## 1. From Aristotle to Boethius



The discussion about future contingents in modern philosophical logic
was revived by J. Lukasiewicz's works on three-valued logic
(1957, 1967). He thought that in order to avoid fatalistic
consequences, one should admit that the principle of bivalence (for
any proposition *p*, either *p* is true or *p* is
false) does not hold good for future contingent propositions. Arguing
that this was realized by Aristotle in Chapter 9 of *De
interpretatione*, Lukasiewicz attempted to formalize
Aristotle's position by introducing a third truth-value (neither
true nor false) for future contingent propositions and giving
three-valued truth-tables for truth-functional basic connectives. Many
authors have followed Lukasiewicz in taking Aristotle to restrict
the principle of bivalence, though they have not ascribed to Aristotle
the details of Lukasiewicz's system, which is problematic
in many respects. In arguing for the deterministic consequences of
unrestricted bivalence, Lukasiewicz himself assumed, and took
Aristotle to assume, that the truth of a proposition entails the
necessity of its truth. Logical determinism, therefore, is to be
avoided by qualifying the truth-values of future contingent
propositions. The critics of this view do not see any entailment
relation between truth and necessity, some of them maintaining that
the illusion of logical determinism has its roots in a tacit
oscillation between a temporal and atemporal predication of truth. The
temporalized reading may be associated with diachronic determination,
certainty, necessity and other time-dependent qualifications. Mixing
these with non-deterministic atemporal predications yields the wrong
idea of fatalism (von Wright 1984: 52-67). It is argued that
even the temporalized predication of truth carries no deterministic
implications. (Sorabji 1980: 96-103; Sorabji's example is
that "even if it has already been true that I am going to swim,
I still retain the power to make it to have been false".)



The majority of Aristotelian scholars believe that the argument in
*De interpretatione* 9 aims at avoiding fatalism by restricting
bivalence for future contingent predictions (Frede 1970, 1985; Sorabji
1980; Craig 1988; Gaskin 1995; Crivelli 2004; Weidemann 2012). The
second interpretation insists that Aristotle's point is not to
deny the truth-value of these statements, but their being true in the
same way as other statements are true. The difference is that while
the truth of other statements is necessary, the truth of future
contingent predictions is not yet similarly determined. This
interpretation is associated with Aristotle's remark that not
everything which is actual and therefore necessary is necessary
without qualification (19a23). This is taken to mean that the
necessity of an event at a certain time does not imply that it was
inevitable. Aristotle speaks about singular future possibilities which
may be realized or remain unrealized and which may or may not cease to
be antecedent possibilities (see *De interpretatione* 19a13-17,
*Nicomachean Ethics* III.5, 1114a17-19, *Metaphysics* VI.3). In the same
way predictions may begin to be necessarily true or necessarily false.
(For various versions of this approach, see Anscombe 1956; Rescher
1963; Hintikka 1973; Fine 1984; Judson 1988.)



The former interpretation, which denies bivalence for future
contingent statements, is called the 'traditional' or
'standard' interpretation. Some Stoics read Aristotle in
this way, as Boethius reports in his second commentary on
Aristotle's *De interpretatione*:



> 
> 
> Now some people - the Stoics among them - thought that
> Aristotle says that future contingents are neither true nor false. For
> they interpreted his saying that nothing [of that sort] is disposed
> more to being than to not being as meaning that it makes no difference
> whether they are thought false or true; for they considered them to be
> neither true nor false [in Aristotle's view], but falsely.
> (*In Perihermeneias* II, 208.1-4, trans. by N. Kretzmann.)
> 
> 
> 



On the basis of a note in Simplicius's commentary on
Aristotle's *Categories* (407.6-13), it is argued
that some Aristotelians also qualified the principle of bivalence.
(For this and other ancient deviations from the principle, see Sorabji
1980: 92-93.) On the other hand, future contingent propositions
were treated as true or false in Stoic logic. The Stoics took the
universally valid principle of bivalence to imply the predetermination
of all future events. (See Cicero, *De fato*, 20-21;
Bobzien 1998: 59-86.) 



