Omniscience is the property of having complete or maximal knowledge.Along with omnipotence and perfect goodness, it is usually taken to beone of the central divine attributes. One source of the attribution ofomniscience to God derives from the numerous biblical passages thatascribe vast knowledge to him. St. Thomas Aquinas (SummaTheologiae I, q. 14), in his discussion of the knowledge of God,cites such texts as Job 12:13: “With God are wisdom andstrength; he has counsel and understanding” and Rom. 11:33:“O the depths of the riches and wisdom and knowledge ofGod!” Another source is provided by the requirements offormulating one or another theological doctrine. For example, thedoctrine of divine providence holds that God has a plan for the worldaccording to which all things are in his care and work out accordingto his good will. As Flint puts it,

to see God as provident is to see him as knowingly and lovinglydirecting each and every event involving each and every creaturetoward the ends he has ordained for them (Flint 1998: 12).

It is thus natural to think than an account of providence requiresattributing vast knowledge to God. (For a dissenting interpretation ofprovidence which does not require complete knowledge, see Hasker2004.) A third motivation for including omniscience among the divineattributes derives from “perfect being theology”. Perfectbeing theology appeals to St. Anselm, who held that God is that thanwhich nothing greater can be thought (Proslogion, c.1077).Anselm expands on what he means by greatness by giving the formulathat “God is whatever it is better to be than not”, and heconcludes that this includes such properties as making other thingsfrom nothing, being just, being happy, and being perceptive,omnipotent, and merciful. Anselm can derive omniscience from this listbecause he holds that “to perceive is nothing else than toknow” (Anselm 1998: 90). Other exponents of perfect beingtheology could simply, and more directly, affirm that it is better tohave knowledge than not; so having knowledge is a property thatcontributes to greatness. Interestingly, the first of these sources,the biblical ascriptions of great knowledge to God, together withadditional passages attributing other perfections to him, as Leftowargues, license a version of the third motivation, perfect beingtheology. On this view, perfect being theology “simply tries toshow what authoritative statements about God’s perfectionsentail” (Leftow 2011: 108).

This entry will address philosophical issues concerning omniscience asa divine attribute or a perfection, without considering its potentialapplication in theology.

• 1. Defining Omniscience
• 2. Additional Features of Divine Knowledge
• 3. Foreknowledge and Human Free Action
• 4. Further Difficulties for Omniscience
  • 4.1 Omniscience and Immutability
  • 4.2 Omniscience and Knowledgede se
  • 4.3 Omniscience and Knowledgede re
  • 4.4 Omniscience and Cardinality
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

1. Defining Omniscience

Since omniscience is maximal or complete knowledge, it is typicallydefined in terms of knowledge of all true propositions, namely, as

(D1)

S isomniscient \(=_{\textit{df}}\) for everypropositionp, ifp is true thenS knowsp.

One might think it important to require, in addition, that anomniscient being also knows which propositions are false. In thiscase,(D1) could be replaced by

(D2)

S isomniscient \(=_{\textit{df}}\) for everypropositionp, ifp is true thenS knowsp and for every propositionq, ifq isfalse thenS knows thatq is false.

This revision is equivalent to(D1), however, given that for every false proposition there is a true oneto the effect that the first one is false.(D1) already requires an omniscient being to know the latterproposition.

Or one might add that omniscience not only requires knowing all truthsbut also believing no falsehoods. That is,

(D3)

S isomniscient \(=_{\textit{df}}\) for everypropositionp, ifp is true thenS knowsp, and there is no propositionq such thatq is false andS believesq.

But(D3) is also equivalent to(D1), at least if it is impossible to believe the denial of a propositionone knows to be true, knows that one knows to be true, knows is thedenial of a proposition one knows, etc. (Oppy (2014: 233) claims, moresimply, that it is not possible to know a proposition if one believesits denial.) In the recent literature, Swinburne (1993: 167 and 2016:175) states a version of(D1) (although in both works he later endorses restricted principles(1993: 181–182 and 2016: 196) to yield what he calls an“attenuated” definition). Zagzebski (2007: 262) endorses(D2). Plantinga ([1974] 1977: 68), Davis (1983: 26), Gale (1991: 57), Craig(1991:6), and others propose(D3).

