Is the only way for philosophy to progress for supposedly eminent philosophers to propose ridiculous arguments so that others can try to knock them down? The purpose of this essay is to try to refute an argument associated with theologian and philosopher Alvin Plantinga for the existence of God. I have written about this argument before, a number of years ago, in a post called "The Modal Ontological Argument", but have decided that I want to revisit it. In particular I want to present an argument for agnosticism that has profound implications for modal logic in general. I shall then move on to considerations of modal logic more specifically. To begin with I will set out a version of the modal argument for the existence of God that is somewhat different to Plantinga's but which will serve as a suitable backdrop to the arguments I want to make later. My modest aim in this essay is to articulate a criticism of both modal arguments for the existence of God and of modal arguments generally.
Consider the following argument, an argument for God, which I shall set out schematically.
P1: It is conceivable that God exists.
P2: If it is conceivable that God exists then it is possible that God exists.
C1: Therefore, it is possible that God exists.
P3: God either exists necessarily or not at all.
C2: Therefore if God exists possibly, then God exists necessarily.
C3: Therefore God exists.
When we scan through this argument we sense that there must be something wrong with it. Somehow it seems to be omitting an important step or two. The first comment I want to make about it is that we can exchange premise 3, "God either exists necessarily or not at all" with an equivalent premise, P3b: "If God exists, then He exists necessarily". If we switch P3 with P3b, this does not affect the argument in the slightest way.
Perhaps we can make the argument seem stronger if we rephrase it in the language of possible world semantics as first proposed by Kripke and Lewis.
P1: It is conceivable that God exists.
P2: If it is conceivable that God exists then there must be at least one possible world at which God exists.
C1: Therefore there must be at least one possible world at which God exists.
P3: God either exists at all possible worlds or in none.
C2: Therefore God exists at all possible worlds.
C3: Therefore God exists at the actual world.
Even with this rephrasing, and even though both forms are valid, we still sense that there must something unsound to it. There is no problem with the first premise I believe – even with the contemporary decline of religion, religious sentiment is rife throughout all human populations and so I think we should cede to the faithful their conviction that at least a few of them can conceive of God. This is a difficult concession for militant atheists to make because atheists such as Richard Dawkins regard faith as a form of delusion. Nevertheless we should make it. So if there is a fault with the argument it must lie with the second or third premise. I shall discuss the second premise a little later in this essay and for the moment want to focus on P3.
What entitles the theologians who sincerely subscribe to this argument and promulgate it to the claim that if God exists he must exist necessarily? From what I understand, originally theologians presented the simplest possible argument for the existence of God: "God exists by definition." God was defined not only as an eternal being, omnipotent, omniscient, omni-benevolent, immutable, self-caused, perfectly just and so on, but also as necessarily existing. This meant that if the world is ruled by an omnipotent, omniscient and omni-benevolent being who is not necessarily existing, this being would, by definition, not be God. This is what entitles theologians to the claim that if God exists he exists necessarily. In modernity, in a contemporary world where atheists are far more plentiful and vocal than during the Middle Ages, theologians and philosophers of religion have engaged in a strategic retreat that Anselm and Descartes would have hated – they have conceded that if God does not exist at all possible worlds He exists in none. Anselm and Descartes would have hated it because they lived in an age when atheism was unthinkable.
We can easily see that there must be something wrong with the argument if we consider that, with a little simple tinkering, we can turn it into an argument for atheism. We effect this 180 degree turnaround in the following way.
P1: It is conceivable that God does not exist.
P2: If it is conceivable that God does not exist then it is possible that God does not exist.
C1: Therefore it is possible that God does not exist.
P3: God either exists necessarily or not at all.
C3: Therefore, if God does not exist possibly, then God does not exist necessarily.
C2: Therefore God does not exist.
How would a typical theist respond to this argument? Just as atheists should humour their monotheistic friends in conceding to them a recognition that the religious can conceive of God, so should theists extend to their atheist opponents the courtesy of believing their atheism to be genuine. Dawkins, Hitchens, O'Conner, and others, despite having a vague sense of the believers' conceptions of God, conceive of Him as not existing. If the theist is to somehow refute the modal ontological argument for atheism, he or she must suppose that there is something wrong with the second or third premise – in exactly the same way as atheists must suppose there to be a problem with the second or third premise of the modal ontological argument for God. There is a great deal of symmetry involved and so this is known as the symmetry objection.
I turn now to a very clever argument I came up with recently, I think a very ingenious argument, an argument for agnosticism. It runs as follows.
