[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

[4.10.1] St Bonaventure on Creatures as God’s Signs

St Bonaventure (the “Seraphic Doctor”, 1217 – 1274 AD), in the work Commentary on the Sentences of Lombard, writes about the ways how all created things signifies God:

  • God created all things, so the whole universe existentially depends on God.
  • All creatures act in the role of signs which point to God; these signs can be of four types.
  • Based on their properties, all creatures signify God as shadows and vestiges; more than that, rational creatures signify it as images and similitudes.
  • Rational creatures (humans, angels) have the power to look to these signs, which leads them to God. This way rational creatures “have God as their ultimate object, whereas all creatures have God as their Cause”.

Bonaventure’s model of creatures as God’s signs is pictured in the following OntoUML diagram:

Bonaventure on creations as signs of God

ClassRationalCreatureClassDescriptionRelations
GodGod creates the creatures whose existence depends on him.creates Creature; provides divine grace to RationalCreature
Creature“All creatures, from rocks to angels, are signs in the sense of shadows and traces of God, for they all bear a relation of causal dependency upon God as their source; but only rational creatures can have the divine as an object of their activities and, for that reason, can conform themselves to the divine will and become likenesses of God.”
PropertyCreatures can be vestiges or shadows based on properties which point to God.characterizes Creature
Shadow“a creature is called a shadow based on its properties which point to God in some type of causality in an indeterminate way.”role of Creature; is Sign
Vestige“a creature is called a vestige based on properties which point to God as triple cause–efficient, formal, and final cause; for example, the properties: one, true, and good.”role of Creature; is Sign
RationalCreature“[…] only rational creatures can have the divine as an object of their activities and, for that reason, can conform themselves to the divine will and become likenesses of God.”subkind of Creature; observes Sign
RationalPowerRational powercharacterizes RationalCreature; subkind of Property
Image“Bonaventure posits […] higher types of semiosis pertinent solely to rational creatures, which are ‘images’ (imago) pointing to the First Principle through its properly rational powers which have their source and highest object in God”role of RationalCreature; is Sign
Likeness“In addition, Bonaventure posits […] higher types of semiosis pertinent solely to rational creatures, which are […] ‘likenesses’ (similitudo) of God to the extent that they are recipients of divine grace and conform themselves to the divine will.” role of RationalCreature; is Sign
Sign“Bonaventure’s semiotics distinguishes four sorts of signs [wich are shadow, vestige, image, similitude...]
All creatures, from rocks to angels, are signs in the sense of shadows and traces of God, for they all bear a relation of causal dependency upon God as their source; but only rational creatures can have the divine as an object of their activities and, for that reason, can conform themselves to the divine will and become likenesses of God.”
points to God

Sources

  • All citations from: Noone, Tim and R. E. Houser, “Saint Bonaventure“, The Stanford Encyclopedia of Philosophy (Winter 2020 Edition), Edward N. Zalta (ed.)

First published: 10/12/2020