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This document is the continuation of the systematic and thematic exposition of Aristotelian metaphysics as a theory of natures, or the ontology of the individual thing.
Because, when expounding Aristotelian metaphysics, we will, in addition to the example of man, often use inorganic beings, and because, among these latter beings, we consider snow crystals especially instructive, we begin by reproducing (as we did in Part I) a few photographs of them from Fourth Part of Website. They will serve us well in the ensuing discussion of the "via praedicationis", that is, the discussion about the aristotelian Predicables and Categories (Predicaments).
In the previous document we considered the four Fundamental Questions, revealing metaphysical presuppositions : Via Quaestionis. Now we will continue our enquiry into Aristotelian Metaphysics (with the help of St Thomas Aquinas) by investigating predication, leading up to an understanding of the aristotelian Categories : Via Praedicationis.
Contents.
c1. Meaning and Extension. Distinction among the several Predicables revisited.
c2. Again, the distinction between Difference (differentia [specifica] ) and
Property (proprium). Genotype and Phenotype.
d1. Substance
d2. Substantia dupliciter dicitur : subiectum et essentia.
d3. The accidental Categories.
d4. Substantia dupliciter dicitur revisited.
Earlier we saw, following AERTSEN (where he is working on an exegesis of Thomistic texts), that by asking a way is opened to knowing. This asking is only then possible when that what we want to know is indeed liable to being 'interrogated'. Asking is always with respect to Beings, and if we suppose that knowledge is possible, then such a being must have a catallel nature (that is, a dual nature, or a nature consisting of two 'parts') in order to be liable for being questioned, because the question itself is also catallel, or can, at least, always be transformed into such a (catellel) question, as shown in the VIA QUAESTIONIS (previous document) (A question only makes sense if there is, apart from something unknown, also something known, because a question must always be a question about something , something that we as such already know).
Our presupposition that says that we can know, leads to the possibility to ask, and this in turn leads to the proposition that that something which we want to know must also be catallel : It is a so-called 'transcendental' argument which leads to ontological conclusions, as KANT uses them to prove, among other things, that everywhere and always causality is at work. The value of such arguments is difficult to assess : WILKERSON, T.E., Kant's Critique of Pure Reason, A COMMENTARY FOR STUDENTS, 1976, discusses them at pp.199.
This catallel nature of question and answer automatically leads us to predication which is inseparably connected with it, because it is in fact here where the catallelism resides, and an investigation of it (that is, of predication) will, according to St Thomas, yield insight into the ontological structures of that what is being questioned. The way of predication is directive as to the questioning of Being and for the way of Being of that what is worthy of being questioned (AERTSEN, p.53).
The answer to the question should in the end become a definitio quid rei (a difinition that says what a given thing is), which will further be used as middle term in the demonstration of a proprium of a given subject (that is, the demonstration that a certain determination is a per se determination with respect to a given subject). Enquiry into the per se -- per accidens predication model yields insight with respect to the Essence, of which the definition is the logical counterpart.
In order to be able to evaluate the via praedicationis properly as to its alleged ability to provide knowledge, and further because predication plays such an important role in Scholastic writings (which have done a great deal of work to explain and further develop Aristotelian metaphysics), it seems to us not superfluous to systematicaly investigate predication by critically evaluating this scholastic tool.
Those terms which are signs that point to extra-mental things (that is, things that are independent of the thinking about them) were called in the Midle Ages primae intentiones. Today they are called terms of the object-language.
Terms that are signs for other terms were called secundae intentiones. Today they are called terms of the meta-language.
It is possible to order terms of first intension (primae intentiones) on the basis of their character (which is a logical undertaking), in virtue of which we classify and name the terms, yielding in this way certain secundae intentiones. For example, the term 'animal' (a term of first intention) relates to the term 'rational' (also a term of first intention) as genus to difference. These latter two are secundae intentiones (second intentions).
This ordering can, among other possibilities, take place by means of distinguishing several ways of predication, and it is this logical activity which make us able to distinguish the so-called predicables. Predication, namely, can be done in different ways (which will be discussed below). I have, in order to gain better insight, tried to use, in addition to classical examples, also other examples.
But before doing so, I must mention a number of consequences that flow from my view of Essence (as outlined extensively in First Part of Website ).
The Essence of a genuine complete being is, in that view, the dynamical law of the dynamical system which can generate that being (which we also call a Totality) from basic elements. This dynamical law is the genotypical aspect of that being. All determinations , on the other hand, together constitute the phenotypical aspect, the concrete Totality, the relevant concrete being. These determinations can be per se with respect to the Essence, or only per accidens with respect to it. All these determinations manifest the in itself invisible Essence out into observable Reality. The formal aspect of the dynamical law is the substantial form of the given being.
Let us now apply all this to the predicables.
The species (logically) expresses this Essence.
The genus (logically) expresses this Essence in an incomplete way.
The difference (logically) expresses an essential quality as a further specification of the Essence.
So those entities to which the species, the genus, and the difference refer, belong to the genotypical domain of the Totality.
All other predicables, namely proprium and accidens, belong, as to what they refer to, to the phenotypical domain of the Totality, because they represent determinations generated by the (physically interpreted) dynamical law, that is, by the Essence of the Totality. They are the phenotypical expression of the Essence
( NOTE 49 ). Genus, Difference, and Species thus stand (with respect to their supposita
( NOTE 50 ) in concrete cases) for the dynamical law or parts of it ( This is worked out more fully below).
However, in far and away most cases the particular dynamical law is not known, and it is because of this that we are forced to work with the phenotypical representatives of dynamical laws.
Apart from signifying the Essence by Genus or Species, indication of the supposita of the predicables by means of phenotypic representatives of them is only necessary, there where a predicable stands for a closer determination
( NOTE 51 ) of the Essence (that is, an aspect of the Essence), and this is the Difference. It accordingly will, out of sheer necessity, be expressed in the form of the (as such taken) phenotypic representative of it. With respect to Man we do this by using the term RATIONALE ( = being rational, that is, being able to discursively think), whereby we must realize that being rational as such is just a determination (because it is phenotypical). But we let being rational nevertheless refer to a part or aspect of the dynamical law (to which the term in fact does not refer, it refers in fact to something phenotypical), which we, as in the case of the dynamical law itself, unfortunately do not know. There where we do not do this (thus there where we pretend to be strict), being rational stands just for a (phenotypic) determination, namely a proprium (a per se determination). We will say more of this below.
REMARK :
Earlier investigations (performed in What is an Individuum? Part III, in the Classical Series of Documents of First Part of Website ) have shown that m e t a p h y s i c a l l y Socrates (or Plato, Peter, etc. for that matter) is not an individual of the species MAN, but of the species SOCRATES. The species Socrates happens to be represented by only one individual, but this is accidental. If Socrates were a member of a monovular twin, then the species SOCRATES would be represented by two individuals, say, Socrates1 and Socrates2. The same goes for Plato, Peter, etc.
Socrates1 consists of a series of stadia (leading from young to old). Together these stadia form the historical individual, Socrates1. Each such a stadium is a here-and-now indivual (semaphoront) of Socrates1. Also Socreates2 consists of a series of stadia together forming the historical individual Socrates2, and each such a stadium is a here-and-now individual (semaphoront) of Socrates2.