P1: It is conceivable that God exists.
P2: If it is conceivable that God exists then it is possible that God exists.
C1: Therefore it is possible that God exists.
P3: It is conceivable that God does not exist.
P4: If it is conceivable that God does not exist then it is possible that God does not exist.
C2: Therefore it is possible that God does not exist.
C3: Therefore it is possible that God exists and possible that God does not exist.
P5: If God is a necessary being, then He either necessarily exists or necessarily does not exist.
P6: If God necessarily exists, then it is not possible that He does not exist.
P7: If God necessarily does not exist, then it is not possible that He exists.
C4: Therefore God neither necessarily exists nor necessarily does not exist.
C5: Therefore God is not a necessary being.
At first glance this argument seems more an argument for atheism than for theism. It seems to suggest that what we are calling 'God' in this argument is by definition not the God of the Abrahamic faiths because the God of the Abrahamic faiths necessarily exists by definition. So we could conclude that because the 'God' of this argument is not a necessary being, God does not exist. An alternative is to suppose that God does exist at some worlds including potentially the actual world, is indeed omnipotent, omniscient and omni-benevolent within the scope of the world where He is present, but does not exist at all possible worlds. It may still be possible to call this being God even if he does not meet all the criteria for God set out by the theologians. This would be a strange way of approaching theology but we cannot rule it out.
If the theist wishes to cleave to her conviction that God exists and is a necessary being she must say that either P3, P4 or P6 is wrong. However she must cede P3 to the atheists just as the atheist must cede P1 to the theists. There is no way for anyone logically minded to suppose that P6 is wrong. So the problem, in her view, must lie with P4. Unfortunately it is impossible to reject P4 without also rejecting P2, because it is of the same logical form, and the theist requires P2 to force through her own argument. Could she pursue such a strategy? What I would like to suggest now is that there is a problem with all three modal arguments, including my own argument for agnosticism, and that this problem arises from modal logic itself. Either the premises in all three arguments in which conceivability is considered an indicator of possibility are wrong, or the premise in both the argument for God and the argument for atheism which we can express as either "God either exists necessarily or not all" or "If God exists, He exists necessarily" is wrong. We may also find that my own argument for agnosticism does not carry us all the way to the conclusion that God is not a necessary being.
Let us first continue considering the implications of rejecting P3 of the argument for God and P3 of the argument for atheism. We will carry out this consideration in the light of my own ingenious argument for agnosticism. Despite seeming, on the face of it, more an argument for atheism than for theism, the Argument for Agnosticism, an argument seeking to show that God is not a necessary being, in fact leads us to a stranger conclusion. If we accept something known as 'modal realism', the view that all possible worlds are in some sense real, a position defended by one of the creators of possible world semantics, David Lewis, then we end up having to suppose that there might be some existing worlds ruled by an eternally existing, omnipotent, omniscient, and omni-benevolent deity and other worlds at which He is absent. God would not be 'contingent' because one meaning of the word 'contingent' is 'dependent on prior circumstances' – rather God would be at the worlds where He exists a 'brute fact'. Is the actual world, a world that hopefully you and I both inhabit, one of those ruled by a being who is perfect in all ways except in terms of necessary existence? Or do we live in one at which He is not present? Leibniz argued that we live in the best of all possible worlds and was satirised by Voltaire through the character of Dr Pangloss for seeming to espouse such a naively optimistic credo. Leibniz held that God was actual and had manifested the best possible world although, of course, he did not frame his credo in the terms of possible world semantics because Lewis and Kripke didn't come along and systematise this form of argumentation until two and a half centuries later. As I understand it, Leibniz did not, in fact, contend that the world did not contain evil at all but rather that God permits a certain amount of evil to exist for His own purposes, purposes that the creators of theodicies seek to explain. What God does not permit is gratuitous evil, gratuitous suffering. Now, imagine that Donald Trump starts a nuclear war with Russia and China tomorrow. Imagine we descend into a nuclear winter and that those who don't succumb to radiation sickness die of starvation or malnutrition. If God is omni-benevolent and does not permit gratuitous suffering, then this possible world must be a world at which God is not present. If we try to imagine God existing at this world, we find that this world must be logically impossible. We reach this conclusion regardless of whether we believe in modal realism or if we take the less strong position of supposing that the world of total atomic destruction is a world God could choose to let exist but chooses not to. If God exists at the actual world, he will not allow Trump to press the big red button. In this way the faithful can posit the existence of God in the actual world to reassure themselves that some kind of nuclear armageddon is unthinkable.
