Wednesday, January 13, 2010

Theoremata Scoti, Partes I-V

Pars I

The first part of Scotus' infamous Theoremata is concerned with the universal, and its relation to the singular existent on the one hand and the intellect on the other hand. There are six main propositions, with explanations and--as always with Scotus--some rabbit trails. This preliminary study will be English-only, since I don't feel like typing in the Latin (hey, if you want real scholarship, read a print journal!), but for the record I'm using as my text Vol. II of Scotus' Opera Philosophica.

I. The intelligible precedes intellection by nature.

"Which is because reception [passio] presupposes an agent and every action is about something." If we are to understand something there must be something to understand. The intellect does not create all of its own intelligible content, any more than the sense power creates the objects of the senses: sight presupposes the visible object as well as light and a working eye. Unlike sight, of course, the intellect can create some of its intelligible content.

II. It is impossible for the first intelligible to be caused by intellection.

"Which is from comparing intellection and the intelligible to the same intellect." Even if the intellect received no information from outside itself it would still have to understand something other than its own concepts: no intellect could know nothing but logic. The intellect itself is an intelligible object before it understands or is understood.

III. We understand the universal first.

Scotus spends a lot of time arguing this point. Unlike, say, Thomas, Scotus admits that the singular is intelligible per se, since for him singularity is a formal property, not some material detritus. Why then is the singular not the first intelligible object? After all, it is the singular thing which acts, not its abstracted universal nature, and so the singular should be the first thing to act on the intellect. Scotus reminds us, however, that there is for us no science of the singular, that the intellect forms a universal by separating the intelligible nature from the leftover singularity. "It is true [that it is the singular which acts], but not insofar as it is singular. For the nature is the ratio of acting." Just as in natural generation the species is multiplied, but not the individual, so in cognition the singular gives rise to an intelligible universal, not a proper concept of the singular.

Our lack of knowledge about the singular per se is neither because we fail to actualize our capacity for it, nor because the singular is unintelligible per se, but because our intellect is too imperfect to achieve it. Just as an intrinsically visible object might not be seen by feeble eyes in weak candlelight, the light of our intellect is strong enough to illumine the nature but not the singularity. Our knowledge then is always imperfect. "For although in a precise comparison the nature is a more perfect knowable than the singularity, nevertheless the cognition of a singular nature is more perfect than that of the nature alone, because it is more distinct."

Scotus goes on to discuss possible reasons for this weakness of the intellect at some length, with more comparisons to the sense powers.

IV. To any universal there corresponds in reality [in re] some grade of entity, in which the things contained under the universal itself coincide.

Scotus says this should be clear from I. and II. For if the universal is not created by the intellect then it must have something corresponding to it in reality. This correspondence is not fictional, but real, or else there could be no true quidditative predication and metaphysics would not differ from logic.

V. In essential predication it is impossible to go to infinity.

Otherwise nothing would be knowable, since we can't pass through an infinite series, nor can our finite intellect apprehend an infinite series all at once. Definition has a limit, and we can really know what something is, even if only confusedly.

VI. It is simply impossible for the first and most universal to be plural.

There cannot be a plurality of first and most universal concepts or grades of entity. In analyzing we always proceed to the simpler concept, and therefore eventually to the first and simplest. And as in any order it is impossible to find two firsts, it is even more so in the highest order, to which multitude is more repugnant.

To conclude:
I. The universal, although produced by the agent intellect, is strictly speaking not caused by it, because something in reality corresponds to it. II. That universal, insofar as it has being in something or with something singular, we first understand as a kind of primary whole object, although the intellect from its imperfection can per se understand the nature as a quasi-part of the primary whole object, and can distinguish this from that [i.e., can distinguish the nature as such from the whole object], while not conceiving the other part, namely the singularity.--For which intellection the action of the agent intellect is required. Whence any part of the first whole object can be first for the intellect, and afterwards the intellect can per se distinguish it from another. Whence a child first distinguishes his father from non-man, then from non-father.

Pars II The second part of the Theoremata is concerned with showing the priority of quality over quantity. I note that, if we accept this, there are some interesting implications for the sciences. Mathematical physics, our paradigm modern science, is primarily concerned with what can be quantified, but for Scotus quantity and the quantifiable are not primary substantial traits.

The editors of the new edition number four main conclusions. Why these propositions are called conclusions in Part II and propositions in Part I is unclear to me. In any case:

I. Quality is naturally prior to quantity.

"Because [quality] is found in every substance, but quantity only in corporeal substances." Quantity can be attributed to separated souls, angels, and so forth, only insofar as they are numerable, i.e. insofar as we can mentally collect them into multitudes. In himself an angel has no dimensive quantity, since he has no dimensions.

