Many Religions, One God? Scrutinizing theReference of God-Concepts

Jonathan Erhardt

October 19, 2014

Draft paper - do not cite without permission. Feedback is welcome.

1 Introduction

The term “interpretatio romana” first appears in a passage in Tacitus’ Germania:

Among the Naharvali is shown a grove, the seat of a prehistoric ritual. A

priest presides in female dress, but the gods commemorated there are, ac-

cording to interpretatio Romana, Castor and Pollux.1

The term refers to the common Roman practice of identifying foreign gods with deities

of their own religion.2 Modern scholars understand it as a form of translation: “In its

true form, the interpretatio graeca/interpretatio romana treats theonyms as appellatives,

thus translating a god’s name from the foreign language into the vernacular; by analogy,

in bilingual texts human names can be translated from one language into another”.3

Behind this practice lies an idea which is expressed by Cicero in the following passage

from De Natura Deorum:

1Tacitus 1985 43.4.2Ando 2005, p. 41.3Graf 2013.

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Tell me now, do we also make out the gods to have the same names as those

by which they are known to us? But in the first place the gods have as many

names as mankind has languages. You are Velleius wherever you travel, but

Vulcan has a different name in Italy, in Africa and in Spain.4

Cicero points out that often one thing has different names in different languages or

communities and suggests that the same holds for gods. He thinks that Zeus may be

identical with Iuppiter very much the same way that the Evening Star is identical with

the Abendstern. The liberal approach to identifying gods from various religions, of which

the interpretatio romana is one instance, also has adherents in contemporary philosophy.

John Hick for example endorses such an approach: “[T]he devout in the various great

world religions are in fact worshipping that one God, but through different, overlapping

concepts or mental icons of him.”5 The German philosopher Hegel on the other hand is

opposed to identifying gods of different cultures in this way and he explicitly mentions

the Roman and Greek gods as instances where this has mistakenly been done.6

How should we decide when gods of different religions can be identified? This is a

rough and ready formulation of the question I mean to explore and answer in this paper.

2 Formulating the Question

In this section I want to clarify the question introduced in the last section. The original

formulation touches on a cluster of related but distinct questions. To keep the discussion

general let us work with the following question schemata:7

(1) Are [god-concept1] and [god-concept2] identical?4Cicero and Rackham 1933 1.83-845Hick 1980, p. 48 f.6Hegel 1956, p. 308.7Examples of god-concepts are “God”, “Jesus”, “Zeus”, “Allah”, “Yahweh”, “Elohim”, and “Odin”. Fora tentative account of what is constitutive of god-concepts see footnote p. 9. In this essay I use “con-cept” and “expression”, and similar linguistic categories and categories of thought interchangeablysince all of them are taken to have extensions: Expressions, designators, etc. inherit their extensionfrom the concepts they express.

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(2) Are “[god-concept1]” and “[god-concept2]” co-referential?

(3) How can we find out whether “[god-concept1]” and “[god-concept2]” are

co-referential?

We can then insert any combination of god-concepts into those schemata to obtain

the questions we’re interested in. Let us call them (1) the metaphysical question; (2) the

semantic question; and (3) the epistemic question. The interpretatio romana gives an

answer to instances of the metaphysical question, and philosophers like Hick and Hegel

also seem to be concerned with instances of the metaphysical question. However, the

central goal of this paper is not to find answers to particular instances of the metaphysical

question, e.g. to the question “Are Allah and Yahweh identical?”, but to find a method

for answering instances of the metaphysical question. When looking for such a method

we can make use of some interesting connections between the metaphysical question, the

semantic questions, and the epistemic question. The first thing to note is that two gods

are identical if and only if the god-concepts referring to them are co-referential. So once

we know the answer to an instance of (2), we also know the answer to the corresponding

instance of (1). So, we are free to either approach (1) directly, or indirectly via (2). And

knowing the answer to (3) will put us in a position to answer (2). Therefore, the central

question of this paper is the epistemic question.

3 Preparing the Ground

Which answers to instances of (3) are correct depends on the semantics of the god-

concepts in question, or, to put it differently, what kind of designators8 god-concepts

are. Consider the following examples of identity-statements flanked by designators:

(4) The Morning Star = the Evening Star.8I understand “designator” as covering all subsentential referring expressions. I also include uses of ex-pressions which are sometimes qualified as non-referring, namely generic interpretations of a nominal(e.g. “cholecystectomy” in “a cholecystectomy is a serious procedure”; see Saeed 2009, p. 26).

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(5) The first human on the moon = the first American on the moon.

(6) The murderer of Mary Ann Nichols = the murderer of Mary Ann Nichols

and Rose Mylett.

(7) The vixen in my garden = the female fox in my garden.

The two designators in (4) are proper names and, according to the received view,

finding out whether (4) is true is an a posteriori project - only empirical research will

tell us whether the two designators are co-referential and hence whether (4) is true.9 (5)

contains two descriptions as designators, but our epistemic access to its truth is exactly

the same as in the case of (4). The two designators are co-referential if and only if there

is a first human who was on the moon and that human was also American. The two

designators are not co-referential if the first human on the moon was not American,

or if the first American on the moon was not human (think of an American version of

Laika). (6), like (5), contains two descriptions, but their content leads to an interesting

difference: Whereas both designators in (5) can designate without being co-referential,

if the designator on the right side of the identity-sign in (6) designates, then the two

designators are co-referential, and (6) is true. The converse does not hold: If Rose

Mylett has been murdered by someone other than the murderer of Mary Ann Nichols,

then the two designators are not co-referential because the right-side designator does not

designate anything. These conditionals can be known a priori simply by understanding

the two descriptions. In (7) both directions hold: If either the left or the right side

designates something, then they are co-referential. This, again, can be known a priori

simply by understanding the two descriptions.

This shows that the method for finding out whether two designators are co-referential

depends crucially on the semantics of the designators. Hence, answers to instances of the

epistemic question depend on the choice of a semantic theory for god-concepts. Various

9Kripke 1972, p. 104.

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theories about the semantics of god-concepts have been proposed by philosophers.10 I

will not go through all of them. Instead, I will focus on what I take to be the strongest

non-descriptivist contender and then argue that it is not adequate. I will then develop

a new descriptivist answer based on a variation of the Ramsey-Carnap-Lewis approach

to theoretical terms. On this view, god-concepts are a special kind of description, and

we can make interesting a priori judgements about whether distinct god-concepts are

co-referential.

