Can we apply the same concepts to both the finite and the infinite?
Is there something distinctive about the infinite that prevents
attribution to it of concepts that we can attribute to the finite? If
so, then this could be a reason for our difficulties in talking about
God — God is infinite, and our concepts, applying, as they do, to
the finite objects of our experience, cannot be `extended' to the
infinite. God's infinity is sometimes used as an explanation of
theological difficulties like the problem of evil or the paradoxes of
omnipotence: we do not really know what we mean when we attribute
*infinite* goodness or power to God.

The mathematical concept of the infinite may be able to shed some light on the theological concept. In mathematics, there is a clearly developed concept of the infinite. We might expect that if there are problems of expressibility related to infinity, they will appear in mathematics as well as in theology. Since the mathematical concept is clearer, the source of any difficulties with it may be clearer as well.

I shall suggest the following conclusions. First, the difficulty that we shall see in pinning down the meaning of `infinite' in its application to God is partly the result of there being two disparate trends in theology: one that tries to find an answer to the problems that come from God's infinity, and one that insists on the impenetrable mystery of the infinite. Second, the development of the mathematical concept of the infinite can shed light on the theological concept not so much by indicating the possibility of a parallel development and clarification of God's infinity; but rather by showing that the attribution of infinity to God may well be — at the present stage of development of the mathematical concept — more figurative than literal. The concepts of the mathematical infinite and the theological infinite may at one time have been quite close; but by now there is at most a metaphorical connexion. And third, infinity is less a cause or a reason for inexpressibility than an attribution resulting from the experience of God as in some degree mysterious.

The following general classifications of infinity are to be developed and refined through a brief historical survey: first, the potential infinite; second, the actual infinite; and third, the theological infinite.

Even in mathematics, there is not a simple dichotomy between the finite and the infinite. Opposed to the finite are the potential infinite and the actual infinite. The potential infinite is an extension of the finite, constructible from the finite by some rule or process that is never in fact completed. The actual infinite, on the other hand, is conceived as an actually existing collection of an infinite number of parts. The actual infinite could be regarded as the completion of a process that builds the infinite from the finite. This is the actual infinite of set theory.

God's infinity, however, is not conceived as one of these species of mathematical infinity. Descartes and Leibniz, for example, make a further distinction between the mathematical infinite and what they call the absolute infinite (and which I shall call the theological infinite). The conception of the theological infinite is not a conception of an infinite collection, but rather of the unbounded or unlimited.

Aristotle distinguished between the potential infinite and the actual
infinite. In none of the experiential sources for the concept of the
infinite does the infinite actually exist. It exists only potentially,
by addition or division. Aristotle argues that saying that the infinite
potentially-is, is not like saying that a statute potentially-is. If a
statute potentially-is, that means that there *will be* an actual
statute. The infinite does not potentially exist in this sense —
there will be no actual infinite. Rather, to say `there is the
infinite', according to Aristotle, means that one thing after another
will be coming into being. The infinite takes place in a succession of
different finite things: by the division of the parts in magnitude; or
by addition in the succession of moments or beings. The infinite has
being only as a process that can be repeated over and over again without
end, but which, at any moment, has only a finite number of
components.^{1} [Aristotle, *Physica,*
translated by R.P. Hardie and
R.K. Gaye, in *The Basic Works of Aristotle,* edited by Richard
McKeon (N.Y.: Random House, 1941), 206a. ]

Aristotle's idea that the infinite has being only potentially and not actually was denied by Cantor. In Cantor's view, a set has to be regarded as a whole, as a totality with all the parts simultaneous. This appears to obviate the distinction between the potential and the actual infinite.

Cantor's actual infinite may not be the same as Aristotle's actual
infinite, even though Cantor represents it as such. As Bochner points
out,^{2} [Salomon Bochner, `Infinity', in
*Dictionary of the
History of Ideas,* vol. 11 (N.Y.: Charles Scribner's Sons, 1973), p.
612.] Aristotle
was not talking about number, but about body — physics
rather than mathematics. On the other hand, Cantor's actual infinite is
in principle constructible by means of a rule or process. Whereas for
Aristotle the infinite has being only *as* this infinitely
repeatable rule or process, Cantor's actual infinite could be seen as
the completion of such a process. This is not to suggest that the actual
infinite is defined by any unique process of construction, but rather
that the actual infinite can be seen as what would result from the
endless repetition of a process. In any case, this process requires a
`subjunctive leap': the actual infinite is not in fact the result of
repeating the process an infinite number of times, but rather represents
what *would* result from infinite repetitions. (Similarly, the
mathematical statement of Zeno's paradox converges to 1, but determining
this limit does not require actually adding up the infinite sum; the
limit tells you what result you *would* get if you *had* added
up the infinite sum.)

