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Pascal’s Wager Explained - Addendum

Daniel J. Castellano


Addendum: Alternatives to Monotheism

Objections to the wager argument often fail to grasp its presuppositions and methodological justifications, already discussed. Since the argument is psychological, it makes certain assumptions about its audience, among which is the belief that the only two viable religious options are monotheism and atheism. This was the state of affairs in Pascal’s time, and it is largely the state of affairs in the West today. Nonetheless, we will here examine the question of how non-monotheistic religions might be considered in a wager argument.

First, let us consider ancient polytheism, historically the most common form of worship. For our purposes, it does not matter whether the deities were many or few, anthropomorphic or animistic, or what the exact hierarchical relationships within each pantheon were. Two general considerations are relevant: (1) as a rule, there was no claim of absolute or total cosmological supremacy for a deity or pantheon, so that (2) polytheistic religions were generally compatible with each other. In polytheistic religions, various deities were invoked to explain different natural phenomena, or they were considered to be protectors of a specific place or people, so there was nothing disloyal about worshiping a new god in addition to previously recognized deities. In this way, each region of the ancient world had an ever-changing pantheon of local divinities, with only the more important gods attaining widespread worship.

This is in striking contrast with Abrahamic monotheism, which explicitly rejects the concurrent worship of other gods. It is not a matter of polytheists being “more tolerant” (the modern liberal notion of tolerance would have been scarcely creditable in antiquity), but rather there was a fundamentally different conception of what constituted a “god.” To the polytheists, divine power was almost always circumscribed: by locale, by natural domain, or even by the cosmos (Heaven and Earth) itself. The gods were therefore generally definable and limited, and so they could be represented by images that symbolized their determinate powers. The Abrahamic God, by contrast, was conceived as completely transcending the cosmos (creating Heaven and Earth), and being without any limit whatsoever. This God could not be defined, and it was manifestly wrong to represent Him with an image, for that would be to circumscribe His power. The God of Abraham was as infinitely far removed from the pagan deities as from the lowliest creature.

Some other ancient religions reached for this nobler conception of divinity: the closest approximation is the god of Zoroaster, and we might see it also in Homer’s portrayal of Zeus, as well as in Akhenaten’s sun worship, and in the Hindu trinity (Brahma, Vishnu, Shiva). Yet none of these had the vision to conceive a Deity that is absolutely without limit, sharing supreme power with none, pre-existing and transcending absolutely everything else that is. This radical transcendence is repeatedly articulated in the Law of Moses, which gave Abrahamic religion a theologically and ritually definite form. Yet God Himself remained completely undefinable, except as a Being absolutely without limit. He was not merely the supreme god, but the only God, and the only pantheon admitted was a host of angels (messengers) who served no purpose but to execute His will or manifest His presence. Thus only the Hebrew religion strictly forbade the worship of other gods (save the short-lived monotheism imposed by Akhenaten). Accustomed to the religious concepts of the times, the Israelites repeatedly lapsed into polytheism, thinking it no vice to worship foreign gods alongside the national God of Israel. Yet the tenor of the prophetic books makes clear that priests and prophets did not see YHVH (“I am ‘I am’” – the self-subsisting existence) as a merely national god. Most strikingly, Elijah realized that God was not to be found in the wind, earthquake, or fire; even the mightiest forces of nature were inadequate representations of the universal God. (1 Kgs. 19:11-12)

This contrast in conceptions of divinity has important implications for our construction of a polytheistic wager argument. First, since the pagan gods are generally definable, they do not meet the unknowability criterion set out in the presuppositions to Pascal’s argument. The pagan gods are quite intelligible in their essence. As to their existence, reason may have something to say here, though it was mute on the question of God’s existence. To the extent that the pagan gods are conceived as existing in the cosmos, in a determinate location, or as the immanent cause of some natural phenomena, our knowledge of physical science has much to say about the probability, or rather the improbability and impossibility, of their existence. Atheists make a theological mistake when they think the scientific refutation of various forms of paganism applies equally to monotheism. This is to mistake the Hebrew God for a god that dwells in a definite location (interpreting “in heaven” literally), or who is immanent in nature, rather than transcending the natural order altogether, being its existential fundament. It is not that atheists are altogether ignorant of the conceptual distinctions between monotheism and polytheism, for indeed they only regard the former as a serious threat, but rather they have a false expectation that physics can answer properly metaphysical questions, if they even acknowledge there is a domain of knowledge beyond natural science.