So the difference between Socrates and Plato is not an individual, and thus accidental, difference (a difference between two individuals of the same species), but a s p e c i f i c difference, i.e. a difference between two different species. In this way we do not have the special feature person as typical for human beings anymore. The clear differences between Socrates, Plato, Peter, etc. are specific differences reflecting correspondingly different dynamical laws (Essences), and are not remarkable anymore, as they should be if Socrates, Plato, Peter, etc. were all just individuals of the s a m e species (biologically, they still are, of course). And indeed, the members of the species Socrates, that is the members of the monovular twin, differ only little (as we see in actual monovular twins), as is to be expected from individuals of the same species.
Having said this, we can, in order to conveniently discuss the findings of Classical Metaphysics, still consider human beings -- figuring as examples -- as if they all belong metaphysically to one and the same species, because here we are not discussing Man but are only discussing what we should understand by the Essence, Genus, Difference, Species, Proprium, or Accident of some given intrinsic thing, whether this thing is Socrates, or a salt crystal, the dog Fido or a water molecule.
Genus and Species, for example Animal and Homo, are each for themselves not closer determined and not analysed, and consequently do not pose a problem. I let them directly refer to, respectively, the genus of the relevant dynamical law and that dynamical law itself. Further down I will say more about it.
Next we will investigate the different ways of predication and show how this investigation gives the five predicables (praedicabilia).
In the human example we will assume that all humans belong to the same species (HUMAN BEING, HOMO), and that the genus (that is, the next higher logical level of generality) is ANIMAL. Further, the difference is (assumed to be) RATIONALE ( = rational, i.e. able to think discursively). (Everywhere 'praedicare' = to predicate).
Sometimes we have, in the examples of the different types of predication (given below), used HAS (instead of IS ). In fact we should always predicate with IS (for example "a human being IS rational"), because in the present context it is always about what something IS.
If we predicate with HAS (if this is a genuine predication at all) then two beings (complete or incomplete) are expressed in the proposition, whether the attribute term is concrete as in "Socrates HAS a nose", or abstract as in "Socrates HAS noseness", or in "Socrates HAS a length of 1.70 meter".
But in substance-accident metaphysics we always want to express the fact that Socrates (and also Socrates-for-example) is one being. And this can only be done by predication with IS. And indeed, all 'predications' (propositions) with HAS can be transformed into equivalent predications with IS :
"Socrates HAS a nose" ==> "Socrates IS nosed"
"Socrates HAS noseness" ==> "Socrates IS nosed"
"Socrates HAS a length of 1.70 meter" ==> "Socrates IS 1.70 meter long"
However, when we would carry out this transformation for all HAS-propositions, many of the resulting IS-predications would look awkward, so we abstain from carrying out such transformations (but know they can be done).
The genus expresses the Essence in an incomplete way (in quid incomplete), it signifies the qualifiable Essence (where the qualification can be done by adding the difference).
The species expresses the Essence in a complete way (in quid complete), it signifies the qualified Essence (but does not mention the qualification explicitly).
REMARK :
The terms (as in the above examples) 'rational', 'saturated', 'vascular', and also 'further qualification of the concrete general crystallization law' are, as first intentions, all belonging in the Predicament of 'Quality', that is, they signify predicamental accidents. Nevertheless, in the above predicative contexts they belong, now as second intentions, all to the Predicable ' Difference'.
Praedicare in quid (1), praedicare in quale quid (2a) and predication of a proprium (2b) are three forms of per se predication : If of something a species, genus, or difference is predicated we get an ens per se ( NOTE 61 ), that is, a necessary unity. For example : the-human-being-Socrates, the-rational-Socrates. Predication of a proprium, on the other hand, results in a necessary twoness, for example : Socrates, who can (as can all man and man alone) laugh ( NOTE 62 ).
The accidental predication (2c) does not result in a necessary unity or twoness, so neither a thing nor a necessary state of affairs, but a contingent state of affairs. For example : Socrates, who happens to be white (Socrates, as an individual of the human species, happens to be white) ( NOTE 63 ).
All up to now mentioned predications are genuine predications (logically per se predications).
The literate is white.
( Socrates, as an individual of the species human being happening to be literate, happens to be white [not all humans are literate, not all humans are white]. It could still be that all literates are white, but this is not a necessary connection : all literates then just happen to be white. In fact also many black people are literate, so in any case literate is a true accident ).
The white is wood.
( " The white" here means : " That white [some]thing overthere", where "that something" must be such that for it to be white is not necessary, implying that here "white" is an accident. "Wood" is a substrate [it carries white], and normally it is then logically a subject ['this wood is white']. Here, however, it is logically a predicate, while "white" [which normally is a predicate] is logically a subject ).
Let me expound this further.
The above predications
The literate is white
The white is wood
are, on the basis of their content accidental predications (in the sense of the last type of genuine predications, discussed above (2c)). This is because not every literate is white, and, respectively, not every white (thing) is wood.
They are, however, quasi predications because of the fact that their subjects (literate, resp. white) should in fact be predicates (Socrates is literate, this wood is white).
The logical subjects (literate, white) of the two quasi predications, clearly connote their own carriers, that's why the terms used (literate, white) are concrete. When their abstract counterparts were used, that is (abstract) terms that only signify a content without connoting the carrier of that content, then our predications would read :
The literateness is white
The whiteness is wood
which is nonsense (because literateness as such is not white, and cannot be white, and whiteness as such is not wood, and cannot be wood).
So the logical subjects must connote the carrier.
When we indicate this connotation more explicitly (then by just using concrete terms), our predications will then look as follows :
" This literate human being is white"
" That white thing there is wooden"
In the last predication we have replaced "wood" by "wooden", because "wood" was meant to signify something like "a concrete piece wood", only implicitly meaning "wooden". We have made that explicit.
We spoke about the SUBJECT and about the CARRIER.
Roughly we can say that a subject is the logical counterpart of a carrier, and that a carrier is the ontological counterpart of a subject. A carrier can also be denoted by 'substrate'.
'Subject' figures in logic, while 'carrier' or 'substrate' figures in metaphysics. But often, namely when no confusion is to be expected, the term 'subject' is used where it is supposed to stand for a carrier.
When referring to determinations, the carrier carries the accidents (determinations), and in Classical Metaphysics this carrier is called 'Substance', that is, that what stands under (the accidents). As is evident, it is paramount for obtaining a healthy updated version of the Substance-Accident metaphysics that we must have a correct and detailed understanding of the carrier-as-such, that is, what it precisely means for something to be a carrier or substrate, especially for the case of something to be the carrier of accidents.
We did this in the documents Revised Ontology of Determinations I and A Supplementary approach : Mereotopology of Reality of the Non-classical Series of Documents in First Part of Website .
Let me reproduce the Section The Totality and its determinations from the first mentioned document ( Revised Ontology of Determinations I ) :
Remark : The just mentioned prime matter is -- as pure potentiality for content, and as ultimate substrate -- a principle of the possibility of radical change and (together with dimensive quantity) a principle of individuation. Prime matter, as ultimate substrate, is necessary for the SUBJECT to become itself a substrate (but only a penultimate substrate).
All this, however, needs some further qualification :
Elsewhere, namely in the Essay on Mereotopology in the Non-classical Series of Documents in First Part of Website , 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 (time, place, thermodynamic conditions) as well as the intrinsic per accidens determinations (like being tanned by the summer sun : "intrinsic" because they are determinations wholly of the Totality or Mereototality, "per accidens" because they just happen to be on the subject). 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 discussion above [the first part of the present Intermezzo], 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 was found to be identical to the whole Mereo-totality minus those particular determinations, and so this SUBJECT still contains, 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.
