of structure (i.e. HAS certain material configurations), and that these enter into an interaction with light in a special way. These structural elements (configurations) themselves are in many cases constantly present in the Totality and belong to the determinations-as-part, which shall be treated of below. The interactions of those structural elements with light can produce different results, dependent on the pool of wavelengths actually present in that light (A red colored Totality will not look red when the light that strikes that Totality does not contain red, i.e. does not contain certain wavelengths). And so the determination-as-interaction can vary, and so is per accidens, while the (mentioned) structural elements of the Totality, when they are a constant possession of the Totality, are per se determinations. Generally taken, the determinations-as-interaction, together with their underlying structural elements of the Totality, already foreshadow possible dynamical laws, which could generate new Totalities, in and by dynamical systems in which the Totality in question could figure as a system element, together with other Totalities.
It is clear that during this interaction a concrete process is taking place.
The physical consideration with respect to the attribution of RED to a Totality (or to a part thereof) thus consists of the description of an interaction.
But because an interaction, taken all by itself, i.e. as such, is not a complete being (it is not some -- ONE -- existing intrinsically patterned thing, but an interaction OF more than one thing), it is necessary that a metaphysical approach with respect to the attribution of a determination (to a Totality), say, an attribution of RED, expresses this fact. Said differently : in a metaphysical context it must be expressed in a metaphysically justifiable predication.
Such a predication, attributing to the Totality T the determination RED, accordingly must look like this :
"This T IS red "
By this way of predication it becomes clear (i.e. it is well expressed) that that which is signified [we shall call this the significatum of ] by the term RED is not a complete being. Only the term T signifies a complete being, namely the Totality T . But because an interaction nevertheless is real, a real event, it is NOT just a not-being, it is only an incomplete being , a ' weakend ' being. The predication
"This T IS red "
precisely reflects the analogy of being : (the term signifying) an incomplete being (namely RED), is predicated of (the term signifying) a complete being (namely the Totality T ).
" Analogy of being " means that, say, a property is in fact not a being, it is a being in an analogical (= comparable) sense only. Also a potential being (like the potential oak which is (in) the acorn) is only a being in an analogical sense, meaning it ' looks ' like a being, because (we know) it can become such a being. Every analogical series is such that its members always refer to a "primary instance", in which the being (or feature) in question is fully expressed.
Aristotle has given a very instructive example : some sorts of food are called healthy, some actions – like taking a walk everyday -- are called healthy, some regions – for example up into the mountains – are healthy. But of course these things, actions and regions are not themselves healthy, i.e. they cannot be said to be in a state of health. All these things are referring to the health of the (human) body, and only such a body can really be in a state of health. So the healthy body is the primary instance of health or healthy.
If only a certain part of the Totality is red, then this part will ' for a while ' be considered as if it were a Totality. We then obtain the following predication :
" This part (of the Totality) IS red "In the subsection PHYSICAL CONTEXT we identified certain structural elements that can be responsible for the Totality being red. So this deternination RED can be traced back to certain parts of the Totality.
Some determinations concern the attribution of a certain concrete part to a Totality (they thus relate to a concrete part OF the Totality). In a physical context such a determination is expressed with the having of that particular part. For example in the predication
" Socrates HAS a nose ".
Here the significatum of [= that which is signified by] the term SOCRATES as well as the significatum of the term NOSE is considered as a thing, a being. Both terms signify something concrete. And because, in this physical context, one is concerned with two things, one cannot say :
" Socrates IS a nose ",
because in this predication only ONE thing is expressed. This predication is false because a whole IS not its part.
When we find ourselves in a metaphysical context, then we know that the proposition
" Socrates HAS a nose "
nevertheless concerns ONE thing, namely one Totality, Socrates. And this fact must be expressed by a proper proposition, when such a proposition wants to be a predication of an incomplete being (i.e. a determination) OF a complete being (as the subject of such a predication). To achieve this we should predicate as follows :
" Socrates IS nosed "
Remark: We also can encounter predications having the same form as the predication " Socrates is nosed ", for example " This nose is curved ", in which NOSE functions as a term, signifyng a complete being, while in reality a nose is not a complete being. The proposition pretends ' for a while ' that the term NOSE signifies a complete, ontologically independent being.
Let me explain and analyse all this.