Several recent discussions of omniscience have attempted to defend amore restricted account than offered by the preceding definitions. Forexample, Langtry (2008: 39) suggests that God is omniscient just incase, for every true propositionp, “either God knowsthatp, or else he does not but his knowing thatpis not precluded by any defect or limitation in his intrinsiccognitive capacities.” Nagasawa (2017) claims that a strongerversion of perfect being theology would hold that God has a“maximally consistent set” of the divine attributes ofknowledge, power, and benevolence. This would allow that a perfectbeing could be omniscient without knowingall truths, ifknowing all truths would reduce the amount of power or benevolence thebeing could possess. Another departure from the traditionalunderstanding presented above appeals to feminist epistemology. Seethe Section 3.1 of the entry onfeminist philosophy of religion, which hints at this possibility in its discussion of “so-calleddivine attributes”, although it limits its discussionto perfect power and divine aseity. Farmer (2010), however, draws moredirectly on feminist epistemology as an application to understandingomniscience. The negative claim in this work is that“propositional ideals of human knowledge” exclude“marginalized and maligned” forms of knowledge. Thusomniscience could be better understood by appealing, positively, tothese other forms of knowledge. Farmer cites “knowing otherpeople in personal relationships”, the “centrality ofcare” which leads to “the acknowledgement of the othernessof the object of knowledge”, and the role of emotion in leadingto knowledge. (Farmer cites (Code, 1993), (Dalmiya 2002), and (Jaggar1989), respectively, for these ideas.) However this approach is to beworked out, the intention is that omniscience would not simply bedefined by reference to knowledge of true propositions.

Another recent development might also be seen as recommending adifferent account of omniscience. This is the suggestion, presentedmost prominently by Zagzebski, that God has the attribute ofomnisubjectivity. According to Zagzebski, omnisubjectivity is“the property of consciously grasping with perfect accuracy andcompleteness the first-person perspective of every consciousbeing” (2008: 232). She adds that “God’s knowledgeof our conscious lives is something like the perfection ofempathy” (2008: 236). Since grasping someone’s subjectiveexperience seems not to be propositional, perhaps the suggestion isthat omniscience involves more than knowledge of propositions. ButZagebski’s claim is, rather, that omnisubjectivity is entailedby omniscience (2008: 232) or entailed by the conjunction ofomniscience and omnipresence (2016: 436), so it is perhaps betterthought of a further extension of divine cognitive perfection and nota rejection of the definitions listed above.

Despite this recent work on omniscience, the main disputes in theliterature center on the traditional definition of omniscience;accordingly, this entry will concentrate on them. These disputes havefocused on the scope of the quantifier in(D1), whether, for example, it includes propositions about the future,whether(D1) requires an omniscient being to change as time goes by, whether itrequires enough for maximal knowledge, and whether it (falsely)presupposes that there is a set of all truths.

2. Additional Features of Divine Knowledge

Omniscience is supposed to be knowledge that is maximal or complete.Perhaps knowledge of all truths, as(D1) puts it, captures that idea. But there are other features that mightbe included in such maximal knowledge when it is had by a perfectbeing. For example, perhaps a perfect being does not merely believeall true propositions but, in addition, could not possibly bemistaken. Perhaps, in other words, such a being isinfallible, that is, necessarily such that any proposition itbelieves is true. Van Inwagen (2006: 26) adds to his variant of(D1) that it is impossible that there is a propositionq suchthatS believesq andq is false, which isequivalent to requiring that necessarily ifS believesp thenp is true. (See also van Inwagen 2002: 221.)It is conceivable that a being might satisfy(D1) by knowing all truths without its being such that it could notpossibly hold a false belief. In that case infallibility adds anadditional component to the standard account given by(D1).