Boethius regarded the Stoic interpretation of Aristotle's view
as mistaken, his interpretation being based on the terms
'definitely' true or false and 'indefinitely'
true or false. These same terms were also used in Ammonius's
commentary (c. 435/445-517/526). Since this work was not known
to Boethius, both authors seem to have known some earlier Greek
discussions in which these qualifications were introduced.
(Ammonius's Greek commentary on *De interpretatione* 9 is
translated by D. Blank and Boethius's Latin commentaries by N.
Kretzmann in the same volume, with interpretative essays by R.
Sorabji, N. Kretzmann and M. Mignucci in 1998.) The contemporary
reconstructions of what Ammonius and Boethius meant can be divided
into two groups. According to one interpretation, Ammonius and
Boethius ascribe to Aristotle the view that the predictions of future
contingent events and their denials differ from other contradictory
pairs, because truth and falsity are not definitely distributed
between them and the propositions are consequently neither definitely
true nor definitely false. In answering the Stoic criticism, Boethius
might have thought that future contingent propositions have the
disjunctive property of being true-or-false, which would mean
something other than simply lacking a truth value. (For various
interpretations of how Boethius restricted bivalence, see Frede 1985;
Craig 1988; Gaskin 1995; Kretzmann 1998.) Another interpretation holds
that Boethian future contingents are not definitely true or false
because their truth-makers are not yet determined, but are true or
false in an indeterminate way. No qualification of the principle of
bivalence is involved. True statements are either definitely true or
simply (indefinitely) true or false (Mignucci 1988, 1998; Seel 2000;
Beets 2003 for Boethius's first commentary). According to both
interpretations, Ammonius and Boethius assumed that the definite truth
of predictions directly implies determinism and that Aristotle denied
the definite truth of all future contingent propositions; it is less
clear how they understood the indefinite truth of these (Sorabji
1998a). Boethius's formulations often suggest that future
contingent propositions are true-or-false. An additional reason for
not treating them as simply true or false is his view of the necessity
of the present. In commenting on Aristotle's remark that
" what is necessarily is when it is" (*De
interpretatione* 19a23), Boethius explains that even though
present things are temporally or conditionally necessary, they may be
generically or antecedently contingent (*In Perihermeneias* I,
121.20-122.4; II, 241.7-243.28). He apparently thinks that
the truth of future contingent statements implies that things cannot
be otherwise, for the assumed actuality of the relevant future
truth-makers means that alternative diachronic prospectives are
rendered temporally impossible. 



In his longer commentary on *De interpretatione*, Boethius says
of God that "he knows future events as happening contingently
and not necessarily so that he does not ignore the possibility that
something else might take place" (*In Perihermeneias* II,
226.9-12). Boethius also stresses that since the truth of future
contingents is not accessible to humans, the predictions of the form
"A sea battle will take place tomorrow" are false in the
sense that they assert the truth of something that cannot be known
(*In Perihermeneias* II, 211.26-213.18). In his later treatise
*Consolatio philosophiae* Boethius states that "I do not
think that anybody would say that those things which are happening now
were not going to happen before they happened" (V. 4.19) In this
treatise, Boethius argues that God is atemporal and has the totality
of changing history present to him. God's knowledge is thus not
foreknowledge since it is not temporally located, but the predictions
of future contingents are true or false from the point of view of
God's eternal knowledge of the things referred to (V.6,
25-32; see also Augustine, *City of God* 11.21). According to Boethius, it is necessary
that if God knows that *p*, then *p*. This
'conditional necessity' does not imply the 'simple
necessity' of *p* (*Consolatio philosophiae* V,
6.27-30). Some medieval authors read this distinction in
Boethius and Augustine as a modal placement solution to the problem of
foreknowledge and free will (Matthews 2004). Thomas Aquinas, for
example, refers to Boethius's distinction using the terms
*necessitas consequentiae* and *necessitas consequentis*
(*Summa contra gentiles* I.67; *De veritate* I.23, ad
13). For Boethius, see Evans 2004; Marenbon 2005; Sharples 2009; Marenbon 2013.



Boethius's remarks on modalities have led some authors to
analyze them by using models derived from modern temporal or tense
logic with branching time theory developed by Prior, Burgess, Thomason
and others. In applying these to Boethius, Bornholdt states that the
models shed light on Boethius's approach even though they were
not intended by Boethius himself (2017: 49; see also Martin 2004:
53-63). Bornholdt extends his formal analysis to later medieval
discussions as well, calling it the Boethian model. For similar
non-historical reconstructions of time logic in some late medieval
theories of future contingents, see the
 SEP entry on future contingents.


