[4.15.9] John Duns Scotus on Logical Possibility and Possible Worlds

John Duns Scotus (the “Subtle Doctor,” 1265/66–1308 AD), in “Ordinatio” writes about modal theory, logical possibility, and how these concepts influence the state of affairs in the world. According to his ideas:

  • God’s divine intellect includes all the simple notae, which are necessary and true propositions, like logical, mathematical, metaphysical truths.
  • Logical possibility is a non-repugnant or non-contradictory relation between two (or more) simple notae. E.g., the simple notae “animality” and “rationality” are non-repugnant since together define “man”.
  • The simple notae related by logical possibility are combined in the divine intellect in contingent divine ideas. E.g., “man”
  • Some divine ideas are necessary and true by definition; these are the necessary propositions. E.g., a priori truths, like “A triangle has three angles.” Others are contingent, with undefined truth value; these are contingent propositions.
  • The divine intellect presents the contingent propositions to the divine will, which decides for some of them by making them true, and with the same act creating them in the world. These are the true propositions. It is noteworthy that the freedom of the divine will is limited to the realm of the contingent propositions.
  • The maximal consistent collection of all the true propositions describes possible worlds, from which one is our real world.

The following OntoUML diagram presents Duns Scotus’s theory of logical possibility and possible worlds:

Duns Scotus’s theory of logical possibility and possible worlds

ClassDescriptionRelations
DivineIntellectGod’s intellect
DivineWill “The divine intellect presents these contingent propositions to the divine will as not yet having a truth value, and the divine will then (in a second instant of nature) contingently determines each to be true or be false.” (Normore, 2003)

“Since God’s [divine] will is the only root of contingency, it follows that ideas necessarily have their content and cannot ground a representation of contingent states of affairs. Conversely, suppose that God’s knowledge of future contingents were based on ideas, then he would not be omniscient, for he would know that Socrates could be either sitting or standing up at T, not that he is sitting at T. Finally, there would be no more difference between God’s knowledge of what is actual and of what is simply possible.” (Anfray 2014)
presents contingent propositions to DivineWill
SimpleNotae“The first stage is God’s natural knowledge of all necessary propositions. These are logically simples and are sometimes called by Scotus [simple] notae. Such notae are related to others according to repugnance or compossibility, independently of any power to bring them about. However, they are not self-subsistent entities, but are the products of God’s intellectual activity, which thus endows them with an ontological status, as intelligible beings. But the logical and modal properties of these entities are not constituted by God’s intellectual activity. Scotus summarizes this by claiming that the possibilia are formally such from themselves (formaliter ex se), but “principially” from God (principiative ab eo). All logical, mathematical, and metaphysical truths, in general all necessary truths, are known at precisely the instant when God produces, thinks things, and produces them in an esse intelligibile. Moreover, since the relations of compossibility [non-repugnance] and repugnance are independent from God’s intellectual activity, any modal truth is necessarily so. This entails that anything possible is necessarily possible.” (Anfray 2014) shared part of DivineIntelect Possibility and DivineIdea
LogicalPossiblityFor Scotus logical possibility is a fundamentally relational idea: “We can intelligibly speak of it only when we are dealing with several notae. Similarly, we can only ask whether notae are consistent when we are dealing with more than one. Thus, in the typical cases the question of whether some possible is possible of itself reduces to the question of the status of a relation among its metaphysical constituents: Are they related of themselves, and in what sense does that relation presuppose its relata?”
Simple notae are true and necessary.
relates between SimpleNotae; defines DivineIdea
Non-repugnance“Scotus articulated a notion of logical possibility as the nonrepugnance of terms and claimed that there is a real power corresponding to every logical possibility.” (Normore, 2003)