Polytheistic gods are generally knowable in their essence and rationally demonstrable to be non-existent, but not in every instance. Let us consider then only those divinities whose essences are unknown, though not absolutely without limit, and whose existence cannot be proven or refuted by reason alone. We still face the problem that the wager is no longer psychologically necessary. This is because the pagan divinities, as a general rule, did not impose universal religious demands on humanity, since they did not have total cosmological supremacy. A pagan might recognize the existence of another nation’s gods without feeling obligated to worship them, and there was nothing in this that was inconsistent with how the foreigner conceived of their gods. The mutual compatibility of polytheistic pantheons eliminates the psychological necessity of the wager, since the gods were generally conceived so that their existence did not necessarily have implications for the lives of all men.

A polytheistic wager argument, then, would have to be in one of three scenarios: (1) a god or gods of cosmological supremacy (e.g., Ahura Mazda or the Hindu trinity), in which case the question of existence is of universal importance, and so a universal psychological necessity; (2) a god whose worship imposes local public obligation (e.g., a national god), in which wagering about the god’s existence is a psychological necessity only for some people (those of that nation); or (3) a god whose worship is optional, even on the supposition of his existence, in which case the wager is not at all psychologically necessary. In the second and third scenarios, most or all of us are free not to wager at all, as reason would command in the absence of evidence.

Suppose we decide to wager on the existence of the lesser pagan deities (Scenarios 2 and 3) anyway, notwithstanding the absence of psychological necessity. First, we can eliminate those whose existence is disproven or rendered improbable by scientific or philosophical knowledge, so that the remainder have a subjective probability of 50%. Following Pascal, if reason cannot decide the issue, we turn to prudence. If these gods offer us a finite possibility of eternal bliss, then it is more prudent to believe in them than to disbelieve in them. Yet we know that this is incompatible with the existence of the Abrahamic God, belief in which is also prudentially preferred. As noted previously, there is no logical error here, but this is only a consequence of the objective incompatibility of subjective probabilities. Still, for those who take the pagan gods as a serious theological possibility, there is now a conundrum over which religion to follow.

Note that there is generally no such conundrum when comparing wagers about different pagan deities. Most polytheistic religions are mutually compatible, so if two sets of gods are prudentially preferred, we can simply worship both sets. Such merging of pantheons occurred many times in antiquity, often motivated by the desire to receive the additional potential blessings of new gods without forsaking those offered by the old. This option does not exist for merging polytheism with monotheism.

Prudence prefers monotheism over polytheism in Scenario 3, since the wager is psychologically necessary only in the case of the God of Abraham. In Scenario 2, monotheism is also obviously preferred for all except those who would be under the local obligation imposed by the pagan god. This excepted minority must choose between the universal God and their local god. On the assumption that the local god exists, he must be a contingent being, as shown by the limits of his power, so there must be some higher god or power upon which he depends. That higher power is either necessary or contingent. If contingent, we must again appeal to a higher power, until we ultimately arrive at a necessary Being. In other words, the existence of the local or contingent god is only possible if the necessary Being exists. That is to say, the god can exist only if there is a God without limit, while God may exist without the lesser god. Therefore, if we are forced to choose between one or the other, we ought to choose God. This is so prudentially uncontroversial that we should not be surprised that monotheism enjoyed such great success in supplanting polytheism, even in historical circumstances where no coercion was applied. Pagans were already accustomed to seeking the protection of ever greater, more powerful gods. It was only a logical extension to seek the protection of the Supreme Being.

We still must contend with those rare instances (Scenario 1) where the pagan conception of divinity rose to that of cosmological supremacy and even perhaps metaphysical necessity. If it is a single deity who is absolutely unlimited, metaphysically necessary, and without peer, then for the purposes of the wager we should say this is just God by another name. It is impossible to determine, by human reason, just what such a God is, and this is a theological question that the wager does not attempt to resolve. In fact, the unanswerability of this question is one of the presuppositions of the wager.

Perhaps we may conceive of a cosmologically supreme, metaphysically necessary divinity whose power is split among several beings. Two apparent examples of cosmologically supreme collectives can be found in the Zoroastrian dyad (Ahura Mazda-Ahriman) and the Hindu trinity (Brahma-Vishnu-Shiva). Such collectives cannot be metaphysically necessary existents unless the individuals that constitute them are metaphysically necessary. A plurality of metaphysically necessary beings is philosophically problematic, but we will ignore such consideration, since Pascal did not believe in philosophical proofs of the unity of God, so it would be disingenuous to enlist them to his aid. Still, we may note that the rational superiority of monotheism was tacitly acknowledged by the ancients, as they tended to make one of their supreme gods superior to the others: Ahura Mazda in the case of Zorastrianism and Brahma in the case of Hinduism. On a deeper level, the Hindus looked to Brahman or “divinity” as the supreme, unlimited fundament of all being, which is just the Abrahamic God by another name.