## 2. Medieval Developments from Abelard to Aquinas



In discussing statements such as "What is known by God
necessarily takes place", Anselm of Canterbury (1033-1109)
distinguished between the antecedent and consequent necessity of
things which are known. The latter is the necessity of a thing's
actuality which is caused by the actuality of the thing itself. The
former is the necessity by which a thing exists because of an external
cause (*Cur Deus homo* 2.17, 125.6-126.2). Neither
antecedent knowledge nor antecedent truth has a compelling effect on
things. In explaining Mary's believing the truth of a prophetic
statement concerning the death of Christ, Anselm writes:



> 
> 
> Therefore, since her faith was true faith, it was necessary that things
> would be as she believed. But if you are once again disturbed by my
> saying "It was necessary...", remember that the
> truth of the virgin's faith was not the cause of his dying
> freely but that her faith was true faith because this was going to
> happen. (*Cur Deus homo* 2.17, 124.27-125.3)
> 
> 
> 



Anselm thought that future contingent statements based on divine
revelation were true without deterministic implications. A similar
view was held by most medieval theologians when they addressed divine
omniscience and prophesy. For Anselm's view, see Knuuttila
2004.



William of Champeaux (c. 1070-1122) dealt with an argument
against the compatibility between contingency and divine omniscience
which was discussed in Augustine's *City of God* (V.9).
In response to Cicero's *De fato* and *De
divinatione*, Augustine refuted the claim that if events can
happen in any way other than God has foreseen, then God can be in
error. William stated that the antecedent of the argument is true but
the consequent is false and therefore the consequence is not valid
(Lottin 1959: 195; Marenbon 1997: 226-227). Peter Abelard
(1079-1142/4), in discussing the same example, applied the
systematic division between modal statements *de sensu* or in
the compounded sense and modal statements *de re* or in the
divided sense. (For Abelard's modal terminology, see *Glossae
super Peri hermeneias* XII.3-46. Later authors used the
expression *de dicto* instead of *de sensu.*)
Abelard's analysis of Cicero's argument was often repeated
in medieval theology, since it was put forward in slightly modified
form in Peter Lombard's *Sententiae* (c. 1157), which
became the standard medieval introduction to theology. Abelard states
that when the proposition "A thing can be otherwise than God
knows it to be" is read as a modal proposition *de sensu*
(It is possible that a thing is otherwise than God knows it to
be), the antecedent is false and the possibility of God's
error as a consequent would not be justified even if the consequence
were valid. When the antecedent is read *de re* (A thing
that is now somehow could be otherwise than God knows it to
be), the proposition is true, but the consequent about
God's error is false, for if things were otherwise, God would
know as they would be. This shows that the consequence is not well
formulated. Following Abelard, Peter Lombard formulated the same view
in stating that "Things cannot be other than as God foreknows
them" is true in the compounded sense and false in the divided
sense. The truth of the compounded sense saves God's
infallibility and the falsity of the divided sense expresses
God's freedom and the metaphysical contingency of the future
(Peter Lombard, *Sententiae* I.38.2; Peter Abelard, *Glossae
super Peri hermeneias* IX.86-99; *Dialectica*,
217.27-219.24). It is assumed here that when a temporally
definite statement is true, its denial may be possibly true. 



Early medieval logicians could deal with singular future statements as
statement types with truth-values changing in accordance with the time
of assertion, as in Aristotle and Hellenistic philosophy. (For the
prevalence of temporally indefinite sentences in ancient philosophy,
see Hintikka 1973: Ch. 4; Bobzien 1998: 66-67, 100-101,
109-111.) In the theological context of timeless divine
omniscience, it was more natural to regard these statements as
temporally definite. Abelard calls statements propositions
(*propositio*) and what is asserted by a statement its
*dictum.* He considered that a statement is true or false when
its *dictum* is true or false. In dealing with prophesy,
Abelard suggested that the *dictum* about a singular event is
first expressed by a future tense proposition and then by present and
past tense propositions. (For the nature of the *dictum*,
contrasted with the 'facts' and 'propositions'
of twentieth-century philosophical jargon, see Marenbon 1997:
202-209). The view of a fixed propositional content was
developed further by twelfth-century authors who were later called
*nominales.* One of the theses of this group was "What is
once true is always true". (See Iwakuma and Ebbesen 1992: 196,
199-201, 205-206 for the relevant texts. For the history
of the principle, see also Marenbon 1992: 58-61 and Ebbesen
1992: 73-74.) This thesis was employed in the discussions of how
the beliefs of Abraham and others who lived before the coming of
Christ and believed various things about him were the same as the
beliefs of those who live after His coming. The reason for asking this
was that the previous beliefs were formulated in future tense
statements and the latter in present or past tense statements.
According to the *nominales*, one could regard as basic a
temporally definite propositional content the meaning of which is
expressed by various tensed expressions depending on when they are
uttered. While tensed statements about temporally definite singular
events have a changing truth-value, the corresponding non-tensed
*dicta* are unchangingly true or false (Nuchelmans 1973:
177-189; for some later examples, see also Nuchelmans 1980;
Lewis 1995; Goris 2001). Peter of Poitiers (c. 1130-1205), one
of the authors taking this approach, argued that while the singular
statements about contingent things are immutably true or false because
of God's eternal choice, their unchanging truth-value could be
otherwise. God does not know contingent things through tensed
statements, since their truth-value is changeable. If God's
knowledge is described by using tensed statements, analogously to the
articles of faith before and after the coming of Christ, one should
read them so that they signify the same (Peter of Poitiers,
*Sententiae* I.7, 133-143; I.12.199-223;
I.14.328-253). This became a well-known position since it was
also employed in Peter Lombard's *Sententiae* (I.39.1;
I.41.3).