A related idea emerges from the suggestion that not only does aperfect beingexist necessarily, but it has its variousgreat-making propertiesof necessity. The suggestion is thata being worthy of worship should not “possess itsvariousexcellences in some merely adventitious manner” (Findlay1948: 180). In that case, another feature of divine knowledge, if Godexists necessarily, is beingessentially omniscient, that is,being omniscient and not possibly lacking omniscience. Essentialomniscience entails infallibility—a being who could not possiblyfail to be omniscient could not possibly be mistaken—but thereverse does not hold, for a being who could not possibly believe afalsehood might nevertheless fail to believe all truths. So essentialomniscience might be another additional component to the standardaccount. In an influential article Pike (1965) has argued for theincompatibility ofessential omniscience and voluntary humanaction (seeSection 3).

Another question that arises about God’s knowledge is whether itis alloccurrent knowledge or whether some of his knowledgeisdispositional. Knowledge of a proposition is occurrent ifthe knower has that proposition in mind. And knowledge of aproposition is dispositional, roughly, if the person knows theproposition but is not currently thinking about it or entertaining it,that is, if the person has a dispositional belief (see Section 2.1 ofthe entry onbelief) in that proposition. Philosophers have answered this questiondifferently. Thomas Aquinas claimed that God’s knowledge was not“discursive” (Summa Theologiae, I, 14, 7), bywhich he meant, in the first place, that God does not first think ofone thing and then think of another, for “God sees all thingstogether and not successively”. On the other hand, Hunt (1995)has argued that taking God’s knowledge of the future to bedispositional can provide a way of reconciling divine foreknowledgewith human free action (see next section). It seems hard tounderstand, however, how someone with the vast ability to beomniscient could fail to be aware of any part of what they know.

A second thing that Aquinas meant by claiming that God’sknowledge is not discursive is that God does not derive his knowledgeby deducing conclusions from other things that he knows. Of course thepropositions God knows stand in logical relations with each other, andthat includes standing in the relation of premisses to validconclusion. Aquinas’s claim, however, is that God does notarrive at a conclusion by deducing it from premisses. In contrast,however, Mavrodes (1988), recognizing the many logical relations inwhich propositions stand to one another, conjectures that all ofGod’s knowledge is inferential.

The usual discussions of omniscience treat it as a special case ofknowledge, although, perhaps, with such additional features as beingarrived at infallibly or through essential omniscience. A standardaccount of knowledge holds that it is justified true belief, plus a“fourth condition” to avoid counterexamples (see, forexample, Chisholm 1989: 90–91). Perhaps, instead, knowledge iswarranted true belief, that is, a true belief produced by ones noeticfaculties functioning properly in circumstances in which they weredesigned to function (see, for example, Plantinga 1993). Or, accordingto another recent proposal, the “Knowledge First” view,knowledge is a general state not to be analyzed by satisfying someother conditions (see Williamson 2000); but even on this suggestion,knowledge entails belief and justification. Thus, on all of theseviews, knowledge involves belief—as did our discussion twoparagraphs back of whether omniscience could include dispositionalbelief. For the most part, however, philosophers have not devoted muchattention to the status of God’s beliefs or the nature of hisjustification. One exception is the claim of Alston (1986) thatGod’s knowledge is not divided into separate beliefs and that infact God does not have beliefs. According to Alston, God has anintuitive, immediate awareness of all truth, which gives him knowledgewithout belief. For criticism of Alston’s view, see (Hasker1988) and (Dickinson 2019).

Whether considerations of perfection require that God’sknowledge includes any of these additional features, most discussionsof omniscience do not focus on whether it includes infallibility,essential omniscience, being “non-discursive”, or notinvolving belief. Instead, they primarily address the range of theknowledge that omniscient requires. Accordingly in what follows wewill consider issues that arise when omniscience is understood alongthe lines of(D1).