Cantor claims that a distinction still remains between kinds of infinite: there are consistent multiplicities, which are infinite sets like the sets of integers; and there are inconsistent multiplicities. These are the infinite sets that in one way or another cause a problem. As he says,

a multiplicity can be such that the assumption that all its elements `are together' leads to a contradiction, so that it is impossible to conceive of the multiplicity as a unity, as `one finished thing' ... the `totality of everything thinkable', for example, is such a multiplicity; later still other examples will turn up.

^{3}[George Cantor, `Letter to Dedekind', inFrom Frege to Godel: A Source Book in Mathematical Logic,ed. Jean van Heijenoort (Cambridge, Mass. and London: Harvard University Press, 1967), p. 114.]

It does not seem likely, however, that Cantor's inconsistent sets point to another species of infinity, or to a problem about infinity as such. Cantor's paradox and its cognates do not rely at all upon the size of their domain — they can be stated as well for finite sets. In other words, although there can be inconsistent infinite sets, there can also be finite sets that are inconsistent for the same reason.

The actual infinite, as I have said, can be conceived as collection of an infinite number of parts, the completion of some process that builds the infinite from the finite. The only problem with actually infinite sets, if there is a problem with them, is that there is not enough time to build them. Nevertheless, they are still the kinds of things that could be built from a collection of parts. The theological infinite, however, is not conceived as an infinite collection, but rather as the unbounded or unlimited; it is not in any sense constructible from the finite because it is not a collection at all, not an extension of the finite.

Descartes puts this as a distinction between the infinite and the
indefinite, between a positive and a negative idea. The actual or
potential infinite of mathematics is more properly called indefinite;
only God is infinite. Indefinite things are those in which we observe no
limits, and perhaps can conceive no limits; but we cannot prove that
they *must* have no limits. What we can call infinite, on the other
hand, is that in which we not only observe no limits, but also can be
certain that there can be no limits.^{4}
[Descartes, *Principles of Philosophy,* in *The
Philosophical Works of Descartes,* 1, trans. Elizabeth S. Haldane and
G.R.T. Ross (Cambridge: Cambridge University Press, 1931), 1, xxvii.]

God is the only thing I positively conceive as infinite. As to other things like the extension of the world and the number of parts into which matter is divisible, I confess I do not know whether they are absolutely infinite; I merely know that I can see no end to them. . . .

^{5}[Descartes, letter to More, 5 February 1649, inPhilosophical Letters,trans., ed. Anthony Kenny (Minneapolis: University of Minnesota Press, 1981), p. 242.]

We have a positive understanding that God is without limits, but

in regard to other things ... we do not in the same way positively understand them to be in every part unlimited, but merely admit that their limits, if they exist, cannot be discovered by us.

^{6}[Descartes,Principles of Philosophy,1, xxvii.]

So Descartes says that there are things other than God that are
apparently without limits; but he separates the unlimitedness of these
other things from the unlimitedness of God by saying that only in the
case of God are we certain that there can be no limits. In all other
cases, according to Descartes, we can say only that we know of no
limits; but there may or may not still *be* limits.

The idea of the theological infinite is, for Descartes, a different
idea from that of the mathematical potential or actual infinite. There
is no way that the idea of the infinite can be derived from the
indefinite — the idea of the infinite is a positive idea that
cannot be constructed from the negative idea of the indefinite. This
distinction between the indefinite and the infinite has a crucial part
in Descartes' proof for the existence of God: since the idea of God is
the idea of an actually infinite being, and I am at most potentially
infinite, I could not be responsible for this idea
myself.^{7}
[Descartes, *Meditations,* in Haldane and Ross, pp.
166f.]

This distinction of the infinite from the merely indefinite may be apt for some objects — we cannot at present prove, for instance, that there are or that there are not ultimate constituents that would limit divisibility of matter. But what about number? We do seem to be able to prove that number is infinite, in virtue of the fact, for example, that the series of positive integers can be put into a one-one correspondence with a proper subset of itself. This is a positive proof of infinity, of the sort that Descartes would reserve only for God. In separating God's infinity from the merely indefinite of mathematics, Descartes perhaps means to retain God's infinity as something absolutely unique, mysterious and strange, in the face of which we stand in awe. But Descartes' definitions of the infinite and the indefinite do not provide as much support for this strangeness as Descartes intended.

