Aquinas’ Five Ways

Aquinas’ Five Ways propose arguments for the existence of a “first cause”, “unmoved mover”, or a “necessary being”, which might, at most, lead to a deistic understanding of a god.
The deistic god implied by Aquinas’ Five Ways would resemble an abstract, uninvolved creator without personal or moral obligations, lacking the defining qualities of the Christian God.
The analogy of gold and a spherical cube of gold illustrates that evidence for one concept cannot logically imply evidence for a concept that is logically incoherent.
Even if Aquinas’ Five Ways provided evidence for a deistic god, this evidence cannot logically entail the existence of the Christian God, whose specific attributes introduce significant logical contradictions.

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Provide me with rigorous formulations of Aquinas’ Five Ways.

1. The Argument from Motion (First Way)

Natural Language Explanation

Premise 1: Whatever is in motion must be moved by something else.
Premise 2: This chain of movers cannot continue infinitely.
Conclusion: Therefore, there must be a first unmoved mover, which is what we call God.

Syllogistic Form

P1: Everything in motion is moved by something else.
P2: An infinite chain of movers is impossible.
P3: Motion exists.
C1: Therefore, there must be a first unmoved mover.
C2: This unmoved mover is what we refer to as God.

Symbolic Logic

Define: $Mx$ : x is in motion
Define: $Cxy$ : x causes motion in y
Statement: $\forall x (Mx \rightarrow \exists y (Cyx))$
Infinite regression negation: $\neg \exists {x_1, x_2, x_3, \dots} (Cx_1 x_2 \land Cx_2 x_3 \land Cx_3 x_4 \dots)$
Existence of motion: $\exists x (Mx)$
Conclusion: $\therefore \exists x (\neg Mx \land \forall y (My \rightarrow Cxy))$

2. The Argument from Causation (Second Way)

Natural Language Explanation

Premise 1: Every effect has a cause.
Premise 2: There cannot be an infinite chain of causes.
Conclusion: Thus, there must be a first uncaused cause, understood to be God.

Syllogistic Form

P1: Every effect has an efficient cause.
P2: Nothing can be the cause of itself.
P3: An infinite chain of causes is impossible.
P4: Causation exists.
C1: Therefore, there must be a first uncaused cause.
C2: This first cause is what we call God.

Symbolic Logic

Define: $Cx$ : x is caused
Define: $Exy$ : x is the efficient cause of y
Statement: $\forall x (Cx \rightarrow \exists y (Eyx))$
Self-causation negation: $\forall x \neg Exx$
Infinite regression negation: $\neg \exists {x_1, x_2, x_3, \dots} (Ex_1 x_2 \land Ex_2 x_3 \land Ex_3 x_4 \dots)$
Existence of cause: $\exists x (Cx)$
Conclusion: $\therefore \exists x (\neg Cx \land \forall y (Cy \rightarrow Exy))$

3. The Argument from Contingency (Third Way)

Natural Language Explanation

Premise 1: Contingent beings exist.
Premise 2: Every contingent being has a cause.
Conclusion: Therefore, there must exist a necessary being, which is God.

Syllogistic Form

P1: Contingent beings exist.
P2: Every contingent being depends on something else for its existence.
P3: Not everything can be contingent.
P4: There must be a necessary being on which all contingent beings depend.
C: This necessary being is what we call God.

Symbolic Logic

Define: $Cx$ : x is contingent
Define: $Nx$ : x is necessary
Define: $Dxy$ : x depends on y
Existence of contingency: $\exists x (Cx)$
Dependency statement: $\forall x (Cx \rightarrow \exists y (Dxy))$
Negation of universal contingency: $\neg \forall x (Cx)$
Conclusion: $\therefore \exists x (Nx \land \forall y (Cy \rightarrow Dyx))$

4. The Argument from Degrees (Fourth Way)

Natural Language Explanation

Premise 1: Things possess properties to varying degrees.
Conclusion: Therefore, there must exist a being of maximal perfection, understood to be God.