3. Foreknowledge and Human Free Action

Knowledge of all true propositions would seem to include knowledge ofall truths about the future, at least if there are truths about thefuture. Thus omniscience would seem to includeforeknowledge.There is a long tradition, however, of philosophers who have thoughtthat divine foreknowledge was incompatible with human free action, or,at any rate, they took arguments for the incompatibility seriouslyenough so as to require either disarming them or limiting what isinvolved in divine omniscience. (Similar reasoning might be given toargue that God’s foreknowledge is incompatible with some ofGod’s own free action. See Swinburne (2016 183) for a such asuggestion. We will follow tradition and consider only the applicationto human action.) Early discussions include ones by St. Augustine(On Free Choice of the Will, Bk. III, ch. 3) and Boethius(The Consolation of Philosophy, Bk. V). They each consideredan argument that may be represented (whereS is any personandA is any action) as:

(1)

If God has foreknowledge thatS will doA, thenit is necessary thatS will doA.

(2)

If it is necessary thatS will doA, thenS is not free with respect to doingA.

Therefore,

• (3)If God hasforeknowledge thatS will doA, thenS isnot free with respect to doingA.

It is somewhat controversial exactly what Augustine’s ownresponse to this argument is (in his formulation it is foreknowledgeof a sinful action and not foreknowledge of human actions moregenerally). An influential interpretation has been given by Rowe(1964) and criticized by Hopkins (1977), who both think that Augustinedenies premiss (2) on the grounds that human actions may be free evenif they come about by necessity. An alternative interpretation hasbeen defended by Wierenga (1989: 60–63), who thinks thatAugustine only explicitly argues against the conclusion of theargument. In any event, it is clearer that Augustine denies theconclusion than that he identifies a flaw in the argument. Boethius,on the other hand, accepts the argument but denies that omniscienceincludes foreknowledge. Instead, God’s perspective is that ofeternity, that is, “the complete possession all at onceof illimitable life”. In other words, God sees everything thatever happens all at once, so he does not, strictly speaking, knowthings ahead of time. (For a more recent defense of this view, seeStump and Kretzmann 1981.)

Subsequent philosophers, however, beginning at least as early asAquinas, identified a flaw in the argument. According to Aquinas(Summa contra Gentiles, I, 67, 10), the first premiss isambiguous between the “necessity of the consequence” andthe “necessity of the consequent”. That is, (1) may beinterpreted as

(1′)

It is necessary that if God foreknows thatS will doA, thenS will doA.

or as

(1″)

If God foreknows thatS will doA, then it is anecessary truth thatS will doA.

On the former interpretation the premiss is true, but under thatinterpretation the argument is invalid, that is, the conclusion doesnot follow. Interpreting the premiss in the second way results in anargument that is valid, but this premiss is false. Just because Godknows a proposition, it does not follow that the proposition is anecessary truth; God knows contingent truths, as well. In either case,the argument fails.

There is a second, more difficult argument for the incompatibility ofdivine foreknowledge and human free action. An early version was givenby Pike (1965), and it has occasioned a voluminous recent literature.(For some of this literature, see the papers and bibliography includedin Fischer 1989.) Developments of the argument typically draw on thefollowing claims:

(4)

A proposition reporting an event in the past is foreverafterwards “fixed” or “unalterable” oraccidentally necessary.

(5)

A contingent proposition that is entailed by an accidentallynecessary proposition is itself accidentally necessary (accidentalnecessity is closed under entailment).

(6)

If a proposition is accidentally necessary at a time, no one isable at any later time to make it false.