In Leibniz there may be somewhat stronger support for the idea that God's infinity is a different sort of thing from mathematical infinity. Leibniz rejects the actual infinite, in the sense of an actually existing whole made up of an infinite number of parts: such a conception, he says, is of use only in mathematics. The infinite analysis of concepts can help to show that God's infinity is a different sort of thing. This infinite analysis is for us a potential infinite. Similarly, a line has an infinite number of points, but these points are present for us only potentially. As this infinite number of points has a use in mathematics, so the infinite analysis of a concept is of use in metaphysics: neither infinite is actual in the sense that it can be grasped by us simultaneously in all its parts. God, on the other hand, is able to grasp the complete concept of a thing. God does not, however, get this understanding by completing the infinite analysis of the concept; instead, he grasps the whole thing all at once. God is not, as you might say, isomorphic with the infinite series, such that his nature is peculiarly suited to carrying out an infinite analysis. Rather, this understanding is not the result of a serial analysis, not the result of carrying to completion the process.Leibniz, like Descartes, makes God's infinity something other than
another species of mathematical infinity. In a sense our idea of the
infinite *is* for Leibniz derived from the finite and from the
impossibility that we should ever come to the end of our ability to
continue adding or dividing. But our ability thus to build the infinite
from the finite, to understand that we can keep applying the same rules
or processes over and over, getting a new result each time, is grounded
in the idea of the theological infinite. The idea of the theological
infinite, which grounds the mathematical infinite, is an idea of an
attribute of God. (That is, God is infinite; and God's other qualities
are in God in the manner proper to an infinite being. Qualities are
determined and limited by the nature of the being in which they inhere;
in an infinite being, there is no limitation of the quality by the
nature of the being.^{8}
[This explication of God's infinity is close to
Aquinas's: cf. *Summa Theologica* 17.]
) This absolute infinite `precedes all
composition and is not formed by the addition of parts'. It is not, that
is, a completed whole, but rather, `an attribute with no
limits'.^{9}[Leibniz, *New Essays on
Human Understanding,* trans. Peter Remnant and Jonathan Bennett
(Cambridge: Cambridge University Press, 1981), 157ff.]

The theological infinite, then, is distinguished from the mathematical infinite in that the theological infinite is defined only by the lack of limits or bounds. This could define the mathematical infinite in only the most naive way — we could say, for instance, that there is no end to number. We have to consider what a limit is, in this sense, and what it means to say that something has or does not have limits. Mathematics shows that the infinite cannot be simply identified with the unlimited: there can be a space that is unlimited but finite; and the real numbers between 0 and 1 are an example of the limited but infinite.

It seems that the idea of the unlimited incorporates these factors: the idea that goodness, power and other qualities are not limited by the nature of God as they are limited by the nature of the other beings in which they are found; the idea that the quality is inexhaustible in God; and the idea that God is a sort of `upper bound' of the quality. But none of these conclusively defines `unlimited' on its own; nor do they add up to a conclusive definition.

In his historical survey of the concept of the infinite, S. Bochner
has suggested that the theological infinite is a qualitative, rather
than a quantitative, infinite. The idea of a qualitative infinite is not
at all clear, however. The qualitatively infinite might be seen as
something that `expresses a degree of completeness or perfection of
something structurable'.^{10}
[Bochner, `Infinity', p. 614.]
According to Aristotle,
completeness rules out infinity altogether: what is complete has nothing
lacking to it, and thus nothing outside of it; but the infinite always
has something outside it — `outside' in the sense that, since the
infinite is an unending process, there is always something that this
process has not yet incorporated: another unit to be added or another
division to be made.^{11}
[Aristotle, *Physica,* 206b-207a.]
Bochner points out that
mathematizations of completeness show that completeness need not rule
out infinity; but to say that completeness need not rule out infinity is
obviously not to say that infinity can be defined in terms of
completeness. It might be suggested that in the qualitatively infinite
the quality is infinitely present. This does not, however, seem to add
anything to the idea of the unlimited. To say that in God being,
goodness, power and so forth are infinitely present is to say no more
than that the quality is not limited by the nature of God, as it
*is* limited by the nature of any creature in which it is
found.

