Incompatible-properties arguments

Incompatible-properties arguments are a family of deductive arguments for the nonexistence of God that proceed not from the existence of evil or the absence of evidence but from the internal incoherence of the divine concept itself. The strategy is to show that two or more of the attributes traditionally ascribed to God — omnipotence, omniscience, omnibenevolence, immutability, aseity, timelessness, perfect freedom, incorporeality, divine simplicity, and others — cannot be instantiated in a single being without logical contradiction. If these arguments succeed, the God of classical theism is not merely unlikely or unsupported by evidence but logically impossible, in the same category as a round square or a married bachelor.^{1, 4, 16}

Theodore Drange (1998) provided the most systematic survey of incompatible-properties arguments, identifying over a dozen distinct pairs or clusters of attributes that have been alleged to generate contradictions. Michael Martin’s Atheism: A Philosophical Justification (1990) developed several of these arguments in detail. Martin and Ricki Monnier’s edited volumes The Impossibility of God (2003) and The Improbability of God (2006) collected the major contributions from both sides of the debate. The arguments are technically demanding — they turn on precise definitions of the divine attributes and on disputed questions in modal logic, the philosophy of time, and the nature of freedom — but their cumulative force is significant: even if any single argument can be resisted by suitably redefining the attribute in question, the pattern of required redefinitions may progressively empty the concept of God of its traditional content.^{1, 4, 16, 17}

The omnipotence paradox

The best-known incompatible-properties argument is the omnipotence paradox, which has been discussed since at least the medieval period. The argument asks: can God create a stone so heavy that God cannot lift it? If God can create such a stone, then there is something God cannot do (lift the stone), and God is not omnipotent. If God cannot create such a stone, then there is something God cannot do (create the stone), and God is not omnipotent. Either way, omnipotence appears to be a self-contradictory concept.^{3, 5}

The standard theistic response, developed by Aquinas and refined by modern philosophers such as Thomas Flint and Alfred Freddoso, redefines omnipotence as the power to do anything that is logically possible. On this view, God cannot create a stone too heavy for an omnipotent being to lift because the description “a stone too heavy for an omnipotent being to lift” is logically incoherent — it describes a state of affairs that involves a contradiction (a being that can lift any weight being unable to lift a particular weight). Since the task is logically impossible, the inability to perform it does not count as a limitation on omnipotence, any more than the inability to create a round square counts as a limitation.^{5, 10, 13}

Critics have pressed the point further. J. L. Mackie argued that the response works only if omnipotence is defined in a way that builds in its own limitations — which is to say that the “omnipotence” being defended is not the unrestricted power over all things that the term naturally suggests but a qualified power subject to the constraints of logic. Whether this qualified omnipotence is sufficient for the God of traditional theism depends on one’s theological commitments: some theists (particularly in the voluntarist tradition, following Descartes) have held that God’s power extends even over the laws of logic, while others (following Aquinas) have held that logical truths are not restrictions on God but reflections of God’s own nature.^{3, 5, 14}

A related puzzle concerns omnipotence and the ability to sin. If God is both omnipotent and perfectly good, can God sin? If God can sin, God is not perfectly good (or at least, there is a possible world in which God is not good). If God cannot sin, there is something God cannot do, and God is not omnipotent. Aquinas resolved this by arguing that sin is a privation — a deficiency of action rather than a positive capacity — so the inability to sin is not a limitation of power but a consequence of perfect power. But this response requires a specific metaphysics of evil (the privation theory) that is itself contested, and critics argue that the concept of a being who necessarily does good eliminates genuine freedom and renders divine moral praiseworthiness empty.^{3, 4, 5}

Omniscience and freedom

A second major cluster of incompatible-properties arguments concerns the relationship between divine omniscience and divine freedom. If God is omniscient, God knows from eternity everything that God will ever do. But if God’s future actions are known in advance — even by God — then those actions are fixed, and God cannot do otherwise. If God cannot do otherwise, God does not act freely. The argument can be stated as follows:^{1, 6}

P1. If God is omniscient, God knows at time t₁ what God will do at time t₂.

P2. If God knows at t₁ what God will do at t₂, then it is determined at t₁ what God will do at t₂.

P3. If it is determined at t₁ what God will do at t₂, then God is not free at t₂ to do otherwise.

P4. If God is not free to do otherwise, God is not perfectly free.