3.1 Evans’ Causal Theory

Sullivan begins her treatise on the semantics of god-concepts with the following thought:

“Until we have good reasons to think otherwise, we should assume that the best semantic

theory for ordinary proper names like ‘Obama’ and ‘Aristotle’ extends to names for

God.”11 She then argues that Gareth Evans’ theory of reference is the best candidate we

currently have.12 According to this view, names are introduced to a community in just

the way Kripke proposes: A person “baptizes” an entity/person, o, with a name n.13

From then on the name, n, is passed on in the community through various sorts of talks.

Speakers at the end of this chain still succeed in referring to o using n, even if they don’t

know much about o. Where Evans’ theory differs from Kripke’s is in the way in which

names are susceptible to reference shift. According to Evans, there is a set of predicates

associated with a name.14 This set may contain items such as “is the president of the10The answers I know of are Alston 1988, 2005; Bishop 1998; Blackburn 1984; Hawthorne and Manley

2012; Helm 1997; Houston 2000; Shaw 1992; Sullivan 2012; and van Inwagen 2006; Most of themagree that god-concepts are proper names, though they differ in their semantic treatment of propernames. Kripke himself remains neutral as to whether the god-concept “God” is a description or aproper name; see Kripke 1972, p. 27. Bishop and Houston are the only philosophers I know whoexplicitly endorse descriptivism about god-concepts. Van Inwagen does not talk in terms of semantics,but he develops a view according to which an entity must have certain attributes to count as God.Plausibly this can be read as a descriptivist account of the concept “God”. Shaw, too, does not talkin terms of semantics, but he talks of names of deities, so it is natural to understand him as sayingthat god-concepts should be treated as proper names.

11Sullivan 2012, p. 2.12Evans and Altham 1973; Evans 1982.13Sullivan 2012, p. 4; Kripke 1972, p. 91; Evans 1982, p. 376.14Sullivan 2012, p. 12.

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US” and “studied in Columbia” for the name “Barack Obama”, and different entries can

have different degrees of importance. This set of predicates is passed on from speaker

to speaker. Important predicates are more often used to identify the person. This set

of predicates can change its content over time, and may even contain false entries. This

is allowed so long as these false entries are caused by the referent in a way that is apt

to produce knowledge.15 If some other entity than o becomes the source of most, or

the most important, predicates of the set associated with a name n over time, then the

reference of n shifts to that other entity. This theory seems very promising for proper

names because it captures our intuition in the Gödel/Schmidt cases16 but also allows

for the phenomenon of reference shift.17

In what follows I argue that this theory, even if it is a very promising theory for proper

names, does not work for god-concepts. Consider the following story:

The Philosophical Tribesman: A tribesman, Frank, lives in Byblos in 5000

BC. He is a very curious person and often thinks about the origin of the

universe. He is completely at loss, and doesn’t have any hypotheses so far.

His friends know about his philosophical inquiries and decide to play a prank

on him. When Frank goes to bed, one of his friends sneaks into his hut and

speaks to him in an eerie voice: “Frank, I know you search for truth, because

I know everything. I will tell you my name: God, the creator of the heavens

and the earth. I have created all living things. I am without limits, nothing

is impossible for me”. Frank believes he is having a vision of the creator of

the universe and is hearing his voice. This experience is life-changing for

Frank. He forms the belief that there is a creator of the universe with the

15Mere aptness to produce knowledge does not guarantee infallibility, or else false entries caused bythe referent would not be possible: “That it is a way of producing knowledge does not mean thatit cannot go wrong; that is why X, by smoking French cigarettes can be the source of the belief Sexpressed by ‘a smokes Greek cigarettes’”. Evans and Altham 1973, p. 200.

16Kripke 1972, pp. 83 ff.17Evans and Altham 1973, p. 206.

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name “God” which has all the attributes the voice claims it has. He begins

to think deeply about God, and engages in philosophical and theological

writing and discusses his experience and his thoughts about God with others.

He comes up with a version of the ontological argument for the existence of

God. Based on philosophical reflection about the words he heard, he believes

that God has all his properties essentially. He formulates a design argument

and struggles with the problem of evil. He takes a deeply religious attitude

towards life. After many years he puts together an astonishingly complex

theological system about God.

We can locate the story of the philosophical tribesman either in a possible world in

which an omnipotent, omniscient, and perfectly benevolent creator of the universe exists,

or we can locate it in a world in which no such entity exists.18 Let’s first have a look

at Frank in the godless world. Suppose Frank one day finds out both that his friends

played a prank on him, and that no personal being created the universe. Should Frank

conclude that God exists, but that he, Frank, had mostly wrong views about him (i.e.

God turned out to be “one of us”, as Joan Osbourne sings); or should he think that God

doesn’t exist after all? I submit that Frank would most likely choose the latter option,

and that he would be right. His personal experience may be an important trigger for

some of his beliefs, and his interest in theories about the origin of the universe and its

creator, but it is not an essential part of the theories he subsequently developed and

the views he arrived at. Yet Evans’ theory suggests the former, because Frank’s friend

is the only external source of predicates associated with the designator “God”. His

friend is the direct causal source of many of Frank’s beliefs about God, namely those he

18There is a problem in relying on possible worlds due to the fact that perhaps an omnipotent, omniscient,and perfectly benevolent creator of the universe exists necessarily and hence there is no possible worldin which he doesn’t exist. To solve this problem I will introduce scenarios, which can be understoodas maximal epistemic possibilities, in section four. Even if such a being exists necessarily, it certainlyis epistemically possible that such a being does not exist. And it is unproblematic to ask about theextension of a concept in this epistemic possibility. In this section I will gloss over these difficultiesand keep speaking of possible worlds.

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formed directly based on the claims made by the voice he heard, and he is the indirect

source of all the other beliefs Frank formed about God, based on philosophical reflections

about the beliefs caused directly by his friend. No other entity has become a source of

predicates associated with the name “God”, and hence no other entity could potentially

be a candidate for a reference shift.

Now, let’s locate Frank in a possible world in which the creator of the universe exists.