Syllogistic Form

P1: Properties come in degrees.
P2: Degrees imply a maximum.
P3: The maximum of any perfection must be caused by something perfect.
C: Therefore, there exists a maximally perfect being (God).

Symbolic Logic

Define: $Px$ : x has property P
Define: $Dxyz$ : x has more of property P than y in respect to z
Define: $Mx$ : x is maximally P
Degree existence: $\exists xyz (Px \land Py \land Dxyz)$
Maximum implication: $\forall x (Px \rightarrow \exists y (My \land Dyx))$
Conclusion: $\therefore \exists x (Mx \land \forall y (Py \rightarrow Dxy))$

5. The Argument from Governance (Fifth Way)

Natural Language Explanation

Premise 1: Natural objects act for an end.
Conclusion: Therefore, an intelligent being must direct nature, understood as God.

Syllogistic Form

P1: Natural objects without intelligence act for ends.
P2: Whatever acts for an end must be directed by intelligence.
P3: Nature exhibits such directed behavior.
C1: Therefore, there must be an intelligent director of nature.
C2: This director is what we call God.

Symbolic Logic

Define: $Tx$ : x tends toward ends
Define: $Ix$ : x is intelligent
Define: $Dxy$ : x directs y
Directed action statement: $\forall x (Tx \rightarrow \exists y (Iy \land Dyx))$
Existence of unintelligent ends: $\exists x (\neg Ix \land Tx)$
Conclusion: $\therefore \exists x (Ix \land \forall y (\neg Iy \land Ty \rightarrow Dxy))$

General Critiques of the Five Arguments

All arguments make an unsupported leap from an abstract cause or mover to the personal God of Christianity.
These arguments rely on outdated medieval physics and metaphysics that modern science may not uphold.
The arguments assume causation is linear rather than potentially circular or networked.
They depend heavily on the principle of sufficient reason, which may not hold universally.

Provide rigorous counter-arguments to Aquinas’ Five Ways.

1. Counter-Argument to the Argument from Motion (First Way)

Critique:
The Argument from Motion assumes a linear, hierarchical causation model rooted in medieval physics, which has been largely replaced by modern understandings of non-linear and networked causation. Quantum mechanics and relativity suggest that causation might not strictly follow a sequential chain.

Infinite Regression: Aquinas dismisses an infinite regress of movers, but cosmological models like oscillating or cyclical universes propose a self-sustaining process without a need for a “first unmoved mover.”
- Alternative Formulation:
  $\forall x , (Mx \rightarrow \exists y , C(yx)), , \neg Mx$
  Explanation: This formulation proposes that for any object in motion (Mx), there is a cause (C(yx)) that moves it. However, an object in motion may simply be part of an infinite chain without a definitive “unmoved” mover.
Assumption of Motion Necessitating an External Mover: Aquinas’s claim that “everything in motion is moved by something else” is contradicted by the law of inertia. According to this law, objects in motion tend to stay in motion without requiring an external mover.
- Inertia Counter-Formulation:
  $\forall x , (Mx \rightarrow (C(yx) \lor Ix))$
  Explanation: Here, if something is in motion (Mx), it could either be due to a cause (C(yx)) or due to inertia (Ix). This suggests that not all motion requires an external mover, as inertial movement can persist without it.
Quantum Uncertainty and Indeterminacy: Quantum mechanics introduces the possibility of random, spontaneous motion without an external mover, undermining the argument that “whatever is in motion is moved by something else.”
- Quantum Movement:
  $\exists x , (Mx \land \neg \exists y , C(yx))$
  Explanation: This states that some objects in motion (Mx) may not have a preceding cause (C(yx)), consistent with quantum events where particles can appear to move randomly without an identifiable cause.

2. Counter-Argument to the Argument from Causation (Second Way)

Critique:
The Argument from Causation assumes a deterministic, linear causal chain, but modern science allows for probabilistic and networked causative interactions.