C. Therefore, if God is omniscient, God is not perfectly free.

This argument is a special case of the broader problem of divine foreknowledge and human freedom, but applied to God’s own actions rather than to the actions of creatures. The theist who resolves the human-freedom version by appeal to divine timelessness (God does not know before the event, because God exists outside of time) can apply the same solution here — but this generates its own difficulties, as discussed below. The theist who resolves the human-freedom version by appeal to Molinism (God’s middle knowledge of counterfactuals of creaturely freedom) cannot straightforwardly apply the same solution to God’s own freedom, because Molinism is designed to preserve creaturely freedom, not divine freedom.^{6, 10, 14}

A variant of the omniscience–freedom problem targets the relationship between omniscience and the ability to learn. If God is omniscient, God already knows everything; there is nothing for God to learn. But a being that cannot learn appears to lack a cognitive capacity that finite beings possess — the capacity to acquire new knowledge. Is this a limitation? Swinburne (1993) has argued that the inability to learn is no limitation if one already knows everything, in the same way that the inability to become healthy is no limitation if one is already perfectly healthy. Critics respond that the analogy is imperfect: learning involves not just the content of knowledge but the process of coming to know, which may be a good in itself that an eternally omniscient being necessarily lacks.^{6, 10}

Timelessness and action in time

Classical theism, following Boethius, Anselm, and Aquinas, holds that God exists timelessly — not within the temporal sequence but in an “eternal now” in which all moments of time are equally present to God. This attribute generates multiple tensions with other divine attributes and with the theistic claim that God acts in history.⁷

The most direct problem is that action appears to require temporal location. To create the universe, to answer a prayer, to perform a miracle, to incarnate as a human being — all of these are events that occur at particular times. If God is timeless, God does not exist at any particular time, and it is unclear how a timeless being can perform temporally located actions. The theistic response typically distinguishes between the act (which is timeless) and its effect (which is temporal): God timelessly wills that the universe exist, and the effect of this timeless willing is the temporal beginning of the universe. Critics such as Drange and Martin have argued that this distinction is obscure: a will that produces an effect at a specific time appears to be a temporally located will, regardless of how it is described.^{1, 4, 7}

A related difficulty concerns the claim that God responds to prayers. If God exists timelessly, God does not experience events in sequence; God does not wait for a prayer to be offered and then decide how to respond. Instead, God’s response to the prayer is timelessly simultaneous with the prayer itself. But this raises the question of whether “response” is the right word: a genuine response requires that the responder take in information and then act on it, which is a temporal process. A timeless “response” that is simultaneous with the stimulus is not a response in any ordinary sense but a pre-established harmony — and if God’s “responses” are timelessly fixed, they cannot be influenced by the content of the prayers, which undermines the point of petitionary prayer.^{7, 8, 14}

Some theists, including Swinburne, have responded by abandoning divine timelessness in favor of divine temporality: God exists in time, experiences temporal succession, and acts at particular moments. This resolves the timelessness–action tension but at the cost of abandoning a central element of classical theism and raising new difficulties (e.g., if God exists in time, was there a time before God acted? What was God doing before creating the universe?).^{10, 7}

Immutability and responsiveness

Divine immutability — the doctrine that God does not change — generates tensions similar to those generated by timelessness. An immutable being cannot undergo any change in properties, including changes in mental states: God cannot go from not knowing that a prayer has been offered to knowing that it has, cannot go from not intending to act to intending to act, and cannot go from one emotional state to another. But the God of the Abrahamic traditions is described as responding to events, being grieved by sin, being pleased by worship, and changing course in response to human action (e.g., God’s decision not to destroy Nineveh after the city repented, as described in the book of Jonah).⁸

The tension between immutability and the biblical portrait of God has led to a longstanding debate in theology. Classical theists typically resolve it by treating the biblical descriptions of God’s emotional responses as anthropomorphic: God does not literally grieve, rejoice, or change his mind, because these are descriptions of changing mental states that an immutable being cannot undergo. The biblical language is accommodated to human understanding but does not describe God as God actually is. Critics argue that this resolution drains the concept of God of personal attributes that are central to theistic devotion and practice — a God who does not genuinely respond to human beings is difficult to relate to as a personal being, and the resulting concept of God may be more akin to the impersonal absolute of philosophical idealism than to the personal deity of Abrahamic worship.^{3, 8, 10}

The tension can be formalized:

P1. If God is immutable, God cannot undergo any change in properties (including mental states).

P2. If God is a personal being who knows what is happening in the world, God’s knowledge changes as the world changes (e.g., God now knows that it is 2026, whereas in 1900 God knew that it was 1900).

P3. A change in knowledge is a change in properties.

C. Therefore, God cannot be both immutable and a personal being with knowledge of changing temporal facts.

This version of the argument targets the compatibility of immutability with omniscience about a changing world. The standard response appeals to the doctrine of divine timelessness: if God exists outside of time, God does not experience changes in knowledge because all temporal facts are equally present to God in the eternal now. But this pushes the problem back to the difficulties with timelessness discussed above.^{7, 8, 14}

The cumulative case and the retreat strategy

Drange (1998) argued that incompatible-properties arguments are most effective not individually but cumulatively. Any single argument can be resisted by redefining the attribute in question: omnipotence can be restricted to logically possible tasks, timelessness can be reinterpreted as atemporal eternity, immutability can be softened to immutability of character rather than immutability of all properties, and so on. Each redefinition may be independently plausible. But the cumulative effect of multiple redefinitions is a concept of God that progressively diverges from the God of traditional theology and ordinary religious devotion.¹

