Two Dozen (Or So) Theistic Arguments

Lecture Notes by Alvin Plantinga


I've been arguing that theistic belief does not (in general) need argument either for deontological justification, or for positive epistemic status, (or for Foley rationality or Alstonian justification)); belief in God is properly basic. But doesn't follow, of course that there aren't any good arguments. Are there some? At least a couple of dozen or so.

Swinburne: good argument one that has premises that everyone knows. Maybe aren't any such arguments: and if there are some, maybe none of them would be good arguments for anyone. (Note again the possibility that a person might, when confronted with an arg he sees to be valid for a conclusion he deeply disbelieves from premises he know to be true, give up (some of) those premises: in this way you can reduce someone from knowledge to ignorance by giving him an argument he sees to be valid from premises he knows to be true.)

These arguments are not coercive in the sense that every person is obliged to accept their premises on pain of irrationality. Maybe just that some or many sensible people do accept their premises (oneself)

What are these arguments like, and what role do they play? They are probabilistic, either with respect to the premises, or with respect to the connection between the premises and conclusion, or both. They can serve to bolster and confirm ('helps' a la John Calvin); perhaps to convince.

Distinguish two considerations here: (1) you or someone else might just find yourself with these beliefs; so using them as premises get an effective theistic arg for the person in question. (2) The other question has to do with warrant, with conditional probability in epistemic sense: perhaps in at least some of these cases if our faculties are functioning properly and we consider the premises we are inclined to accept them; and (under those conditions) the conclusion has considerable epistemic probability (in the explained sense) on the premises.

add Aquinas' fifth way: this is really an argument from proper function, I think

I. Half a Dozen (or so) ontological (or metaphysical) arguments

(A) The Argument from Intentionality (or Aboutness)

Consider propositions: the things that are true or false, that are capable of being believed, and that stand in logical relations to one another. They also have another property: aboutness or intentionality. (not intensionality, and not thinking of contexts in which coreferential terms are not substitutable salva veritate) Represent reality or some part of it as being thus and so. This crucially connected with their being true or false. Diff from, e.g., sets, (which is the real reason a proposition would not be a set of possible worlds, or of any other objects.)

Many have thought it incredible that propositions should exist apart from the activity of minds. How could they just be there, if never thought of? (Sellars, Rescher, Husserl, many others; probably no real Platonists besides Plato before Frege, if indeed Plato and Frege were Platonists.) (and Frege, that alleged arch-Platonist, referred to propositions as gedanken.) Connected with intentionality. Representing things as being thus and so, being about something or other--this seems to be a property or activity of minds or perhaps thoughts . So extremely tempting to think of propositions as ontologically dependent upon mental or intellectual activity in such a way that either they just are thoughts, or else at any rate couldn't exist if not thought of. (According to the idealistic tradition beginning with Kant, propositions are essentially judgments.) But if we are thinking of human thinkers, then there are far to many propositions: at least, for example, one for every real number that is distinct from the Taj Mahal. On the other hand, if they were divine thoughts, no problem here. So perhaps we should think of propositions as divine thoughts. Then in our thinking we would literally be thinking God's thoughts after him.

(Aquinas, De Veritate "Even if there were no human intellects, there could be truths because of their relation to the divine intellect. But if, per impossibile, there were no intellects at all, but things continued to exist, then there would be no such reality as truth.")

This argument will appeal to those who think that intentionality is a characteristic of propositions, that there are a lot of propositions, and that intentionality or aboutness is dependent upon mind in such a way that there couldn't be something p about something where p had never been thought of.

(B) The argument from collections.

Many think of sets as displaying the following characteristics (among others): (1) no set is a member of itself; (2) sets (unlike properties) have their extensions essentially; hence sets are contingent beings and no set could have existed if one of its members had not; (3) sets form an iterated structure: at the first level, sets whose members are nonsets, at the second, sets whose members are nonsets or first level sets, etc. Many (Cantor) also inclined to think of sets as collections--i.e., things whose existence depends upon a certain sort of intellectual activity--a collecting or "thinking together" (Cantor). If sets were collections, that would explain their having the first three features. But of course there are far to many sets for them to be a product of human thinking together; there are many sets such that no human being has ever thought their members together, many that are such that their members have not been thought together by any human being. That requires an infinite mind--one like God's.