For the important argument (taken from the document on Mereotopology in First Part of Website) revealing not only what is precisely the carrier-only (that is, in the case of a true Totality -- fully-fledged substance, substance in the broader sense -- : SUBSTANCE (s.str.)), but also (within that carrier-only) the boundary between the genotypic and phenotypic domain of a true Totality, see this ( NOTE 64a ).
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.
End of quotation from First Part of Website.
The next Figure summarizes all the above results about the ontological constitution of a real being :
Above we had investigated predication, and the enquiry into the ways of predication yields the following predicables (praedicabilia) :
In order to obtain a better understanding of the Praedicabilia we will, in what follows, try to indicate several distinctions, whereby it automatically becomes evident that this is not so easy as seems at first sight (that is, when we would only consider the human example) :
The distinction between genus and species ( NOTE 66 ) on the one hand, and differentia, proprium and accidens on the other, consists in the fact that the first are 'whatnesses', while the last are 'qualities' or 'traits'.
The distinction between the accidens on the one hand, and proprium and difference (differentia) on the other, is that one or another accident (signified by the accidens) can at one occasion be present on a given individual subject, at another time not (anymore) ( This either with respect to time, or to 'space', which latter means qua extension of the qualification (accident) over the (set of) individuals of the species ( Some individuals have the qualification, others don't).
This is not the case for proprium and differentia.
The distinction between proprium and differentia is in fact very hard to ascertain. Often it can only be so ascertained in an arbitrary fashion.
If we ask :
"How can a human being be (typically) qualified?" then we can say either :
"He is capable of laughing", or (we can say) :
"He is rational".
Which one of these would be the essential quale (differentia) cannot be ascertained just like that. Conventially one says that it is "rational" that is this essential quale, while taking "capable of laughing" to represent the proprium. But this is an arbitrary decision. We will return to this problem later.
The distinction between proprium and accidens (which both must be in a subject) is that the accidens, with respect to a given subject, can vary (that is, replaced by another) in space or time, while a proprium is always present in the subject : So it goes for " The human being laughs" that "laughs" is an accident (because he does not always laugh), while for " The human being is capable of laughing" "capable of laughing" is a proprium (because he carries this capability always with him).
Further, can (and must), together with a given proprium (in its definition), (also) a certain appropriate subject be mentioned, wherby it applies that this appropriate subject belongs to one species or one (higher) genus for which it is a proprium. So when we consider all individual white (physical) bodies, then those bodies that are always white, do not represent a genus or species, and therefore white is not a proprium
( NOTE 67 ).
In Book I of the Topica Chapter V, Aristotle defines four praedicabilia :
Definition, Proprium, Genus, and Accidens.
The Definition consists of Genus and Differentia, and can, therefore, in the list be replaced by the Differentia. So we get :
Genus, Difference, Proprium, and Accidens.
The fact that the Species is not mentioned forms a special problem ( Porphyry [3rd century A.D.] does enter the Species in his Introduction to the Categories ) : Science is not about particulars (because these are contingent), but about necessities. A species is only predicable of particulars (like Socrates : "Socrates is a human being") (what is [by definition] subsumed under a species are just individuals), that's why Aristotle does not enter the Species here : All terms are predicated of the species : For demonstrative science the Species is the ultimate subject of predication (Indeed, science is about species and higher generalities, it is about iron and about metals, it is about light and sound, it is about the silk worm, butterflies and insects, it is about the mammoth, man and mammals. It is never about the dog Fido or the greek philosopher Socrates, that is, it is never about individuals in the sense of particulars).
In order to understand well what is coming next, it is perhaps useful to give here the Categories (or, equivalently, the Predicaments), which will be treated further below. Together they form the most fundamental generic diversity within the domain of Being (s.l.).
Generic diversity originates by that which makes possible different types of predications about the subject -- as it is said by St Thomas in In Metaph. V, lectio 9, nr. 891/2 :
What the subject is.
What the measure of the subject is.
What the disposition of the subject is.
To what the subject is related.
What the subject 'possesses' (has on it).
When the subject is.
Where the subject is.
What the pose of the subject is.
What the subject does.
What the subject undergoes.
This results, after maximally generalizing, in the ten highest Genera.
What then is the precise difference between these Categories (Predicaments) and the above considered Predicables?
c. The difference between praedicabilia and praedicamenta and the difference between predication and signification.
From what has been written in the Section on Predicables it is clear that the predicables are terms of second intention ( that is to say, terms such as 'genus', 'species', 'proprium', 'difference', 'definition', 'accidens', and also the term 'predicable' ), while the predicaments (categories) are terms of first intention
Recall that terms of first intention are signs signifying extra-mental things (A human being [that is, Socrates, or Plato, or Peter, etc.] IS an animal [ = collection of all sensitive organisms] ). Terms of second intention are signs signifying other terms (of first or second intention) ( The term 'animal' is a genus, that is the term 'animal' is a generic term. In the proposition "animal is a genus" the term 'animal' refers to a certain type of terms [namely a genus, of which 'animal' is an instance], it [as 2nd intention] does not refer to extra-mental things like sensitive organisms ).
This difference (between predicables and predicaments) gets relief in the following :
The term 'color', belonging in the accidental predicament 'Quality', and which (term) can be predicated in a per se manner of, for example, 'red[ness]' (i.e. in virtue of the essence of red[ness] ), is the genus of 'red[ness]'. That is to say, because the predication " Red[ness] is a color" is an essential predication (here predicare in quid with respect to an auxiliary being [namely red(ness) ] ), the term 'color' is a genus (it is not a species, because the subject is not individual). The term 'color' thus belongs in the Predicable 'Genus'. It is established now what kind of term the term 'color' is, namely a genus. And this genus is, as genus, a term of second intention.
As a term of first intention 'color' signifies something in extra-mental reality. It signifies a collection of things which are such that we can legitimately attribute the formal content color to it. When we, in steps, generalize 'color' we obtain a sequence of higher and higher genera. And the highest genus in this sequence (red-color- ...) is 'Quality'. Now we know that 'color' belongs in the Predicament 'Quality' (and because red[ness] is [per se] a color, 'red[ness]' also belongs in this Predicament.
'Red' as predicated in " The sun is red " is, however, the predicable 'accidens' (because here the term is used in an accidental predication [the sun is not always red] ), while 'red' is always (also) a predicamental accident (because it is a quality of a given individual being, that is, it belongs in the predicament of Quality, and is as such an ontologically dependent being)
( NOTE 68 ). So the various members (red, color) in the same Predicament (Quality) can differ as to in which Predicable (genus, species, difference, etc.) they belong :
Color belongs to the predicable 'Genus'. Predicative context : red is a color (predicare in quid [ = essential predication] with respect to a qualification [as subject] ).
Red belongs to the predicable 'Accidens'. Predicative context : the sun is red (accidental predication).
Capable to laugh is a quality (i.e. not as term, but in virtue of that in reality to which the term 'capable of laughing' refers). The term signifies something which cannot stand on its own 'feet' (i.e. which is ontologically dependent, it cannot exist all by itself) but must be in a subject (must be carried by a substrate), so this term is a predicamental accident (that is, the term belongs in one of the nine Predicaments that come after the Predicament of 'Substance', in the present case, the Predicament of 'Quality').
But when the term capable to laugh is predicated of human being (as in : "a human being ( = species) is capable of laughing") it is the predicable ' Proprium'. The term capable to laugh is the predicable ' Proprium' because it can be predicated only as proprium.
So as a term of first intention 'capable to laugh' is a (predicamental) Accident, while as a term of second intention it is the Predicable ' Proprium'. Also here the difference between predicables and predicaments is evident.