Martin and Monnier (2003) described this as the “retreat strategy”: when confronted with an incompatible-properties argument, the theist retreats to a weaker definition of the problematic attribute. Omnipotence becomes the power to do anything logically possible; timelessness becomes everlastingness; immutability becomes constancy of character; omniscience is qualified to exclude knowledge of future free actions (open theism). Each retreat resolves the immediate contradiction but at a cost: the resulting God is less powerful, less knowledgeable, less transcendent, or less stable than the God of classical theism. Taken together, the retreats may produce a being that is barely recognizable as the God of Anselm, Aquinas, or the Nicene Creed — a being that is very powerful but not omnipotent, very knowledgeable but not omniscient, very constant but not immutable.^{4, 16}

Theists have responded that the redefinitions are not retreats but clarifications. Swinburne’s The Coherence of Theism (1977; rev. ed. 1993) is the most systematic attempt to formulate a coherent set of divine attributes that avoids internal contradiction. Swinburne argues that the attributes have always required careful philosophical articulation, and that the process of refining their definitions is a normal part of theological inquiry, not a concession to atheistic arguments. He defines omnipotence as the ability to do anything logically possible for a being with God’s other attributes, omniscience as knowledge of all true propositions (with disputes about whether this includes future contingents), and abandons timelessness in favor of divine temporality. The resulting concept of God is, Swinburne argues, fully coherent and fully adequate for theistic purposes.¹⁰

Critics respond that the adequacy of Swinburne’s reformulation depends on what one takes to be essential to theism. If classical theism — the theism of the great medieval thinkers, the ecumenical creeds, and the dominant theological traditions of Christianity, Islam, and Judaism — is the target, then Swinburne’s reformulation concedes that classical theism is incoherent and replaces it with a different, more modest conception of God. Whether this revised theism is still “theism” in a theologically meaningful sense is itself a matter of debate. Oppy (2006) has argued that the cumulative effect of the required modifications is to erode the concept of God to the point where it is unclear what explanatory or devotional work the concept still performs.^{15, 20}

Further incompatibilities

Beyond the major arguments discussed above, the literature contains numerous additional incompatible-properties arguments, each targeting a different pair or cluster of attributes. A brief survey of the most significant:

Omniscience and incorporeality. Some forms of knowledge appear to require a body. Knowing what it is like to feel pain, taste chocolate, or experience sexual desire requires having the relevant sensory apparatus. If God is incorporeal, God lacks this apparatus and therefore lacks experiential knowledge of embodied states. This is a limitation on omniscience. The response that God can know the propositional content of embodied experiences without having them may be adequate for propositional knowledge but appears to leave out a genuine kind of knowledge — knowledge by acquaintance — that finite embodied beings possess and an incorporeal God does not.^{1, 4, 6}

Perfect justice and perfect mercy. Justice requires that wrongdoing be punished in proportion to its severity. Mercy requires that punishment be mitigated or forgiven. A being that is perfectly just must never under-punish; a being that is perfectly merciful must always mitigate punishment. These requirements appear to conflict: any act of mercy is, to that extent, a departure from strict justice, and any act of strict justice is, to that extent, a failure of mercy. Theistic responses typically distinguish between different senses of justice and mercy, or argue that divine grace provides a framework within which both can be satisfied simultaneously (e.g., the Christian doctrine of atonement). Critics argue that the atonement doctrine introduces new problems (the justice of punishing an innocent substitute) rather than resolving the original tension.^{1, 3}

Omnipresence and incorporeality. Classical theism holds that God is both omnipresent (present everywhere) and incorporeal (lacking a body). But presence is ordinarily understood as a spatial relation, and spatial relations require extension — a body or at least a spatial location. What does it mean for a non-spatial being to be “present” at a spatial location? Theists have offered various accounts: omnipresence as causal influence (God acts at every point in space), omnipresence as epistemic access (God knows what is happening at every point in space), or omnipresence as constitutive (space exists within God). Each account redefines omnipresence in a way that diverges from its ordinary spatial meaning, raising the question of whether the resulting concept is still meaningfully called “presence.”^{1, 10, 14}

Divine simplicity and multiple attributes. The doctrine of divine simplicity, affirmed by Aquinas and the Catholic theological tradition, holds that God has no parts or composition: God’s essence is identical with God’s existence, God’s omnipotence is identical with God’s omniscience, and each of God’s attributes is identical with every other attribute and with God’s essence. Plantinga (1980) argued that divine simplicity entails that God is a property (since God is identical with each of his properties), and that properties cannot be persons, which means that a simple God cannot be a personal being. Alternatively, if God’s omnipotence is literally identical with God’s omniscience, the two words mean the same thing when applied to God, which empties each attribute of its distinctive content.^{9, 19}

The breadth and variety of incompatible-properties arguments mean that no single theistic response can address them all. Each argument targets a different logical joint in the concept of God, and the resources available for resolving one argument (e.g., abandoning timelessness) may exacerbate another (e.g., the tension between divine temporality and immutability). The theist who wishes to maintain the full set of classical divine attributes faces a complex, multi-front defense in which concessions made on one front may create vulnerabilities on others. Whether this defense can succeed — whether a fully coherent and theologically adequate concept of God can be articulated — remains one of the central open questions in the philosophy of religion.^{1, 14, 15}