The theological formulations by Peter Abelard, Peter Lombard and Peter
of Poitiers discussed above exemplify twelfth-century deviations from
the Aristotelian thesis "What is necessarily is when it
is". This was traditionally understood as implying the principle
of the necessity of the present, which was not questioned in ancient
modal theories (Knuuttila 1993: Ch. 1). Since God's knowledge
about contingent things was regarded as unchangeable, the contingency
of this knowledge (in the sense that it could be different) also
implied the denial of the Aristotelian equation of immutability with
necessity, a denial regarded as an explicit doctrine of the
*nominales* (Iwakuma and Ebbesen 1992: 194). The new modal
paradigm, which is more or less consciously applied in these
discussions of God's will, power, and knowledge, could be
characterized as the model of simultaneous or synchronic alternatives.
There are three main examples of it in early medieval philosophy. 



Abelard assumes that at a given instant of time, what is actual is
necessary as no longer avoidable, but he argues that unrealized
alternatives are possible at the same time in the sense that they
could have happened at that time. Some of the alternatives of a
singular being are real counterfactual alternatives. These are
unrealizable because of some previous change in the conditions of the
subject, and some are merely imaginable alternatives, such as
Socrates's being a bishop, which never had a real basis in
things. While often employing traditional ideas about necessity and
possibility, Abelard also developed ideas pertaining to simultaneous
alternatives. (See Martin 2003; Knuuttila 2008: 537-538.)



Gilbert of Poitiers (1085/90-1154) stressed the idea that
natural regularities which are called natural necessities are not
absolute, since they are chosen by God and can be overridden by divine
power. This had become a widespread theological view in
Gilbert's time. Gilbert explained it in the light of the
Augustinian view of God's acting by choice between alternative
providential options and omnipotence as an executive power. There is
an interesting formulation of Plato's 'Platonitas'
in Gilbert. This is said to include all of what Plato was, is and will
be as well as what he could be but never is. Even though Gilbert does
not explain why there is a modal element in the individual concept, it
was probably needed in order to speak about Plato in alternative
possible histories or, as in Abelard, about Socrates as a bishop.
Gilbert seems to have been the first to formulate an individual
concept in this way (Knuuttila 1993, 75-82; Marenbon 2007: 158-159).



A third context of the systematic interest in simultaneous
alternatives was the new twelfth-century theory that declarative
singular statements or their contents should be primarily treated as
temporally definite and as having an unchanging truth-value. All
propositional contents pertaining to contingent things have a
truth-value on the basis of God's eternal choice. These
truth-values would be otherwise if the providential design of the
world were different in relevant respects. Robert Grosseteste
(1168/75-1253) taught that the opposites of actualized
contingent things are no longer realizable possibilities, though they
are possible alternatives in the sense that they could have been
included in God's eternal providential choice. Actual history is
an explication of one of the divine alternatives with respect to which
things are primarily called necessary, possible or impossible.
Necessities and possibilities at this basic level are called
modalities 'from eternity and without beginning'.
Mathematical truths exemplify these 'simple' necessities.
In addition, there are necessities and impossibilities which have a
beginning and which are eternal contingencies in the sense that they
depend on God's free choice (*De libero arbitrio*
168.26-170.33; 178.28-29). The contingency of the divine
acts of knowledge and will is associated with an atemporal causal
priority between the powers and their acts (178.24-26).
Grosseteste's views are compared with those of Duns Scotus in
Lewis (1996).