The Predicaments (Aristotelian Categories) refer to the way of b e i n g. Therefore they, and the subordinates of each one of them, are, as terms, terms of first intention.
The Predicables refer to the way of p r e d i c a t i o n. Therefore they are terms of second intention.
St Thomas states in In VII Metaphysica nr. 1331, following the Stagirite ( = Aristotle), that (predicamental) accidents, strictly speaking, do not have a true quod quid est, that is, a definition, because in the definition of a given accident we must always include something extrinsic with respect to it, namely the subject. Insofar as one nevertheless wants to speak of the 'essence' of a predicamental accident (because predicaments are terms of first intention -- predicables do not have an essence), then one can do so only by way of analogy and via an abstract term, for instance the essence of whiteness (and not of white, which is a concrete term).
The predicables classify terms into groups, but, as we've said, only from a predicative context : The term 'capable to laugh' is in itself not a proprium, but a predicamental accident. But 'capable to laugh' insofar as this is said from something in a per se way (per se predication) is a proprium (And this is directly related to the extension of the terms or concepts [a concept is a natural sign, while a term or word is the corresponding conventional sign] ).
The way of predication (i.e. the different ways in which a predicate can be appropriate for a subject) is here accordingly the criterion for distinguishing the different predicables.
The problem with this, however, is that the 'way of predication' is also called a criterion for distinguishing the different predicaments from each other (Aristoteles, Metaphysica V, 7, and St Thomas In V Metaphysica, lectio 9, nr. 890 :
Unde oportet, quod ens contrahatur ad diversa genera secundum diversum modum praedicandi, qui consequitur diversum modum essendi
( NOTE 69 ) ). So the via praedicandi here leads, according to St Thomas, to an understanding of the different ways of being expressed in the Predicaments (Categories).
William of Ockham (14th century) indeed states (according to the interpretation of MOODY, E.A., The Logic of William of Ockham, 1965, p.69, note 1) that the predicaments are not ways of predication, but ways of signification.
The name 'predicaments' suggests that it is about ways of predication, but the way of predication as such does not yield a distinction among the predicaments at all :
Socrates is (a) human being, Socrates is 1.70 meter long, Socrates is pale, Socrates is shoed, Socrates is cutting, etc.
If we look into the per se / per accidens character of such predications (and that is only possible after we have considered the signification (meaning)), we can distinguish between the predicables, that is, we can then determine whether a term is a proprium, accidens, genus, etc. is.
So it is the Predicables that are distinguished on the basis of ways of predication (and not the Predicaments). But distinguishing between ways of predication can only take place on the basis of the signification (meaning) of the terms. It is directly on this that the Predicaments are based. So the meaning of the terms determines directly into what Predicament the term belongs, while the predicative context determines to what Predicable the terms belong.
The Predicaments (Categories) are terms, as incomplex signs, for things (that is, to represent things by referring to them). They are not elements of propositions (predications), i.e. no parts of complex signs (propositions). Signification must precede predication, because the truth of propositions depends on the signification (meaning) of the terms. The Predicaments belong in that part of Logic which deals with the 'simplex apprehensio', that is to say, the first act of reason (the apprehension of the concept), and not the second act, the proposition. The Predicaments are ways of description of a given thing in which the degree of interiority of this description varies with the predicaments. Indeed, the description of a thing as ' having shoes on' (belonging in the Predicament ' Habitus' ) is very external, while 'being white' (belonging in the Predicament of 'Quality' ) is already more intrinsic, while something like ' being a human being ' (belonging in the Predicament of 'Substance' ) is the most intrinsic way of description (way of signification).
So in this way we get the Predicaments as highest genera of these way(s) of description of a thing ( That is to say, by maximally generalizing such descriptions [shoed, white, human being, etc.] we arrive at the ten upper genera, Habitus, Quality, Substance, Quantity, Relation, etc.)
( NOTE 70 ).
If we consider a given term in ordere to determine its logical and ontological status, we first look to what this term means, and that is here, to what in extra-mental reality it refers, if it refers to that reality at all, and in so doing : detached from any possible propositional or predicational context. That is we consider its signification. If this term indeed refers to something in extra-mental reality then it is a term of first intention. Such terms are classified by the system of Predicaments. In fact all terms of first intention can be reduced to ten types, classes or (highest) genera, the ten Predicaments. As to in what Predicament a given term of first intention belongs is determined solely from its signification, that is, from its meaning, apart from any predicational context.
When we now consider the given predication in which the term happens to figure, we determine, again on the basis of the term's signification -- and that is now on the basis as to in what Predicament the term belongs -- the present predicative context of the term, that is the per se / per accidens nature of the predication and in what way the term figures in the predication, that is, what status the content to which it refers has : does this content completely or incompletely express the Essence of an intrinsic being, is it the content (quale) that completes the incompletely expressed Essence, is it the content that can, diagnostically replace the Essence, or is it the content that is accidentally attributed to the given thing? On the basis of this we determine as to what Predicable the given term belongs.
For example, the term 'rational' means some qualitative content. Therefore, logically, it belongs, as a term of first intention, in the Predicament 'Quality'. In the predication " A human being ( = species) is rational " this qualitative content is that what completes the incomplete Essence as it is expressed by the term 'animal'. That is, here the term 'rational' is, as a term of second intention, a difference, that is, it belongs to the Predicable ' Difference '.
So logically the term 'rational' belongs, as term of first intention, to the Predicament 'Quality', which is an accidental predicament, while as term of second intention it, as figuring in the predication " a human being ( = species) is rational ", belongs to the Predicable ' Difference '. And this means that although 'rational' is logically an accident its significatum does not reside in the phenotypic domain but in the genotypic domain of the given thing.
So ontologically the significatum of the term 'rational', as it figures in the predication " a human being ( = species) is rational ", is not something that is generated by the Essence (that is, is not a phenotypic expression of the Esssence), but is part of the Essence.
Realize, that the predicational context does not influence or determine the meaning (signification) of the term, but only its status, namely its ontological status (phenotypic, genotypic), as well as its logical status (as to what Predicable it belongs).
In our example we assume that 'rational' in the predication " a human being ( = species) is rational ", stands for the completion of the incompletely expressed Essence. The Essence is the specific dynamical law governing the dynamical system human being. The incomplete Essence is then the general dynamical law, while that what contracts this general dynamical law to our specific dynamical law is that what is supposed to be signified by the term 'rational' (We will return to this topic further below).
All this leads us to the question that asks what then indeed is the the distinction between predication and signification.
If there is a difference at all then it seems to be as follows :
Signification is the apprehension (simplex apprehensio) of the individual essence or, equivalently, the quod quid erat esse
( NOTE 71 ) of a thing, that is, the transforming of an object into a 'significant' object which exposes its 'pointe'. Next we apprehend the quod quid erat esse of another thing, and after that, of another thing, etc. And on the basis of the character of all these individual essences we form classes and subclasses.
This quod quid erat esse can also -- mutatis mutandis -- refer to a quantity, a quality, etc. The Predicaments signify the whatness, and that is here the most general whatness, of either an ontologically independent being (substance), or of an accidental or per se determination of it. In fact the predicaments signify always (also in the case of accidental predicates) the whatness of the thing (how it is determined in itself, or how it is determined per accidens ) and, in so doing, they indicate the degree of interiority of this whatness [description].
The explicit emplacement of a thing (s.l.) or a group of things in a definite class by means of an assertion is then predication ( 'Socrates is a human being' [Socrates is a thing belonging in the category of Substance], 'A human being is an animal' [Every human being (is a thing that) belongs in the category of Substance], ' Redness is a color' [Redness is a thing that belongs in the category of Quality] ).