And suppose again that Frank finds out about both the prank and the existence of the

creator of the universe. Should Frank say he had many wrong beliefs about God, namely

beliefs about God being the creator of the universe etc., or should he say he had mostly

correct beliefs about God, but that he mistakenly assumed God revealed himself to him

in a vision, and that he heard God’s voice? I think the latter is more plausible, but

Evans’s theory points to the former. That his triggering experience turned out to be a

prank shouldn’t make it the case that all his theological convictions are false, despite

the fact that there actually is a being with almost all the properties he ascribed to God,

and which thus fits his theological theory so nicely.

It’s noteworthy that Evans’ theory also provides the wrong results if we assume that,

for some reason, the initial baptism failed. In this case, the theory tells us that God

does not exist in both possible worlds: In neither of these worlds has the name been

connected to an entity by baptism, and in neither of these worlds has reference shifted

to an entity at a later stage. But this is implausible for the possible world in which

an omnipotent, omniscient, and perfectly benevolent creator of the universe exists. It

seems that this semantic accident, the failure of baptism, should not render all of Frank’s

theological convictions false, considering there is some other entity about which almost

all his theological beliefs are true.

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3.2 “God” as a Theoretical Term

Why does Evans’ theory give us the wrong result for god-concepts if it works so well for

most proper names? I think the following passage from the Jewish Encyclopedia gives us

a first hint: “[The name of God] represents the Hebrew conception of the divine nature

or character and of the relation of God to His people. It represents the Deity as He is

known to His worshipers, and stands for all those attributes which He bears in relation

to them and which are revealed to them through His activity on their behalf.”19 Even

if we are not sure how precisely this passage has to be understood, it certainly doesn’t

seem like the same is true for any other ordinary name. Usually, proper names do not

“represent a conception of the nature or character” of the entities they denote.

The explanation for this difference, it seems to me, is this: God-concepts are not

ordinary proper names, they are theoretical terms which are similar to proper names

only insofar as they have at most one entity in their extension. The theories they are

part of are folk-theologies.20 We all have more or less elaborate folk-theologies. Our

folk-theologies might originate from ancient accounts written down by various authors,

or they might come from philosophical or theological literature on the topic, or from

autobiographies of religious people. They might also get their content mostly from

what we take to be experiences we have made with a god. Sometimes our own folk-

theology might be quite simple, but we defer to an expert who has a more elaborate

folk-theology, perhaps a priest or a person with more religious experience. These folk-

theologies contribute to the meaning of god-concepts and, together with the world,

determine their extension.

This suggestion gives us a natural reading of the passage from the Jewish Encyclopedia.

Just as the term “proton” does not only denote a certain type of entity, but represents

19Jewish Encyclopedia, section “Names of God”.20Arguably this is constitutive of god-concepts. A concept is a god-concept if and only if it has a central

place in a folk-theology, where a folk-theology is a theory about the meaning and the origin of theuniverse and the place of human beings in it. This allows for borderline-cases, but that seems onlyplausible: Is “Heracles” a god-concept or not?

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its role in particle physics (e.g. how protons relate to the elementary charge), so does

the name of God not simply denote an entity, but represents the Hebrew conception of

the divine nature or character of God.21

This suggestion might sound odd at first, but I think this impression stems from a

wrong conception of what it means to be a theoretical term. A theoretical term is

simply a term introduced by a theory. The theory introducing the term need not be a

very elaborate theory, and it need not be a strictly scientific theory (“Jack the Ripper”,

for example, is a theoretical term introduced by a theory about the murders of Mary

Ann Nichols, Annie Chapman, Elizabeth Stride, Catherine Eddowes, and Mary Jane

Kelly). A theoretical term need not denote a purely hypothetical entity (e.g. “H2O”).

Nor need it denote something invisible (e.g. “Golgi apparatus”). And theoretical terms

can denote things which are extremely important and valuable to us (e.g. “phenomenal

consciousness”). Theoretical terms do not denote a special category of entities, they are

simply introduced into our vocabulary as a part of a theory.

In what follows I will assume that god-concepts are theoretical terms, and I will apply

a variation of the Ramsey-Carnap-Lewis method to them in order to a) get the right

result in the Philosophical Tribesman story and b) develop an answer to the epistemic

question.

3.3 Ramsifying Theologies

If god-concepts are theoretical terms, then they come as parts of theories, and I have

called these theories folk-theologies. How do folk-theologies relate to religions? Each

religion has several associated belief-systems and systems of religious practice. Belief-

systems are simply sets of beliefs with religious content which are (or were, in the case21By “represents” I mean that the theory which introduces the term “proton” gives us the right inter-

pretation of the term, and the right interpretation includes such sentences as “its charge is definedas the elementary charge”. The right interpretation of a theoretical term like “proton” is captured inits Carnap sentence; see the section “Ramsifying Theologies” for further details. None of this is thecase with proper names: They do not get their proper interpretation by a theory which introducesthem.

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of extinct religions) held either by individual adherents of a religion, or by groups of

adherents. In the former case we can talk of individual belief-systems, and in the latter

of shared belief-systems. So, in the case of the interpretatio romana the relevant belief-

systems are either canonical Greek and Roman mythology (shared belief-systems), or

the concrete religious beliefs of specific Roman and Greek citizens (individual belief-

systems). The semantic account for god-concepts I will develop here works for god-

concepts of both individual and shared belief-systems, but it is easier to implement the

procedure for arriving at the right semantics of a specific god-concept with individual

belief-systems on which the individual holding that belief-system is authoritative.22

The beliefs which belong to a specific religious belief-system fall into two categories:

Theoretical beliefs and beliefs about religious experiences. In the first category we might

find, for example, in Alvin Plantinga’s version of Calvinism such items as “God is es-

sentially good”, “God created the universe”, “Human beings suffer from transworld

depravity”, etc. In the latter category he might have things like “God was the cause of

the light of unimaginable power and grandeur and sweetness I saw one gloomy evening

in Harvard”,23 or similar items. We then create a big conjunction of all these sentences.

This conjunction is the folk-theology of a belief-system.

The folk-theology will contain two kinds of terms: Theoretical terms, or T-terms, and

old terms, or O-terms. T-terms are terms which are either introduced by the theory, or

terms whose meaning is substantially different in the theory than in ordinary language.

Examples of such terms are “God”, “sin”, “redemption”, “faith”, etc. T-terms can

denote individuals, species, states, properties, activities, actions, or anything else. All

terms which are not T-terms are O-terms. O-terms are just the ordinary terms of our

natural languages.