In virtue of (4), propositions reporting God’s past beliefs areaccidentally necessary. If it is true thatEighty years ago Godbelieved that Jones will mow his lawn tomorrow (to usePike’s example), then that proposition reports a past event and,thus, is now accidentally necessary. Now from the assumptions that Godis omniscient and that God believesp, it follows thatp. If we strengthen the first assumption to hold either thatGod isessentially omniscient or that he isinfallible (seesection 2 above), the propositionGod believes p by itself entailsp, that is, it is not possible that God believepandp be false. Let us develop the argument under one ofthese stronger assumptions. Then sinceGod believes that Joneswill mow his lawn tomorrow entailsJones will mow his lawntomorrow, given that the former is accidentally necessary andthat the latter is contingent, it follows, with the help of (5), thatJones will mow his lawn tomorrow is also accidentallynecessary. But then, in view of (6), no one, not even Jones himself,is able to make it false that Jones will mow his lawn tomorrow. Ifthere is nothing Jones can do to avoid mowing his lawn tomorrow, thenhe does not do so freely. This action was chosen arbitrarily, and sothe argument is supposed to show that no action that God knows aheadof time will be performed is free; divine foreknowledge isincompatible with human free action.

This argument requires a number of nontrivial assumptions. So there isno lack of places for an objector to attack, and, in fact,philosophers have tried various ways of discrediting the argument,none of them entirely convincing. Ockhamists (named after William ofOckham) try to defend the claim that many propositions apparentlyreporting God’s past beliefs are not wholly about the past, andthus are not accidentally necessary. Accordingly, Plantinga (1986) andsome of the authors of the papers in Fisher (1989) on the distinctionbetween “hard” facts and “soft” facts deny(4). But it has proven remarkably difficult to provide clear andpersuasive principles for determining which propositions apparentlyabout the past are not completely or really about the past.

An alternative defended by the sixteenth-century Jesuit, Luis deMolina, is to deny (5), the principle that accidental necessity isclosed under entailment of contingent propositions (Freddoso 1988:58). Of the assumptions required for the argument, however, (5) hasseemed to many to be the least controversial, at least if we really dograsp the modality of accidental necessity. For a simple argumentagainst (5), see (Wierenga 2016:102).

Finally, it remains open to deny (6), to hold that even if it isalready accidentally necessary that Jones mow his lawn tomorrow, heneverthelesshas it within his power to do something, forexample, spend the day indoors, which is such that if he were to doit, it would be false that he mows his lawn (Plantinga 1986: 257).Jonescan remain indoors tomorrow, and if he were to do that,the past would have been different; in particular, God would neverhave believed then that Jones would mow his lawn tomorrow. See alsoMavrodes (1983) for a defense of the claim that events of the past arenow preventable. Some philosophers object, however, to this sort ofcounterfactual power over the past.

We have just looked at three strategies for rejecting the argument.Some theistic philosophers, however, are happy to accept it. Oneposition accepts the argument and gives the Boethian response, likethat given to the first argument above, that God’s mode ofexistence is eternity, so he does not have foreknowledge. On thisview, it does not matter that divine foreknowledge is incompatiblewith free human action, because God’s omniscience does notinclude foreknowledge (see, for example, Stump and Kretzmann 1991).Other philosophers have objected that regardless of whether God iseternal rather than everlasting, it does not suffice to reply to theargument simply by appealing to God’s eternity. Plantinga(1986), Zagzebski (1991), and others claim that an exactly analogousargument could be constructed using the premiss that 80 years ago itwas then true, and so now accidentally necessary, that God eternallyknows that Jones mows his lawn tomorrow. According to this revision ofthe argument, divineeternal knowledge would be asincompatible with human free action as divineforeknowledgeis; so the Boethian response leaves the argument unchallenged.