(I might digress for a moment. It may seem that the Black Death, the Holocaust, and the genocide of the Palestinians in Gaza and the West Bank seem like examples of gratuitous suffering that took place and are taking place in the actual world. It is the job of Christian apologists to explain why these examples of suffering are not gratuitous. However the purpose of this essay is not to discuss the Problem of Evil but rather arguments for the existence or non-existence of God derived from considerations of modal logic. The Problem of Evil is something I have spent more time on elsewhere in this blog.)
Having considered sketchily some implications of rejecting P3 of both the argument for God and P3 of the argument for atheism, of assuming that God is not a necessary being, let us now imagine that we want to reject P2 of the argument for God and P2 of the argument for atheism. I want to pick on these two propositions, the first stating that if the existence of God is conceivable it is necessary, and the second stating that if the non-existence of God is conceivable it is necessary, because I believe that this is the best way of exposing the serious defects of this type of modal argument. I will show later in this essay that these defects occur because people have erroneously thought possible world semantics to be a metaphysical theory when in reality it should be considered an epistemic theory.
Where does the idea that conceivability equals possibility come from? Apparently it can be traced back to Hume and Descartes. Both thought that if after a period of contemplation one could find no logical contradiction in an imagined state of affairs, then the state of affairs would be possible. Descartes thought that he could conceive of his soul as something separate from his body and thus that it must be possible for his soul to be separable from his body. This furnished him with some confidence in his own theory of mind-body dualism or substance dualism. The axiom that conceivability inevitably entails possibility is a notion still widely embraced by philosophers today. For instance, the very famous essay by David Chalmers in which he introduced the notion of the 'hard problem of consciousness' relies on a thought experiment. He imagines a world full of apparent humans and other sophisticated beings who lack consciousness. Because the world full of zombies is superficially exactly the same as this one but the beings in it lack consciousness, consciousness must be an added extra that materialist science cannot explain. Chalmers argues that because the zombie world is conceivable it must be possible. Another example of a relatively recent philosopher who employed modal logic in his reasoning is Hillary Putnam. Putnam defended his theory of 'meaning externalism' by imagining a world in which the stuff that behaves like water and is called water by the inhabitants of this world is not H2O but rather XYZ. It is by definition necessarily not water because its composition is XYZ and water is necessarily H2O. Putnam also argued that because this world is conceivable it is possible.
I would like now to present a modal argument of the same structure as the ones I have already presented but concerning not God but rather water. It runs as follows.
P1: It is conceivable that water is not H2O.
P2: If it is conceivable that water is not H2O, then it is possible that water is not H2O.
C1: Therefore, it is possible that water is not H2O.
P3: If it is possible that water is not H2O, then it is not necessary that water is H2O.
C2: It is not necessarily true that water is H2O.
I imagine my readers will want to say, straight away, that because the conclusion must be false, either the first or second premise must be false. I share the same intuition. But why does an argument of this general form seem so obviously unsound when we apply it to water but so inconclusive when applied to the existence or non-existence of God? The arguments are indeed of the same general form. The answer to this question involves the fact that we live in a world in which it is universally accepted that the chemical composition of water is H2O. I have never heard of a single person making the case that all science is wrong and that the actual composition of water is XYZ. It is because it seems to us inconceivable that water could have some other chemical composition that Saul Kripke, the other co-creator of possible world semantics, presented the identity of water as H2O as a necessary a posteriori truth. It is necessary that water be H2O, he argued, because water is H2O in all possible worlds, and it is a posteriori because we had to discover this identity empirically, through chemistry. It was this idea that was picked up by Putnam. The debate between theists and atheists, however, is evidence that many can conceive of God existing and that many can conceive of God not existing. It is because we have evidence that some people can conceive of God existing and others can conceive of Him not existing, but lack evidence that anyone in the world today seriously conceives of water as something other than H2O, that the arguments concerning God's existence or non-existence seem so inconclusive while the argument I presented above seems so obviously false.
However, has it always been the case that it is impossible to conceive of water as something other than H2O? It was not until 1784 that Henry Cavendish showed that mixing oxygen with hydrogen, an element he had discovered, created water. In 1811, Italian chemist Amedeo Avogadro established that water was two parts hydrogen and one part oxygen. Before then any number of hypotheses concerning the makeup of water may have been tabled and all of them were conceivable. The ancients, I think, regarded water as elemental – it could be mixed with solutes but could not itself be considered to break down into simpler components that prima facie shared no characteristics with what we call water at all. So it was once conceivable to imagine that water might not be H2O, either because hydrogen and oxygen had not yet been discovered or because its chemical composition had not been fully established and this information not yet disseminated to the wider public. Doesn't this mean that if it was once conceivable that water might not be H2O, it was once possible that water might not be H2O?