Summarizing :
Signification is a relation (implicitly having it posited) between sign (signum) and signified (significatum), or, equivalently, between sign and the thing which corresponds to it outside the anima intellectiva (reason) : This sign is first of all a so-called natural sign (intentio animae, Ockham, Summa Totius Logicae I. 1) which has a conventional sign as an effect (that is a spoken or written word).
Predication is a relation between terms in virtue of their signification (meaning).
The meaning (significatio) of terms ( = incomplex signs) ultimately is formed by ostensive definition (that is, via pointing to the signified (significatum) while at the same time mentioning the term).
As soon as we know the meaning of the terms (and if they are thereby univocal or considered as univocal) then we have a number of descriptions of things. If we make these descriptions as general as possible, then we are left with a number of fundamental ways or types of description (ways of signification), which indicate the whatness of a thing in as general a fashion as possible. These most general ways of description differ among each other, with respect to -- as has been said -- the degree of interiority of the description of the thing.
In this way we obtain the Categories or Predicaments. The supposita ( = that for which they stand) of these most general descriptions are principles of being , as was stated earlier.
C1. Meaning and Extension. Distinction of Predicables revisited.
The meanings of terms also give directly their relative extensions. By means of these extensions (ranges of reference, which are themselves thus based on the meanings, significations of the terms) we can determine whether a given term belongs to the Predicable accidens, proprium, genus, species or difference ( In the context of discursive science the species does not belong here, while -- according to me -- it does so belong in the context of metaphysics). The relative extensions are, however, not sufficient. This is so, because, for instance, the relative extensions of accidens and species on the one hand, and the relative extensions of genus and species are identical :
(where Ext(X) = extension of X, > = larger than, < = smaller than, acc = accidens, diff = difference (differentia specifica) ) :
Ext(acc) > Ext(species)
Ext(genus) > Ext(species)
The other extensions are (the species not being accounted for) :
Ext(diff) < Ext(genus)
Ext(diff) = Ext(proprium)
Ext(diff) < Ext(acc)
Ext(genus) < Ext(acc)
Ext(genus) > Ext(proprium)
Ext(proprium) < Ext(acc)
So here we find the following equal relative extensions :
Ext(diff) < Ext(genus)
Ext(diff) < Ext(acc)
Ext(acc) > Ext(proprium)
Ext(acc) > Ext(diff)
Ext(genus) > Ext(proprium)
Ext(genus) > Ext(diff)
So in order to determine whether a given term belongs in this or that Predicable, the relative extension is not sufficient.
For to detect a distinction between, say, genus and accidens their extension with respect to that of the difference is of no use, because :
Ext(diff) < Ext(genus) [ = Ext(genus) > Ext(diff) ]
Ext(diff) < Ext(acc) [ = Ext(acc) > Ext(diff) ]
but also their extension with respect to that of the proprium is of no use, because :
Ext(genus) > Ext(proprium)
Ext(acc) > Ext(proprium)
How then must we discriminate between, say, genus and accidens?
This can only be done by considering the way of predication (predication per se / predication per accidens, and within predication per se : predication in quid and predication in quale, and within predication in quale : predication in quale quid ( = predication of the difference) and predication of a proprium.
This way of predication takes place on the basis of the signification ( = meaning) of terms. From these meanings, that is to say, from the terms' intentions, the absolute extensions follow. The extensions consequently are the necessary result of the intentions. Nevertheless we discriminate between, for instance, an accidens such as 'white' and a proprium such as 'capable of laughing' on the basis of how their extensions turn out to be : Because 'capable of laughing' turns out to occur exclusively and always in the species MAN, we call it a proprium with respect to MAN. And because 'white' turns out to occur also beyond MAN, it is in any case not a proprium with respect to MAN (as appropriate subject). Is it in the nature of WHITE also to occur in other things than humans? Probably so. Is it in the nature of CAPABLE OF LAUGHING to occur exclusively and necessarily in MAN? Probably so.
So the term 'white' signifies some formal content, and 'capable of laughing' also signifies some (other) formal content (implying that they both logically belong in the Predicament of 'Quality'). But their extension (range of signification) turns out to be different. In fact, WHITE is a replaceable determination, and so implies a substrate (on which it can be replaced by another determination [in te same Predicament] ), while CAPABLE OF LAUGHING is a non-replaceable determination (it is always present in any given human being), and thus does not imply a direct substrate (only an ultimate substrate, namely prime matter).
In this way we decide to which Predicable a given term belongs by considering the empirically assessed extension, in the case of proprium and accidens (where the extension of 'capable of laughing' suggests it to stand for a non-replaceable determination, while the extension of 'white' suggests it to stand for a replaceable determination).
But with this we cannot ascertain whether the term 'capable of laughing' is a proprium or a difference , because the extensions of proprium and difference are equal.
The distinction between proprium and difference could be that a proprium refers to an ontologically dependent entity (while implying an appropriate subject), while the difference refers directly to the last over-forming, which has itself integrated as to become over-formed matter (integrated such that it is now over-formed matter) and is thus ultimately an ontologically independent entity
( NOTE 72 ).
A second distinction (related to the first one) could be that a proprium is always and exclusively present with the Essence, without, however, necessarily following from it, while a difference is a formal content that necessarily follows from the Essence, and that means here : necessarily is the Essence : the difference explicitly signifies the last over-forming and implicitly the rest, and thus it signifies the Essence.
However, these distinctions lack sense as long as we cannot objectively ascertain whether something, for instance that which represents CAPABLE OF LAUGHING, does or does not comply with the mentioned criteria. Does CAPABLE OF LAUGHING comply with the criterion that it is always and exclusively concurrent with the Essence (and with it with MAN) without necessarily following from that Essence? The first part of this criterion can be empirically verified, but as regards the second part we cannot indicate anything that would convince us that CAPABLE OF LAUGHING does not necessarily follow from the Essence, and that RATIONAL does necessarily follow from it : RATIONAL is always and exclusively present at the Essence (that is, always present in MAN), but does it then necessarily follow from the Essence or not? Whatever answer we give -- in the present stage of the discussion (but see already NOTE 72) --, the answer is stipulative instead of being ascertained on the basis of enquiry.
Before we investigate this further, we can establish that the predicables Genus, Species and Accidens do not pose problems :
The predicable accidens has as suppositum
( NOTE 73 ) a per accidens determination ( = replaceable determination).
The predicables genus and species have as suppositum the Essence.
The genus expresses that aspect of te Essence that commonly occurs in the subsumed Essences (For example the genus animal refers to a common nature that is present in MAN, as well as in DONKEY, HORSE, DOG, etc.).
So genus and species do not have as suppositum one or another determination, but the Essence itself.
But, as said, proprium and difference give problems, at least in Classical Metaphysics. In my revision (as has been laid down above, especially in NOTE 72, and as will be expounded further below) of this sproblem I have given an answer : We can say that, with respect to MAN (but then generalizing all this), the features RATIONAL and CAPABLE OF LAUGHING are ontologically equivalent. Both are generated by the dynamical law, both are permanent and so do not involve inherence, both are phenotypic essential parts (namely certain material substructures of the human body), both are generated by that part of the dynamical law that we call the difference. This difference is the over-forming of the generic part of the dynamical law, and so is a genotypic essential part. In the definition of MAN we can (phenotypically) let represent this difference by either the feature RATIONAL or the feature CAPABLE OF LAUGHING. Both are propria.