A variant: perhaps a way to think together all the members of a set is to attend to a certain property and then consider all the things that have that property: e.g., all the natural numbers. Then many infinite sets are sets that could have been collected by human beings; but not nearly all--not, e.g., arbitrary collections of real numbers. (axiom of choice)

This argument will appeal to those who think there are lots of sets and either that sets have the above three properties or that sets are collections.

Charles Parsons, "What is the Iterative Conception of Set?" in Mathematics in Philosophy pp 268 ff.

Hao Wang From Mathematics to Philosophy chap. 6: iterative and constructivist (i.e., the basic idea is that sets are somehow constructed and are constructs) conception of set.

Note that on the iterative conception, the elements of a set are in an important sense prior to the set; that is why on this conception no set is a member of itself, and this disarms the Russell paradoxes in the set theoretical form, although of course it does nothing with respect to the property formulation of the paradoxes. (Does Chris Menzel's way of thinking bout propositions as somehow constructed by God bear here?)

Cantor's definition of set (1895):

By a "set" we understand any collection M into a whole of definite well-distinguished objects of our intuition or our thought (which will be called the "elements" of M) Gesammelte Abhandlungen mathematischen und philosophischen, ed. Ernst Zermelo, Berlin: Springer, 1932 p. 282.

Shoenfield (Mathematical Logic) l967 writes:

A closer examination of the (Russell) paradox shows that it does not really contradict the intuitive notion of a set. According to this notion, a set A is formed by gathering together certain objects to form a single object, which is the set A. Thus before the set A is formed, we must have available all of the objects which are to be members of A. (238)

Wang: "The set is a single object formed by collecting the members together." (238)

Wang: (182)

It is a basic feature of reality that there are many things. When a multitude of given objects can be collected together, we arrive at a set. For example, there are two tables in this room. We are ready to view them as given both separately and as a unity, and justify this by pointing to them or looking at them or thinking about them either one after the other or simultaneously. Somehow the viewing of certain objects together suggests a loose link which ties the objects together in our intuition.

(C) The argument From (Natural) numbers

(I once heard Tony Kenny attribute a particularly elegant version of this argument to Bob Adams.) It also seems plausible to think of numbers as dependent upon or even constituted by intellectual activity; indeed, students always seem to think of them as "ideas" or "concepts", as dependent, somehow, upon our intellectual activity. So if there were no minds, there would be no numbers. (According to Kroneker, God made the natural numbers and man made the rest--not quite right if the argument from sets is correct.) But again, there are too many of them for them to arise as a result of human intellectual activity. Consider, for example, the following series of functions: 2 lambda n is two to the second to the second .... to the second n times. The second member is ##2 (n); the third 3#2(n), etc. (See The Mathematical Gardener, the essay by Knuth.) 6**2(15), for example would be a number many times larger than any human being could grasp. , for example, is to the We should therefore think of them as among God's ideas. Perhaps, as Christopher Menzel suggests (special issue of Faith and Philosophy) they are properties of equinumerous sets, where properties are God's concepts.

There is also a similar argument re properties . Properties seem very similar to concepts. (Is there really a difference between thinking of the things that fall under the concept horse and considering the things that have the property of being a horse?) In fact many have found it natural to think of properties as reified concepts. But again, there are properties, one wants to say, that have never been entertained by any human being; and it also seems wrong to think that properties do not exist before human beings conceive them. But then (with respect to these considerations) it seems likely that properties are the concepts of an unlimited mind: a divine mind.

(D) The Argument From Counterfactuals

Consider such a counterfactual as

(1) If Neal had gone into law he would have been in jail by now.

It is plausible to suppose that such a counterfactual is true if and only if its consequent is true in the nearby (i.e., sufficiently similar) possible worlds in which its antecedent is true (Stalnaker, Lewis, Pollock, Nute). But of course for any pair of distinct possible worlds W and W*, there will be infinitely many respects in which they resemble each other, and infinitely many in which they differ. Given agreement on these respects and on the degree of difference within the respects, there can still be disagreement about the resultant total similarity of the two situations. What you think here--which possible worlds you take to be similar to which others uberhaupt will depend upon how you weight the various respects.