Modern philosophy is a kind of conversation engaged in by academics in articles published in journals. It does not seem to me to really progress – rather provocative ideas and arguments appear and become fodder for a continuing discussion. There is a major split in Western philosophy between what is known as continental philosophy or postmodern philosophy on the one hand and what is known as either Anglo-American philosophy or analytic philosophy on the other. I myself used to be much more of a postmodernist because the English department at Auckland University were much more fans of Derrida than of Saul Kripke. Over the last several years I have taken a crash course in analytic philosophy however. Within analytic philosophy, there are certain big names that have changed the direction of the conversation, such as Chalmers and Nagel. Plantinga is big in the space of philosophy of religion. Philip Goff has recently become associated with the bold new notion of panpsychism. However the two big names that have most influenced modern analytic philosophy are Saul Kripke and Hillary Putnam. In contrast to a continental tradition that descends from Nietzsche in which it could be claimed that there is no such thing as truth at all and that 'reality is a social construction', Putnam and Kripke have sought to defend what Bertrand Russell called 'a robust sense of reality'. They have claimed that not only is there a set of propositions that are true but that they are necessarily true. Kripke thought that a name like Christopher Luxon refers to the same individual in all possible worlds. He thought there was something necessary associated with names. For Kripke, the sentence "The person we call Shakespeare is not Shakespeare" is self-contradictory, almost non-sensical. It is necessarily false. The notion that water is necessarily H2O was originally proposed by Kripke and then picked up by Hillary Putnam and used by Putnam as a dialectical tool when setting out his theory of 'meaning externalism' as I mentioned earlier and discussed in a recent post. There is something like a paradox here because Kripke helped invent modal logic and Putnam enthusiastically embraced it.
The argument I am making here is most a threat to the theories proposed by Kripke and Putnam that true propositions can be divided into a necessary camp and a contingent camp. It is a threat to them because both espouse possible world semantics but claim that some propositions are necessary. I am claiming that because it was once conceivable that water might not be H2O, it is still conceivable today that water is not H2O. All it takes for it to be conceivable is for a single person who is not acquainted with chemistry at all, a backwoods man, to sit in his homemade chair and after deep reflection decide that water is a simple indivisible substance. For something to be conceivable, it only has to be conceivable to a single person. And if the claim originally proposed by Hume and Descartes, "If something is conceivable it is possible" is true then we are forced to conclude that water might possibly be something other than H2O. In order to explore this puzzle we might consider the notions of possibility and impossibility. Oddly, impossibility comes in different degrees. Something is logically impossible if the conception of it involves a logical contradiction, a logical contradiction that is apparent a priori to someone sitting in his or her armchair. Examples of logically impossible concepts and propositions supposedly include 'a square circle' or '2 + 2 = 5'. However something can be metaphysically impossible or something can be nomologically impossible. In Putnam's twin-earth thought experiment, he effectively proposed that the identities we discover through chemistry are necessary but that the laws of physics are contingent, might be different.
What conclusion does this discussion force on us? We must suppose that the rule that if something is conceivable then it is possible is too permissive. If we can use the same rule of thumb to prove that God exists in all possible worlds, exists in no possible world, or exists in some possible worlds but not others, then it seems there must be something wrong with this rule and so perhaps we should abandon it. It might be that we have to abandon the rule that conceivability entails possibility even if we want to defend the ordinarily quite unquestioned verity that water is identical to H2O. If we continue to subscribe to the rule, then the only necessary truths are analytic a priori truths such as "all bachelors are unmarried", "two plus two equals four" and "a sphere is a surface in three dimensional space where all points of the surface are equidistant from the centre". If we suppose that conceivability entails possibility, then ALL a posteriori propositions must be contingent, possibly true or possibly false. So we could conclude that we should abandon therefore the rule first proposed by Hume and Descartes and instead suppose that one can conceive of states of affairs that are impossible. This is especially the case for all followers of Kripke and Putnam. If there are to be any necessary truths apart from analytic a priori truths, then we must presume that conceivability is no indicator of possibility.