That to which a proprium refers is phenotypic and not replaceable.
That to which an accidens refers is phenotypic and replaceable.
That to which a difference refers is genotypic and not replaceable.
In the following we will precisely and in more detail go through all this :
We have been able to established that the Essence of a genuine intrinsic complete being is identical to the dynamical law governing the dynamical system that can generate this being from basic elements.
In almost all cases (of such beings) we are not able to explicitly formulate this dynamical law (it is simply unknown). But for the exposition of the status of genus, species, and difference this is not necessary. These status we can, and will, illustrate with the help of a number of simple abstract dynamical laws, expressed in a mathematical form ( These laws are fictitious, i.e. without (possibility of) physical interpretation, but that is no obstacle because here it is about laws as laws). Such dynamical laws can come in all kinds of forms among which that of a polynomial (i.e. a mathematical expression involving more than one term). Let us give an example :
Xn+1 = 3Xn2 + 2Xn +7
Here Xn and Xn+1 refer to consecutive process states, and Xn2 means : Xn multiplied by itself, that is, the square of Xn .
Xn , Xn+1 , Xn+2 , etc. are variables, and that means that they are each for themselves, as it were,
a 'box' provided with a name (that is, the name of the variable, as we have here for example "Xn", or "Xn+1", or "Xn+2" ), and into such a box we can put one or another chosen or computed value. We then have a box with the name (pasted onto it), say, "Xn", and a value, say, 5 (put into it). We can change that value at will. So we can replace the value 5 in box Xn by the value 8. We then say that the variable Xn first had the value 5, while later the value 8 has been attributed to it.
The meaning of the above given expression (which is supposed to represent a dynamical law) is as follows :
The new process state, Xn+1 , is generated from the previous ('old') process state, Xn , namely -- in the present case --, as follows : The new state, Xn+1 , becomes equal to : Three times the square of the old state Xn ( = 3Xn2 ), plus two times that old state ( = 2Xn ), plus 7.
If we thus start with a value for Xn , then we can compute the value of Xn+1 as indicated above.
And then a new state is generated from the previous state.
From this new state a next state can in turn be generated (and thus calculated) by repeating the procedure. This we do by placing the computed value of Xn+1 back into Xn (that is, we rename the value that was computed for Xn+1 to "Xn" ) and introduce it back into the expression Xn+1 = 3Xn2 + 2Xn +7 (that is Xn , wherever it occurs in te expression, gets this new value). We can then calculate this next state. This can be continued as far as we want to, and what we get is a whole series of consecutive states. And because in this procedure every time the newly obtained value is intoduced back into the expression (the formula) as (now) representing the 'old' one (this we call 'iterating'
( NOTE 74 ) ), we have to do with a feedback system ( feedback often occurs in organisms). Such type of dynamical system one calls a recursive system.
So here we have given an example of a polynomial dynamical law (polynomial, because Xn+1 = 3Xn2 + 2Xn +7 is a polynomial, that is, it consists of more than one term, in the present case three [trinomial] ).
There are many such polynomial laws (to come up with) and these relate to each other as genera and species.
In order to understand these genera and species we must have a closer look to the just given polynomial 3Xn2 + 2Xn +7 (which stands for the value of the state that follows upon Xn , or said differently, which belongs to the dynamical law Xn+1 = 3Xn2 + 2Xn +7 ) :
In this polynomial '3' is the coefficient Xn2 , '2' is the coefficient of Xn and '7' is a constant.
The highest power of Xn is here 2, and therefore we call 3Xn2 + 2Xn +7 , and of course also 3X2 + 2X +7, a quadratic polynomial (and Xn+1 = 3Xn2 + 2Xn +7 a quadratic polynomial dynamical law).
The general form of such a quadratic polynomial can be denoted as follows :
a1Xn2 + a2Xn + a3
In the above discussed polynomial, 3Xn2 + 2Xn +7 , we thus have :
a1 = 3
a2 = 2
a3 = 7
There are, of course, also polynomials in which the highest power of Xn is larger than 2, as for instance the polynomial 2Xn3 + 5Xn2 + 7Xn +1 (where Xn3 means : Xn times Xn times Xn ). This is a polynomial in which the highest power of Xn is 3, and such a polynomial is called a cubic polynomial. The general form of this type of polynomial is :
a1Xn3 + a2Xn2 + a3Xn + a4
We are now able to give the most general form of a p o l y n o m i a l, and with it, at the same time, the most general form of a p o l y n o m i a l d y n a m i c a l l a w :
Xn+1 = a1Xnm + a2Xnm-1 + a3Xnm-2 + . . . + ak-2Xn2 + ak-1Xn + ak
where a1 , a2 , a3 , . . . , ak-2 , ak-1 are the coefficients of respectively Xnm , Xnm-1 , . . . , Xn , and where ak is a constant.
The most simple polynomial is where the highest power of Xn is equal to 1. The general form of such a polynomial is :
a1Xn + a2
The dynamical law corresponding with this polynomial reads :
Xn+1 = a1Xn + a2
and such a law one calls a linear dynamical law. A species of it is, for example, Xn+1 = 3Xn , where, accordingly a1 = 3, a2 = 0 .
From the above given general form of a polynomial dynamical law, which we can consider to represent an Uppergenus, we can derive a number of genera, namely the Linear dynamical laws, the Quadratic dynamical laws, the Cubic dynamical laws, etc. These genera have, as direct subsumpts
( NOTE 75 ), not yet true species, but subgenera. But when we descend along the line general-special we'll finaly arrive at lowest genera.
Every lowest genus consists of one or more species (these latter are thus direct subsumpts of the former). An example of directly (i.e. skipping intermediates) a species
( NOTE 76 ) of the (higher) genus Linear dynamical laws (which genus is : Xn+1 = a1Xn + a2 ) is : Xn+1 = 5Xn + 17 .
As we saw earlier, the genus Cubic polynomials looks like this :
a1Xn3 + a2Xn2 + a3Xn + a4
and the corresponding genus Cubic polynomial dynamical laws looks like this :
Xn+1 = a1Xn3 + a2Xn2 + a3Xn + a4
This genus is a high genus, that is to say that it contains possible subgenera as its (logical) subsumpts.
An example of a highest subgenus (of that genus) is :
Xn+1 = a1Xn3 + a2Xn2 + 14Xn + a4
A lower (and at the same time the lowest possible) subgenus is for example :
Xn+1 = a1Xn3 + 8Xn2 + 12Xn + 2
To the same group of lowest subgenera belongs for example :
Xn+1 = a1Xn3 + Xn2 + 6Xn + 4
To another group of lowest subgenera belongs for example the subgenus:
Xn+1 = 3Xn3 + a2Xn2 + 7Xn + 20
Because in such a (lowest) subgenus there is only one variable coefficient left, specification of it (that is, giving this coefficient a definite numerical value) -- and that is the determination of this (lowest) subgenus -- directly results in a species. The just mentioned subgenus (but of course also all other lowest subgenera) can now also simply be called a genus. It is then the genus of, for example, the following species :
Xn+1 = 3Xn3 + 5Xn2 + 7Xn + 20
Another species of the same genus is for example :
Xn+1 = 3Xn3 + 7Xn2 + 7Xn + 20
Yet another species of this same genus is for example :
Xn+1 = 3Xn3 + 7Xn + 20
where the coefficient of Xn2 is thus equal to 0.