Here the significatum of the term NOSED is not a concrete part of Socrates, but it is WHAT (among others) Socrates IS ( Besides " nosed ", there are other predicates, also signifying what Socrates is ). The way of expressing by means of such a predication shows that the proposition refers to only ONE complete being, namely Socrates. Besides this, reference is made to just a dependent determination, an incomplete being.
Socrates being nosed refers, it is true, to a concrete part of Socrates, namely his nose, but this part is AS nose (i.e. insofar as it is a nose) not ontologically independent, because a nose is not an intrinsic Totality. The nose is not a product of a special dynamical law, and thus it has no Essence. Therefore it is, considered in itself, i.e. considered apart from the organism, only an aggregate, an aggregate of molecules. This is valid for every part of an organism, meaning with " part " not a fragment but an anatomically distinct part. A (conceptual or concrete) fragment of an organism is not a determination of an organism at all.
In the case of Crystals though, matters are different (See for their structure the Essay on Crystals).
An isolated macroscopic part of a crystal (for instance a piece that is broken off, or a region of the crystal considered as isolated part) is nonetheless a pure, complete being. This is because every crystal has a periodic structure, and that means that it consists of a repetition of a certain microscopical unit, the so-called unit cell ( This is a concrete microscopic region that is being repeated periodically along three spatial directions, and in this way building up the crystal. The unit cell is fully integrated into the framework of the crystal. Such a unit cell contains at least one formula unit of the relevant chemical substance, and has (as such defined) the same dimensionality as the crystal lattice itself.). Also when such a (crystalline) fragment does not show (crystal-)faces --- either because of lack of sufficient space to grow in, or because of the irregular surface of fragmentation, resulting from (conceptually or otherwise) breaking the crystal into pieces, i.e. resulting from isolating a part (piece) of the crystal, or, finally, because of the fact that the flat surfaces we (sometimes) see on a crystal fragment are not genuine crystal faces but cleavage planes --- the specific and for the crystal species constant angles, remain : angles (between the faces), that we can observe in a complete crystal that has grown unimpededly. Those angles remain, because the possibility of generating faces -- being directed (i.e. positioned) among each other according to those determined angles -- is already given by and in the periodic structure of the crystal interior. In any (macroscopic) fragment of a crystal the whole structural build-up, including the angles, remains conserved, i.e. is already present. The conservation of those specific angles is a consequence of the conservation of the whole specific phenotypic identity of the crystal in any fragment separated from that crystal. This identity is : The Spacegroup + Chemical Composition (See the Essay on Crystals, mentioned above).
Characteristic anatomically distinct parts, often with diagnostic significance, which we encounter in the case of Organisms, do not occur in the case of single Crystals. Only in crystal twins and the like, do they generally occur. Isolated macroscopic parts of a single crystal, are, as has been said, complete beings of the same species as the crystal itself. When those parts are not isolated, they cannot be considered as parts, they are fully integrated in the crystal ( NOTE 2 ).
But conceptually or actually isolated parts of a concrete unit cell, that are moreover microscopical parts (fragments), have, each for themselves, lost the specific nature of that crystal, and are moreover not beings at all -- unless such a part consists of one individual atom or molecule or when it happened to be precisely one or another chemical formula unit of either the chemical substance represented by the crystal, or of another chemical substance - in which cases they are specifically other (in a metaphysical sense) beings (namely single atoms or molecules), different from the crystal. They are (except in the cases mentioned) not beings because such a fragment of the unit cell has -- with respect to its own structure (the structure of the fragment) -- no relation with one or another special dynamical law which should have generated it. Let me explain this :
A case in which such a part of the unit cell is not a genuine being at all, could be the following : The unit cell – as the repetitional unit of the crystal, having, by definition, the same dimensionality as the crystal lattice itself – often comprises half atoms or even quarter atoms (i.e. [conceptual] fragments of atoms), which we can illustrate by the following diagram of a crystal lattice, in which we confine ourselves (for reasons of clarity) to two dimensions only, i.e. to a 2-dimensional crystal lattice and its 2-dimensional unit cell :
Part of a two-dimensional crystal lattice with motifs, as such belonging to the Plane Group (a Plane Group is the 2-dimensional analogue of a Space Group) C2mm.
The lattice is such that its points occupy the four corners and center of each repeated rectangle. Each lattice point is provided with a (chemical) motif.