If we presume that conceivability is no guide to possibility, but we still want to retain some notion of possibility, how then shall we decide what is possible and what is necessary? Modal logic is at the heart of modern analytic philosophy and so there is formidable resistance to change. Nevertheless many eminent philosophers in the Anglo-American tradition down the years have questioned whether our notions of necessity and possibility are correct. It may be that we attribute necessity to those beliefs we are absolutely stubbornly unwilling to give up, such as the belief that water is fundamentally H2O, and attribute possibility to those beliefs we are more uncertain about. Analytic philosophers who have taken this cynical even somewhat postmodern step into an area normally more the province of continental philosophers include Wittgenstein, Quine, and Ayers. It seems to me that this skepticism regarding the foundations of the philosophical method occurs to all major philosophers at some point in their careers even while the professorial herd remain in the tunnel, looking neither to the left or the right, never seriously wondering if the words 'necessary' and 'possible' might have meanings other than the conventional ones assigned to them to by modal logic. It is instructive to consider how foundational these terms are in philosophy but not in the other sciences or humanities, that this is a problem particular to philosophers.
Oftentimes a philosopher, even an eminent one, expresses contradictory views. (I am probably one such myself.) For instance Hume famously proposed his Doctrine of Necessity which I shall quote:
"It is universally allowed, that matter, in all its operations, is actuated by a necessary force, and that every natural effect is so precisely determined by the energy of its cause, that no other effect, in such particular circumstances, could possibly have resulted from it."
Hume seems to be arguing that everything that happens materially happens necessarily. If so, there is no such thing as possibility. This contradicts his other doctrine, the principle that conceivability entails possibility. Readers who remember my original post about this topic, "The Modal Ontological Argument", may recall that I argued, following Sam Harris, that there is no possibility, only necessity. All truths are necessary truths. If so the premise in the first modal argument I presented, in the argument for the existence of God, "God either exists necessarily or not at all", is trivially true because all meaningful propositions about the world are either necessarily true or necessarily false. There is only one world, the actual world. The proposition concerning God, "God exists necessarily or not at all" can be extended to cover all existing and non existing entities. It is a metaphysical statement that applies to everything. If we take this view, then how can we explain our ordinary language usage of words like 'possible'? The proposition "God is conceivable" might be rephrased as "I can imagine the God of the theologians existing but cannot be sure." It is thus, arguably, an epistemic statement. The second premise, "If God is conceivable, God is possible" moves us from the world of the mental to the world of the metaphysical in a way reminiscent of Anselm's original ontological argument for the existence of God. It seems to conflate metaphysics with epistemology, seems to crush them together although seemingly acting as a bridge between the two categories. However if all facts about the world are necessary and if when we conceive of potentially counterfactual scenarios we may sometimes be imagining impossible worlds we must suppose that this premise is false and thus, insofar as the argument for God, the argument for atheism, and the argument for agnosticism depend upon a premise of this general form, none of them are sound. This explains our intuition that there is something wrong somewhere with these arguments.
Human beings are epistemically limited. I do not not know the names and occupations of my neighbours but do know that they necessarily have names. If I say that Jones next door might be a plumber, I am not expressing a view that Jones's ontological status is in flux or in some way indeterminate, that it can only be resolved if I knock on his door and perform an observation, bur rather that I think Jones might be a plumber but am unsure. If I say that it is possible that it will rain tomorrow I am expressing uncertainty about whether it will rain or not but I still regard the shower if it occurs to be necessary. If we follow this train of thought all the way to its final destination, we might be led to jettison not only possible world semantics as invented by Lewis and Kripke but all talk of possibility at all. But this would go too far. We have words like "possible", "plausible", "probable", "likely" and "unlikely" in our language because they serve a useful purpose. However these words are primarily not responses to the metaphysical nature of reality but rather expressions of our epistemic uncertainty. So what I would like to advise is that we do indeed toss possible world semantics into the dustbin of history but that we keep the language and concepts of modal logic. We do so by assuming that the language and concepts of modal logic are entirely epistemic and not metaphysical at all. I believe in doing so we are simply following in the well worn path trodden by other philosophers such as Wittgenstein, Quine, and Ayers.
We arrive now at the twist in my argument. If you heed my advice to regard modal language and concepts as entirely epistemic, we can in fact retain the principle proposed by Hume and Descartes that conceivability always entails possibility. The major difference between the theory I am now proposing and possible world semantics relates to the meaning of the word "necessary". If Bob says, "Water is necessarily H2O", what he is really saying is, "I am absolutely confident that water is H2O.". If Jill says, "P is possible and Q is necessary" what she is saying is that her belief in Q is greater than her belief in P, that in fact her belief in Q is as strong as she can make it.