The Quadratic polynomial dynamical laws constitute, as has been said, yet another genus, the genus Quadratic polynomial laws. This genus has the following general form :
Xn+1 = a1Xn2 + a2Xn + a3
A lowest subgenus of it is for example :
Xn+1 = a1Xn2 + 5Xn + 2
A species of that lowest subgenus then is for example :
Xn+1 = 3Xn2 + 5Xn + 2
And another species is for example :
Xn+1 = Xn2 + 5Xn + 2
Another lowest subgenus is for example :
Xn+1 = 2Xn2 + a2Xn + 3
A species of this subgenus is for example :
Xn+1 = 2Xn2 + 18Xn + 3
Yet another species of this same subgenus (which we can simply call genus) is for example :
Xn+1 = 2Xn2 + 3
where a2 has the value 0 ( NOTE 77 ).
We now have, by way of simple examples (of dynamical laws) an idea as to what we should understand by the suppositum ( NOTE 78 ) of a term that is predicated as the predicable genus, with respect to (genera of) true complete beings, and also the suppositum of a term that is predicated as species (also with respect to true complete beings).
If we now inspect the two mentioned species of the genus
Xn+1 = 2Xn2 + a2Xn + 3 (where a2 as coefficient shows the incomplete specification of the Essence),
namely (the species)
Xn+1 = 2Xn2 + 18Xn + 3
and
Xn+1 = 2Xn2 + 3,
then the differences (differentiae specificae) are, respectively : {18} and {0}
(where the notations are done in the form of sets : "{18}" means : "a set containing just one element, namely the number eighteen" ).
Upon generation of the respective Totalities as a result of those dynamical laws (if we assume that we here indeed have to do with Totality-generating dynamical systems), these differences cause phenotypic determinations, such as RATIONAL (in the case of MAN) (these determinations are thus generated).
Such a determination accordingly represents an aspect of the Essence, said differently, such a determination is a phenotypic aspect of the corresponding aspect of the Essence (which itself is genotypic), or, yet in another way formulated, such a determination is the expression of an aspect of the Essence ( = dynamical law, which, as dynamical law of that Totality-generating dynamical system, was (and is) in operation).
Now suppose that Xn+1 = 2Xn2 + 18Xn + 3 is the dynamical law (in its purely mathematical form) of every human individual
( NOTE 79 ). And suppose further that its direct genus is : Xn+1 = 2Xn2 + a2Xn + 3, then the determination RATIONAL would be reducible to {18} (the determination RATIONAL is a certain definite material [and thus phenotypical] substructure of the [brain of the] human body, and this substructure is co-generated by that what is signified by the term {18} [and indirectly by the term 'rational'] ). The term {18} is predicated of the species as the difference :
" Xn+1 = 2Xn2 + 18Xn + 3 ( = species) IS {18} ( = difference) "
where " IS {18}" means : " has its coefficient a2 equal to 18 ",
and where Xn+1 = 2Xn2 + a2Xn + 3 is the genus.
In this proposition the specification of the genus, namely that a2 in this genus is specified to be equal to 18, is predicated of the species (like we say HOMO est RATIONAL). Here "a2 = 18" (or simply "18") can be seen as the name of this particular difference. It signifies directly and explicitly that what precisely in reality is "a2 = 18", and indirectly and implicitly the genus, namely precisely that genus (Xn+1 = 2Xn2 + a2Xn + 3) of which "a2 = 18" is a specification, turning this genus into the species Xn+1 = 2Xn2 + 18Xn + 3.
So if we say that a certain material substructure, 'making the difference' in the sense that it specifically qualifies a given Totality, is generated by that part of the dynamical law which is signified by the difference term (which part of the dynamical law is the part that over-forms or specifies the generic part, and is the '18' in the above example), we must realize that we're here speaking about that what is directly and explicitly signified by the difference term. In fact the difference term in addition refers, but now implicitly so, to the rest of the dynamical law, and thus the mentioned material substructure is generated, not solely by the part of the dynamical law that is explicitly signified by the difference term, but (is generated) by the whole dynamical law, i.e. the (fully) specified generic law (where, then, as a result, this generic law has become the the specific law).
Still to discuss is how to establish the distinction (if there is any) between difference and proprium.
Here we speak about two things, one possessed by another.
But if we want to express the unity of Socrates + nose -- and then we find ourselves in a metaphysical context -- we predicate with IS :
Precisely the same we should do with the mentioned material structures representing the features RATIONAL and CAPABLE OF LAUGHING.
A special part of the dynamical law, namely that part which over-forms (that is, specifies) the generic part of the law, is responsible for the generation of specific and permanent determinations, like, for instance, RATIONAL and CAPABLE OF LAUGHING in MAN. Terms directly referring to such a (specifying) part of the dynamical law (of whatever being) belong in the Predicable difference.
The use we made above of a fictitious and simple dynamical law to indicate the supposita of genus, species and difference, of course embodies a very simplistic representation of the real state of affairs. It only gives a rough simplified analogy of that what really is the case in the constitution of every human individual.
Earlier (in the above mentioned document in First Part of Website) we had found that determinations can in fact be reduced, (1) in some cases to corresponding concrete parts of, or concrete structures in, the Totality, and (2) in other cases to concrete interactions of the Totality with external agents (these latter give the per accidens determinations).
The ultimate form, however, of many such determinations, such as (to be) RATIONAL
( NOTE 81 ) and the like, are high-level features, that is, features residing at a high structural (morphological) level of the given Totality, features which present themselves out into reality, it is true, but are not visible as a definite individual material local substructure, such as Socrates' nose. They are materially scattered all over the Totality, or (scattered) over a more or less large material part of the Totality, and this means that these features are not present anymore at a low level. They are called emergent features or phenomena. Said differently, they are epiphenomena , they are generated on top of the lower morphological levels.
Of course there are also many determinations that reside at a low material level in the form of small parts of the Totality.
C2. Again, the distinction between Difference and Proprium. Genotype and Phenotype. The per accidens nature of Determinations.
Earlier we have distinguished between per accidens determinations and per se determinations of a Totality.
However, Classical Metaphysics holds that all determinations are per accidens, even a proprium
( NOTE 82 ) (which is supposed to accidentally always go along (together) with the Essence).
Now it could be the case that this classical position is correct (or partly correct) after all, namely in virtue of the following reasons :
Determinations belong (according to my revision) to the 'phenotypic' domain or range of a being, that is, they belong to the concretum end of the principle-concretum duality, that is, the duality constituted by a principle and that which is determined by that principle) ( The Essence lies in the 'genotypic' domain or range of a being, and with that it belongs to the principle end of that duality).
Determinations (except those that represent the setting of the Totality with respect to Time and Place) are reducible to concrete parts (sometimes scattered) or concrete structures of the Totality, and thus originate (as to a certain aspect of them) necessarily from the Essence.
But it is possible that such a concrete part or structure later -- that is, after its generation -- becomes damaged, or even -- as a result of such an act of damaging -- totally disappears, without the Essence being changed or destroyed (the latter would mean a substantial change of the Totality into one or more other specifically different Totalities). In this way a given human individual can, as a result of disease or accident, lose certain capacities, without causing the individual to die or lose its identity.
Crystals are more sensitive in this respect (i.e. they are eidetically
( NOTE 83 ) less stable) : A change in chemical composition (except where this is just a substitution of one atomic species by a different but similar atomic species) directly entails a substantial change, that is, the Totality turns into a specifically different Totality
( NOTE 84 ).
