The philosopher regarded by some as the first metaphysician and modal theoretician to reflect systematically on the nature of possibility, necessity, and impossibility is the Greek presocratic philosopher and founder of the “Eleatic” school of philosophy, Parmenides, born around 515 BC. His one surviving work, On Nature, is a fragmentary poem describing the poet’s mystical journey by chariot to the temple of an unnamed goddess who instructs him in the two ways in which human beings approach reality, the “Way of Truth” and the flawed “Way of Appearance” or mere “Opinion” (doxa). In her discourse on the Way of Truth, the goddess further distinguishes three ways in which reality may be thought about or conceived: “that it is and must be,” “that it is not and it cannot be,” and “that to be and not to be are the same yet not the same.”
What Parmenides meant by these three paths (along with much else in his opaque and oracular poem) has been the subject of much debate, but one interpretation relevant to the history of the possibles has seen his three-fold path as an early distinction between the three modal categories of necessity, impossibility, and possibility, respectively. On this reading, Parmenides’s “what is and must be” refers to those things which are necessary, “what is not and cannot be” to those things that are deemed to be impossible, and the intermediate realm of “what both is and is not” is presumably his way of characterizing the merely possible.
 Merrill Ring relates Parmenides’s interest in modality to the likelihood of his mathematical training among the Pythagoreans:
If, as there is good evidence for, he did begin his intellectual career among the Pythagoreasn, he was there exposed to sophisticated mathematical thought. One clear and obvious feature of mathematical discussion is frequent use of the various modal notions. For instance, an early mathematical discovery was that the result of multiplying any integer by 2 has to be an even number. A more complicated realization was that it is impossible to construct a right triangle whose hypotenuse is shorter than iether of the other twos sides. Even possiblity is easily spotted in mathematicians’ talks: “Can (say) 2,372 be divided by 3 without remainder?”
Very probably, Parmenides’ interest in modal concepts arose from his exposure to the frequent use of those notions in the mathematical work of the Pythagoreans. (Ring 91).
Metaphysics of the Music, part 21
We can see, then, that while Thomas is certainly keen, in the words of G.B. Phelan, to give “due consideration for the rôle of the perceiving subject in the apprehension of the beautiful,” going so far as to define “the beautiful as having a necessary reference to a subject,” there is nevertheless an “intransigent objectivism” to his account of beauty. This leads us, finally, to a consideration of the existential realism lying beneath Thomas’s theory of being. Existentialism in this context refers to the insight—now widely regarded as one of if not the central principle of Thomas’s metaphysical thought—that the act of existence, signified by the Latin infinitive esse, is the “actuality of all acts and the perfection of all perfections.” As the existential Thomists of the twentieth century argued, in identifying a thing’s act of existence as the “act of acts,” Thomas inaugurated a veritable revolution in metaphysics and the theory of knowledge, at the heart of which was the realization that, contrary to the “essentialism” of much of the metaphysical tradition both before and after him, it is not a thing’s intelligible, contemplatable essence or form, but its actual, real, concrete existence in the world that, in the words of Armand Maurer,
holds the primary place in the order of being. While not neglecting other aspects of being, such as form and essence, St. Thomas offers a radically new interpretation of being by emphasizing its existential side. This was a decisive moment in the history of Western metaphysics, for St. Thomas was transforming previous Greek and mediaeval conceptions of being, which gave primary place to form.
 Phelan, “The Concept of Beauty in St. Thomas Aquinas,” 162.
 Maurer, “Introduction,” in Aquinas, On Being and Essence, trans. Maurer, 10.
The answer, according to Aquinas, is “No.” As James F. Ross explains, for Aquinas
ceasing to cause existence in creatures would not be the same as giving them an active tendency toward nonbeing, because God does not cause nonexistence in them, but ceases to cause them to be, to “give them being.” (“Aquinas on Annihilation,” 181, citing De Potentia Dei 5.3 ad 1)
In other words, annihilation is not a “causing a thing not to be,” but is rather a “no longer causing a thing to be.” It matters where you put the “not.” Annihilation, in short, is not something God can do, but something that he can not do, namely continuing to create something once he has created it. Annihilation is God’s ability not to create.