In recent years perhaps the most widely accepted response to theargument is to accept it but to deny that omniscience extends toknowledge of the future. Geach (1977) held that apart from“present trends and tendencies” there is no future to beknown. Swinburne (1993 and 2016) holds that omniscience does notinclude foreknowledge of future free actions. Hoffman and Rosenkrantz(2002) give a careful account of omniscience, intentionally limitingGod’s foreknowledge to truths that are “causallyinevitable”, where causally inevitable events are not freeactions. Indeed a recent movement within philosophy of religion,so-called Open Theism, has been developed with the explicit aim ofleaving the future “open”, and thus unknown to God,precisely so as to leave room for human freedom. Hasker (1989, 2004)has been a leading figure in this group, as have been the contributorsto Pinnock (1994). In a similar vein, Mawson recommends that theistswho think that God is in time should say “that God suspendsjudgment on everything that will actually happen in the future.”Instead, on this view omniscience extends to the future only inknowledge of “the probabilities of particular futuresdeveloping” (Mawson 2019: 38–39). A view according towhich God has at least some knowledge of the future that goes beyondGeach’s “present trends” and Hoffman andRosenkrantz’s “causally inevitable” has beendefended by Fischer (2016: 26ff.; 2022, 67ff; see Iwanicki andKarczewska 2024 for criticism). According to Fischer,we havetrue beliefs about the future, for example, what our friends will dotomorrow, and such beliefs can be formed when we are in a“knowledge-conferring situation” (roughly, what is addedto justification to avoid the Gettier Problem). But God can form thosekinds of beliefs, too. Furthermore, since God is omniscient and knowsthat he is, he knows when he has such a belief, he knows that it istrue, and has evidence, namely, his omniscience, entailing that it istrue (2022, 67). In this way God can even “bootstrap” hisway to certainty. We saw at the outset of this essay that one of themotivations for attributing omniscience to God is to be able todevelop a doctrine of divine providence. Nevertheless those who denythat God’s knowledge extends to future free actions, or extendsonly in a limited way, will have the difficult task of stating oraccepting a doctrine of providence, if God does not know what freeagents will do.

For a fuller discussion of these issues, see the entries onforeknowledge and free will andmedieval theories of future contingents.

4. Further Difficulties for Omniscience

Philosophical issues involving foreknowledge and free action are oflong-standing interest, with a history of discussion from lateantiquity through the present day. Several other questions aboutomniscience are of more recent vintage, some of them raising moretechnical issues. This section will consider four more recentobjections.

4.1 Omniscience and Immutability

As time goes by, many things change. It is tempting to think that asthings thus change, propositions reporting what is the case change intruth value. In a provocative paper, Kretzmann (1966) argued thatbeing omniscient requires knowing different things at different times,and thus is incompatible with being immutable. This would constitutean objection to classical theism, according to which omniscience andimmutability are both taken to be central attributes of God.Kretzmann’s argument was anticipated by Franz Brentano(1838–1917) in the following passage (not published until1976):

If anything changes, then it is not the case that all truths areeternal. God knows all truths, hence also those which are such onlyfor today. He could not apprehend these truths yesterday, since atthat time they were not truths—but there were other truthsinstead of them. Thus he knows, for example, that I write down thesethoughts, but yesterday he knew not that, but rather that I was goingto write them down later. And similarly he will know tomorrow that Ihave written them down. (Brentano,PhilosophischeUntersuchungen, English translation in Chisholm 1979: 347)

According to this objection, then, some propositions change theirtruth values over time, and a being who knows all true propositionsaccordingly changes beliefs. So, if God is omniscient, he is notimmutable (Kretzmann’s formulation) or eternal (Wolterstorff1975) or timeless (Davis 1983). Variations on this objection have alsobeen given by Kenny (1979), Prior (1962), and Grim (1985).Philosophers who have objected to the argument includeCastañeda (1967), Kretzmann himself subsequently in Stump andKretzmann (1981), Kvanvig (1986), Pike (1970), Swinburne (1993, butnot 2016), and Wierenga (1989, 2002).

This argument, which appeals totemporal indexicals such asthe present tense and the words “now” and“yesterday”, has an analogue in an argument that appealstofirst-person indexicals. That is the subject of the nextsection; it will be convenient to consider replies to the twoarguments together.