The notion of inexhaustibility, of not being able ever to come to the
end, is also relevant here. For instance, you could never come to the
end of God's infinite mercy: you could never sin to much or too often to
be forgiven. Inexhaustibility cannot define the mathematical infinite
— something could be practically or virtually inexhaustible, and
yet be (hugely) finite. The class
of the first 10^{100} positive integers is inexhaustibly large in the
sense that you could never come to the end of counting them; but it is
not infinite. On the other hand, we have seen that the mathematical and
the theological conceptions of the infinite are not the same. So the
fact that inexhaustibility does not define the mathematical infinite is
not conclusive evidence against its defining the theological
infinite.

We might try defining theological infinity as maximality — so
that saying that God is infinitely good, for instance, means that God is
more good than anything else possible. This `upper bound' conception of
God's infinity is close to the definition of God as `that than which
there can be no greater'. The fact that this definition is relative to a
class of *possible* things, rather than to a class of actual
things, means that at least there is nothing contingent or variable
about the definition.

This definition of the theological infinite, however, does not fully answer the question of what we mean when we attribute infinity to God. The impact of the infinite on our ability to think about and talk about God is determined by a decision to accept or reject what we might call a `purity postulate'. By `purity' I mean the notion that if God is infinitely good, then there is in God no trace or mixture of evil; if God is powerful, there is in God no trace or mixture of inability; and so forth. We can accept or reject this purity postulate while retaining the definition of God's infinity as maximality. It seems that this postulate of purity is independent of the attribution of infinity to God.

Clearly something could be more good than anything else possible, and
still not be *purely* good, more powerful than anything else
possible, and still not *purely* powerful, and so forth. And in
this case, God could still be said to be infinitely powerful — to
be more powerful than anything else possible — but still not be
powerful enough to eradicate evil altogether. In this case, *pure*
power, *pure* goodness, would be an impossibility. On the other
hand, we might say that this does not capture adequately what we mean to
say when we say that God is unlimited. We might want to say that if
God's power is infinite, then there cannot be a certain point beyond
which it does not extend. If there were, that would be a limit; and
hence God's power would be only hugely finite.

The point is that there is no agreement about how far God's lack of limits reaches, no agreement about the acceptance or rejection of this idea of purity. Both Descartes and Leibniz define theological infinity as the lack of limits. But Leibniz does not claim that God can contravene the laws of logic; and Descartes does. For Leibniz, God's power is unlimited in the sense that God can do anything logically possible. For Descartes, God's power is unlimited altogether. Descartes says that God could make a mountain without a valley, or make it the case that 2 + 3 5: that we cannot conceive these things is no indication of a limit to God's power. We need not see a paradox or a contradiction as indicating a limit to God. We can see it, instead, as indicating a limit to our minds.

The idea of God's infinite goodness as the upper bound of possible goodness brings to light one of the sources of the difficulty of defining theological infinity as the lack of limits. In this connexion, it seems that there are always two trends in theology: one that wants to make sense out of God's infinity; and one that wants to preserve God's infinity as an unexplored — and unexplorable — mystery. The definition of `unlimited' and the attitude towards the mystery of the infinite are interwoven. Essentially, the point is that there is no agreement about the extent to which God is unlimited, and hence no agreement on the content of the concept of God's infinite goodness, infinite power and so on.

Can God contravene the laws of logic? Can God do evil so that a greater good will come? We can answer these questions either way, and the meaning of `unlimited' will vary as the answers vary.

Ivan Karamazov wants an explanation of evil that will be understandable for his `finite Euclidean mind': the only answer he gets says that understanding is impossible; and the most he could attain would be an acceptance stemming from mystical love that somehow transcends his own limits. Here is one of the points where the mathematical concept of infinity cannot help us clarify the concept of theological infinity. There are these two trends in theology: one that wants an answer to the problems that seem to come from God's infinity; and one that insists upon the mystery of the infinite. These are not trends that you find in mathematics. And in mathematics a contradiction indicates error: in theology, however, a contradiction can be taken also as indicating that the subject matter lies beyond our grasp.

It seems that the development of the mathematical concept of the infinite has gone on increasingly independently of the theological concept of the infinite. The mathematical infinite has become, particularly during this century, an ordinary, unmysterious operational concept. The theological infinite, however, retains its connexion with mystery. What Bochner calls the "secularization" of infinity has taken place within the realm of the mathematical. In mathematics, there may not be universal agreement about the philosophical meaning of infinity, but there is at least agreement about methods and goals; and there are means of determining, to some extent, the suitability of conceptions of the infinite. In theology, there is no such agreement.