Self-Causing Events: Some quantum cosmology theories suggest that certain phenomena may emerge spontaneously, challenging the assertion that “every effect has a cause.”
- Self-Causation:
  $\exists x , (Cx \land \neg \exists y , Exy)$
  Explanation: This implies the existence of events (Cx) that lack an external efficient cause (Exy), supporting the idea that some effects could be self-causing.
Circular and Networked Causation: Many systems exhibit networked causation, where causes do not follow a simple linear sequence but are interconnected, sometimes circularly, without the need for a first cause.
- Causal Network:
  $\exists x, y , (Exy \land Eyx)$
  Explanation: This suggests a scenario where two entities (x and y) cause each other, representing a circular causative relationship, which does not necessitate a first cause.
Principle of Sufficient Reason (PSR): The PSR underpins the idea that every effect must have a cause. However, at the quantum level, events often occur probabilistically, challenging the PSR’s applicability to the entire universe.
- Probabilistic Events:
  $\exists x , (Cx \land \neg \exists y , (Exy \lor Py))$
  Explanation: Here, some events (Cx) lack a sufficient reason or preceding cause (Exy or Py), reflecting the probabilistic nature of certain quantum phenomena.

3. Counter-Argument to the Argument from Contingency (Third Way)

Critique:
The Argument from Contingency relies on the premise that contingent beings require a necessary being for existence. However, multiverse theories offer alternative explanations without requiring such a being.

Multiverse Theory: Some cosmological theories propose that our universe is just one of countless universes, allowing for contingent existence without a necessary being.
- Multiverse Contingency:
  $\forall x , (Cx \rightarrow \exists y (Cy \land Dyx))$
  Explanation: In this formulation, each contingent entity (Cx) depends on another contingent entity (Cy), which may itself rely on another, forming a chain within a potentially infinite multiverse rather than requiring a necessary being.
Questioning Necessity: The idea of a “necessary being” is controversial; some argue that contingency might be self-explanatory, as the universe could be a “brute fact.”
- Brute Fact Argument:
  $\exists x , (Cx \land \neg \exists y , (Nx \land Dyx))$
  Explanation: This suggests that a contingent entity (Cx) may exist without needing a necessary being (Nx), supporting the notion that contingency might not need further explanation.
Self-Referential Contingency Chains: All beings might be contingent without requiring a necessary being, as self-referential systems or chains of dependency could explain existence.
- Self-Referential Contingency:
  $\forall x , (Cx \rightarrow \exists y (Cy \land Dxy))$
  Explanation: This expresses that each contingent being (Cx) depends on another contingent being (Cy), allowing for a self-sustaining chain without invoking a necessary being.

4. Counter-Argument to the Argument from Degrees (Fourth Way)

Critique:
The Argument from Degrees suggests that variations in properties imply a maximally perfect being. This is problematic due to subjective and relative interpretations of perfection.

Subjective Nature of Perfection: Concepts like “goodness” and “beauty” are subjective, meaning that perfection may not exist as an objective maximum.
- Subjective Property:
  $\neg \exists x , (Mx \land \forall y , (Py \rightarrow Dxy))$
  Explanation: This suggests there is no universal entity (Mx) that embodies perfection to a degree exceeding all others (Dxy), as “perfection” is relative to subjective standards.
Degrees Without Maximums: Not all properties imply a highest degree. For example, temperature can theoretically increase infinitely, challenging the idea that all degrees imply an absolute maximum.
- Non-Maximal Gradation:
  $\forall x, y , (Px \land Py \rightarrow \exists z , (Dxyz))$
  Explanation: This represents that for any two entities with a property (Px and Py), there is always a degree difference (Dxyz), but no ultimate maximum is required.
Relative, Contextual Properties: Properties like “strength” or “wisdom” may be contextually defined, undermining the idea of an absolute, maximal being.
- Relative Properties:
  $\forall x, y , (Px \rightarrow (Py \rightarrow Rxy))$
  Explanation: Here, properties (Px) are relative and comparative (Rxy) rather than pointing to an absolute maximum, which implies that no ultimate or perfect entity is needed.

5. Counter-Argument to the Argument from Governance (Fifth Way)

Critique:
The Argument from Governance assumes that natural objects acting for an end implies guidance by an intelligent being. However, evolution and self-organizing systems demonstrate that order can arise without conscious direction.