I’m presently working through Anselm’s Cur Deus Homo (“Why God Became Man”) as part of my “theology of the possible” project. One of the things, however, that I’ve wanted to do for some time is a study comparing Anselm’s work with Tolkien’s own Middle earth version of Cur Deus Homo, the Athrabeth Finrod ah Andreth (in Morgoth’s Ring, vol. 10 in The History of Middle earth). Both texts make the case for the “necessity” of the Incarnation as the divine means for dealing with evil in the world. David Herlihy gives this summary of the central argument of Anselm’s dialogue:
Anselm attempted with with still greater boldness to show the logical relationships linking three fundamental Christian beliefs: the infinite nature of God, the fact of original sin, and the incarnation of Christ. Anselm argued that the degree of an offense was measured by the dignity of the one offended. Original sin was therefore an act of infinite evil, as it offended God himself. But the worth of an apology or act of atonement was measured by the dignity of the one conferring the apology. Man, therefore, while capable of a sin of infinite magnitude, could not as a finite creature offer equal atonement. Only a man of infinite worth could do this, i.e., a man who was also God. If God wished to save man, argued Anselm, the only suitable way for him to do so was to allow his son to become one of them, to offer atonement for the human race. (Medieval Society and Culture 162)
Metaphysics of the Music, part 20
As to what it is in the beautiful object that is responsible for eliciting the affective response in the individual, Thomas lists the three objective properties of beauty—integrity, proportion, and clarity—touched on at the end of the last chapter. By integrity or perfection, Thomas means something close to what Tolkien has in mind in his requirement that sub-created, secondary world’s exhibit the “inner consistency of reality.” Integrity, in other words, refers to a thing’s completeness, wholeness, or togetherness, its having and displaying the structure and requisite parts proper to a thing of that particular essence or nature. The second aesthetic property of proportion, sometimes referred to as harmony or consonance, is of Pythagorean extraction and designates in Thomas’s usage a sense of qualitative proportion that he calls convenientia, or what Liberato Santoro-Brienza describes as an “intrinsic attunement” or “correspondence between inner and outer reality, appearance and essence, matter and form.” It is the harmony of beauty, in other words, that is especially involved the aforementioned, pleasing correspondence obtaining both between the parts and metaphysical principles within the object and between the object and the sensory faculties of the perceiver. Finally, there is the aesthetic criterion of clarity, or brightness or “splendor,” i.e., the shining forth of form or radiating of intelligible light from the beautiful object, an idea that Robert Wood suggests is further linked to the Greek word doxa or “glory” and which Tolkien gives us an apt image of in the Ainulindalë when the Ainur first glimpse the world, newly created by the Flame Imperishable of Ilúvatar, as “a cloud with a living heart of flame” (S 20).
 For an analysis of these properties in light of their development in Western thought prior to Aquinas, see chapter four of Eco, The Aesthetics of Thomas Aquines, “The Formal Criteria of Beauty,”64-121.
 Santoro-Brienza, “Art and Beauty,” 72.
 Robert Wood, Placing Aesthetics, 109.
 Wood, Placing Aesthetics, 105.
Metaphysics of the Music, part 19
Another debate that has revolved around Thomas’s conception of beauty concerns the exact mental processes that are involved in individual judgments of beauty, or what Delfino refers to as the “epistemology of beauty.” As Delfino summarizes the debate,
[s]ome Thomists, like Jacques Maritain, have held that it [the perception of beauty] is an intuition, a direct, immediate knowledge of an object… [A] person perceives beauty through sense intuition, and that the intellectual act of abstraction is not present in aesthetic experience. Eco disagrees, noting that to know whether or not the things before us (for example, this cat) has clarity, order, and integrity requires us to have conceptual knowledge (in this case, of cat), which the act of abstraction furnishes. But Eco contends that abstraction by itself is not enough. Aesthetic perception occurs at the end of the intellectual act of judgment whereby we say something about the actual existence of the thing before us… [Armand] Maurer’s view overcomes the negative aspects of Eco’s view while remaining faithful to the basic structure of Aquinas’s epistemology. In agreement with Maritain, Maurer holds that our aesthetic perception of physical things is grasped through sense intuition and is non-conceptual, but, in accord with Eco, aesthetic perception is completed in the intellectual act of judgment. However, Maurer disagrees with Eco by contending that, in the aesthetic perception of physical things, the judgment is not the result of a reasoning process involving concepts. Maurer does not deny that the concept of the thing that we experience as beautiful is present in the intellect. The intellect’s nature is to abstract the concept. Still, in aesthetic experience, we do not give primary focus to the concept and rational analyses. Instead, we focus on the beauty of the thing. (Delfino, “The Beauty of Wisdom,” 42-3)