A possible unit cell is indicated (yellow). Each motif represents (the point symmetry of) the constituent atoms or atomic groups. The unit cell consists of four quarter motifs and one whole motif (together making up two whole motifs). Such a quarter motif, occurring (only) at the corners of the rectangles) could easily contain, in addition to some complete atoms, a quarter atom (i.e. only one quarter of a certain atom), for instance in the case where the motif represents an atomic group with one of its atoms precisely in the center of that motif, i.e. coinciding with a lattice point. It is clear that one such a quarter motif – taken as a fragment of the unit cell – containing a quarter atom (i.e. containing a fragment of an atom) – cannot be a genuine being.
[See for crystals and crystal lattices the Essay The Structure of Crystals revisited (Special Series), and also the Essays on the Internal Structure of Crystals (Also in the Special Series) ].
So what we see is the following :
But when it comes to Atoms and Molecules, then they seem -- in the case of (their being constituents of) organisms as well as (constituents) of crystals -- to be beings on their own, whether they are isolated or not. They are generated by dynamical laws of their own and so do not seem to have any ontological relation with the (macroscopical) Totality, i.e. they do not seem to be ontologically integrated in the Totality. So atoms and molecules, also when they are not isolated from the Totality, seem nonetheless each for themselves to be genuine beings, and so Totalities. This is why crystals and organisms do not seem to be genuine (i.e. complete, or absolute) continua. They are, to be sure, closely situated towards the continuum-side of the dimension (scale)
Continuum ----------- Aggregate ,
but their (smallest) parts do not seem to be virtual (do not seem to exist in a virtual -- versus actual -- way). They would be virtual if crystals and organisms were absolute continua, because an absolute continuum does not have actual parts (only potential parts). But we must enter a caveat here.
Figure 1. Scanning tunnelling microscope image of atoms.
Here we can actually see atoms, but what we see, and by what method we see, can also be explained in terms of seeing determinations of some supra-atomic whole.
( After COVENEY & HIGHFIELD, 1991, The Arrow of Time )
Remark: Confining ourselves to Real Totalities, i.e. inhabitants of the Real World (this World is contrasted with an Ideal World, See for this distinction the Essay on The Universal ), we can add the following : Because alongside a metaphysical interpretation, every Real Totality moreover admits of a physical interpretation which acknowledges (the existence of) actual parts, a Real Totality never seems to be absolute, i.e. never (seems to be) an absolute continuum, and, so never seems to be an absolute being. But as such, a Real Totality points to (the existence of) absolute beings, because of a general principle which says that a MOTIF is never without a BACKGROUND. Such absolute beings could relate to dynamical laws in their formal (i.e. mathematical) aspect. They could be the "Separated Entities ", anticipated by Aristotle, and they could make up the already mentioned Ideal World.
Figure 2. Structure of C60 (Buckminsterfullerene). 60 Carbon-atoms are arranged in hexagonal and pentagonal rings, resulting in a soccer ball structure of the molecule. Molecules like this are generally called " Fullerenes "
( After BALL, 1994, Designing the Molecular World )
Figure 3. A layer of C60 molecules on the surface of gold. The picture is obtained using a scanning tunnelling microscope, which can reveal much finer detail than a light microscope. The spherical molecules appear as bright peaks. Their hexagonal and pentagonal rings (See previous Figure) cannot be resolved here as the C60 molecules are thought to be spinning rapidly. Because here we have to do with one layer only, it does not yet represent the C60 crystal, so the molecules, visible in this picture, must be interpreted as actual molecules (not yet determinations of a larger whole).
( After BALL, 1994, Designing the Molecular World )
Remark concerning the above figure and the one below : C60 molecules are each for themselves complete entities (See figure 2). Such a molecule is symmetrical and so does not seem to exhibit any differences in electrical charge at different sides of the molecule -- (In for example a Water molecule such differences are present, because of the special three-dimensional structure of that molecule) -- and thus the C60 molecules will just pile up when their kinetic energy is low. One layer, representing the beginning of this piling up, we see in the above figure. But maybe some weak (electrostatical) forces nevertheless do play a role, but, if not, then the ' crystals ' of the figure below (crystals, consisting of 90 % C60 and 10 % C70, obtained from a solution in Benzene) are not each for themselves a Totality, but an Aggregate, resulting from just a piling up of molecules. But if those crystals turn out to represent, each for themselves, a REPEATABLE set of properties, then we must consider them as Totalities, be it ' loose ' Totalities. We must keep in mind, the fact that when a molecule (or an atom for that matter) passes from actual to virtual, nothing mysterious happens to that molecule. The only thing that happens to it is its INTEGRATION into a larger whole, which implies that it will take some effort (in terms of energy) to liberate it again from the framework of that whole.
