The higher levels are genera (e.g. animal is a genus), the lower are species (e.g. man is a species). According to Aristotle, being at the top of the tree is not a genus: the ten categories at the second level of this diagram are the highest genera. Also, note that Socrates and Plato, at the bottom, are not distinct species: they share the same specific nature, they have the same definition. So the lowest species in that part of the diagram is man.
Species of the same genus are distinguished from one another by specific differences: man is differentiated from other species of animals by being rational. The lowest species (below which there are only individuals sharing the same specific nature) was called the lowest or ultimate species, and the difference distinctive of an ultimate species is called an ultimate difference. According to Scotus the individuals of an ultimate species are differentiated from one another by what he calls an individuating difference, or "Thisness", in Latin haeceitas (haec meaning "this", -eitas being the termination corresponding to our "-ness" to form an abstract noun). Going upwards through the diagram there are "differences" at each level at which sub-division occurs: for example, animal is differentiated from other sub-genera of living bodies by being sentient. A definition combines genus with difference. You can define man as a rational animal, "rational" being the difference, "animal" the genus. Or you can combine some or all of the intermediate differences with a higher or the highest genus. You could define man as a material, living, sentient, rational substance. Substance is the highest genus, material, living etc. are differences dividing and sub-dividing the genus, and rational is the ultimate difference differentiating the ultimate species.
Is everything good? According to the scholastics (following Augustine, who was following Plotinus) everything is good insofar as it is real. Evil is a lack of some reality or perfection that should be there. So goodness and being are coextensive--whatever can be called in some way a being is good.
Are things true? According to Aristotle and most modern philosophers, only statements can be true or false. But Anselm, in a little book called Of Truth, convinced medieval thinkers that there is a wider sense in which things also can be said to be true: the sense is which we might say that something is a genuine so-and-so, or that it is true to its type.
Is every being one? According to the neo-Platonists everything is either absolutely simple (and thus absolutely one), or else it consists of many part or elements that have to be unified, held together somehow to keep the thing in being. (See Proclus in PHIL252 Supplement, p.105.) So every being is one either of itself or by being unified.
Another transcendental is res or thing: every reality is a thing. (Our word "reality" comes from "res".) In English I don't think we say that every reality is a thing: "thing" in English applies only what the Aristotelians called substances, i.e. independently existing things, are things. But the scholastics used res more widely, to say for example that a thing's whiteness is a thing: qualities are things inhering in substance-things.
To summarise the doctrine of transcendentals, every being is a thing, is one, is true, is good: these terms are coextensive--whatever comes under one comes under all the others, and like being they all apply to everything coming under any of the ten highest genera. Among the materials distributed at the beginning of the course was an extract from Thomas Aquinas, On Truth; the extracts give Thomas Aquinas's treatment of the transcendentals. Pause the tape while you read those extracts.
Besides the mutually convertible transcendentals we've just been talking about (whatever is any of them is also each of the others, so they are coextensive), Duns Scotus recognised other disjunctive transcendentals: that is an either-or pair of terms, one or the other of which is applicable to any being whatsoever, and thus coextensive in disjunction with being, thing, one, etc. These pairs include finite-infinite, necessary-contingent, simple-composite.
Although the transcendentals are mutually convertible (singly or in disjunction), they are not synonymous. Being, one, true, etc. have different meanings, i.e. there are differences distinguishing the transcendentals from one another. So besides the ultimate differences distinguishing the ultimate species, and (on Scotus's view) the individuating differences, and the various other differences that sub-divide the ten genera, there are also the differences that distinguish the transcendentals from one other. There are also the differences that distinguish ten supreme genera, the different ways of being. For example, independence of being differentiates substance from the nine other categories.
Why must some propositions be evident without proof? Suppose you offer an argument to prove something, then I challenge the premisses of your argument, and you produce more arguments to prove those premisses, and I question some of the premisses of those arguments, and so on. Aristotle says that you can't go on forever producing premisses for arguments to prove the premisses of arguments, etc., etc.: if any proof is to succeed, there must be premisses that don't need proof, premisses that are self-evident.