"Quality is in substance by reason of form, quantity by reason of matter." Form is primary over matter, ergo, etc. Note that this would not be accepted by earlier Franciscans who would admit matter in the angels, but not dimensive quantity, which they would attribute to corporeitas.

"Again, quality is the principle of acting, quantity [is] not. Quality is that by which an agent alters [something]. But alteration precedes augment[ation]. It is impossible for quantity to be induced except through the action of quality, [but] not conversely."

II. Qualities are attributed to God as perfections, not so quantities.

That is, some quality can be seen as a pure perfection, and when existing in an infinite mode can be identified with God himself. For any quantity, however, this is simply nonsense. There cannot be an actually infinite quantity.

III. Qualities have many species in both spiritual and corporeal [things], as light, etc., by which entities attain their ends, as man [attains] beatitude through grace and charity, etc. But continuous quantity has only three species and no being attains its end through it.

This is losing the pithy aphoristic edge a bit, but is there a shorter way to say it? Since quality pertains to the form more than quantity, one can see how it helps to attain a thing's end. No thing attains its end, however, merely or primarily by being a certain size, mass, etc., even if a certain quantity is a sine qua non of its natural perfection. Quantity is of the same sort for everything; it's general, not specific. In other words:

"[Quantity] accompanies any species according to its actuality, not so quantity. According to it is the order of the universe and natural place and motion and rest. According to them as objects are distinguished the powers of the soul."

IV. A being has more perfect [quality] the more perfect it is. Not so with quantity. Neither an angel nor a man has as much quantity as the earth does.

A more perfect tree has more perfect flourishing. A more perfect man has more perfect intelligence. But if my quantity were to increase much I would get less perfect, not more!

This covers about the first third of Part II. The rest is devoted to what I called in my last post one of Scotus' frequent rabbit-trails. Not because they're pointless, but because they lead you down into a hole. Like the rabbit-hole in Alice in Wonderland, Scotus' digressions can sometimes wander into a wonderland of argumentation, in which everything is brilliant and stuffed to the rafters with things to consider, but you never know quite where you are, who's talking, how things got so tangled up, or what's at stake. So here. After the discussion of quality and quantity Scotus starts thinking about accidental inherence in general and asks, "What can be the subject of an accident?" Not God, since he is completely perfect and so not in potentiality to receive new forms. Only things with some perfection--i.e. per se actual existence--and some imperfection can be the subject of accidents. He then considers arguments that 1) substantial form, 2) accidental form, 3) matter, and 4) angels don't meet these criteria, before opposing them.

Pars III

Part three of the Theoremata is divided into subsections, labeled by the editors "A" and "B". These appear to be two versions or two drafts of the same train of thought: Scotus gives some definitions, draws some corollaries, and makes some conclusions, all about conceptual analysis. Then he starts over with the same material, but takes it in another direction. This post looks at the first subsection.

Definition 1: I call that which terminates the act of understanding a concept.

"A concept is called either "object" or "intelligible" or "intellected" [intellectum] or "intention". The first is most common, because [it pertains] to all [intelligible] potencies. The second is common, because [it pertains] to the object understood either in potency or in act. The third is proper [i.e. is properly a concept]. The fourth is how the Arabs Avicenna and Averroes understand it. But just as "intention" is said equivocally of the object and of the act, so also is "concept". But here I take it to be the object."

Definition 2: That is said to be conceived first which is adequated to the intellect.

Scotus explains that by adequation he means that in the "first" concept what is understood is the whole object, not some part of the object.

Definition 3: Whatever is essentially included in the first concept is conceived per se.

For instance, whenever a species is conceived its genus is automatically conceived per se, and so for similar cases. When I conceived of "triangle" I also ipso facto conceive of "figure".

Definition 4: That and only that is perfectly conceived, of which nothing is concealed which is essentially included in it.

"'Perfect' is here understood [to mean] the act, not insofar as it is elicited from its potency, but insofar as it is compared to its object, namely so that nothing intrinsic to the object is unknown, in whatever mode it is being known."

Definition 5: A concept which cannot be analyzed into [simpler] concepts is simply simple.

Definition 6: A concept which is per se one, yet is analyzable into [simpler] concepts, is not simply simple.

For example: "triangle" can be analyzed into simpler concepts, namely "figure", "side", "three", etc. It is a simple concept--it can be grasped as a per se whole--but it isn't simple simpliciter.

Corollary: Therefore "essentially" belongs to more than is said "in quid".