A not uncommon answer to theological difficulties is to say that the
difficulties stem from God's infinity: we cannot grasp the infinite, so
we cannot answer the questions. But mathematics shows that, while we may
not be able to *encompass* the infinite — we cannot actually
pass through all the numbers in an infinite series — we can still
*grasp* the infinite, and by finite means. Mathematical concepts
like `addition' can be applied to both finite and infinite collections.
Certain concepts have been reworked so as to encompass both finite and
transfinite operations; the concepts of finite arithmetic do not
automatically carry over into transfinite arithmetic. For instance
`addition', although it is a concept that is *applicable to* both
the finite and the transfinite, does not behave in the same way in both
cases: the property of commutativity, for instance, is not assured for
the addition of transfinite ordinals. A similar sort of restructuring of
the concepts seems not to be possible for theology. As long as there is
some insistence on preserving the mystery of the theological infinite,
any agreement about restructuring concepts to encompass the infinite is
prevented. Moreover, there are standards in mathematics for this
restructuring of concepts — whether the extended concepts
*work.* In theology, though, there is not even any agreement about
whether concepts applied to God *ought* to `work'. If God
essentially transcends our knowledge, then there is no reason to believe
that the concepts we apply to God should `make sense'.

At this point we are faced with grave difficulties in defining the theological conception of the infinite. The theological conception of the infinite is defined by Descartes and Leibniz as a lack of limits. But there is no agreement about nor, apparently, any means of determining, how far this lack of limits reaches and what effect it has on predication. Furthermore, the conception of the unlimited is, according to mathematics, strictly independent from the infinite. And we have to ask how infinity could be an explanation for the difficulty in extending predicates from the mundane to the absolute, when there is no comparable degree of difficulty encountered in extending concepts from the finite to the infinite in mathematics. The link between the mathematical and the theological concepts of infinity seems at this point so tenuous that we might wonder whether `infinity', used of God, is not simply equivocal.

We might explore the possibility of a figurative attribution of infinity to God. Saying that God is infinite is meant to suggest that God shares the unending and mysterious quality of the infinite. Even the mathematical infinite remains a fascinating and compelling concept. Escher's pictures and some of Borges's stories, though based on aspects of mathematical infinity, have a power to cause delight or anxiety. Maybe it is this power, present even in the rationally defined concept, that is most relevant. Clearly, there is such a figurative use of infinity. I might say that something is infinitely beautiful to me: by this I should mean that I could never get tired of looking at the object and that its beauty comes from some as it were inexhaustible and mysterious source — mysterious in virtue of the fact that I cannot fully understand or articulate the reasons for the object's power over me. `Infinitely' here incorporates the mystery and the inexhaustibility, as well as suggesting a scope or a depth beyond the ordinary.

Perhaps there is a development of `infinite' as an attribute of God
from the literal to the figurative. Before all the developments in
mathematics — before our own century particularly, and before the
seventeenth century altogether — the mathematical concept of the
infinite was as tied to mystery as is the theological concept. In that
context it was not senseless to say that God is literally infinite. But
now, the mathematical concept of the infinite, and mathematical methods
for dealing with it, make it impossible to suggest that God's infinity
is the *reason* for any difficulties in thinking or talking about
God. We cannot, now, simply stand in awe of the infinite and claim that
it is not like anything else — mathematics shows that the infinite
is in many respects not all that unlike the finite.

What we may be seeing here is a case where the term was originally used literally, and then retreated to a metaphorical status, because of the development and `secularization' of the infinite. Another possibility is that theological infinity has always been a mathematical metaphor conveying mystery and immensity, but that the metaphor has retained a meaning that has gradually been lost on its home ground. (Similar, perhaps, to the exemplar `Man is a wolf', which can be used to convey characteristics no longer believed to be possessed by wolves.)

The mathematical infinite cannot provide a direct, positive clarification of the meaning of the theological infinite. What the concept of the infinite can express about God does not lie in the gradual mathematical demystifying of the concept, nor even in the residual strange bits of the mathematical infinite, but rather in the wonder (or dread) we have felt in being introduced to infinite series or set theory, or in looking at Escher's pictures, or at the sky at night. Infinity fascinates us. The meaning of the metaphor of the infinite, as opposed to the useful operational infinite, is no more (or no less) than the mystery and wonder attached to the incomprehensibly immense. It may be that there is, historically, a literal source common to the mathematical and the theological infinite, but these concepts have diverged as the mathematical meaning has become more clear and less mysterious.