Only a substitution of an atomic species for a different but similar atomic species, or the replacement of atomic species, only at the crystal surface, by other atomic species (similar or strongly differing), for instance in the case of a light weathering of the crystal (surface), can be interpreted as just an exchange of a given determination (first case) or just an 'illness' of the crystal (second case) (and thus -- in both cases -- the crystal's specific identity staying the same), and need not be interpreted as a substantial change. The crystal remains what it was. Substitution or (superficial) weathering never involves a macroscopic anatomical part of the crystal (by means of that part being lost or replaced), because crystal doesn't have such parts, it is everywhere (i.e. at every location [larger than its unit cell] in the crystal) the same with respect to structure. So in the case of substitution or weathering the erasion of one or another existing per se determination is out of the question. Rather a determination is exchanged (in the case of substitution), or, in the case of weathering one is added : weathered (Of course we can, before that had happened, say that the crystal had the determination unweathered, but this looks more like a privation of a determination). And the exchange between one particular ratio obtaining between two atomic species (in the crystal) and another such ratio (as such an exchange takes place in substitution) is per accidens with respect to the crystal's Essence. The same applies to the case of superficial weathering : The determination weathered is a per accidens determination, because it is induced by certain external factors that accidentally prevailed, and --ex hypothesi -- having affected the crystal's surface only.
But because a crystal has no (macrocopic) anatomical parts, per se determinations of it cannot (together with these parts) be erased while the Essence remaining the same. The per se determinations are all all-pervading determinations. In a crystal there are, in contrast to organisms, no per se determinations intrinsically connected with certain macroscopic anatomical parts of the crystal (which parts could then get lost) resulting as such in such a 'per se' determination to be in fact -- abeit in a weak sense -- a per accidens determination (like we do see it in the case of RATIONAL or CAPABLE OF LAUGHING). In a crystal it is such that if there are per se determinations at all, then they are genuinely per se determinations. And this is denied in Classical Metaphysics.
In organisms, which always possess (macroscopic) anatomical parts, that can execute certain biological functions, and thus embody certain capacities, matters are, as we saw, different : There per se determinations, if they are embodied in such anatomical parts, can be erased after their initial generation (as we said, as a result of disease or accident), making such determinations (insofar as they are phenotypic) weakly per accidens determinations.
So in complex beings, such as organisms, some per se determinations can -- while the Essence remains the same -- be erased or replaced by other determinations, making these determinations, in a sense (that is, in a very weak sense) per accidens determinations. Such determinations are, among others, RATIONAL and CAPABLE OF LAUGHING : normally they remain -- as specific proprium -- present in the human individual, but they can get lost.
Such changes, as a result of damage of some local structure embodying a proprium, can result in privations, but also in an exchange of functions (the new 'function' is in such cases not always very useful for the organism involved).
Now it is possible to indicate the real distinction between proprium and difference :
While a d i f f e r e n c e can never be erased or exchanged (by another difference) without destroying or changing the Essence of the involved being, a p r o p r i u m can, in some cases, namely some propria in complex beings, be erased or exchanged while the Essence of the involved being remains the same.
A difference (that is, one or another difference) directly refers to the Essence, as Classical Metaphysics asserts to hold, as I have shown above by means of example-laws (i.e. fictitious dynamical laws in their not physically interpreted mathematical form). As long as no substantial change takes place, the Totality (the thing, the being) does not experience an exchange of difference because it does not undergo an exchange of its Essence. The suppositum of the difference belongs to the 'genotypic' domain of the Totality, and is per se with respect to the Essence concerned.
The corresponding local material structure generated by the dynamical law, especially in virtue of its (specific) over-forming, is a determination and as such residing in the 'phenotypic' domain of the thing concerned. This material structure, can, where the causal path between it and the dynamical law is long, be erased or exchanged, making, as has been said, this determination a per accidens determination in a weak sense. Because the difference is a part of the dynamical law of the Totality it is, as the dynamical law itself, an all-pervading formal content, that is a content that is everywhere present in the Totality, it cannot be erased or exchanged by the destruction of some material part of that Totality.
A proprium (that is, one or another proprium) always refers to a determination (as Classical metaphysics also holds), and therefore it always refers to something in the phenotypic domain of the Totality.
While the signification of a given difference goes all the way down to the dynamical law (that is, to the Essence of the Totality), the signification of a given proprium halts at the corresponding local material structure, that is, it remains in the phenotypic domain of the Totality.
The local material structure, which is the significatum of the given proprium, can, where the causal path between it and the dynamical law is long, be erased or exchanged, making also this determination a per accidens determination in a weak sense.
If the proprium happens to be an all-pervading formal content of the Totality, it cannot be erased or exchanged by the destruction of some material part of that Totality.
We can illustrate the case of non-erasable or non-exchangeable determinations by looking at crystals :
In crystals there is -- as in all simple beings -- a much shorter path of dependency between the genotypic domain (the dynamical law, or Essence) and the phenotypic domain of the Totality (that is, the individual crystal).
The Space Group of a given crystal is, as expounded in First Part of Website, the description of the total symmetry of the crystal, thus including that symmetry which is visible only at the microscopic level. From this it is evident that the Space Group of a given crystal is a (qualitative) determination (and thus residing in the phenotypic domain of the crystal). This determination is, however, an all-pervading determination, that is, a determination that is present everywhere in the crystal. So it is not connected with one or another particular concrete part of the crystal. It is connected with the whole crystal individual. The Space Group concerned remains the same in all growing stages of a given individual crystal, but a number of other crystal species possess the same Space Group (that is, have the same total symmetry). So the Space Group is a generic proprium.
Something similar can be said about the Chemical Composition of a given crystal. It can also be considered as a (qualitative) determination of the crystal. It is also an all-pervading determination, and also residing in the phenotypical domain of the crystal. And, like the Space Group, it is a generic proprium, because other crystal species can have the same chemical composition.
The Space Group PLUS Chemical Composition (S + C) also remains the same in all growing stages of the given crystal, but does not as such occur in any other crystal species.
And of course also S + C is phenotypic, and therefore a determination (and thus it is not the Essence itself, it is generated by the Essence). So we can consider S + C to represent a proprium, namely a s p e c i f i c proprium.
Hoewever, S + C is an all-pervading determination and cannot, therefore, as such be destroyed or exchanged while the dynamical law (the Essence) remains the same (as, in contradistinction to this, is so with respect to RATIONAL and CAPABLE OF LAUGHING in the case of a human individual, because in a human individual the causal path leading from the dynamical law to the corresponding local material structures, respectively embodying these features, is much longer than the corresponding path is in crystals and other simple beings).
S + C (Space Group plus Chemical Composition in crystals) evidently is a direct consequence of the dynamical law (which here is the relevant crystallization law).
S + C is the immediate (phenotypical) expression of the Essence of the given crystal.
Consequently, the proprium S + C (or, expressed better, the suppositum of the proprium S + C [where S, as well as C is named, and thus where "S + C" is a term] ) is a genuinely per se determination , and not a per accidens determination in any sense.
So indeed there exist propria that are truly per se with respect to the Essence of the given Totality, at least in crystals
( NOTE 85 ).
And, as we have seen in the NOTE just given, also organisms have such truly per se propria, namely in the form of their specific DNA structure, in addition to not truly per se propria, such as RATIONAL and CAPABLE OF LAUGHING.
Let's summarize these findings.
Figure above : Causal connections between the dynamical law, DNA instructions, DNA chemical structure, generated material structures, and high-level features.
The complete set of DNA instructions forms the pen-ultimate dymamical law of the given organism.
In the next document we will continue with the Predicables, and reconsider them within a mereotopological framework, that is, we consider a given genus, species, difference, proprium, and accidens in terms of parts and boundaries, in this way supplementing our understanding of them.
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