Scotus next offers two premises establishing or assuming that his definitions have actual counterparts. There is something which can be conceived first and perfectly, and there are some concepts which are distinct.

From all the foregoing Scotus now draws several conclusions and corollaries:

Conclusion 1: The analysis of concepts has a stopping-point [status].

Here Scotus inserts a brief discussion of the inability of a finite power, such as the human mind, either to grasp infinites all at once or to be able to run through an infinite series. This is relevant to the following conclusions.

Conclusion 2: No concept [which is] one "in quid" can be predicated of all others.

There is no concept--call it a--which designates "what" something is as a whole which can be predicated of every other such concept. There is no common "what" under which every such concept can be subsumed. This is because, if there were, no other concept other than this hypothetical one a would be simply simple as defined above, since every other concept would include a as a factor or constituent. Therefore one and the same concept--every concept except for a--would include a concept of an infinite in itself, or rather would include actual infinities. For any concept other than a would include both a and something else, and that something else would include a and something else, and so on to infinity.

In addition to this argument Scotus offers two more for the same point.

Corollary: There is nothing in common between the concept of a genus and a difference, nor does one include the other; similarly with matter and form.

"Figure" does not include "Three Sides", when the difference "Three Sides" is added to "Figure" to produce "Triangle". We can't define "Triangle" as "Three-sided Figure with three sides". And so forth.

Another Corollary: Nor is a superior difference, which is included in a genus, included in an inferior difference. Otherwise definition would be pointless [nugatio] and there would be a progression to infinity with difference, because they would differ by their own differences.

This point is similar to the last one. "Animal" cannot include "Rational" and "Rational" cannot include "Animal", since the one is determinable by the other and vice versa.

Conclusion 3: The analysis of concepts will come to a stop at some first [concepts].

Definitions, etc., must be in terms of things which are themselves not reducible to something.

Corollary: a determining and a determinable never include one concept, nor does one of them include the concept of the other per se.

As though it follows from the foregoing, Scotus finishes this subsection, without further explanation or argument, with a conclusion which seems to contradict the theory of conceptual univocity which he holds elsewhere:

Conclusion 5: No identical concept is per se common to the created and the uncreated.

What to make of all this? Stay tuned for more!

* * *

In Theoremata Part III, section B, Scotus starts in the same place as in section A, with the definition of the concept. Here, however, the treatment is fuller and soon veers off down an alternative path. This sort of thing is not unprecedented elsewhere in Scotus' works. It appears that more than once he will begin a treatment of a topic, change his mind about how he wants to approach it, and start over. But because of the unfinished state in which he left so many of his works, both versions end up in posthumous editions of the book as though they were distinct parts. For another example, see the QQ. In Metaphysical VII, questions 14 and 15.

All right, beginning again with the definition of a concept:

I call a concept an object understood in act, namely as it is in the intellect, not as the form [exists in itself], but as it is in the act of thought [in esse cognitum].

"Here 'to be in' is nothing except having an actual relation to the intellect, or the intellect [having an actual relation] to it, or either to either."

It's clear that Scotus is trying to be more clear here than in the parallel definition in section A. The follow-up explanation in part A was about terminology, but here instead Scotus goes on to define subsets of concepts, perhaps a more useful task. He divides concepts into several varieties and explains their differences:

"Every concept [which is] per se one is either altogether simple--that is, of which either nothing is conceived, or else the whole is--or it is not altogether simple, but rather incomplex." *{Interpolated note: That is, it is not composed of potency and act, as [for instance in the concept] of an infinite being.} "Infinite being" is not simple, because I can conceive "Infinite" and "Being" separately, but it's not a complex concept either, since "Infinite" is not exactly a determining characteristic of "Being"--since the latter, after all, is neither a genus nor in a genus.

"A concept is called analyzable, when it essentially includes several concepts, of which one can be conceived without the whole." For instance, "Triangle" can be analyzed into "Three" and "Plane Figure", etc., which can be conceived apart from "Triangle".

"Of concepts which are not per se one, [there are some] which are called aggregate, such as 'white man'; and about a fourth kind, called complex, and a fifth, called discursive, see below."

Now Scotus adds some remarks about how these varieties of concepts are related to one another.

"Every concept [can be] compared to any [which is] not altogether the same as itself: either it is primarily diverse from itk, if it agrees with it in no concept; or different, if it agrees in something and differs in something; or ordered, for instance if one whole [concept] includes another, but not conversely, the one is called including and the other included. Only an analyzable concept can be different [in the just-defined sense] and can include primarily diverse [concepts]; and an included one can itself be either simple or analyzable."