Metaphysics of the Music, part 18
For all its similarities with Kant’s idealistic aesthetics, there is nonetheless an intractable, objective or mind-independent character to Thomas’s conception of beauty. The more beauty a thing has the more existence or being will be implicated in that beauty. One aspect to this principle for St. Thomas is his definition of beauty as “that which pleases when seen” (ST1.5.4 ad 1). In direct contrast to Kant, therefore, Thomas establishes as one of the defining features of beauty the pleasure or delight the object of beauty is able to bestow on its perceiver through the senses, which makes beauty at some level presuppose the existence of a perceiver-independent object capable of acting on the senses in this aesthetically pleasing manner. For Thomas, human sense faculties have as their proper activity and end the perception of sensible objects, especially beautiful sensible objects, and aesthetic pleasure or delight consists in this activity being brought to completion—that is to say, in the sensible properties of the object of beauty first stimulating and gratifying the senses, and in their turn effecting a corresponding intellectual apprehension of and satisfaction in the form or internal structure of the physical object. In this manner a harmonious, pleasing, and nature-fulfilling correspondence is established between the object and the perceiving subject and between the subject’s own perceptual and intellective faculties.
 “[P]ulchra enim dicuntur quae visa placent.” Although Thomas’s definition emphasizes visual beauty, Santoro-Brienza makes the point that “visio is further qualified as apprehensio. Sight stands for all perception in general, but particularly for the perception of sight and hearing, and not for taste, touch, and smell, if reference is to beauty.” Santoro-Brienza, “Art and Beauty,” 69. As for Thomas’s above definition of beauty in terms of “that which pleases when seen,” there has been some discussion whether or not Thomas is here to be understood as stating his own personal view on the matter. Eco, in a lengthy note in the bibliography of his Art and Beauty in the Middle Ages, takes Maritain in his Art and Scholasticism to task, lamenting that “[e]xpressions such as pulchrum est id quod placet are accepted as authentic Thomistic formulae by people who do not care, or perhaps are not aware, that this is a definition devised by Maritain himself. What Aquinas actually wrote was pulchrum dicuntur quae visa placent. The difference is considerable. Maritain’s proposition is a dogmatic attempt to define once and for all the ontological character of beauty. Aquinas’s is more like a sociological finding. It means, ‘Things which give pleasure when they are perceived are called beautiful’, and this is to introduce the problem, not solve it.” Eco, Art and Beauty in the Middle Ages, 128. Murphy, however, has taken Eco to task in his turn: “A grammatical point can be made in defence of Maritain’s interpretation: how does St Thomas use the phrase dicuntur elsewhere? Each of his arguments for the existence of God concludes with a similar phrase, e.g., ‘one is bound to arrive at some first cause… and this is what everybody understands by God.’ Whilst distinguishing finite being from the self-subsistent being of God, St Thomas says: ‘the first cause is above being insofar as it is infinite being; ‘being’ (ens), however is called that which participates in being in a finite way, and this being is proportionate to our intellect.’… One would hesitate to conclude that this is the product of a sociological survey. Eco hangs too much on the use of the present passive plural. St Thomas uses the present passive singular and the gerundive, (dicitur, dicendum) more often. This is because, in the scholastic Quaestio, the master’s reply to the ‘problem’ set quaeritur, ‘it is asked’) usually commences with dicendum, ‘it ought to be said’. But the meaning of the verb appears to be interchangeable. Thus, St Thomas writes elsewhere: ‘let that be called beauty, the very perception of which pleases.’ (‘pulchrum autem dicitur id cuius ipsa apprehensio placet.’ [ST1-2.27.1 ad 3]).” Murphy, Christ the Form of Beauty, 209. G.B. Phelan has also defended the formula “pulchrum est quod visum placet” as a valid though not complete interpretation of Aquinas’s own definition “pulchra dicuntur quae visa placet.” Phelan, “The Concept of Beauty in St. Thomas Aquinas,” 174.
 Santoro-Brienza, “Art and Beauty,” 70.