Self-Organization and Evolution: In evolutionary biology, complex structures arise through natural selection, which does not require intentional guidance.
- Evolutionary Mechanism:
  $\forall x , (Tx \land \neg Ix \rightarrow (Dyx \lor Exy))$
  Explanation: This implies that natural objects (Tx) can act toward ends without intelligence (Ix), as their behavior can be explained by evolutionary mechanisms (Dyx or Exy).
Non-Teleological Processes: Many natural phenomena, such as thermodynamic systems, operate without purpose or intentionality, challenging the notion that natural ends imply design.
- Law-Based Behavior:
  $\forall x , (Tx \rightarrow (Lx \lor Ix))$
  Explanation: This states that natural objects with a tendency toward ends (Tx) are either following physical laws (Lx) or intelligent direction (Ix), but intelligent design is not the only explanation.
Anthropomorphic Fallacy: The argument projects human intentionality onto natural processes. Just because humans design with purpose doesn’t mean nature requires intelligent guidance.
- Fallacy of Intent:
  $\exists x , (Tx \land \neg \exists y , (Dyx \land Iy))$
  Explanation: This suggests that certain tendencies toward ends (Tx) occur without an intelligent director (Iy), indicating that natural objects can behave purposefully without requiring a guiding mind.

General Critiques of All Five Arguments

Jump from Abstract to Specific: Each argument attempts to leap from a general first cause or mover to the specific characteristics of the Christian God, which is unwarranted, as even a successful argument would not confirm a personal, omniscient, or omnipotent deity.
Outdated Physics and Metaphysics: The arguments rely heavily on Aristotelian physics and metaphysical assumptions that have been largely replaced by modern scientific understandings of causation, motion, and contingency.
Linear Causation Assumption: Each argument assumes that causation is linear, while modern science reveals that causation can be circular or networked, as in ecological systems or feedback loops.
Principle of Sufficient Reason (PSR): All arguments rely on the Principle of Sufficient Reason (PSR), positing that everything must have an explanation. However, the PSR is not universally accepted, and some argue that the universe could exist as a brute fact without needing an external explanation.

Provide an essay on the conceptual gulf between the deistic god the Five Ways, if valid, would entail and the specific God of the Bible.

The Conceptual Gulf between the Deistic God of Aquinas’ Five Ways and the Christian God of the Bible

Aquinas’ Five Ways propose arguments for the existence of a “first cause,” “unmoved mover,” or a “necessary being,” which might, at most, lead to a deistic understanding of a god—an abstract, remote, and fundamentally impersonal force responsible for the existence and order of the universe. However, there is a profound conceptual gulf between this philosophical conception and the specifically personal, interventionist, and morally engaged God of the Bible. This essay explores the limitations of Aquinas’ arguments, even if they are accepted as valid, and contrasts the deistic god they imply with the numerous logical incoherencies surrounding the Christian God. Additionally, it introduces an analogy to illustrate a fundamental flaw in attempting to link evidence for a deistic god to the specific attributes of the Christian God, as evidence of gold can never be evidence of a spherical cube of gold.

The Deistic God of the Five Ways

The god implied by Aquinas’ Five Ways, assuming they are valid, would resemble a deistic god—a being or force that initiated the universe and perhaps established natural laws, but one that remains remote and uninvolved in the affairs of humanity. Such a god is defined by abstract philosophical principles, lacking the characteristics traditionally associated with the biblical God, such as omnibenevolence, omniscience, and omnipotence, along with an active interest in human morality and salvation. Here’s a brief summary of how each of Aquinas’ arguments points only to a general “first cause” or “necessary being” rather than the specifically Christian God:

Argument from Motion suggests a “prime mover” that initiates motion in the universe, but it does not entail a god who interacts with human history or enforces moral laws.
Argument from Causation points to a “first cause” in a chain of causes but does not imply a god who intervenes in the physical or moral world after initiating it.
Argument from Contingency suggests the existence of a “necessary being” that prevents infinite regress, yet it says nothing about the being’s personal qualities, moral attributes, or intentions.
Argument from Degrees hints at a maximal standard for properties like “goodness,” but does not entail a god with active will or personality.
Argument from Governance implies a designer who orders natural processes, but this designer could be as impersonal as the laws of nature themselves, without any specific involvement in human affairs.