For the sake of argument, let us suppose there is nothing rationally problematic about a cosmologically supreme, metaphysically necessary, unlimited divinity divided among several distinct entities. As cosmologically supreme entities, each of these mini-pantheons are as incompatible with each other as they are with monotheism, though they would seem to meet the presuppositions of the wager as surely as does the latter. We should therefore consider each of these special polytheistic alternatives (Scenario 1) as an independent possibility.

One of the more common objections to the probabilistic aspect of Pascal’s argument is that we ought to consider all the various polytheistic possibilities on equal terms with monotheism. I have shown why most of historical paganism does not merit such equal treatment, though there are some notable exceptions. Instead of a two-way wager between God’s existence and non-existence, perhaps we could have a four-way wager among monotheism, Zoroastrianism, Hinduism, and atheism. Using the principle of indifference, we should assign a subjective probability of 25% each (or lower if there are more possibilities). Note that this hurts the probability of atheism no less than monotheism, though atheist critics arbitrarily decide to split only the monotheistic share of probability with the polytheists.


In this table, we separate the probability of a wager being correct (0.25) from the conditional probability of eternal life (mi, zi, hi, ai) given the correctness of (1) monotheism, (2) Zoroastrianism, or (3) Hinduism. We naturally assume that the one who chooses the correct religion has at least some small advantage in terms of the probability of eternal bliss. That is, m1 > z1, h1, a1; z2 > m2, h2, a2; and h3 > m3, z3, a3. As in the conventional Pascal wager, prudence again disfavors atheism, since it is suboptimal if one of the other three possibilities turns out to be correct, and the atheist is no better off than anyone else if atheism is correct. However, there appears to be no prudential basis for choosing among the three theistic possibilities. Since these possibilities are mutually exclusive, we can only believe in one of these religions, so the best strategy is to choose one of these at random or by some arbitrary criterion and avoid atheism.

What if there were infinitely many mutually exclusive theistic possibilities meeting the same criteria (Scenario 1) as those described? The factor of 0.25 would become infinitesimally small, and we might then consider that atheism is no longer at a strategic disadvantage. This is because each theistic religion r has an infinitely small chance p of being correct, so its expectation value is greater than that of atheism only by the difference p(rn - an)E, where the infinitesimal smallness of p seems to counter the infinite greatness of E. However, even if p and E balanced each other out, religion r would still have a finite advantage in the difference rn - an. The only way for atheism to be strategically equivalent to theistic religion would be for p to converge to zero more rapidly than E goes to infinity, or for the inverse of p to represent a higher order of infinity than E. Since p is real, the cardinality of 1/p can be no greater than that of the continuum. This means E would have to represent a merely countable infinity. Yet even the most banal notion of eternal life includes the infinity of the continuum, and this is not even counting the magnitude of the bliss, or any other ineffable qualities that may enhance this beatific life. Even on the most generous assumptions, then, theism retains a strategic advantage over atheism, however marginal. It is roughly analogous to setting the poor odds of someone who buys a lottery ticket against the one who has no ticket at all.

This discussion assumes without proof that the apparent polytheistic alternatives to monotheism are indeed genuinely distinct and viable alternatives. In fact, metaphysical reasoning can show that any plurality in God contradicts the idea that He is, in His entirety, metaphysically necessary. Once we isolate what is truly metaphysically necessary in the Deity, we essentially have monotheism, regardless of what name we give to the Supreme Being or how we speculate about His nature. Pascal did not trouble himself with polytheistic alternatives because they were not given credence by any intellectual, and this in turn was a legacy of the philosophical culture he inherited. As much as Pascal disdained philosophy, he was very much in its debt for having effectively reduced the wager argument to two possibilities.

Even today, no Western intellectual of note seriously contemplates a plurality of supreme beings. The pagan gods of old were “gods” only in the broader sense of immortal living beings. As soon as one contemplates cosmological supremacy and metaphysical necessity, the rational need to refer everything to a single principle or being becomes apparent. Even atheists recognize this need, as they feel a monotheistic compulsion to subject physical principles to unification schemes, though this requires speculating beyond the observable evidence. As for modern “pagans,” they have nothing of the ancient rustic faith that there really are multiple personal gods. Their religion is more of a poetic nature-worship that is in cultural reaction to Christianity and its transcendent God. The modern pagans have more of a spiritual kinship with atheists in their awe of nature and worship of the immanent, as they allow themselves no other spiritual outlet, having rejected the transcendent a priori. Though there are no true polytheists outside those who still keep the ancient religions, the basic pagan attitude remains in all those who seek ultimate principles within the natural world and its contingency.