We can understand the concept of non-repugnance as the contratry of repugnence: the concept of ‘chimera’ is internally incoherent in the sense that the metaphysical constituents out of which the common nature of chimera would be composed (the notae) simply cannot be combined, and that is why there is a further repugnance between ‘chimera’ and ‘being something’. But this repugnance presupposes that ‘chimera’ is itself a complex term in which several notae are combined.Achimera is perhaps an animal with the head of a lion, the body of a goat, and the tail of a serpent. These notae are themselves complex and could be analyzed in the same way. On Scotus’s view, we eventually reach simple notae. Suppose we ask then whether all simple notae are possible – and further, whether they are possible of themselves.” (Normore, 2003)
characterizes LogicalPossibility
DivineIdea“According to Scotus, all combinations of compatible [non-repugnant] notae are objects of God’s knowledge, which he calls also [divine] ideas. Scotus is less explicit on the content of ideas than on their ontological status, but it is likely that an idea is an intellectual representation of any object, either of an individual like ‘Socrates’ or of a common nature like ‘man’ and that it contains everything that can be grasped by God through his intellect alone. An idea would be something like the deductive closure of all necessary truths concerning a given object. For instance, God’s intellect produces the notae of animality and rationality and these, being intrinsically nonrepugnant, can be combined in a single subject, man. And man can be combined with an individual differentia to produce a possible individual, say ‘Socrates.’ The idea of Socrates contains all the properties grounding necessary truths concerning him: that he is a man, that he is a rational animal, and that it is possible that he is sitting at T, and so on. However, it does not include the property of sitting at T, because it is a contingent truth. This leads Scotus to reject theories that ground God’s knowledge of future contingents on his ideas. First, they can ground only analytical, thus necessary truths. Moreover, ideas are intellectual representations, excluding any volitional element. They are therefore purely natural occurrences in God’s mind.” (Anfray 2014)
Necessary Proposition“Scotus has as a basic notion in his modal picture that of a nonepugnant collection of notae. Second, he claims that having thought the notae, the divine intellect naturally and in a single instant of nature considers all nonrepugnant combinations of them. Some of these combinations are such that it would be repugnant for their elements not to be so combined. These correspond to necessary propositions.” (Normore, 2003)
Necessary propositions are true and necessary.
subkind of DivineIdea; shared part of DescriptionOfPossibleWorld
ContingentProposition“Scotus has as a basic notion in his modal picture that of a nonepugnant collection of notae. Second, he claims that having thought the notae, the divine intellect naturally and in a single instant of nature considers all nonrepugnant combinations of them. […] Others are such that it is not repugnant for their elements either to be so combined or not. These correspond to contingent propositions.” (Normore, 2003)
Contingent propositions are contingent and have undifined truth value.
subkind of DivineIdea; shared part of DescriptionOfPossibleWorld
TrueProposition“The divine intellect presents these contingent propositions to the divine will as not yet having a truth value, and the divine will then (in a second instant of nature) contingently determines each to be true or be false. The divine will thus contingently determines a maximal consistent collection of contingent propositions to be true. Such a maximal consistent collection of [true] propositions is a description of (or, on some views, is) what both Leibniz and twentieth-century modal theorists would call a possible world.” (Normore, 2003)
True propositions contingent and true.
subkind of ContingentProposition; shared part of DescriptionOfPossibleWorld; defines and creates Thing
ThingAn object, a substance, a state of affairs in a possible world.exclusive part of PossibleWorld
DescriptionOfPossibleWorld “The divine will thus contingently determines a maximal consistent collection of contingent propositions to be true. Such a maximal consistent collection of [true] propositions is a description of (or, on some views, is) what both Leibniz and twentieth-century modal theorists would call a possible world.” (Normore, 2003) defines PossibleWorld
PossibleWorldA possible world, our world is an instance of that.

Sources

  • Normore, Calvin G., “Duns Scotus’s Modal Theory”, The Cambridge Companion to Duns Scotus, Cambridge University Press 2003, ed. Thomas Williams
  • Anfray, Jean-Pascal Anfray, “Molina and John Duns Scotus”, A Companion to Luis de Molina, Brill, 2014
  • Williams, Thomas, “John Duns Scotus“, The Stanford Encyclopedia of Philosophy (Winter 2019 Edition), Edward N. Zalta (ed.)

First published: 27/5/2021

[4.1.2] Eriugena’s Cosmology

Irish monk and philosopher John Scottus Eriugena (800? – 877? AD) in its masterpiece Periphyseon (On the Division of Nature) elaborates an original Christian and Neoplatonic (see also [2.4.2][3.2.1][3.3.2][3.4][3.7.3]) cosmology, where

  • “Nature” includes God and the creations, the totality of things that are and are not.
  • God expresses Himself in creation, and creation culminates in the return to the divine.
  • Being and non-being is defined as a set of dialectic modalities, so a thing “may be said to be under one mode and not to be under another.”