We can now apply a method to the folk-theology which was originally developed

22For a general statement of the view that it is easier to extract individual folk-theories (folk-theologiesor other folk-theories) than shared folk-theories see Jackson 2000, pp. 31 ff.

23Plantinga 1973, p. 51.

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by Frank Ramsey24 and later modified by Rudolf Carnap25 and David Lewis26. We

introduce what has been called the Ramsey sentence of the folk-theologies in question.

The Ramsey sentence of a theory T is an expression T* which is like T, but where all

T-terms have been replaced by variables, and where an existential quantifier binds each

of the variables.27 The Ramsey sentence of a Christian folk-theology might look like this:

“There is an x, such that x is a personal being of supreme power and knowledge and

moral superiority, this x created the universe, ...” The Ramsey sentence is not logically

equivalent to the original folk-theology, but it is equivalent with respect to what can be

said in the vocabulary of the O-terms and logical vocabulary.28 Then we can formulate

a Carnap sentence which consists of a conditional of the Ramsey sentence of the folk-

theology and the folk-theology itself.29 The Carnap sentence says that if the Ramsey

sentence of a folk-theology is true, then the folk-theology is true. If we take the Ramsey

sentence but remove the existential quantifiers, then we get the realization formula of

the folk-theology in question. Any set of entities, be it persons, substances, actions, etc.,

which satisfies the realization formula is a realization or a realizer of the folk-theology.

We can also call this set a truth-maker of the folk-theology. Thus the set of God, Jesus,

The Holy Spirit, the authors of the books of the bible, etc. would be a realization of a

generic Christian folk-theology. If they existed, then the Ramsey sentence, the Carnap

sentence, and therefore the folk-theology itself would be true. In most folk-theologies

there will be a single T-term, or a small number of them, which occupy a central place in

that theology; these are the god-concepts. We can also speak of realizers of god-concepts

instead of realizers of a whole folk-theology. A realizer of a god-concept is simply an

entity which satisfies that part of a realization-formula which deals with the variable

replacing the god-concept in question. If an existing entity is a realizer of a god-concept,

24Ramsey 1990.25Carnap 1966.26Lewis 1970.27Braddon-Mitchell and Nola 2009, p. 2.28Braddon-Mitchell and Nola 2009, p. 2 f.29Lewis 1970, p. 430.

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then the god-concept refers to that entity.30

3.4 Perfect and Imperfect Realizers

This basic approach needs refinement or else it fares no better than Evans’ causal theory

in the Frank case. Part of Frank’s folk-theology is that God revealed himself to Frank in

a vision, and that God created the universe. But neither in the godless universe nor in

the universe with a creator is there a single thing which satisfies these two roles. Hence

there is no realizer of Frank’s folk-theology: “God” as he uses it is denotationless, and

his folk-theology is false. So the Ramsey-Carnap-Lewis approach outlined so far leads

to a different but equally implausible result as Evans’ causal theory.

The reason for this implausible result is that we have only allowed for perfect realizers

so far. A perfect realizer is a single entity or set of entities which satisfies the whole

realization formula. But we can also allow for imperfect realization. An imperfect

realizer is a single entity or a set of entities which satisfies not all but most, or at least a

significant portion of, the realization formula. Whenever there is an imperfect realizer of

a folk-theory T, then there is a theory T’ which can be obtained by a slight weakening of

T and which is perfectly realized. In the case of Frank the weaker theory simply gets rid

of “x revealed himself to Frank in a vision”. We can then make the following assumption

about god-concepts: A god-concept denotes the best existing (perfect or imperfect)

realizer. This gives us the right results in the Frank case. In a godless universe there is

no realizer for “God” because nothing satisfies most of the realization formula of Frank’s

folk-theology. In a theistic universe the creator satisfies most of the formula and is thus

denoted by “God”.

30Lewis 1970, p. 432.

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3.5 The Scrutability of Reference and the Weighting-Function

This more liberal version of the Ramsey-Carnap-Lewis method brings us closer to the

right result in the Frank case, but it has two unsatisfying features: It doesn’t tell us

how much of the realization formula an entity has to satisfy to count as an imperfect

realizer, and it doesn’t allow us to give different weight to different parts of the realization

formula. That God created the universe is presumably more important for fixing the

reference of “God” as the concept is used in the Christian tradition than that he slew

Onan who didn’t want to conceive a child with his dead brother’s wife (Genesis 38:8-10).

So an entity might well be an imperfect realizer of “God” if it didn’t slay Onan, but

perhaps not if it didn’t create the universe.

We can fix these shortcomings by introducing a reference-inequation and a weighting-

function for each variable in the realization formula standing for a god-concept.31 Con-

sider the following inequation:

(EssP1 x EssP2 x ... x EssPn x (P1 + P2 + ... + Pn)) ≥ M

Let us call it the reference-inequation because an entity is the referent of a specific god-

concept if and only if the equation is true for the entity in question. M has an arbitrary,

non-zero value and stands for the threshold above which an entity counts as (at least)

an imperfect realizer of a god-concept. Let us assign 1 to M. If the left side of the

equation is equal to or higher than M, and the whole equation turns out to be true, then

the entity in question counts as an (at least) imperfect realizer. Predicates assigned

to a variable which stands for the god-concept in question in the Ramsey sentence

of a certain folk-theology correspond to elements on the left side of the inequation.

Or, to put it differently: Statements about the god in question in the folk-theology

31The idea of weighting elements of the realization formula is not new, but can be found in Braddon-Mitchell and Nola 2009, p. 9. But to my best knowledge nobody has actually implemented thissuggestion so far. I will restrict my solution to god-concepts, but the same approach could be appliedto all variables in the realization formula. It could also be generalized to Ramsey sentences of theoriesother than folk-theologies.

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under consideration correspond to elements on the left side of the inequation. “EssP1”,

“EssP2”, etc. stand for properties which every possible realizer of a certain god-concept

has. Nothing which doesn’t have these properties is a perfect or imperfect realizer of the

god-concept in question. If an entity has a specific essential property then we assign the

value 1 to the corresponding EssP; if it doesn’t have it we assign the value 0. We can

also use EssPn to add negative essential properties: No entity with a certain property is

a realizer of a god-concept. For this we simply assign the value 0 if the entity in question

has that property, and 1 if it doesn’t have it. If we assign a 0 to any of the essential

properties, then the value of the left side of the inequation will be 0, the equation turns

out to be false, and the entity in question is no perfect or imperfect realizer.