We might still claim to find in infinity a reason for difficulty in
attributing concepts to God, in virtue of the fact that the theological
infinite is incommensurable with the finite as well as with the
potential and actual infinities. As I am using `incommensurability'
here, incommensurability can be said to involve an insurpassable gap, a
discontinuity,
the suspension of addition . . . we have a positive value that, no
matter how often a certain amount is added to itself, cannot become
greater than another positive value, and cannot . . . because they are
the sort of value that, even remaining constant, cannot add up to some
other value.^{12}
[James Griffin, *Well-Being* (Oxford: Clarendon
Press, 1986), pp. 85ff.]

Whatever the theological infinite *is,* it is not constructible
from the finite — not in fact and not in principle. We cannot get
there from here; there is no process by which we *would* get to the
theological infinite. This has been emphasized in the discussion of
Descartes and Leibniz above. And we may wonder whether this
insurpassable gap means that whatever measure we use for the finite and
the `mundane' infinite, is not a measure for the theological
infinite.

We could try saying that the same concepts cannot apply both to the finite and to the theological infinite, because of this incommensurability. The same concepts can, however, apply both to the finite and to the actual or potential infinite, because these types of infinite are constructible, at least in principle, from the finite. And then the fact that concepts stretch from the finite to the infinite in mathematics would not rule out the possibility of infinity's being an explanation for expressibility problems in theology.

A relevant point here is the idea that, while we know that God is
good, we do not know what it is for God to be good: we do not know the
truth-conditions or criteria for God's goodness. According to this idea,
just adding on to the mundane concept of goodness will not get us to a
real understanding of God's goodness. God's goodness is not just bigger,
so to speak, than human goodness; it is *different,* on a different
scale altogether. If I, for instance, were to have power added to me,
even to infinity, I can imagine I should be able to move large pieces of
furniture without help, work for hours and hours, and so forth. But this
is not what `infinite power' means for God. If I had infinite power, I
should have infinite *human* power; I should still not be able to
create something in its being ex nihilo. Again, the point is that God's
power is not limited by the nature of God, as my power is limited by my
(human) nature. We might wonder if there is a sort of conceptual gap
here: while we can imagine what it would be like (give the
truth-conditions) for a mundane quality to be increased to infinity, we
cannot grasp what is infinite on another scale altogether.

This line of thought, though, is also questionable. It need not be impossible to grasp what is infinite on another scale altogether; it may simply be that we have not yet found the scale, not found a useful model. Even if two things are incommensurable in the sense defined, it need not follow that the same concepts do not apply to both. Certainly my intellect is incommensurable with Leibniz's in this sense: no matter how many of me were working together, we should in all likelihood not have invented calculus — but the same concepts of intellect apply to both me and Leibniz.

It seems that incommensurability, too, can be seen as a figurative expression of God's transcendence. God's infinity is said to transcend mundane infinity, the sort of infinity that we can construct and grasp, not because we are barred from reaching the theological infinite by some practical considerations, as someone might say that we are barred from reaching the actual infinite. Rather, we cannot reach the theological infinite because we have no process for constructing it, no means of reaching it.

If `infinite', used of God, is a figurative expression of mystery,
immensity, and transcendence, then it is not a cause or reason for
problems with expressibility. `Absolutely infinite' does not give us a
new and useful piece of knowledge about God, the way that `denumerably
infinite' *does* give us new and useful knowledge about the
rational numbers. It is not so much that we `discover' that God is
infinite, and thereby discover a good explanation for the difficulties
of predication that we have experienced. We might just as well say that,
experiencing God as mysteriously unlimited and, so to speak,
unimaginably large, we attribute to God a term that expresses —
among other things — wonderful and fascinating mystery and
inexhaustibility in other matters.

It may be that the proposition `God is infinite' can be taken
literally only when infinity in general is shrouded in mystery. When
infinity is `secularized' and mathematical infinity is given an
increasingly clear and unmysterious meaning, `infinite' can be
understood of God only figuratively. In this figurative meaning,
`infinite' is meant to suggest the ever-present fascination and, as it
were, unwieldy vastness of the infinite. We cannot somehow extend the
mathematical concept of the infinite in order to gain a deeper
understanding of the nature of God. Instead, comparison of the
mathematical with the theological concept brings into light the
experience of God as the mysterious unspeakable.^{13}
[I am grateful to Hans Herzberger for his comments on
earlier drafts of this material. I am also grateful to Edwin Mares for
his suggestions.]

*Department of Philosophy,
McMaster University,
Hamilton, Ontario,
Canada, L8S 4K1*