4.2 Omniscience and Knowledgede se

Kretzmann (1966) raised a second problem for omniscience. He held thateach of us possesses special “first-person” knowledge,knowledge not available to anyone else. He illustrates this with theexample of what Jones knows when he knows that he himself is in thehospital. What Jones knows is not simply the proposition that Jones isin the hospital, for he might fail to believe this proposition if hishospitalization is for amnesia. Conversely, Jones could know thatJones is in the hospital by reading an account in a newspaper but failto know thathe is in the hospital, if he is mistaken aboutnot only who he is but where he is. Thus, what Jones knows is supposedto be something other than the proposition that Jones is in thehospital and something that no one other than Jones can know.Accordingly, if omniscience requires knowing everything that anyoneknows, God cannot be omniscient without being identical to Jones.Kretzmann took this to show the incompatibility of divine omnisciencewith “the doctrine of a personal God distinct from otherpersons” (1966: 420). Put more carefully, the objection purportsto show the incompatibility of divine omniscience with the existenceof persons distinct from God who have self-knowledge. In the versionadvocated by Grim (1985), given that we do have first-person ordese knowledge, there is no omniscient God. Nagasawa (2003, seealso 2008) gives an objection to Grim that appeals, in part, to theclaim that omniscience is a “epistemic power” (which hetakes to be included in divine omnipotence).

Given the structural similarity between the objection frompresent-time knowledge and the objection fromfirst-person knowledge it is not surprising that philosophershave given parallel replies. (See Sosa 1983a,b on the analogy betweenfirst-person and present-time knowledge.) What is perhaps moresurprising is that it has, for the most part, been opponents of theargument who have attempted to supply the details of exactly what theobjects of knowledge and belief are in the case of knowledge of thepresent and of oneself. On the one hand, perhaps the propositions weknow when we know what day it is are eternally true. In this case,what changes is our access to the propositions in question, ratherthan the propositions themselves. Kvanvig (1986) holds that suchknowledge involves a special access to or a “direct grasp”of a proposition, which leaves it open that God could believe the samepropositions without thereby ending up with present-time knowledge orfirst-person knowledge of someone else. Wierenga (1989: 48–53)has proposed an account of the objects of present-time andfirst-person belief according to which these propositions involvehaecceities or individual essences of persons and times. Onthis view, one gets a first-person belief by believing a propositionincluding his or her own haecceity, and one gets a present-time beliefby believing a proposition involving the haecceity of a moment of timeat the time in question. This leaves it open that Godbelieves the same propositions we do. He does not get a first-personbelief about someone else, because the relevant propositions do notinclude his own haecceity. And whether he gets a present-time beliefdepends on whether he believes these propositions involving thehaecceities of moments of timeat their times orat hiseternal perspective. It is not knowing the propositions thatmakes him temporal; it is whether he believes in time or out of time.For criticism of this proposal, see Craig (2000) and Torre (2006). Butfor a recent positive presentation, see Swinburne (2016:175–182).

A second kind of reply is available, one that does not appeal to aspecial kind of grasping or an exotic type of proposition. Rather, ittakes its cue from recent work on indexicals, according to which somepropositions areperspectival, that is, true at someperspectives or indices and false at others. On this view, theproposition,I am in the hospital, which Jones believed at\(t\) when he was then in the hospital is true at the index of\(\langle\textrm{Jones}, t\rangle\) but false at many other indices,such as \(\langle\textrm{Smith}, t\rangle\) or\(\langle\textrm{Jones}, t + \textrm{one month}\rangle\). Anyone canbelieve the eternal truth that this perspectival proposition is trueat \(\langle \textrm{Jones}, t\rangle\), but only Jones is able tobelieve the perspectival propositionat\(\langle\textrm{Jones}, t\rangle\). More generally, one can believeperspectival propositions only at the perspectives or indices one isat. Wierenga (2002: 155) suggests that if something like this is thecorrect account of first-person and present-time beliefs, then thedefinition of omniscience,(D1) above, should be replaced with

(D4)

S isomniscient \(=_{\textit{df}}\) for everypropositionp and perspective \(\langle x, t\rangle\), (i) ifp is true at \(\langle x, t\rangle\) thenS knowsthatp is true at \(\langle x, t\rangle\), and (ii) ifS is at \(\langle x, t\rangle\) andp is true at\(\langle x, t\rangle\), then at \(\langle x, t\rangle\)Sknowsp.