Similarly, if you define something, and I ask for definitions of some of the terms used in your definition, you will define those terms in other terms; I may ask for definitions of those; and so on. But there must be concepts that a person can understand without definition: otherwise nothing could ever be defined.. According to Scotus, simply simple concepts are not explainable by analysis or definition; they cannot be defined, but they don't need to be.
Before we return to Scotus's text there are a few more preliminaries. First, the ultimate premisses, the self-evident propositions that need no proof, the medievals said were per se nota, meaning evident or known ("nota") through themselves ("per se"), not through some other proposition functioning as a premiss in a proof. They distinguished several kinds of perseity; we'll come back to this point in a minute.
The whole quiddity, or any part of the quiddity, was said to be predicated quidditatively, or in quid. Thus if you say "Socrates is human" or "Socrates is an animal", or "Socrates is rational", these are quidditative predications, in which some or all of what answers the question "What is it?" is affirmed of it.
According to the Aristotelians there are characteristics implicit in the essence but nevertheless not part of it. For example, a rational animal has a sense of humour, is capable of laughing at what reason recognises as incongruity. To have a sense of humour is not part of the essence of a rational animal but is necessarily connected with it. Such a characteristic is called a property. Other things outside the essence and not necessarily connected with it are accidents, like being white or being short. A predication in which the predicate is a property, e.g. "Socrates has a sense of humour", or an accident, e.g. "Socrates is white" or "musical", is not quidditative. (Hyman and Walsh use "definitionally" for "quidditatively".)
First, there are the propositions that modern philosophy calls analytic, such as "every bachelor is unmarried", which is true, as we might say, by definition of the terms. Substitute the definition of bachelor for the word bachelor, and the proposition becomes: "Every unmarried man is unmarried". In Aristotle's language, these are propositions in which the predicate is part of the definition of the subject. Another example is: "Every man is rational", equivalent (when you substitute the definition) to "Every rational animal is rational".
The second kind of per se proposition is one in which the subject is part of the definition of the predicate or of something presupposed to the predicate--e.g. "Some substance is rational", which is true because man is a rational etc. substance. The predicate, rational, presupposes something, in this case man, of which substance is predicable per se in the first way. See Aristotle, Posterior Analytics, I.4, 73a35-73b. Another example of the second sort of per seity: "Every number is either odd or even". Only numbers can be odd or even, so number is part of the definition of odd, and also of even.
When the subject of the proposition is part of the definition of the predicate the proposition is per se in the second way. When the predicate is a part of the definition of the subject, the proposition is per se inx the first way. In both cases the scholastics said that the predicate was "contained in" the subject. In a proposition per se in the first way, the subject contains the predicate quidditatively or essentially, because the predicate is the whole or a part of the quiddity or essence; the predication is in quid. If you substitute the whole definition for the subject, you will see the predicate terms in it, "contained" in it--every rational animal is rational.
In a proposition per se in the second way, they said that the predicate is contained in the subject, but this time "virtually"--meaning that if you divide the subject (in constructing a porphyrian tree), the predicate will eventually turn up as one of the sub-divisions, or as a difference distinguishing one of the sub-divisions. Thus in the proposition (which is per se in the second way), "Some substance is rational", "rational" is virtually contained in substance because the division of substance will eventually come to a sub-genus or species of which rational is the difference. "Every number is odd or even" is per se in the second way, and if you divide the subject number, one of the subdivisions will be into odd and even. So with a per se proposition of the first kind, the predicate is contained in the subject in the sense that if you substitute the definition of the subject for the subject you will find the predicate as one of the terms of this definition--"Every rational animal is rational". With per se propositions of the second kind the predicate is contained, as they said, virtually in the subject, meaning that if you divide and subdivide the subject you will come (immediately or eventually) to the predicate as a sub-genus or species or difference. "Virtually" is not a very illuminating word. Concepts in this odd sense "virtually" contained are "found under" what contains them, as a sub-heading in a porphyrian tree, but not found in the concept of the subject when you spell out its definition.