This was an innovative theory for dealing with future contingent
statements as omnitemporally true or omnitemporally false or, if these
were tensed, as antecedently true or antecedently false. The
truth-values of statements about contingent things, though temporally
immutable from the beginning of the world and also immutably known by
God, were metaphysically contingent. The consequence from knowledge or
truth to necessity, whether causal or semantic, was denied. The
contingency of the created order was based on God's eternal and and
free providential choice that involved the acts of the created will as free.
Anselm formulated this traditional view, following Augustine, as
follows: "It is both necessary that God foreknows what will come
to be and that God foreknows that something will freely come to
be" (*De concordia praescientiae et praedestinationis et
gratiae Dei cum libero arbitrio*, 1.1; cf. Augustine, *On Free
Choice of the Will*, 3.3.8). Anselm argued that that predictions
are true or false and their truth can be understood as the
correspondence to what will happen, although what will contingently
happen is not known to human beings without supernatural help. This
was the standard view of the possibility of prophesy. (See the above
quotation from Anselm's *Cur Deus homo*; Peter Abelard,
*Glossae super Peri hermeneias*, IX.69-85; Anonymous,
*Summa Duacensis*, 129-130.)



Early medieval authors were well acquainted with the conception of
God's eternal and timeless knowledge in Augustine and Boethius.
This aspect of the question of the divine knowledge and future
contingents became a central issue in Thomas Aquinas, who discussed
the philosophical theory of future contingents by following Aristotle
and Boethius rather than twelfth-century innovators. According to
Aquinas, God atemporally grasps all combinations of things in
particular times by one eternal vision. Temporal things are timelessly
present to God, who has direct knowledge of them and their temporal
order, though none of them is past or future with respect to His
cognition (*Scriptum super libros Sententiarum* I.38.1.4-5; *Summa contra
gentiles* I.66; *Summa theologiae* I.14.9, 14). Things seen
as actual are necessary by supposition (i. e., with respect to
God's knowledge and providence), but many of them are contingent
with respect to their proximate causes (*Scriptum super libros Sententiarum* I.38.1.5,
*Summa contra gentiles* I.67, *Summa theologiae* I,
14.13, *De veritate* 2.12). The ultimate source of the
actuality of the created order is the divine free will (*In libros 
Perihermeneias* I.14, 197). Aquinas assumes that a metaphysical view of
the truth or falsity of all temporally definite propositions implies
that everything happens of necessity (*In libros Perihermeneias* I.13,
173). In order to avoid this wrong idea, one should deal with future
contingent propositions like Boethius as disjunctively true or false.
Their definite truth-values known by supernatural omniscience are
beyond human cognitive capacities, except the various degrees of
probabilities corresponding to certain types of causes (*In
libros Perihermeneias* I.13, 172, 174). However, in the doctrine of divine
providence, all historical propositions are definitely true. This is
called Aquinas's providential determinism (Porro 2013:
121-127; Posti 2017: 82). While there are prophetic predictions
of future contingents through a revelatory participation in divine
knowledge, their truth remains a supernatural matter (*Summa
theologiae* II-2, 171.3, 6). Speaking about God's atemporal
knowledge as divine prescience is a temporal projection of the divine
mode of knowing. For various interpretations of Aquinas's view,
see Wippel 1985; Craig 1988: 99-126; Goris 1996; Marenbon 2005;
Knuuttila 2010.



Medieval critics found the allegedly Thomist idea of the presence of
each instant of time to God's non-temporal eternal vision
problematic because of the transitivity and symmetry of the relation
of simulaneity. (See John Duns Scotus, *Lectura*
I.39.1-5, 23, 28, 87, and further references in Hoenen 1993:
169-70.) One could also ask how Aquinas's view of
God's essential simplicity and immutability is compatible with
the view that God's eternal choice could be otherwise and the
voluntary acts of created beings could be other than what is known by
God (see Stump 2003: 100-127).


## 3. Interpreting Aristotle



Mignucci's account of how Ammonius and Boethius understood the
distinction between definite and indefinite truth is roughly speaking
the same as the explanation of these terms in Peter Abelard's
interpretation of *De interpretatione* 9. Abelard believed that
Aristotle assumed that future contingent statements are true or false,
though not determinately true or false before the actuality of the
things to which they refer (*Dialectica* 213.17-20).
Abelard used the notions of 'determinate/indeterminate'
instead of the Boethian 'definite/indefinite', as most
medieval authors did. In this interpretation, he retained the
principle of bivalence for all assertoric statements, but rejected the
universal application of the stronger principle that every assertoric
statement is determinately true or determinately false. According to
Abelard, the notions of 'determinate' or
'indeterminate' apply primarily to the truth-makers of
assertions and secondarily to assertions themselves:



> 
> 
> But as the obtaining of future contingent states of affairs is
> indeterminate, similarly the propositions which enunciate these are
> said to be indeterminately true or false, for those which are true are
> indeterminately true and those which are false are indeterminately
> false, in acccordance with the indeterminate obtaining of what is
> predicted. *Dialectica* 211.30-32)
> 
> 
> 



Abelard was interested in the question of whether the
present truth of statements about future contingent events are
themselves determinate; i. e., whether "The sentence
'Socrates will eat tomorrow' is true", if true, is
determinately true. Denying this, he restricted the principle that all
past and present true propositions are determinately true. Abelard
also distinguished between determinateness and certainty. Future
contingent propositions may be certain if they are revealed by angels,
for example, but they are not knowable of themselves and not
determinately true. (See *Glossae super Peri hermeneias*
IX.19-42; *Dialectica* 211.32-212.23; Lewis
1987.)