Illustrative interlude: Chicago Tribune, June 15, l986:

"When it comes to the relationship between man, gorilla and chimpanzee, Morris Goodman doesn't monkey around.

"No matter where you look on the genetic chain the three of us are 98.3% identical" said Goodman, a Wayne State University professor in anatomy and cell biology.

"Other than walking on two feet and not being so hairy, the main different between us and a chimp is our big brain" said the professor. . . . . the genetic difference between humans and chimps is about 1.7 %.

"How can we be so close genetically if we look so different? There's only a .2 % difference between a dachshund and a Great Dane, yet both look quite different (sic)," Goodman said.

"He explained that if you look at the anatomies of humans and chimps, chimps get along better in trees than people, but humans get along better on the ground. (Or in subways, libraries and submarines.)

How similar uberhaupt you think chimps and humans are will depend upon how you rate the various respects in which they differ: composition of genetic material, hairiness, brain size, walking on two legs, appreciation of Mozart, grasp of moral distinctions, ability to play chess, ability to do philosophy, awareness of God, etc. End of Illustrative interlude

Some philosophers as a result argue that counterfactuals contain an irreducibly subjective element. E.g., consider this from van Fraassen:

Consider again statement (3) about the plant sprayed with defoliant. It is true in a given situation exactly if the 'all else' that is kept 'fixed' is such as to rule out the death of the plant for other reason. But who keeps what fixed? The speaker, in his mind. .... Is there an objective right or wrong about keeping one thing rather than another firmly in mind when uttering the antecedent? (The Scientific Image p. 116)

(This weighting of similarities) and therefore don't belong in serious, sober, objective science. The basic idea is that considerations as to which respects (of difference) are more important than which is not something that is given in rerum natura, but depends upon our interests and aims and plans. In nature apart from mind, there are no such differences in importance among respects of difference.

Now suppose you agree that such differences among respects of difference do in fact depend upon mind, but also think (as in fact most of us certainly do) that counterfactuals are objectively true or false: you can hold both of these if you think there is an unlimited mind such that the weightings it makes are then the objectively correct ones (its assignments of weights determine the correct weights). No human mind, clearly, could occupy this station. God's mind, however, could; what God sees as similar is similar.

Joseph Mondola, "The Indeterminacy of Options", APQ April l987 argues for the indeterminacy of many counterfactuals on the grounds that I cite here, substantially.

(E) The Argument from physical constants

(Look at Barrow and Tipler The Anthropic Cosmological Principle)

Carr and Rees ("The Anthropic Principle and the Structure of the Physical World" (Nature, l979)):

"The basic features of galaxies, stars, planets and the everyday world are essentially determined by a few microphysical constants and by the effects of gravitation. . . . several aspects of our Universe--some which seem to be prerequisites for the evolution of any form of life--depend rather delicately on apparent 'coincidences' among the physical constants" ( p. 605).

If the force of gravity were even slightly stronger, all stars would be blue giants; if even slightly weaker, all would be red dwarfs. (Brandon Carter, "Large Number Coincidences and the Anthropic Principle in Cosmology", in M. S. Longair, ed, Confrontation of Cosmological Theories with Observational Data l979 p. 72 According to Carter, under these conditions there would probably be no life. So probably if the strength of gravity were even slightly different, habitable planets would not exist.

The existence of life also depends delicately upon the rate at which the universe is expanding. S. W. Hawking "The Anisotropy of the Universe at Large Times" in Longair p., 285:

"...reduction of the rate of expansion by one part in 1012 at the time when the temperature of the Universe was 1010 K would have resulted in the Universe's starting to recollapse when its radius was only 1/3000 of the present value and the temperature was still 10,000 K"--much too warm for comfort. He concludes that life is only possible because the Universe is expanding at just the rate required to avoid recollapse".

If the strong nuclear forces were different by about 5% life would not have been able to evolve.

The same goes for the weak interaction force.

So if the weakness of the gravitational force relative to the electromagnetic force, or the strength of either the strong or weak forces were altered even slightly one way or the other, the universe would have been largely different, so different in fact that life could not exist. Pat Wilson, "The Anthropic Cosmological Principle" unpublished.