On "what the univocity of being is", compare the top paragraph on p. 562.
Some comments on p. 575. He says, "As to the first, I say that being is not univocally predicated definitionally [i.e. quidditatively, as part of the quiddity] of ... ultimate differentiae [differences], nor of the proper attributes of being itself". By the proper attributes of being he means the transcendentals: so being is not predicated, as part of their definition, either of the ultimate differences (such as "rational", the ultimate difference characteristic of man, an ultimate species) or of the transcendentals--one, true, good, etc. The ultimate differences and the transcendentals are "simply simple" concepts that do not have any definition, so it is not possible to predicate of them part of their definition. Thus you can't say that "rational" is a being that has some differentiating character, because rational is not a being, it is what ultimately differentiates some beings from others. At the other end of the scale, with the transcendentals, which are coextensive with being (either singly, or in disjunctive pairs) you can't say that The One is a being that has some differentiating character, because there are no beings that do not have this transcendental character of oneness.
To recapitulate: quidditative predication (or "definitional" predication in the terminology of this translation) means that "S is P" where P is part or the whole of the definition of S--e.g. "Man is rational" or "Man is animal", assuming that man is defined as a rational animal. Now ultimate differences do not have definitions of the form "such-and-such being" ("rational being"), and neither do the transcendentals. So you can't say "S is a being" where S is an ultimate difference or a transcendental ("rational is a being", "one is a being").
Now read the second argument, in the paragraph beginning "second". Some comments. According to the Aristotelians, if a being is composite it will nevertheless be well unified if its components are related as potency and act: e.g. if one is form which so to speak shapes the other as matter--the matter and its form constitute a close unity, an "essential" unity. Contrast this with the looser unity of something that consists of two parcels of matter each with its own form--this is a juxtaposition of two beings, not one composite unified being. The Aristotelians called this an accidental unity. Artifacts are accidental unities: a house, for example, consists of many distinct entities (bits of wood, bricks, etc.) juxtaposed in an organised way. A social body is an accidental unity: the individual persons that make it up are distinct individual entities. Individual persons, rational substances, on the other hand, are essential unities; their parts are related as matter and form and constitute a close unity.
Similarly, Scotus says, a complex concept is unified if its constituents are not merely juxtaposed but are related as quasi-form and quasi-matter--as determinable (or "shapeable") and determining: linguistically, as noun and adjective. Thus "rational animal" ("rational" being an adjective, "animal" a noun) is an essential unity, in which the generic concept animal is "determined" to this species of animal by the determining difference, rational.
The word "primarily" in the middle of the paragraph translates primo, a technical term that can be explained perhaps as meaning "by virtue of being precisely that". For example, if you say that the interior angles of an isosceles triangle add to 180 degrees, that does not hold primo of isosceles triangle, since it is true of an isosceles triangle not by virtue of being that, of being an isosceles triangle, but by virtue of being a triangle. See Aristotle, Posterior Analytics I. 4, 5, 73 b25ff (in the material distributed). So by "primarily diverse" Scotus means different by virtue of being what they are, and not by virtue of including some differentiating part. Notice in the third last line of p.575 the word "resolution"; this is the process of analysing concepts (or anything else) into parts not further analysable.
Being is sufficiently divided into created and uncreated, and created into the ten categories and their sub-genera and species. "Definitional" division means division into essential parts by differing definitions. So what Scotus is saying in this paragraph is that the transcendentals, such as "one", "finite", "infinite", are not kinds of being, genera or species of being, since the transcendentals are coextensive with being--everything that can be called a being can be called "one", etc.
Turn back to p.575, to the paragraph beginning "I reply to the question", and re-read the last sentence. He has clarified what the univocity of being is and to what (i.e. to or of what it is predicable): being is predicable of all the kinds of being--created and uncreated, and, under the heading "created being", of the ten categories and all their subgenera and species, but not of the ultimate differences of the ultimate species, nor of the transcendentals. "From this", he says, "I go to the proposed position"--This is the second article of the solution. So turning back to p.576, read the paragraph beginning "As to the second principal article".