The 'traditional' view of truth and bivalence in Aristotle
is put forward in an anonymous early twelfth-century commentary on
*De interpretatione*, edited by M. Dal Pra, which is often, and
probably mistakenly, attributed to Abelard. Applying Boethius's
distinction between definitely and indefinitely true statements, the
author argues that future contingent statements are merely
disjunctively true or false (*tantum sub disjunctione*);
100.13-19; 112.8-113.3). They are true-or-false.



While Abelard thought that the universal validity of the principle of
bivalence was an Aristotelian view, thirteenth-century commentators
argued for the traditional interpretation. Albert the Great and Thomas
Aquinas took Aristotle to be arguing in *De interpretatione* 9
that if every contradictory pair divides truth and falsity in a
determinate way and the members are consequently determinately true or
false, all things must determinately be or not be. They thought that
Aristotle then refuted the consequent by referring to various
contingent things. It follows that the antecedent cannot be true and
future contingent propositions are not determinately true or
determinately false. They are true-or-false under disjunction (Albert
the Great, *Liber Perihermeneias*, I.5.4-6,
418-422; Thomas Aquinas, *In libros Perihermeneias*,
I.13, 170-172; I.15, 202-203). The same interpretation of
Aristotle is found in Arabic commentators Abu Nasr
al-Farabi and Averroes. (See *Al-Farabi's*
*Commentary and Short Treatise on Aristotle's* De
interpretatione, trans. F. Zimmermann, lxviii, 75-76,
78-79, 91-92, 244-245, and Averroes's *Middle Commentary on Aristotle's* De interpretatione, 82va.)
Al-Farabi's own view was that future contingents
are either true or false (94-96; Marmura 1985; Adamson 2006).
The traditional interpretation of Aristotle's view was put
forward by many later Latin commentators such as John Duns Scotus,
*Quaestiones in libros Perihermenias Aristotelis*, I.7-8
(179-181), trans. Buckner and Zupko; Walter Burley,
*Commentarius in librum Perihermeneias Aristotelis*, 92,
95-96; William Ockham, *Expositio in Librum Perihermenias
Aristotelis* I.6.15; Peter Auriol, *Scriptum in I
Sententiarum* I.38.3, 817-828; Gregory of Rimini,
*Lectura super I Sententiarum* I.38.1.1 (238-243); Peter
of Ailly, *Quaestiones super libros Sententiarum* I.11.1A). In
his *Supercommentary on Averroes's Commentary on
Aristotle's* De interpretatione, the Jewish philosopher Levi
ben Gerson (Gersonides, 1288-1344) states that positing a truth
value for future contingents leads to absurdity (83r; Rudavsky 1985:
166). However, John Buridan read Aristotle in the same way as Abelard.
All assertoric statements are true or false though those about future
contingents are not determinately true or false (*Questiones longe
super librum Perihermeneias* I.10). Since theologians usually
thought that divine omniscience and prophecy presupposed unrestricted
bivalence, the discussion of future contingents was divided into
historical constructions of Aristotle's view, mostly in
accordance with the traditional interpretation, and the systematic
discussions in theology that mostly refuted this for doctrinal
reasons. Later examples of the traditional interpretation of
Aristotle's view include George of Brussels, *Logica magistri
Georgii inserto textu Bricoti*, 51rv; Iodocus Trutfetter,
*Summulae totius logicae* II.1 (LL3v-4v); *Veteris
artis...Perihermeneiasque expositio* (g1r); see also Baudry
1989 (ed.), *La querelle des futurs contingents (Louvain
1465-1475). Textes inedits*, 206. (For medieval
interpretations, see Weidemann 1994; Gaskin 1995; Knuuttila 2010.)