In summary, the Five Ways argue only for a minimalistic, detached god, limited in scope to the function of creating or sustaining the universe and not necessarily involved in human morality, salvation, or even self-awareness. This god lacks personality, consciousness, and moral obligations—attributes essential to the Christian understanding of God.

The Specific Attributes of the Christian God and Logical Incoherencies

In contrast, the God of the Bible is portrayed as personal, omniscient, omnipotent, omnipresent, and omnibenevolent. This God not only created the universe but also intervenes in history, speaks to prophets, performs miracles, judges the wicked, rewards the righteous, and sacrifices Himself in the form of Jesus for humanity’s salvation. However, several logical incoherencies arise when these characteristics are closely examined, which highlight the stark difference between the deistic god Aquinas’ arguments might entail and the Christian God.

Omniscience and Free Will: The Bible asserts that God is omniscient, knowing all things, including human thoughts and actions before they occur. Yet, the Bible also asserts that humans have free will to choose between good and evil. This raises a logical contradiction: if God knows future actions with absolute certainty, then human choices must be predetermined, rendering free will an illusion. This makes the concept of sin, and thus the notion of divine judgment, problematic, as it would mean that humans are punished for actions they could not freely choose.
Omnipotence and the Problem of Evil: The Christian God is defined as omnipotent, able to do anything within His nature. However, the existence of suffering and evil in the world presents a severe challenge to this attribute. If God is both omnipotent and omnibenevolent, why does He permit needless suffering and evil acts, such as natural disasters or the actions of malevolent individuals? The classic theodicy arguments attempt to justify this by proposing that evil exists to allow free will or as a means to greater goods, but these explanations often feel unsatisfactory and appear to undermine God’s supposed benevolence or omnipotence, particularly in cases of pointless suffering where no greater good can be discerned.
Incarnation and Divinity: The Christian doctrine of the Trinity presents another major logical tension. The idea that God is simultaneously three distinct persons (Father, Son, and Holy Spirit) while remaining one singular being seems to defy logic and has been termed a “mystery of faith.” Yet, logical analysis suggests that a being cannot be fully three distinct persons while also fully one being without violating the principle of non-contradiction.
Moral Incoherencies: The Bible portrays God as morally perfect, yet several biblical narratives seem inconsistent with this portrayal. For example, the commanded genocides in the Old Testament and instances where God appears to condone slavery and punish individuals or groups disproportionately for minor offenses raise questions about the coherence of God’s purported moral perfection. If God’s moral laws are unchanging, as often claimed, these actions seem difficult to reconcile with a consistent standard of moral benevolence.

These logical and moral inconsistencies highlight the conceptual difficulties in aligning the abstract deistic god implied by Aquinas’ Five Ways with the specific characteristics of the biblical God.

Analogy: Evidence of Gold and the Spherical Cube of Gold

To illustrate the logical incoherence of attempting to connect evidence of a deistic god to the specific God of the Bible, we can use the analogy of gold and a spherical cube of gold. Imagine discovering a nugget of pure gold. This discovery can serve as evidence that gold exists, with certain properties such as malleability, shininess, and atomic structure. However, this evidence does not imply, nor could it ever imply, the existence of a “spherical cube of gold.” Such an object is logically incoherent—a cube cannot be spherical by definition, as the two shapes are mutually exclusive.

In a similar way, even if Aquinas’ Five Ways provided evidence of a deistic god, this would be merely evidence of an initial cause, an ultimate mover, or a necessary being. This evidence cannot logically entail the existence of the Christian God, as the specific attributes of the biblical God introduce logical contradictions that do not logically follow from evidence of a deistic god. For instance, the omnipotence and omnibenevolence of the Christian God conflict with the observable existence of suffering, just as a spherical cube conflicts with the definitions of “sphere” and “cube.”