See? That's much more thorough! But the second definition is identical to its counterpart in section A:

Definition 2: That is said to be conceived first which is adequated to the intellect.

The third definition is going in the same direction as its counterpart, but is less clear and making a slightly different point:

Definition 3: Whatever is included in the primary [object] understood is per se not primary.

The fourth definition is similar to its counterpart but formulated differently:

Definition 4: [Something is] perfectly known on the part of the object when nothing pertaining to the object lies concealed.

And two corollaries:

Corollary: Therefore a simple [object], if it is conceived, is conceived perfectly. [Second corollary:] An analyzable [concept] may happen to be conceived imperfectly.

At this point Scotus starts doing something different than in section A. There are no new versions of definitions 5 and 6, but rather than moving directly to his conclusions, there's some additional business. After explicitly making the assumption that there are in fact some analyzable concepts, he looks in some more detail at how the different varieties of concepts are related to each other.

"Some concepts are not included [in others], such as the concepts of all singulars and lone [objects]. All others are included in these and are abstracted by analyzing from these." There follows an interpolated note, to the effect that things are conceived by us confusedly before being conceived distinctly. The main text goes on to say that something is conceived distinctly when conceived according to the way it is distinguished from other things; but is conceived confusedly when indistinctly. Therefore not everything which is not a first or primary object is conceived confusedly, because (for instance) a genus is conceived as distinctly in the concept of a definition as it is per se, yet then it is not conceived primarily, but the definition is primary.

Here Scotus reminds of the principle that "everything per se one and not simple is [contituted] from act and potency or from matter and form." He indicates that this is Aristotelian boilerplate, before going on to draw the following conclusion:

There is some unique and simple act of any composite.

"From that [act] is the unity of the composite in itself and [its] distinction from something else. For the act distinguishes, therefore it is proper. But it is unique, because anything belonging to the composite is potential with respect to it and so is not the act of this composite, although with respect to anything else in the composite it can be called an act. For the some [reason it is] simple; otherwise something belonging to it would be a further act."

Now Scotus seems to be wandering away from conceptual analysis and just doing straightforward metaphysics; for this reason the editors don't number this conclusion with the ones he draws from the definitions. But since this seems like enough for one post already, I will save the conclusions proper for the next sequel.

* * *

Pars IV

The fourth part of Scotus' Theoremata contains little worthy of comment. It consists of a (largely scattered and unconnected) series of notes on some of the questions in books VIII and IX of Scotus' QQ in Metaphysicam. The notes are mostly about the construction of a composite substance, the causes of its constituents and of the whole, and of the causation effected by each. There are no settled conclusions and no immediately discernible order in the notes, and so I'm going to omit any translation from the text.

Part IV supports what I've been suspecting about the nature of the Theoremata, namely that it seems to be a set of--not drafts, exactly--but of preliminary studies on questions that interest Scotus and which he discusses at much more length elsewhere. He's working out in a systematic way the consequences of various approaches to the problems set out in the various parts. Because of this none of it should be taken as Scotus' final word on anything without confirmation from one of the more authoritative works.

This sketch of an interpretation is particularly relevant for how to approach part V, which contains much of interest and which is very disconcerting at first. We'll see tomorrow how plausible it is.

Pars V

art five of Bl. Duns Scotus' Theoremata is a kind of deconstruction of natural theology. In it he attempts to find the fundamental principles upon which natural theology rests and shows how the whole edifice comes tumbling down if those principles are not sufficiently rigorously established.

The context in which we should understand this part seems to me to be clarified by a remark Allan Wolter makes in the Preface to his edition of Scotus' De primo principio, namely that this latter work "may be the most carefully thought out attempt of any schoolman to prove the existence of God within the epistemic norms for demonstration laid down in Aristotle's Posterior Analytics." Anyone familiar with that work will appreciate the justice of that remark, as well as the nature of Scotus' project in proving God's existence and attributes. For the subtle doctor is not satisfied with providing "reasons" to accept God's existence or "ways" by which it can be proved; he wants to provide a really rigorous demonstration, one which if properly grasped will give the human mind certain knowledge.

The fifth part here is jumbled. It is clearly divided into three parts, but the parts seem to have been mixed up, with the apparent beginning only coming in around paragraph 70 in the critical edition, and the final third seeming to be put first. Paragraph 70 is where I start.

Assumption 1: In essentially ordered things one must posit a first, which is unique in that ordered series, and cotemporal with it.

Assumption 2: There is an essential order in every kind of cause.