“P1”, “P2”, etc. stand for cluster properties. Not every possible realizer of a god-

concept has a specific cluster property, but having that property brings an entity closer

to being a perfect or imperfect realizer. If an entity has that property, we assign a value

to it. Which value depends on how much weight we give the property in fixing the

referent for a god-concept. We can also allow that some parts of the Ramsey sentence

of the folk-theology do not play any role in fixing the referent. For this we simply drop

these properties from the reference-inequation. If a single property turns out to be both

necessary and sufficient, then we simply add the property as both an essential and a

cluster property with value 1 if the object has that property. If several properties are

necessary and collectively sufficient - as in the case where a classical analysis of a god-

concept in terms of necessary and sufficient conditions is possible - we add each of them

both as essential and cluster properties.

If an entity has all the essential properties and enough but not all of the cluster

properties, so that the left side of the inequation has a value equal to or above M, and

the equation turns out to be true, then the entity counts as an imperfect realizer of the

god-concept in question. If an entity has all of the essential properties and the cluster

properties, then it is a perfect realizer.

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What we now need is a weighting function which determines for each god-predicate in

the realization formula whether it corresponds to an essential or to a cluster property,

and, if it stands for a cluster property, which values it can take. One way of doing this

would simply be to go through all the predicates and make individual decisions, where

the value 1 is assigned if a cluster property is extremely important, 0.5 if it is fairly

important, etc.32 The problem with this approach is that it requires us to do something

similar to a classical conceptual analysis, only that it is even more demanding: We

need to both find the properties ascribed to the god in question by to folk-theory and

make up our mind about the weighting of the individual properties. The history of

conceptual analysis gives us plenty of reasons to be pessimistic about our ability to

do this. Even in the cases where it is plausible that a classical analysis in terms of

necessary and sufficient conditions is possible, philosophers have always managed to find

counterexamples: Either cases where the conditions are satisfied and yet the concept

does not seem to be applicable, or cases where the conditions are not satisfied and yet

the concept seems to be applicable.33

But there is a better approach than doing the weighting directly. What a look at the

history of conceptual analysis also reveals is that there is a surprising level of agreement

on the classification of individual cases. Most philosophers agree that Gettier cases are

counterexamples to the justified-true-belief analysis of knowledge.34 It seems that while

the history of conceptual analysis gives us inductive reasons to be sceptical about our

ability to do the weighting directly (and conceptual analysis in general), it also gives

inductive support to the following principle:

The Scrutability of Reference: For any referring expression E, once we know

32Important means here simply that a property brings the entity in question a long distance towardsbeing an imperfect realizer of a certain concept. We can also talk of importance in a relative sense:A property can be more important than another property if having the property brings an entity alonger distance towards being an imperfect realizer than having the other property.

33For a short survey of some of the classical counterexamples see Chalmers 2012, pp. 12 ff.34For a dissenting voice see Hetherington 1998.

16

enough about the world, we are in a position to know what E refers to.35

According to the Scrutability of Reference we are in a position to know what a god-

concept refers to once we know enough about the world. In the Frank case, for example,

we were able to know that his concept “God” doesn’t refer to anything in the atheistic

universe, but refers to the creator in the theistic universe. We can now apply the method

of possible cases36 to assign weight to the different god-predicates. We simply imagine

various possible candidates for a realizer of a god-concept and see whether we think the

god-concept in question would refer to them if they existed. If all possible candidates

which we judge to be the referents of a god-concept share a property, then that property

is an essential property. For cluster properties the procedure is more complicated. We

imagine different combinations of cluster properties and see whether the concept refers

to the resulting candidate. If it does, then we know that, together, they are above the

threshold. We can then try small variations of those candidates above the threshold

to get precise values for individual cluster properties. This is admittedly a tedious

procedure, but I see no way around it.37

This step illustrates the advantage of comparing folk-theologies of individual belief-

systems. I am authoritative about my own folk-theology, and it seems highly plausible

that the Scrutability of Reference holds for my own concepts.38 Things are a lot more

difficult for shared belief-systems and the associated folk-theologies. I am presumably

not in a position to judge whether a certain candidate realizer is an imperfect realizer for

the god-concept of a certain version of Calvinism. I don’t think this is a big disadvantage;

it simply means that we have to leave this job to religious authorities and experts in the

35Chalmers 2012, p. 34.36Frank Jackson coined this term; see Jackson 2000, pp. 31 ff. But the basic idea goes back to Carnap

1955.37If it turns out to be too complicated to find the right weighting due to the large number of predicates

and possible cases we can rely on computational methods to find a weighting which is consistentwith all our verdicts in numerous possible cases. An example of a method which has been used tofind application rules for concepts based on a database of cases is inductive logic programming, seeMooney 2003, pp. 381 ff.

38Jackson 2000, pp. 31 ff.

17

case of shared belief-systems.

Suppose we have a complete weighting of the individual elements of the realization-

formula of a specific folk-theology. We are then in a position to say of every possible

entity whether it is a perfect, imperfect, or no realizer of a specific god-concept. From

this we can easily obtain a complete mapping from possible worlds to extensions: We

simply scan possible worlds for perfect and imperfect realizers. The reference-inequation

can therefore be seen as a tool for representing or expressing intensions of concepts,

understood as functions from possible worlds to extensions.39 What is interesting about

this way of representing the intension of a concept is that it is compatible with cases

where classical definitions of a concept in terms of necessary and sufficient conditions

are available, and also cases where we’ve only found approximate definitions. In the

latter cases the reference-inequation might still be fairly compact, but the corresponding

conceptual analysis in terms of necessary and sufficient conditions might be so disjunctive

and complicated that we haven’t found it yet.40

3.6 Are All God-Concepts Theoretical Terms?

It is plausible that all god-concepts are parts of folk-theologies,41 but this does not settle

the question whether all god-concepts are theoretical terms. Consider the case of “Jesus”.