From this it is clear that Nature tends to resist any clearcut categorization of her creations.
Figure 4. Fullerene crystals (reddish brown).
They consist mainly of C60 , with about 10 % of C70 . See also next Figure.
( After BALL, 1994, Designing the Molecular World )
Because the C60 Fullerene molecules are spherical, they can either stack (and in this way forming crystals) according to Hexagonal Closest Packing (HCP) or according to Cubic Closest Packing (CCP). The crystals of C60 Fullerene turn out to be structured according to Hexagonal Closest Packing (KLEIN & HURLBUT (Jr), 1999, Manual of Mineralogy, 21st edition, p.193). This means that the crystalline structure consists of layers of spheres (C60 molecules) that are stacked on top of each other as follows : We have a layer of spheres (where the latter lie as close together as possible), let it be called layer A. A second such layer, let us call it B, is placed on top of the first layer in such a way that the spheres of this second layer lie in the dimples between the spheres of the first layer. So now we have AB. For adding a third layer as close as possible to the second layer we have two possibilities : either the spheres of the third layer come to lie precisely above the spheres of the A-layer, which means that the third layer can be considered to be an A-layer. If we repeat this way of stacking we get the stacking sequence ABABAB ..., which is Hexagonal Closest Packing. If, on the other hand, the spheres of the third layer come to lie not above the A-spheres, but at new positions (as seen from above), we have to do with a positionally new type of layer which we can call C. If we repeat this way of stacking we get the stacking sequence ABCABCABC ..., which is Cubic Closest Packing.
(a) : The hexagonal closest packing of C60 molecules (Buckminsterfullerene) as revealed by high-resolution transmission electron microscopy (HRTEM). These complex carbon molecules are of synthetic origin and have not been found in nature. Scale is in nanometers (nm) : 1nm = 10 Angstrom (1 Angstrom = 10-8cm).
(b) : A computer calculated image that replicates the observed structure image in (a).
( (a) and (b) After KLEIN & HURLBUT, 1999, from WANG & BUSECK, 1991, Packing of C60 molecules and related fullerenes in crystals : A direct view. Chemical Physics Letters, v. 182, pp.1-4.).
(c) : Illustration of the structure of a C60 molecule.
(After KLEIN & HURLBUT, 1999, Manual of Mineralogy)
Earlier we considered the ontological status of anatomical parts, and spoke about the transformation of a proposition expressing itself physically into a proposition expressing itself metaphysically, exemplified by the corresponding propositions
" Socrates HAS a nose "
" Socrates IS nosed "
Comparable considerations are relevant with respect to the remaining intrinsic determinations.
Let us, as an example, consider the determination LENGTH.
When we say
" Socrates HAS a length ",
then this proposition suggests two beings, but this is just appearance because LENGTH is an abstract term, and so is not signifying a complete being, but a principle (i.e. the expression predicates in the manner of attributing a principle). When we specify that determination with, for example, 1.70 meter, then we can say
" Socrates HAS a length of 1.70 meter ".
Also in this case the way of predicating is still dominated by the attribution of a principle, namely LENGTH. But as soon as we make the predication concrete :
" Socrates IS 1.70 meter long ",
(then) the fact of there being only ONE Totality, namely Socrates, is clearly expressed. And of this Totality an ontologically dependent intrinsic condition is predicated, namely the determination 1.70 METER LONG. The significatum of the term 1.70 METER LONG is, to be sure, really present but is not a complete being (with an Essence of its own). It is a secondary being. The proposition clearly states what Socrates IS, not what he has.
Of course we could also predicate as follows :
" Socrates HAS 1.70 meter longitude ",
but this is equivalent to the aforementioned proposition
" Socrates HAS a length of 1.70 meter ",
This proposition attributes a principle to Socrates, not a part. What it attributes is a determination taken in itself (taken apart from its subject). And a determination-taken-apart is not a thing, nor a part of a thing. In some classical systems it is considered as a thing, but such views are superseded. Of course Socrates HAS this principle, but this principle expresses in fact what Socrates IS. With determinations such as 1.70 long it is, by the way, direct clear that they (i.e. the terms) do not signify a concrete part of Socrates.
In all considerations of this kind we must keep on realizing that the real, complete, individual being (the Totality) always forms the center , the point of reference, of a metaphysical contemplation.
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