A draft of Eriugena’s cosmological model is presented in the following OntoUML diagram:

Eriugena on nature
ClassDescriptionRelations
ModeOfBeingEriugena defines “five ways of interpreting” (quinque modi interpretationis) the mode of being, the way in which things may be said to be or not to be.
“One of the striking features of this complex—and certainly, in this form, original—account is that being and non-being are treated as correlative categories: something may be said to be under one mode and not to be under another. Attribution of being is subject to the dialectic of affirmation and negation.”
charaterizes Thing
1stModeOfBeing“According to the first mode, things accessible to the senses and the intellect are said to be, whereas anything which, ‘through the excellence of its nature’ (per excellentiam suae naturae), transcends our faculties are said not to be.” descendant of ModeOfBeing
2ndModeOfBeing“The second mode of being and non-being is seen in the ‘orders and differences of created natures’, whereby, if one level of nature is said to be, those orders above or below it, are said not to be:
For an affirmation concerning the lower (order) is a negation concerning the higher, and so too a negation concerning the lower (order) is an affirmation concerning the higher. (Periphyseon, I.444a) According to this mode, the affirmation of man is the negation of angel and vice versa (affirmatio enim hominis negatio est angeli, negatio vero hominis affirmatio est angeli, I.444b). This mode illustrates Eriugena’s original way of dissolving the traditional Neoplatonic hierarchy of being into a dialectic of affirmation and negation: to assert one level is to deny the others. In other words, a particular level may be affirmed to be real by those on a lower or on the same level, but the one above it is thought not to be real in the same way. If humans are thought to exist in a certain way, then angels do not exist in that way.”
descendant of ModeOfBeing
3rdModeOfBeing“The third mode (I.444c–445b) contrasts the being of actual things with the ‘non-being’ of potential or possible things still contained, in Eriugena’s memorable phrase, ‘in the most secret folds of nature’ (in secretissimis naturae sinibus). This mode contrasts things which have come into effect with those things which are still contained in their causes. According to this mode, actual things, which are the effects of the causes, have being, whereas those things which are still virtual in the Primary Causes (e.g., the souls of those as yet unborn) are said not to be.”descendant of ModeOfBeing
4thModeOfBeing“The fourth mode (I.445b–c) offers a roughly Platonic criterion for being: those things contemplated by the intellect alone (ea solummodo quae solo comprehenduntur intellectu) may be considered to be, whereas things caught up in generation and corruption, viz. matter, place and time, do not truly exist. The assumption is that things graspable by intellect alone belong to a realm above the material, corporeal world and hence are timeless.”descendant of ModeOfBeing
5thModeOfBeing“The fifth mode offered by Eriugena is essentially theological and applies solely to humans: those sanctified by grace are said to be, whereas sinners who have renounced the divine image are said not to be.”descendant of ModeOfBeing; characterizes Human
ThingEriugena claims, that “nature” (natura), is “the general term for all things that are and all things that are not”, including both God and creation.
Species“Echoing similar divisions in Augustine (De civitate Dei Bk. V. 9, PL 41: 151) and Marius Victorinus (Ad Candidum), nature’s four ‘divisions’ or ‘species’ are: that which creates and is not created (i.e., God); that which creates and is created (i.e., Primary Causes or Ideas); that which is created and does not create (i.e., Temporal Effects, created things); that which is neither created nor creates (i.e., non-being, nothingness).”characterizes Thing
GodPeriphyseon Book One examines the first division, God understood as a transcendent One above, and yet cause of, all creation. God transcends everything; He is, following Pseudo-Dionysius, the “negation of all things” (negatio omnium, III.686d). According to Eriugena—who in this respect is following a tradition which includes Augustine and Boethius as well as Dionysius and other Greek authors—the Aristotelian categories are considered to describe only the created world and do not properly apply to God (I.463d). God cannot “literally” (proprie) be said to be substance or essence (ousia, essentia), nor can He be described in terms of quantity, quality, relation, place or time. He is “superessentialis” (I.459d), a term which, for Eriugena, belongs more to negative theology than to affirmative. His “being” is “beyond being”. Eriugena particularly admires a Dionysian saying from the Celestial Hierarchy (CH iv 1; PG 3: 177d1–2): to gar einai panton estin he hyper to einai theotes (“for the being of all things is the Divinity above being”, III.686d) which he translates as esse omnium est superesse divinitatis, (“the being of all things is the super-being of divinity”, III.686d, I.443b; see also I.516c; III.644b, V.903c). This is perhaps Eriugena’s favorite phrase from Dionysius. (Indeed, Maximus Confessor had also commented on it in I Ambigua xiii, PG 91: 1225d, a passage well known to Eriugena who translated the Ambigua.) Sometimes, instead of invoking the Dionysian formula superesse divinitatis, Eriugena speaks of the “divine superessentiality” (divina superessentialitas, III.634b), or—quoting Divine Names I 1–2 (PG 3: 588b–cb)—of the “superessential and hidden divinity” (superessentialis et occulta divinitas, I.510b).