Scotus says, "a two-fold primacy concurs in it, namely the primacies of commonness and virtuality". That is, it is the highest common predicate of everything that can be called a being, and contains virtually the ultimate differences etc. of which it is not predicable as part of their quiddity. He does not mean that it is both common and virtual with respect to each and every thing: rather, with respect to each and every thing it is either common or virtual. The rest of the paragraph should be clear enough. Bear in mind that "definitionally" means "as part of their definition".
To sum up the position he is maintaining: Being is first in that it stands at the top of the tree, is coextensive with the most extensive concepts (one, true, good, etc.) and is predicable of all the genera, sub-genera and species lower down the tree, though not of the ultimate differences (but still, these are differences of species of beings).
In the next short paragraph ("But what I have supposed") at the end an amendment needs to be made to the text. For "because as should be obvious I treat them equally" substitute: "To make this clear I explain them [these reasons] a little". Some amendment is also needed for the next sentence: "while doubting whether the differentia contracting being to such a concept is such a being or not", should read: "while doubting concerning the differences contracting being to such a concept". For example, we are certain that a man is a being of some sort, even though we may doubt that "rational" is the contracting difference. "Contracting" here means "narrowing down", another metaphor for division. We may not be certain that rationality is what distinguishes human beings from other beings (such as other animals), but we are certain that humans are beings of some sort. Compare the argument of this paragraph with p.562, second paragraph (beginning "And I prove univocity so understood").
Returning to p.577, read the first new paragraph, "The second argument I treat so". This argument assumes that we cannot directly perceive substance; all we can directly perceive or directly know are the accidents of substance: when we see a human being, we see his or her outward shape, colour, etc., not their essential humanity. So if all we knew directly were accidents of material substances, then we could not form concepts of material substances, or of immaterial substances. If we do have such concepts, the perception of material accidents must somehow convey to us a wider concept of being, applicable also to substance and to immaterial beings. We get the wider concept by analysis or definition of the concept of accident, since an accident is defined as something that is in something else that simply is. So what simply is, substance, is mentioned in the definition of accident.
The argument is, then, that since we can know directly only material accidents, and yet we have a concept of substance, then it must be that we get that concept by analysis of the concept of material accidents; but this can only be if being in general (as prior to its division into substance and accidents, subdivisions of being) is contained in the concepts of material accidents.
The second half of the paragraph is an argument to prove that we do not directly know the substances underlying the accidents; this is the point assumed in the first half. The phrase "in its absence" should be changed "to be absent"; in other words, if something present is knowable as present, then when it is absent the intellect knows that it is absent. The argument turns on a point of Catholic doctrine, namely that the consecrated host on the altar only looks like bread, but has had its substance changed to the substance of Christ--this is the doctrine of transubstantiation. If we could directly perceive substance, the we would know that the substance of the bread was no longer there; but we don't know this, it requires faith.
Compare the paragraph you've just read with p.562, last paragraph, "I argue the second principal proof thus". The last two paragraphs are applications to the present question of arguments used in Dist. 3, q.2, as Scotus says in the second last para. of p.576.
Returning to p.577, the next paragraph ("The proposed position ..." extends the second argument to cover matter and form, the essential constituents of a material substance. We can't perceive the substance, only its accidents, a fortiori we can't perceive the matter and form that constitute the substance. So if we can form concepts of these constituents, it must be that they come under a concept we can form from perceptions of material accidents, and the only concept wide enough to cover matter, form, substance and accidents is being. So just as he argued in question 2 that we must have univocal concepts common in the same sense to God and creatures because otherwise we could have no knowledge of God, so here he argues that being must be common to the things he has been talking about and to material accidents because otherwise we could have no knowledge of them, since all we know directly are material accidents. Of course the things he's been talking about are not just beings--their concept is contracted or narrowed by differences in some way: but, as he argued in the first argument we can be certain that they are beings of some sort even while we doubt concerning their differences. This is the end of the fourth cassette.
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