## 4. Later Medieval Views



An influential late medieval approach to future contingents was
included in John Duns Scotus's theory of metaphysics as a
transcendental science in which the meaning of the univocal notion of
being (*ens*) was defined as 'that to which to be is not
repugnant'. Beings in this metaphysical sense are actual things
as well as non-actual possible things, the imagined actuality of which
does not include a contradiction. In the Augustinian tradition
metaphysical possibilities were ultimately based on the divine essence
and represented the ways in which it could be imitated by created
things. According to Scotus, when God as an omniscient being knows all
possibilities, he seemingly does not know them by turning first to his
essence. Possibilities can be known in themselves; in fact, they would
be what they are even if there were no God. Scotus calls the
propositional formulations of pure possibilities logical possibilities
(*possibile logicum*). These express things and states of
affairs to which it is not repugnant to be. Possibilities as such have
no kind of existence of their own, but are real in the sense that they
form the precondition for everything that is or can be. (For
Scotus's modal theory, see Vos *et al.* 1994; Knuuttila
1996; Normore 1996, 2003; Honnefelder 2005.) Scotus takes it as an
obvious fact that there are contingent states of affairs which could
have not been at that very moment of time at which they are
(*Ordinatio* I.2.1.1-2, 86). This idea of simultaneous
alternatives differed from the traditional view of the necessity of
the present and played and important role in Scotus's
metaphysics.



All possibilities of being receive intelligible or objective being as
the objects of God's knowledge. Some of these are included in
God's providential plan of creation and will receive actual
being. The description of a possible state of affairs at a certain
moment consists of compossible possibilities. Since finite beings are
contingently actual, alternative possibilities are possible with
respect to the time of their actuality, but they are not compossible
with what is actual. According to Scotus, impossibilities are
incompossibilities between possible ingredients, such as
Socrates's sitting at a certain time and Socrates's not
sitting at that same time (*Lectura* I.39.1-5, 62-63;
*Ordinatio* I.35, 32, 49-51; I.36, 60-1; I.43, 5-7, 14).



Scotus's modal metaphysics incorporates many ideas similar to
those in the early medieval model developed by Abelard and the
*nominales*, such as the denial of the necessity of the
present, the distinction between immutability and necessity and the
universal validity of bivalence. Giving up the Thomistic view of the
atemporal presence of the flux of time to God, Scotus explains
God's knowledge of the truth-value of future contingent
propositions as his knowing which of the possible scenarios will be
actual and which will not (*Lectura* I.39.1-5, 44). The
definite truth-values of the propositions about possible future events
do not make them necessary, many of these being acts of the will which
as a free cause chooses between alternatives without being determined.
(See Vos *et al.* 1994; Soder 1999; for some discussions
of Scotus's view of the free acts of the will, see Dumont 2001;
Normore 2003: 141-145; Langston 2010.) 



Scotus famously attempted to explain the contingency of God's
eternal choice by distinguishing between the instants of nature in
God's mind that represent conceptual succession without
separation or interval, for example, the instant of encountering
opposite alternatives and the instant of choosing one of these. Future
contingent propositions founded on God's eternal choice are
determinately true or false in such a way that they could be
otherwise, independently of whether they are known or not to humans
(*Ordinatio* I.38.2, 426) These ideas are not found in
Scotus's early questions on Aristotle's *De
interpretatione* that mostly follow Boethius's views on
future contingents, adding some more elaborated analyses of the
structure of future-tense propositions: they may signify that it is
true now that something will be or signify that something will be
(*Opus* 2.1.7-9). See the translations and commentary in
Buckner and Zupko 2014. 



Ockham followed Scotus in believing that God's choice could be
other than it is and that future contingent propositions are true or
false just as Scotus explicated, but he was dissatisfied with
Scotus's instants explanation, admitting that he did not have
any of his own (*Ordinatio* d. 38, 578, 581, 584-5; Adams
1987: 1130-1136. Ockham also criticized the view that God knows future free acts
through his own acts of the will as their partial cause, which he,
like many of his contemporaries and later commentators, treated as
Scotus's position (*Ordinatio* d. 38, 582-583). This was
Henry of Ghent's view to which Scotus first subscribed but then
qualified his acceptance. (See Hoenen 1993: 177-179; Soder
1999: 177-183; Schabel 2000: 43-46.) Scotus thought that there
are many contingent propositions known by God that are not simply
chosen but rather permitted such as those about creaturely sins and
other acts of free will (see Frost 2010).



In Scotus' theory, the synchronic alternatives of a future free
act remain possibilities though not compossibilities at the instant of
that act. He thought that these "logical potencies"
expressed by propositions with non-repugnant terms are not sufficient
for freedom that requires "real potencies" for
alternatives at an instant of time with respect to the same instant
(see Dumont 1995). Ockham did not accept this part of Scotus's
denial of the necessity of the present, thinking that real capacities
for oppositions are diachronic (*Ordinatio* d. 38, 581). Opposite
real capacities without temporal succession at an instant were found
problematic by Thomas Wylton, an early critic of Scotus's ideas
who, while largely following Boethius, put forward some propositional
distinctions similar to those in Scotus's questions on *De
interpretatione*. See the edition and comments in Schabel 2011b;
Bornholdt 2017: 116-120.