These are called "assumptions" here, because the ability to prove them is precisely what is called into doubt in this part, although it is on these principles that, for Scotus, natural theology--knowledge about God which cam be proved from natural things and insofar as he is the cause of things known to us--rests. Of course they are not "assumptions" for Scotus absolutely, because he spends a lot of time in other works trying to prove them. But here he says, "These two propositions are assumed, of which the first has three parts [i.e. that God is 1) first, 2) unique, 3) cotemporal with his creation], [but] the second is simple. But although either of these parts, namely 'first', 'unique', [and 'cotemporal'], may be probable, still it would be difficult or perhaps impossible for us to prove it simpliciter by necessary argument and by purely natural [reason]."

Conclusion 1: In the genus of efficient cause one must posit a unique first efficient [cause], which exists now in the nature of things.

This follows from the two assumptions, and this cause is called God.

Conclusion 2: Every efficient [cause] is more perfect than its effect or equally perfect, because nothing acts to a greater extent than it is in act.

Conclusion 3: God is more perfect than every effect.

From Conclusions 1 and 2. If God is the cause of everything else he must be at least as perfect as everything else.

Corollary: And so [God] is the most perfect of all and the highest in every difference of being, which simply implies a perfection, among which are one, true, good, necessary etc., because whatever is such is simply a perfection in some way . . . Put here the boundary of wha tis knowable about God by natural necessary reason; and this is supposing those first two assumptions.

This is classic scotism, showing that natural theology is developed by showing that God must contain in a supereminent way all pure perfections. But the conclusions are only as solid as the ground they're built on, and Scotus now begins to explore the difficulty with providing true demonstrations of natural theology's foundations.

How can the first part of the first [assumption] be proved, namely [that God is] "first" more in essentially ordered causes than [in] accidentally [ordered ones] [since in accidentally ordered causes there is no first cause simpliciter]? How can the second part by proved, [that God is] "unique"? How can it be proved [that God is] "cotemporal?

A primary difficulty that Scotus brings up here is how can it be proved by demonstrative arguments that the God who created the world--the temporally "first" cause--is the same as the principle which stands at the head of the chain of essentially ordered causes in the world now? How do you prove that the creaturely order of secondary causes need to be conserved in being by the first cause, even after their initial creation? Scotus sees that the Big Bang does not prove that God exists now, but only that there was an first cause in the sense of an initial one. Our impulse, of course, is to appeal to God's eternity or immutability, but if the foundations of natural theology haven't been secured yet, we can't appeal to its posterior conclusions. And if we can't prove that the initial cause is identical with whatever is the current "first" [in the ontological, not the temporal sense], then what happens to our natural certainty that God is "one" and "unique"?

The second assumption does not seem to be proved necessarily. For if many effects are so coordinated among themselves, so that none of them has the character of an effect with respect to another--as with a cow and an ass--why are all causes so ordered, that the first [in one causal chain] is always the cause of another [causal chain]? If this name "God" is given to some numerically identical first efficient [cause], it follows from this that it cannot be proved that God exists in the real world now, because if he no longer existed the coordination [of causes in the world] would remain through another [first cause, another God] univocal with him.

Again, remember that Scotus has not yet made his argument for the incompossibility of two first causes, because in this work the conceptual apparatus with which to do so hasn't been developed yet. From comments he makes later on it seems that what Scotus is showing what kinds of problems a thinker proceeding along Aristotelian lines, with principles and arguments from the Physics, is going to run into.

Beyond this, Scotus continues, the second assumption does not prove that any God exists, even a new one like the first, if it cannot be proved that conservation of the created order is needed as much as the original act of creation. Otherwise we can only conclude that a first cause is necessary for the world's becoming, not for its being. Whence it follows only that either exists or did exist once, as from a house it can be proved that a builder exists or did exist once.

Therefore these things, which it seems cannot be proved by necessary arguments from merely natural [reason], are laid out in order in the conclusions, as well as some others which cannot be proved.

That is, if these primary propositions of natural theology turn out to be unprovable, so are whatever less known propositions which follow from them and depend on them.

I omit any detailed discussion of the rest of Part V, in which Scotus lays out the "unprovable" conclusions systematically. It's rather horrible reading, a kind of anti-Contra gentiles in which Scotus insists at great length that unless he who builds metaphysical systems builds his house upon the rock, he labors in vain that builds it.

In any case, the problems that he lays out here are not solved here. The reader must go to the De primo principio or other theological writings to see how Scotus deals with them. As I said yesterday, what seems to emerge is that the Theoremata is a kind of testing-ground where Scotus is working out the consequences of different approaches before giving them a more authoritative treatment elsewhere.

* * *

This series on the Theoremata is incomplete. I may or may not someday get around to bloganalyzing the other parts.

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