If we take this second position, hold that modal language and concepts are epistemic in nature, we can rephrase the argument for the existence of God that I set out at the beginning of this essay in the following way.
P1: Jill can conceive that God exists.
P2: If Jill can conceive that God exists then God seems to her to at least possibly exist.
C1: Therefore it seems to Jill that God at least possibly exists.
P3: Jill is either absolute confident that God exists or absolutely confident that God does not exist.
P4: If Jill is absolutely confident that God does not exist then it would not seem to her at least a little possible that God does exist.
C2: Therefore Jill is absolutely confident that God exists.
In order to make the argument as clear as possible, I have added a premise that was not there in the original. The argument may seem odd because Jill appears to shift from a position of simply entertaining in her mind the possibility that God might exist to full blown conviction but this shift, if you look at the argument carefully, although odd, does not make the argument invalid. However, and this is the important thing, by treating modality as epistemic rather than metaphysical, we no longer have an argument for the existence of God but rather an argument for why Jill might believe in God
We can also rephrase the argument for atheism in the following way.
P1: Bob can conceive that God does not exist.
P2: If Bob can conceive that God does not exist then it seems to him at least a little possible that God does not exist.
C1: Therefore, it seems to Bob that God at least possibly does not exist.
P3: Bob is either absolutely confident that God exists or absolutely confident that God does not exist.
P4: If Bob is absolutely confident that God exists then it would not seem to him at least a little possible that God does not exist.
C2: Therefore Bob is absolutely confident that God does not exist.
Here we have an argument not that God does not exist but rather for why Bob might not believe in God.
Finally, we can rephrase the argument I came up with myself, the argument for agnosticism.
P1: Andrew can conceive that God exists.
P2: If Andrew can conceive that God exists then it seems to him at least a little possible that God exists.
C1: Therefore, it seems to Andrew at least a little possible that God exists.
P3: Andrew can conceive that God does not exist.
P4: If Andrew can conceive that God does not exist then it seems to him at least a little possible that God does not exist.
C2: Therefore, it seems to Andrew at least a little possible that God does not exist.
C3: Therefore, it seems to Andrew at least a little possible that God exists and at least a little possible that God does not exist.
P5: If the God Andrew conceives of is the God of the theologians, then Andrew is either absolutely confident that God exists or absolutely confident that God does not exist.
P6: If Andrew is absolutely confident that God exists then it would not seem possible to him that God does not exist.
P7: If Andrew is absolutely confident that God does not exist then it would not seem possible to him that God exists.
C4: Therefore, the God Andrew conceives of is not the God of the theologians.
In rephrasing the argument for agnosticism this way I am not being absolutely rigorous, am being a little playful, but the general thrust of the argument should be clear. I shall summarise the argument so far. We can understand the theory of possible world semantics as being either a metaphysical theory or an epistemic theory. If we regard the most popular theory of modal logic as being a description of metaphysical reality, then the flaw in many arguments that rely on modal logic is that the premise, "If something is conceivable then it is possible" is not true. It involves a move from epistemology to metaphysics that is not licensed. It might be that everything that happens happens necessarily, that there is only one world, the actual world, and that when conceive of supposedly 'possible' worlds we are really conceiving of impossible worlds. If we regard modal logic as something epistemic, on the other hand, although we can retain the principle that conceivability equals possibility, we can no longer reach either the conclusion that God exists or the conclusion that God does not exist.
I turn now, at last, to Plantinga's actual argument. It is very simple, consisting of a single premise and a conclusion.
P: The necessary being possibly exists.
C: Therefore the necessary being actually exists.
Because the argument is so short it requires a great deal of unpacking. Similarly to Kripke and Putnam, Plantinga views all the truths of the actual world as being of two sorts: contingent or necessary. Contingent truths are truths that hold in some possible worlds, including the actual world, but not all possible worlds. Necessary truths hold in all possible worlds. There is confusion in philosophy and theology about the word 'contingent' because it has more than one meaning. Sometimes the word is intended to refer to the fact, as already indicated, that some propositions are true in some possible worlds but are not true in other possible worlds. Sometimes however it means 'dependent on other facts.' The word 'necessary', when applied to truths, sometimes means true in all possible worlds and sometimes means 'not dependent on other facts'. God is supposed to be necessary in both senses of the word.