According to this definition, God can be omniscient without having thede se beliefs of others, and whether his knowledge changesover time depends, not on the mere fact of his omniscience, but on thefurther question of whether he has his beliefs at temporalindices.

4.3 Omniscience and Knowledgede re

Another question about omniscience is whether it is really completeknowledge unless it is extended tode re (see the supplementonthede re/de dicto distinction in the entry onpropositional attitude reports) knowledge, that is, knowledge with respect to specific individualsthat they have certain properties (or with respect to particular pairsof individuals that they stand in certain relations, etc.). This issuehas not received much discussion in the literature, but Prior (1962)called attention to it by taking the claim that God is omniscient toentail

(7)

For every \(f\) and \(x\), if \(f(x)\) then God knows that\(f(x)\).

Prior read (7) as “God knows everything about everything”but it could be given a more explicitlyde re formulation as“every property and every individual is such that if theindividual has the property then God knows of that individual andproperty that the former has the latter”. Despite the woodennessof the expression, it does seem, as Prior says, that this is aproposition “which a believer in God’s omniscience wouldwish to maintain”. The question then becomes whether(D1) (or(D4)) includes such knowledgede re.

Of course, if(D1) does not capturede re knowledge, it would be simple enoughto add an another clause to it

… and for every thingx and every propertyP,ifx hasP, thenx is such thatSknows thatx hasP.

On the other hand, perhaps no such emendation is necessary. Manyphilosophers have defended an account ofde re belief aboutan object in terms of having somede dicto belief about thatobject while also bearing a relation of acquaintance to it, that is,while being epistemicallyen rapport with the object (seeChisholm 1976, Lewis 1979, and Kaplan 1968). Perhaps, God has animmediate or direct awareness of everything and that relation issufficiently intimate to put him into epistemic rapport witheverything. In that case, ifde re knowledge is thusreducible tode dicto, then God’s satisfying(D1) (or(D4) would give him completede re knowledge. On this last point,see Wierenga (2009: 134).

4.4 Omniscience and Cardinality

Another recent concern is whether it really is possible to know alltruths. Grim (1988) has objected to the possibility of omniscience onthe basis of an argument that concludes that there is no set of alltruths. The argument (byreductio) that there is no set\(\mathbf{T}\) of all truths goes by way of Cantor’s Theorem.Suppose there were such a set. Then consider its power set,\(\wp(\mathbf{T})\), that is, the set of all subsets of\(\mathbf{T}\). Now take some truth \(t_1\). For each member of\(\wp(\mathbf{T})\), either \(t_1\) is a member of that set or it isnot. There will thus correspond to each member of \(\wp(\mathbf{T})\)a further truth, specifying whether \(t_1\) is or is not a member ofthat set. Accordingly, there are at least as many truths as there aremembers of \(\wp(\mathbf{T})\). But Cantor’s Theorem tells usthat there must be more members of \(\wp(\mathbf{T})\) than there areof \(\mathbf{T}\). So \(\mathbf{T}\) is not the set of all truths,after all. The assumption that it is leads to the conclusion that itis not. Now Grim thinks that this is a problem for omniscience becausehe thinks that a being could know all truths only if there were a setof all truths. In reply, Plantinga (Plantinga and Grim 1993) holdsthat knowledge of all truths does not require the existence of a setof all truths. Plantinga notes that a parallel argument shows thatthere is no set of all propositions, yet it is intelligible to say,for example, that every proposition is either true or false. A moretechnical reply in terms of levels of sets has been given by Simmons(1993), but it goes beyond the scope of this entry. See alsoWainwright (2010: 50–51) and Oppy (2014: 223–244).

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