In the debate about the historical Jesus, most of the claims of the Gospels concerning the

life of Jesus have been rejected by some scholar at some point. John Dominic Crossan,

for example, rejects the virgin birth, the raising of Lazarus, and the resurrection.42 He

strips Jesus’ life of all supernatural elements. But if “Jesus” is a theoretical term, then

Crossan should presumably not say that Jesus was an ordinary human being, he should39Chalmers 2002, pp. 145 ff.40Consider, for example, a simple case where the reference inequation of a concept contains three cluster

properties, and any two of them are sufficient for reference. The explicit analysis of that concept interms of necessary and sufficient conditions will be fairly complex: It will contain three disjuncts,and each disjunct will consist of a conjunction of two property-ascriptions. The reference-inequation,on the other hand, will simply have three weighted properties.

41And my account on p. 9 entails that all god-concepts are parts of folk-theologies.42Crossan 1995.

18

say that Jesus did not exist, since he thinks the Galilean Jew who was born between

around 5 BC and died around 33 AD did not satisfy most of the realization formula of

a generic version of Christianity. Yet neither Crossan nor his critics frame the debate

as one about the existence of Jesus. This is some evidence that “Jesus” is a proper

name and not a theoretical term, even if it is nowadays part of many folk-theologies,

and many people are inclined to qualify “Jesus” as a god-concept due to its role in those

folk-theologies.43 Hence it seems fairly plausible that not all god-concepts are theoretical

terms.

Compare the situation to theological and philosophical debates about God. The-

ologians and philosophers argue about which attributes God has, and there is much

controversy concerning his nature, but this debate does not parallel the one about Je-

sus. There is no debate about the historical God where scholars doubt whether he really

had any supernatural powers. Such statements about God lacking all supernatural pow-

ers sound infelicitous, and the reason for this, I take it, is that any entity without any

supernatural powers would simply not be a referent of the concept “God”. It therefore

seems that the concepts “Jesus” and “God” have different semantics, despite the fact

that both are god-concepts.

If not all god-concepts are theoretical terms, then the domain of application of my

answer to the epistemic question developed in the next section is limited. But as long as

many god-concepts are theoretical terms, the method remains interesting and relevant.

4 Answering the Epistemic Question

Now we have the all the necessary ingredients to develop an answer to the epistemic

question. The epistemic question, as you might remember, is this:

43This does not settle the question of the right semantics for proper names. In particular it is compatiblewith the idea that proper names have descriptive content (as suggested by, e.g., Braddon-Mitchell2004), it merely excludes the view that the descriptive content of proper names is determined by thetheories in which they figure.

19

The Epistemic Question: How can we find out whether “[god-concept1]”

and “[god-concept2]” are co-referential?

I will proceed in two steps. First, I will develop an answer based on a simplified

version of the above account of theoretical terms – a version which only allows for

perfect realizers. I will then consider a natural attempt of expanding this method to an

account which allows for imperfect realizers, and show why it fails. I will then suggest

a more sophisticated version which solves these problems.

4.1 The Simple Method

Let’s first work with the simple version of the above account of theoretical terms and

allow only for perfect realizers. On this simplified view an entity is a realizer of a god-

concepts if and only if it satisfies that part of a realization-formula which deals with

the variable replacing the god-concept in question. We can then formulate the following,

fairly simple criteria for two god-concepts being necessarily, contingently, and impossibly

co-referential:

The Simple Version: Two god-concepts from two folk-theologies are nec-

essarily co-referential if and only if every realizer of one god-concept is also

a realizer of the other god-concept, and vice versa. Two god-concepts from

two folk-theologies are contingently co-referential if and only if some but

not all realizers of one god-concept are realizers of the other god-concept.

And two god-concepts from two folk-theologies are impossibly co-referential

if and only if no realizer of one god-concept is also a realizer of the other

god-concept.

Some remarks on these criteria: Realizers are to be understood as possible realiz-

ers. So even if two god-concepts are in fact co-referential, they are still not necessarily

20

co-referential if there are merely possible worlds where they have distinct realizers. More-

over, we only quantify over possible worlds in which at least one of the god-concepts has

a realizer. So, even if there are possible worlds in which neither of the two god-concepts

is realized, they still count as necessarily co-referential if in every possible world in which

one has a realizer, the other has the same realizer, and vice versa. This seems like a

sensible terminological convention, since most theists are interested in knowing whether

some religions have the same god, on the assumption that one of these religions is true

and its god exists. Figure 1 shows the situation with Venn diagrams: Two god-concepts

are necessarily co-referential if the set of realizers of one is identical with the set of real-

izers of the other. They are contingently co-referential if the set of realizers of one is not

identical with the set of realizers of the other, but they have a non-empty intersection.

And two god-concepts are impossibly co-referential if the sets of their realizers have an

empty intersection.

This result is not very interesting. Firstly, it is at best an approximation. If we do

not accept imperfect realizers, then we end up with the wrong result in the Frank case,

and hence we do not have the right semantics for Frank’s god-concept and other god-

concepts. Secondly, we only seem to get co-reference in cases where people have exactly

the same folk-theology,44 or cases where people have deferential elements in their folk-

theologies (e.g., when someone believes that God has all the properties his pastor says

God has), or cases where the properties assigned to a god by one folk-theology is a proper44As far as the god-concepts under consideration are concerned, they may differ in other areas, since

this does not influence the extension of their god-concepts.

21

subset of the predicates assigned to a god by another folk-theology. This would lead to

the implausible result that even within a certain religious tradition most people would

not refer to the same deity, for there usually are variations between their folk-theologies

which are not captured in any of these three categories.

4.2 The Improved Method

Let us therefore find an answer to the epistemic question based on the more complicated

semantic theory, which allows for both perfect and imperfect realizers. A natural idea

might be this: We simply understand “realizer” in the simple version to include both

perfect and imperfect possible realizers. The set of all realizers of a folk-theology is

then the union of the sets of all perfect and imperfect realizers. Plausibly a number of

folk-theologies of distinct religions have something like the following sufficient conditions

for something to be an imperfect realizer of their god-concepts: A candidate realizer has

created at least large parts of the universe, is a person, very powerful, extremely knowl-

edgeable, and extremely good. Perfect realizers, on the other hand, will have features

like being omniscient or having created the whole universe, etc., but also properties

which are more specific, such as the property of having appeared to Saul on the road

to Damascus. So, one might suspect that the following holds for the god-concepts of

the grand religious traditions: The sets of their imperfect realizers are non-identical; the

sets of their perfect realizers are non-identical; but the unions of their sets of perfect

and imperfect realizers are identical. In other words: No matter which of the perfect or

imperfect realizers of one god-concept exist, it will be at least an imperfect realizer of

the other. For such folk-theologies this criterion for necessary co-reference might seem

to yield the right result, and so it seems fairly plausible that the god-concepts of such

folk-theologies are necessarily co-referential.