Ockham believed, as Scotus did, that future contingent propositions
are true or false, that created wills are non-determined free causes,
and that God knows contingent events without their being
simultaneously present to God. (For Ockham's view, see Adams and
Kretzmann 1983; Normore 1982.) While Scotus preferred to distinguish
God's eternal knowledge and choice from the temporal order
sharply (*Lectura* I.39.1-2, n. 28, 85; *Ordinatio* I.40,
n. 8), Ockham thought that they can be treated as temporally past.
This led him to ask how God's foreknowledge as something past
and hence seemingly necessary is compatible with the contingency of
future things. Ockham's answer was that even though God's
foreknowledge is past, its content is future, and the past truth of
future contingent propositions in God's immutable but contingent
knowledge does not fall under the necessity of the past (*Ordinatio*
d. 38, 387-8; *Tractatus de praedestinatione*
515-516). Many influential late thinkers embraced Ockham's
view. (See Robert Holkot, *Sent.* II.2 in *Seeing the Future
Clearly*, 127, 145-146; Gregory of Rimini, *Lectura super I Sententiarum*
I.38.2.3 (302-303); Pierre d'Ailly, *Quaestiones super libros Sententiarum* I.11.3S.) This is also the hallmark of what is called the
Ockhamist view of divine foreknowledge in contemporary philosophical
theology (Zagzebski 1991: 66-97).



Walter Chatton was a contemporary critic of Ockhams's views
about future contingents and divine knowledge. He also addressed the
theories of Scotus, Wylton, and particularly Peter Auriol, his main
source of inspiration, but mostly avoided formulating his own
position. For an English translation with a commentary of his main
treatise on future contingents, see Bornholdt 2017; see also the
 SEP entry on Walter Chatton.
 Peter Auriol put forward an original revision of the usual
theological position that while future contingent propositions were
neither true nor false in Aristotle, this was not acceptable
concerning divine knowledge. Auriol argued that since these
propositions lack a truth value, even God is aware of the future in an
"indistant" way that does not imply that future contingent
propositions should be treated as true or false. Auriol's
indistant knowledge abstracts from temporality and simultaneity and is
allegedly compatible with God's necessary immutability and human
free will (Schabel 2000: 67-123). Auriol's position
inspired much critical discussion until early sixteenth century. It
came to be regarded as heretical when a Papal commission made a
decision about the theses of Peter de Rivo, who defended a view
similar to that of Auriol. Some of de Rivo's statements were
officially condemned in 1474 by Pope Sixtus IV (Baudry 1989 (ed.), *La querelle des futurs contingents (Louvain 1465-1475). Textes inedits*; Schabel 1995-96, 2000:
315-336, 2003a).



English fourteenth-century authors often commented on the
terminological distinctions between determinate and indeterminate
truth and falsity. Ockham characterized all prospective truths,
whether necessary or contingent, as immutable and therefore
determinate, but there were other suggestions as well. Walter Burley,
Richard of Campsall, Arnold of Strelley, and Robert Holkot preferred
to call true propositions about future contingent things as
indeterminately or contingently true. Some commentators have argued
that speaking about this special mode of being true or false was an
attempt to modify bivalence by formulating an idea of many-valued
logic, see Normore 1982, 1993; Gelber 2004: 224-250. For further
texts and studies on late medieval controversies related to
foreknowledge, freedom and future contingents, see Genest 1992;
Schabel 2003a, 2003b, 2007, 2011a, 2011b; Schabel, Friedman, and Balcoyiannopoulou
2001; Rossini and Schabel 2005; Thakkar 2005, 2010. 



A central question for those who gave up the Thomist view was how God
can eternally know the acts of the will which is a free cause? An
influential answer was offerred in the theory of middle knowledge by
Luis de Molina (1535-1600). In addition to the knowledge of all
possibilities and the possibilities which will be actualized in the
providentially chosen history, God has a third kind of knowledge
(*scientia media*), which comprises the hypothetical truths
about possible beings. In creating the world, God knows what possible
creatures would do in any possible situation (Freddoso 1988).
Molina's 'middle knowledge' theory about
counterfactuals of freedom was actively debated in the sixteenth and
seventeenth century and has remained a living issue in the philosophy
of religion (Dekker 2000).