God is a “nothingness” (nihilum) whose real essence is unknown to all created beings, including the angels (447c). Indeed, Eriugena argues in a radical manner, following Maximus Confessor, that God’s nature is infinite and uncircumscribable, such that He is unknown even to Himself, since He is the “infinity of infinities” and beyond all comprehension and circumscription. In the Periphyseon, Eriugena repeats the position of the De Praedestinatione that God does not know evil, and, in a genuine sense, God may be said not to know anything; his ignorance is the highest wisdom.”
According to the First Mode of Being “God, because of his transcendence is said not to be. He is ‘nothingness through excellence’ (nihil per excellentiam).”
creates PrimaryCause; returns to God; subkind of Thing
Creates NotCreatedCreates and not createdcharacterizes God; descendant of Species
neitherCreated norCreatesNeither created nor createscharacterizes God; descendant of Species
PrimaryCauseThe main focus of the Second Book of the Periphyseon is an analysis of what Eriugena terms “the Primary Causes” (causae primordiales) which are the patterns of all things located in the mind of God and function as the timeless and unchanging causes of all created things. This doctrine represents an eclectic combination of various earlier doctrines, including the Platonic theory of Forms or ideai, Dionysius’ discussion of the divine names, and Augustine’s revival of the Stoic notion of eternal reasons (rationes aeternae).
God’s mind, understood as the logos or verbum, contains in one undivided Form all the reasons for every individual thing. These reasons (rationeslogoi) are productive of the things of which they are the reasons. Their number is infinite and none has priority over the other, e.g., Being is not prior to Goodness, or vice-versa. Each is a divine theophany, a way in which the divine nature is manifested. The very nature of these Causes is to flow out from themselves, bringing about their Effects. This “outflowing” (πρόοδοςproodosprocessioexitus) creates the whole universe from the highest genus to the lowest species and “individuals” (atoma). In his understanding of this causal procession, Eriugena accepts Neoplatonic principles: like produces like; incorporeal causes produce incorporeal effects; an eternal cause produces an eternal effect. Since the causes are immaterial, intellectual and eternal, so their created effects are essentially incorporeal, immaterial, intellectual, and eternal. Eriugena, however, thinks of cause and effect as mutually dependent, relative terms (Periphyseon, V. 910d–912b): a cause is not a cause unless it produces an effect, an effect is always the effect of a cause.
creates CreatedEffect;
subkind of Thing
Creates isCreatedCreates an is Createdcharacterizes PrimaryCause; descendant of Species
CreatedEffectBy nature, they are eternal and incorruptible, but Eriugena also thinks of individual created things as located spatially and temporally. He seems to think there are two kinds of time: an unchanging time (a reason or ratio in the divine mind,Periphyseon, V.906a) and a corrupting time. Place and time are definitions in that they situate or locate the things they define, and since definitions are in the mind, then place and time are in the mind (Periphyseon, I.485b). Following Gregory of Nyssa, Eriugena holds that the sensible, corporeal, spatio-temporal appearances of things are produced by the qualities or “circumstances” of place, time, position, and so on, which surround the incorporeal, eternal essence. The whole spatio-temporal world and our corporeal bodies are a consequence of the Fall, an emanation of the mind. Eriugena is somewhat ambiguous about this. His considered position appears to be that God, foreseeing that man would fall, created a body and a corporeal world for him. But this corporeal body is not essential to human nature and in the return of all things to God, the body will be absorbed back into the spiritual body (spirituale corpus) and the spiritual body back to the mind (mens, intellectus, νοῦς). The corporeal world will return to its incorporeal essence, and place understood as the extension will return back into its cause or reason as a definition in the mind (Periphyseon, V.889d).returns to PrimaryCause; subkind of Thing
isCreated doesNotCreateIs created and does not createcharacterizes CreatedEffect; descendant of Species
Human“I declare that man consists of one and the same rational soul conjoined to the body in a mysterious manner, and that it is by a certain wonderful and intelligible division that man himself is divided into two parts, in one of which he is created in the image and likeness of the Creator, and participates in no animality … while in the other he communicates with the animal nature and was produced out of the earth, that is to say, out of the common nature of all things, and is included in the universal genus of animals. (Periphyseon, IV.754a–b)”subkind of CreatedEffect
RationalSoulRational soul (see above)exclusive part of Human
Body“But this corporeal body is not essential to human nature and in the return of all things to God, the body will be absorbed back into the spiritual body (spirituale corpus) and the spiritual body back to the mind (mens, intellectus, νοῦς). The corporeal world will return to its incorporeal essence, and place understood as the extension will return back into its cause or reason as a definition in the mind”exclusive part of Human
CorporealBodyCorporeal body (see above)phase of Body
SpiritualBodySpiritual body (see above)phase of Body

Sources

First published: 14/05/2020