Throughout this discussion, I have considered atheism only in its modern form, which is a denial of anything transcending the natural world. Accordingly, it is taken for granted that such atheism denies an afterlife; this was true in Pascal’s day as well as our own. However, it has not always been so, and it is conceivable for there to be an afterlife even in atheistic religions and philosophies. This is believed to have been the case in the purer form of Buddhism, and no deity is required in Daoism either. In such belief systems, eternal life is considered to be a consequence of the cosmic order, though there is no deity governing this order. We might say such systems profess only an impersonal god, or no god at all, depending on how we define the term. To the extent that they posit anything about ultimate reality, they are rationally compelled to admit some supreme individual subsistent (even the nirvana of Buddhism, though described as nothingness, is spoken of as if it were a positively experienced state). The “god” of these religions, much like Brahman in Hinduism, is a non-rational suppositum that exists in itself, having every aspect of personhood except rationality. It might be said that even some secular atheists acknowledge such a “god,” which they call Nature.

From the perspective of Pascal’s wager, atheistic religions are more closely analogous to monotheism and polytheism than to secular atheism, insofar as they posit the possibility of eternal bliss, upon which the prudential evaluation of the wager depends. Although they have no personal deity, they posit a metaphysically necessary cosmic order with some suppositum underlying it. Religions such as Buddhism impose a psychological necessity to wager, insofar as they force us to confront the possible reality of a cosmologically supreme order. They effectively force us to deal with at least the impersonal aspects of the divine, the existence of which has bearing on how we are to conduct ourselves in life. Dealing with the utterly transcendent and unknowable, we again can only apply subjective probability and the principle of indifference. By the same prudential calculus already articulated, atheistic religion is strategically superior to secular atheism.

It remains to be seen if there is any basis for choosing between belief in a personal or impersonal divinity. The latter possibility was not taken seriously by Europeans in Pascal’s time, since the perfection of God was generally assumed to entail intelligence. Again Pascal benefited from the Scholastic philosophical legacy he tried to ignore. If we are to be true to the wager’s presupposition that we cannot reason any aspects of the divine nature save its complete absence of limits, it would seem that we cannot decide whether there is thought in God. It may be argued that denying thought to God would be to impose a limit, but it is conceivable (ignoring rigorous metaphysics) that thought would be every bit as burdensome to the Deity as corporeality. Still, if the absolutely infinite Deity were to lack thought, it must possess some superior power that makes the lack of thought no deficiency at all. We cannot, per Pascal’s presuppositions, presume to resolve the question of divine personhood through reason. Indeed, Spinoza and other modern philosophers have made powerful arguments for a God who is impersonal, yet no less supreme and unlimited. In fact, it is contended that the perfection of the divine nature requires such impersonality, and it is but a clumsy anthropomorphism or overly literal figure of speech to ascribe any sort of intellection to God.

If we cannot admit a rational basis for choosing between a personal or impersonal Deity, perhaps there is a prudential basis. It might seem that an impersonal Deity is oblivious of our actions, so there is no point in modifying our behavior on that assumption. However, the atheistic religions do posit a cosmic moral order, and the absence of intelligence in the Supreme Being is not construed to be a deficiency, even in its more philosophical conceptions. Applying the same calculus as we used for the polytheistic alternatives, the wager argument gives us no basis for choosing between a personal or impersonal God. This is perhaps as Pascal would have wanted it, as he considered speculation about the divine nature to be fruitless and immaterial to man’s religious duty. If you wish to say God is not a rational person in any sense we would understand, you may do so, but this does not in any way diminish the fact that an infinite God necessarily has effective “knowledge” of all creation, or something more perfect than knowledge. The practical implications for man are not changed an iota, so these alternative conceptions of Deity might as well be grouped together with monotheism, as far as the wager argument is concerned.

The treatment of these alternatives exposes the limitations of the wager argument as a case for Abrahamic monotheism. While all versions of the argument make clear that secular atheism is an imprudent strategy, it does nothing to choose between theologically correct and erroneous religion, which was surely as critical a moral and salvific distinction for Pascal as that between theism and atheism. The wager may save man from one kind of religious error, but it leaves him exposed to countless others that could be just as grievous. While Pascal was able to make a prudential argument against atheism without appealing to natural theology, the rejection of this discipline leaves us without any natural basis for choosing among theologically distinct religions. This, perhaps, is as Pascal would have preferred, since he located the salvific act entirely in the granting of supernatural grace. Of course, if we are to deny a positive role for reason and natural ethics in the act of religious conversion, then all arguments, including Pascal’s wager, would be useless except to confirm the faithful.

Main Essay: Pascal’s Wager Explained

© 2011 Daniel J. Castellano. All rights reserved. http://www.arcaneknowledge.org

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