22

4.2.1 Counterexamples

Plausible as this seems, there are counterexamples which show that, even if these con-

ditions are satisfied, the two god-concepts are not necessarily co-referential.

c1 and c2 in figure two represent god-concepts. Suppose both of them have one possible

perfect and one possible imperfect realizer. r1 is the perfect and r2 the imperfect realizer

of c1. r2 is the perfect and r1 the imperfect realizer of c2. This means that c1 and c2

satisfy the condition for necessary co-reference specified above: The unions of their sets

of perfect and imperfect realizers are identical. But now let us consider a world in which

both r1 and r2 exist, as depicted in figure 2. Since r1 is a perfect realizer of c1, it will

be denoted by c1. And since r2 is the perfect realizer of c2, it will be denoted by c2.

Hence c1 and c2 are not co-referential, despite the fact that they share a common set

of realizers. Hence they are at best contingently co-referential. But not even this is

guaranteed. A number of theists believe that the realizer of their god-concept exists

necessarily – there is no possible world in which their god fails to exist. Suppose r1

and r2 both exist necessarily. The situation depicted in figure 2 then obtains in every

possible world. Hence they are impossibly co-referential. So, unless we know whether

r1 and r2 exist necessarily we cannot make a judgement about whether c1 and c2 are

contingently co-referential, or necessarily not co-referential. It therefore seems that we

are much more limited in making a priori judgements about whether two god-concepts

are co-referring than on the simple view which allows only for perfect realizers.

23

But this does not mean total defeat. In what follows I will try to recover some

interesting conditional claims about co-reference. And since we’re trying to answer the

epistemic question, I want to connect these conditional claims with the background

knowledge a person trying to answer an instance the metaphysical question might have.

I will argue that, given certain facts about the background knowledge of a person, we

can still make interesting claims about whether it epistemically necessary, epistemically

contingent, or epistemically impossible for that person that two god-concepts are co-

referential.

4.2.2 From Metaphysical to Epistemic Possibility

To make the connection between the background knowledge of a person trying to answer

an instance of the metaphysical question and the semantics of god-concepts, it is useful

to work with epistemic possibilities instead of metaphysical possibilities, and with epis-

temically possible realizers instead of metaphysically possible realizers in formulating

the intension of a god-concept. There are two reasons for this.

The first reason has to do with our way of expressing the intension of god-concepts

by means of the reference-inequation. We observed that the reference-inequation allows

us to get a mapping from possible worlds to extensions, and hence allows us to express

the intension of a concept. But there is a problem with this: Two god-concepts can have

distinct reference-inequations but the same intension. To see this, let us consider a case

where two god-concepts have distinct sets of imperfect realizers but the same perfect

realizer. And let us suppose that this perfect realizer exists necessarily. In this case, the

reference-inequation of the two god-concepts differ, but their intension, understood as a

function from possible worlds to realizers, is the same. This means that the reference-

inequation is more fine-grained than the intension. We can still recover the intension

from the reference-inequation, and hence see the reference-inequation as containing the

intension, but we cannot recover the reference-inequation from the intension. To restore

24

a perfect correspondence between reference-inequations and intensions we can quantify

over epistemic possibilities and epistemically possible realizers.45 Let us say that a

sentence S is epistemically possible if and only if there is a scenario that verifies S.46

And let a scenario be a maximal hypothesis about how things are.47 On this view there

are more scenarios than possible worlds: If r1 exists necessarily, then there is no possible

world in which r1 does not exist. But there is a scenario in which r1 does not exist, for

this is a viable hypothesis about how things are. (A hypothesis held by atheists.) And let

a perfect realizer of a god-concept be an element of a scenario which satisfies all the parts

of the realization formula dealing with the variable standing for the original god-concept.

An imperfect realizer of a god-concept is an element of a scenario which satisfies enough

of the realization formula dealing with the variable standing for the original god-concept.

This re-establishes the 1:1 correspondence between intensions and reference-inequations.

In the case where we have two god-concepts with distinct reference-inequations, but

with an identical necessary existing perfect realizer, there is an epistemic possibility or a

scenario in which this realizer doesn’t exist, and where one god-concept has an imperfect

realizer but the other doesn’t. Hence their distinct reference-inequations are mirrored

in their intension, understood as a function from scenarios to extensions. So, there are

theory-internal reasons for working with epistemic possibilities and epistemically possible

realizers – this allows us to express intensions with reference-inequations.

But there is a second reason, which has distinctly to do with the epistemic question.

45David Chalmers has suggested identifying primary intensions with functions from epistemically possi-ble worlds to extensions for similar reasons; see Chalmers 2008. He wants primary intensions to playthe role we associate with meaning, and intuitively two concepts can have distinct meanings evenif they are co-referential in every metaphysically possible world in which they refer. The concepts“Morning Star” and “Evening Star”, for example, seem to differ in meaning, despite the fact that theyare co-referential in every metaphysically possible world in which they refer. What we have called“intension” corresponds to his primary intension: It is the aspect of meaning which is connected tocognition and mastery of concepts, and which is available a priori upon (perhaps idealized) reflectionto competent speakers. Where the current account differs is that it introduces the reference inequa-tion as a kind of descriptive content, whereas Chalmers is agnostic when it comes to the existence ofsuch descriptive content; see Chalmers 2006 p. 91f.

46Chalmers 2006, p. 81.47This is an approximate and intuitive conception of scenarios. For further details see Chalmers 2006,

pp. 83 ff. and Chalmers 2011, pp. 74 ff.