Similarly for the number of neutrinos, and for the mass of the neutrino

Before doing much of anything with this (and for Oxford, maybe only mention it and work harder with others) look again at: "The SAP also Rises: . . . " American Philosophical Quarterly, Oct. l987

Davies, P. C. W., The Accidental Universe, l982:

All this prompts the question of why, from the infinite range of possible values that nature could have selected for the fundamental constants, and from the infinite variety of initial conditions that could have characterized the primeval universe, the actual values and conditions conspire to produce the particular range of very special features that we observe. For clearly the universe is a very special place: exceedingly uniform on a large scale, yet not so precisely uniform that galaxies could not form; expansion rate tuned to the energy content to unbelievable accuracy; values for the strengths of its forces that permit nuclei to exist, yet do not burn up all the cosmic hydrogen, and many more apparent accidents of fortune. p. 111

And what is impressive about all these coincidences is that they are apparently required for the existence of life as we know it (as they say).

Some thinkers claim that none of this ought to be thought surprising or as requiring explanation: no matter how things had been, it would have been exceedingly improbable. (No matter what distribution of cards is dealt, the distribution dealt will be improbable.) This is perhaps right, but how does it work? and how is it relevant? We are playing poker; each time I deal I get all the aces; you get suspicious: I try to allay your suspicions by pointing out that my getting all the aces each time I deal is no more improbable than any other equally specific distribution over the relevant number of deals. Would that explanation play in Dodge City (or Tombstone)?

Others invoke the Anthropic Principle, which is exceedingly hard to understand but seems to point out that a necessary condition of these values of the physical constants being observed at all (by us or other living beings) is that they have very nearly the values they do have; we are here to observe these constants only because they have the values they do have. Again, this seems right, but how is it relevant? What does it explain? It still seems puzzling that these constants should have just the values they do. Why weren't they something quite different? This is not explained by pointing out that we are here. (a counterexample to Hempelian claims about explanation) Like "explaining" the fact that God has decided to create me (instead of passing me over in favor of someone else) by pointing out that I am in fact here, and that if God had not thus decided, I wouldn't have been here to raise the question.

Another approach:


We examine the question of whether the present isotropic state of the universe could have resulted from initial conditions which were "chaotic" in the sense of being arbitrary, any anisotropy dying away as the universe expanded. We show that the set of spatially homogeneous cosmological models which approach isotropy at infinite times is of measure zero in the space of all spatially homogenous models. This indicates that the isotropy of the Robertson-Walker models is unstable to homogeneous and anisotropic perturbations. It therefore seems that there is only a small set of initial conditions that would give rise to universal models which would be isotropic to within the observed limits at the present time. One possible way out of this difficulty is to suppose that there is an infinite number of universes with all possible different initial conditions. Only those universes which are expanding just fast enough to avoid recollapsing would contain galaxies, and hence intelligent life. However, it seems that this subclass of universes which have just the escape velocity would in general approach isotropy. On this view, the fact that we observe the universe to be isotropic would simply be a reflection of our own existence.

We shall now put forward an idea which offers a possible way out of this difficulty. This idea is based on the discovery that homogeneous cosmological models do in general tend toward isotropy if they have exactly the same escape velocity. Of course, such "parabolic" homogeneous models form a set of measure zero among all homogeneous models. However, we can justify their consideration by adopting a philosophy which has been suggested by Dicke (1961) and Carter (1968). In this approach one postulates that there is not one universe, but a whole infinite ensemble of universes with all possible initial conditions. From the existence of the unstable anisotropic model it follows that nearly all of the universes become highly anisotropic. However, these universes would not be expected to contain galaxies, since condensations can grow only in universes in which the rate of expansion is just sufficient to avoid recollapse. The existence of galaxies would seem to be a necessary precondition for the development of any form of intelligent life. Thus there will be life only in those universes which tend toward isotropy at large times. The fact that we have observed the universe to be isotropic therefore only a consequence of our own existence. 319

Spatially homogeneous models can be divided into three classes: those which have less than the escape velocity (.e., those whose rate of expansion is insufficient to prevent them from recollapsing), those which have just the escape velocity, and those which have more than the escape velocity. Models of the first class exist only for a finite time, and therefore do not approach arbitrarily near to isotropy. We have shown that models of the third class do in general tend to isotropy at arbitrarily large times. Those models of the second class which are sufficiently near to the Robertson-Walker models do in general tend to isotropy, but this class is of measure zero in the space of all homogeneous models. It therefore seems that one cannot explain the isotropy of the universe without postulating special initial conditions.. . . .