According to the mainstream theological tradition, all material facts, all facts pertaining to the physical world, are contingent. This is why we can ask the question: "Why is there something rather than nothing?" It is because we can conceive of a possible world that is empty of anything material or physical. The mainstream theological tradition holds that the only explanation for the material universe is that there is a necessary being who created it and keeps it running. This doctrine goes back at least as far as St Augustine and perhaps to Plato. Plantinga is following in the footsteps of Kripke and Putnam in asserting that there are both necessary and contingent facts. However the main example used by Kripke and Putnam of a necessary truth is the identity of water as H2O whereas Plantinga is making an assertion concerning existence.
We can start to see the problem with Plantinga's argument if we ask why Plantinga seems to imply that there is only a single necessary being. What if there is more than one necessary being? Perhaps the actual world and all possible worlds contain two necessary beings, Jehova and Satan, a force for Good and a force for Evil as the Manichaeans thought. Perhaps there is a pantheon of necessary beings – Zeus, Hera, and all their children and relations. (This story involves us disregarding the fact that Zeus and Hera had Titan parents.) We might then go on to wonder why Plantinga could not have said, "The necessary island possibly exists," "The necessary golden mountain possibly exists" or "The necessary unicorn possibly exists." It seems that, in the absence of any criteria for deciding what is necessary and what is contingent, we can slap the word "necessary" in front of any concept and then by asserting that the concept is possible conjure anything we want into existence. We might also wonder if some or all of the quotidian things we ordinarily encounter and consider to exist might necessarily exist. I have a table in my apartment. Perhaps this table exists necessarily – perhaps, despite appearances to the contrary, it is self-caused and exists in all possible worlds. Perhaps, as I have suggested, everything that exists necessarily exists. These considerations seem to suggest that the word 'necessary' as used by Plantinga is ill-defined. In the end, if we accept that the word 'necessary' is meaningful, the sole premise in Plantinga's argument can be simply expressed as, "Whatever is necessary is possible", a trivial truism. Plantinga's argument may comfort those theists who do not examine it closely but I don't think does anything to persuade atheists to change their minds.
Planting seems to be saying simply, "Whatever is necessary is possible", yet Plantinga's argument is indeed intended to be an argument for the existence of God. It seems to me that Plantinga, in his statement that the necessary being possibly exists, is smuggling in other properties theologians and Christian philosophers of religion take to be necessary of God, such as omnipotence, omniscience, and omni-benevolence. These other properties are held by theologians and Christian philosophers to be essential to the single necessary being. Plantinga I believe intended to imply more than he actually said and those of faith who find solace in Plantinga's argument read into it more than he actually said. If Plantinga is implying more than the simple statement that if necessary beings exist possibly then they exist actually, where do these additional properties associated with 'the necessary being' come from? Perhaps Plantinga relies on scripture. More likely though, because Plantinga is trying to present a natural-philosophy argument for the existence of God, he is thinking of the argument Anselm proposed in his Proslogian in the eleventh century. This is one of the first and most influential of the ontological arguments for the existence of God. Anselm argued that if God exists then He is a perfect being. Anselm went on to say that he can conceive of this perfect being. One of the perfections associated with this perfect being would be necessary existence. Anselm argues that because he can conceive that God exists, God must exist in the actual world. The essay you are now reading, which is too long already, would be far too long if I did a deep dive on Anselm. Suffice it say that the problem with Anselm's argument is that there is no reason why we should not suppose that he could conceive that God exists – and be wrong. I cannot justify this claim here for lack of space.
Anselm's argument, I propose, can be simply stated as "I can conceive of God existing and so God necessarily exists." Plantinga and those others who present modal ontological arguments are making a weaker claim, "I can conceive of god existing and so God possibly exists." We can now unpack Plantinga's argument, incorporate into it the assumptions Plantinga and other theologians are making when they propose it, by presenting it in the following way.
P1:The Perfect Being is conceivable.
P2: If the Perfect Being is conceivable it is among other things conceived of as the sole necessarily existing being.
P3: The necessarily existing being possibly exists.
C1: Therefore the necessarily existing being actually exists.
C2: Therefore the Perfect Being actually exists.
P4: The Perfect Being is God.
C3: Therefore God exists.