25

Epistemic space – the set of all scenarios – has an interesting feature: It shrinks with

growing knowledge.48 If I find out that nothing exists necessarily, then it becomes epis-

temically impossible that the creator of the universe exists necessarily. All the scenarios

in which the creator of the universe exists necessarily are eliminated from (my) epis-

temic space. So, if I find out that r1 and r2 do not exist necessarily, then I can make

the following judgement about the two god-concepts c1 and c2: They are contingently

co-referential, since it is impossible that their respective perfect realizers exist neces-

sarily, where the modality in question is epistemic possibility. And if I come to know

that at most one of r1 and r2 exists in any possible world, then I can say that c1 and

c2 are necessarily co-referential, where this expresses again epistemic possibility. This

gives us an attractive way to accommodate for background knowledge in our judgements

concerning the co-reference of god-concepts of distinct belief-systems.

4.2.3 Recovering Conditionals

We now have an elegant framework which lets us combine both purely semantic facts

about god-concepts which are accessible a priori and additional background knowledge

in order to make judgements about whether two god-concepts are co-referential. We can

now make some general claims about the co-reference of god-concepts:49

(8) If I know that i) the union of perfect and imperfect realizers of “[god-

concept1]” is identical to the union of perfect and imperfect realizers

of “[god-concept2]”, and I know that ii) there is at most one entity

which is a realizer of “[god-concept1]” and “[god-concept2]”, then “[god-

concept1]” and “[god-concept2]” are necessarily co-referential.48Chalmers 2011, p. 61. Chalmers introduces the notion of deep epistemic possibilities, ways things

might be, prior to what anyone knows. Scenarios can also be understood as maximal deep epistemicpossibilities to avoid that growing knowledge reduces the number of scenarios. But, as we will seeshortly, for our purpose it is useful that epistemic space is dynamic.

49As above, necessary co-reference does not imply existence. It simply means that for all scenarios, if oneof the god-concepts has a perfect or imperfect realizer in that scenario, then they are co-referentialin that scenario.

26

(9) If I know that i) the union of perfect and imperfect realizers of “[god-

concept1]” is not identical to the union of perfect and imperfect realizers

of “[god-concept2]”, that ii) the intersection of the union of perfect and

imperfect realizers of “[god-concept1]” and the union of perfect and

imperfect realizers of “[god-concept2]” is not empty, and iii) I do not

know whether any realizer of either “[god-concept1]” or “[god-concept2]”

exists necessarily, or I know that no realizer exists necessarily, then

“[god-concept1]” and “[god-concept2]” are contingently co-referential.

(10) If I know that i) the intersection of the union of perfect and imperfect

realizers of “[god-concept1]” and the union of perfect and imperfect

realizers of “[god-concept2]” is empty, then “[god-concept1]” and “[god-

concept2]” are impossibly co-referential.

For all god-concepts which are theoretical terms i) in (8) to (10) and (ii) in (9) can be

known simply by analysing the reference-inequation of the two god-concepts in question.

The reference-inequation is knowable a priori in the case of our own god-concepts, and

can be obtained by applying the method of possible cases as outlined above. If we want

to make judgements about whether the god-concepts of others are co-referential, then

we have to get involved in empirical investigations and apply the method of possible

cases to them. This would fall in the domain of experimental philosophy. ii) in (8) can

in some cases also be known a priori simply by analysing the reference-inequations of

our own god-concepts. This is the case if we ascribe uniqueness-properties as essential

properties to realizers of a god-concept, i.e., properties which only one entity per scenario

can have. An example of such a property is “is the only creator of the universe”. In the

case of god-concepts of others, we again have to apply the method of possible cases to

find out whether they ascribe uniqueness-properties to realizers of their god-concepts.

But even if the religion in question (ours or another person’s religion) does not ascribe

uniqueness-properties, we can come to know ii). Suppose our reason for believing in

27

a specific god has to do with inference to the best explanation. We believe that the

god-hypothesis is simply the best explanation of the existence of the universe. Such an

argument arguably only supports one candidate realizer of a god-concept per universe.

Postulating more than one realizer would presumably violate Ockham’s razor and hence

not count as the best explanation. Hence we can plausibly know ii) as well, even if no

uniqueness-properties are involved, albeit in a different way than i). The case is slightly

different for iii) in (9). As long as I do not know whether any candidate realizer of

a god-concept exists necessarily, there are scenarios in which they do and scenarios in

which they don’t. This is enough to exclude counterexamples to contingent co-reference

based on necessary existing realizers. So, in this case lack of knowledge is enough to

get contingent co-reference. And if I come to know that no candidate realizer exists

necessarily, then this still keeps the result intact – only necessary existing realizers could

potentially lead to counterexamples such as the one discussed above.

So, while we could not recover a completely general answer to the epistemic question,

the conditionals (8) to (10), together with our account of theoretical terms, still give us

some interesting results which are applicable to a fairly large class of god-concepts. It is

noteworthy that this answer to the epistemic question allows for practical implementa-

tion. It would be a fairly straightforward matter to design a questionnaire with enough

possible cases to get at least a decent approximation of the reference-inequation of the

god-concepts of the sample group. We could then make judgements about whether two

god-concepts of two individuals are (epistemically) necessarily, contingently, or impossi-

bly co-referential.

5 Conclusion

In this paper I have developed a method for finding out whether two god-concepts of

distinct religions are co-referential. This method does not make the work and insight of

various theologians, philosophers, anthropologists, etc. on the question of the identity of

28

the gods of distinct religions superfluous; it only offers a way to systematize their work:

We can use their insights to extract the folk-theologies from various shared belief-systems

and do the weighting of the god-concepts involved in these systems. The method gives

an epistemic privilege to individual folk-theologies over folk-theologies associated with

shared belief-systems. This seems intuitively right, from a religious perspective as well

as from a philosophical perspective.

One last thing is noteworthy. The method developed here suggests that there is such

a thing as conceptual arrogance. If a person either assigns to every predicate of her

realization formula an essential property in the reference-inequation, or she assigns to

every god-predicate which corresponds to a cluster property an equally small value, such

that almost all of them have to be satisfied by a candidate realizer in order to be above

the threshold, then she accepts that her god-concepts do not refer, even if a slightly

more modest version of her religion would be realized. She thereby risks intra-religious

splits: It could turn out that the god-concepts of two conceptually arrogant adherents

of the same religion are necessarily not co-referential. This may suggest that we should

be conceptually modest. But perhaps there is a lower limit for conceptual modesty in

the light of religious practice. Perhaps we can only have the religious attitudes to which

our beliefs call us towards the referent of a god-concept which satisfies some minimal

conceptual constraints.50

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