The most attractive answer would seems to come from the Dickie-Carter idea that there is a very large number of universes, with all possible combinations of initial data and values of the fundamental constants. In those universes with less than the escape velocity small density perturbations will not have time to develop into galaxies and stars before the universe recollapses. In those universes with more than the escape velocity, small density perturbations would still have more than the escape velocity, and so would not form bound systems. It is only in those universes which have very nearly the escape velocity that one could expect galaxies to develop, and we have found that such universes will in general approach isotropy. Since it would seem that the existence of galaxies is a necessary condition for the development of intelligent life, the answer to the question "why is the universe isotropic?" is "because we are here". 334

C. B. Colling and S.W. Hawking, "Why is the Universe Isotropic?" The Astrophysical Journal, March 1, l973

Here you had better look up Alan Guth , "Inflationary Universes: A possible solution to the horizon and flatness problems, Physical Review D, 23, 1981 347-356, and some other pieces mentioned by John Earman, "The SAP also Rises: . . . " American Philosophical Quarterly, Oct. l987

From a theistic point of view, however, no mystery at all and an easy explanation.

(F) The Naive Teleological Argument


The world is a complicated thing. There are lots and lots of different bits of matter, existing over endless time (or possibly beginning to exist at some finite time). The bits of it have finite and not particularly natural sizes, shapes, masses, etc; and they come together in finite, diverse and very far from natural conglomerations (viz. lumps of matter on planets and stars, and distributed throughout interstellar space). . . . . Matter is inert and has no powers which it can choose to exercise; it does what it has to do. yet each bit of matter behaves in exactly the same way as similar bits of matter throughout time and space, the way codified in natural laws. . . . . all electrons throughout endless time and space have exactly the same powers and properties as all other electrons (properties of attracting, repelling, interacting, emitting radiation, etc.), all photons have the same powers and properties as all other photons etc., etc. Matter is complex, diverse, but regular in its behaviour. Its existence and behaviour need explaining in just the kind of way that regular chemical combinations needed explaining; or it needs explaining when we find all the cards of a pack arranged in order. EG 288

Newton: Whence arises all this order and beauty and structure?

Hume Dialogues: Cleanthes: Consider, anatomize the eye. Survey its structure and contrivance, and tell me, from your own feeling, if the idea of a contriver does not immediately flow in upon you with a force like that of sensation. The most obvious conclusion, surely, is in favour of design, and it requires time, reflection and study to summon up those frivolous, though abstruse objections which can support infidelity.

The idea: the beauty, order and structure of the universe and the structure of its parts strongly suggest that it was designed; it seems absurd to think that such a universe should have just been there, that it wasn't designed and created but just happened. Contemplating these things can result in a strong impulse to believe that the universe was indeed designed--by God.

(Hume's version may be very close to a wholly different style of "argument": one where the arguer tries to help the arguee achieve the sort of situation in which the Sensus Divinitatis operates.)

(G) Tony Kenny's style of teleological argument

(h) The ontological argument


  1. Another argument thrown in for good measure.

Why is there anything at all? That is, why are there any contingent beings at all? (Isn't that passing strange, as S says?) An answer or an explanation that appealed to any contingent being would of course raise the same question again. A good explanation would have to appeal to a being that could not fail to exist, and (unlike numbers, propositions, sets, properties and other abstract necessary beings) is capable of explaining the existence of contingent beings (by, for example, being able to create them). The only viable candidate for this post seems to be God, thought of as the bulk of the theistic tradition has thought of him: that is, as a necessary being, but also as a concrete being, a being capable of causal activity. (Difference from S's Cosmo Arg: on his view God a contingent being, so no answer to the question "Why are there anything (contingent) at all?"