The problem with this argument is that it is invalid. To be a Perfect Being, the necessarily existing being must have attributes in addition to necessary existence. We thus cannot make the move from C1 to C2. There is no reason why I couldn't say that the existence of the table is my apartment is necessary – but I would not then be entitled to say that the table in my apartment is a Perfect Being. We could attempt to manipulate this argument into something that is valid but I contend that to be an argument for the existence of God, any modal ontological argument still require two premises either or both of which may be false. The first is, "If God exists, then he necessarily exists." The second is, "If I can conceive of God, then He possibly exists." Consider the first. What license do we have to say that if God exists he exists necessarily? In order to be a foundation for an argument for God, one needs to rely either on scripture or on Anselm's Perfect Being theology. However if we reject these two authorities, we can find no reason why my own argument, the argument for agnosticism, an argument I am proud of, might not be the best argument. Perhaps we are only entitled to say "I don't know." Even if we grant the first of these two premises, we could still say that the second is false. We could say that the principle first proposed by Hume and Descartes is not sound, that conceivability is no guide to possibility.
These two objections arise if we treat modal logic as a description of metaphysical reality. How could we rephrase Plantinga's argument if we suppose that modal logic is simply a description of epistemic reality, what we can and cannot know about the world? I shall rephrase Plantinga's argument in a way that fits with the second interpretation.
P: The being that Plantinga absolutely confidently believes to exist seems to him to possibly exist.
C: Therefore the being that Plantinga absolutely confidently believes to exist actually exists.
This is again invalid. In fact the premise is just a tautology and nothing follows from a tautology. To believe something to be true does not make it true. Perhaps we could make another stab at rephrasing Plantinga's argument in a way that includes the concession modern theologians often make and this could make it both valid and sound.
P: The being that Plantinga either absolutely confidently believes to exist or absolutely confidently believes not to exist seems to him to at least possibly exist.
C: Therefore the being that Plantinga either absolutely confidently believes to exist or absolutely confidently believes to not exist actually exists.
This argument is no longer based on a tautology but it is still invalid. In fact the premise in this newly minted version of Plantinga's argument only leads to one valid conclusion.
C: Therefore the being that Plantinga either absolutely confidently believes to exist or absolutely confidently believes to not exist he believes with absolute confidence must exist.
Modal arguments, understood epistemically, only give reasons for belief and say nothing about the existence or non existence of the subjects of these arguments.
The purpose of this essay has been to consider a modal ontological argument for the existence of God and another argument of the same form that, with a little tinkering, presents itself as an argument for atheism. My intention was neither to try to prove that God exists nor to try to prove that he does not exist. Rather I have been seeking to show that modal logic is inherently self-contradictory and thus an inadequate foundation for any argument of this sort. Possible world semantics as invented by Lewis and Kripke and weaponised by Putnam is flawed because it confuses metaphysics with epistemology. To be a metaphysical theory Kripke and Putnam need better criteria for establishing which truths are necessary and which are contingent. Plantinga at lease relies on scripture and Perfect World theology to justify a claim of the sort, "If God exists, He exists necessarily." He can rely on the principle proposed by Hume and Descartes that if something is conceivable it is possible. Yet the confusion in modal logic between metaphysics and epistemology is evident here too: in his brief argument he seems to be employing the word 'necessary' in a metaphysical sense and the word 'possible' in an epistemic sense. Putnam by contrast simply asserts, in his essay "The Meaning of Meaning", without evidence, that the identity "water = H2O" is necessarily true. It may seem that this essay has Plantinga as its bete noir but the real targets of my ire are Kripke and Putnam.
If possible world semantics is a metaphysical theory then it must rely on something like "Conceivability entails possibility" to establish what is possible and foundations such as scripture or Perfect Being theology to establish what is necessary, to define what is necessary. None of these foundations can really be relied on. If, by contrast, possible semantics is an epistemological theory it only tells us what people believe and hints at why they might believe it.
I'll finish this essay by re-emphasising an obvious claim I made early on in it. Some people believe in God and some people don't. Some people can conceive of God and still do not believe He exists. In the world today, there seems no reason to believe in God. The age of miracles is past and it seems science can explain everything. Yet there are many who persist in believing ing God, perhaps to entertain some hope in their lives and some hope of an afterlife. It might be that God, to backslide into the Kripkean heresy, may turn out to be an a posteriori metaphysically necessary truth. We may find evidence that God exists in some comparable way to the way water was discovered to be H2O in the eighteenth century. Believers may say that we already have a posteriori evidence that Christianity is true. We have eyewitness testimony of miracles and two resurrections in the Gospels. All I am saying in this essay is that if one wants either a conclusive argument for God or a conclusive argument against Him, we cannot rely on Modal Logic to do the heavy lifting for us.