Conclusion

The Five Ways, even if sound, lead only to the existence of a deistic god—a god defined by minimal qualities necessary for creating or sustaining the universe. This deistic conception falls far short of describing the Christian God, whose attributes introduce significant logical and moral incoherencies when examined. Just as the existence of gold does not imply the existence of a “spherical cube of gold,” the existence of a deistic god does not logically imply the existence of the Christian God. The conceptual gulf between the two is profound, and the logical contradictions inherent in the Christian God’s attributes further underscore the impossibility of bridging this gap through Aquinas’ philosophical arguments alone.

Quiz

#1: What is the primary difference between the deistic god suggested by Aquinas’ Five Ways and the Christian God of the Bible?

Answer:

The deistic god is an abstract, uninvolved creator, while the Christian God is depicted as personal, interventionist, and morally engaged.

#2: Which concept in physics challenges Aquinas’ assumption that “everything in motion must be moved by something else”?

Answer:

The law of inertia, which states that objects in motion remain in motion without requiring an external mover.

#3: How does quantum mechanics contradict Aquinas’ Argument from Motion?

Answer:

Quantum mechanics allows for random, spontaneous motion without an identifiable mover, challenging the premise that all motion requires an external cause.

#4: In what way does the Argument from Causation face a challenge from circular and networked causation?

Answer:

Circular and networked causation allow for mutual or interdependent causes, removing the necessity of a single first cause.

#5: What is the Principle of Sufficient Reason (PSR), and why is it questioned in modern philosophy?

Answer:

The PSR states that everything must have an explanation. It is questioned because quantum events often occur probabilistically, lacking deterministic causes.

#6: How does the Argument from Degrees lead to the idea of a maximally perfect being, and why is this idea problematic?

Answer:

The Argument from Degrees assumes that gradations imply a maximum. However, perfection is often subjective or context-dependent, making a “maximally perfect being” philosophically contentious.

#7: What analogy is used to illustrate the flawed reasoning in linking evidence for a deistic god to the Christian God?

Answer:

The analogy of gold and a spherical cube of gold, suggesting that evidence of gold cannot be evidence for a logically incoherent concept like a spherical cube.

#8: Explain the logical incoherency involving God’s omniscience and human free will in Christian theology.

Answer:

If God is omniscient and knows all actions before they occur, human free will becomes illusory, as choices would be predetermined, making sin and judgment problematic.

#9: How does the Problem of Evil challenge the notion of an omnipotent and omnibenevolent God?

Answer:

If God is omnipotent and omnibenevolent, the existence of needless suffering and evil is difficult to reconcile, as an all-powerful, good God would presumably prevent such suffering.

#10: Describe the logical issue related to the Trinity in Christian doctrine.

Answer:

The Trinity proposes that God is simultaneously three distinct persons and one being, which seems to violate the principle of non-contradiction, as it implies both unity and distinct plurality.

#11: How does Aquinas’ Argument from Governance imply a guiding intelligence, and what natural process challenges this implication?

Answer:

Aquinas argues that natural objects act toward an end, implying guidance. However, evolutionary biology shows complex order can arise through natural selection without a conscious designer.

#12: Summarize the overall conclusion about the Five Ways and their failure to support the existence of the Christian God.

Answer:

The Five Ways suggest only a minimalistic, deistic god responsible for creation, which lacks the attributes and personal involvement ascribed to the Christian God, making them inadequate to prove the biblical God’s existence.

Provide 15 discussion questions relevant to the content above.

In what ways does the deistic god implied by Aquinas’ Five Ways differ fundamentally from the God described in the Bible?
Can Aquinas’ Five Ways provide any foundation for belief in the personal, interventionist God of Christianity, or do they only argue for a distant first cause? Why or why not?
How does the law of inertia challenge Aquinas’ assumption that “everything in motion is moved by something else”?
Given the randomness observed in quantum mechanics, is it still reasonable to assume a linear chain of causation as Aquinas does in the Argument from Motion?
What are the strengths and weaknesses of using the Principle of Sufficient Reason (PSR) as a basis for proving the existence of God?
How does the Argument from Contingency rely on a “necessary being,” and are there alternative ways to account for existence without this concept?
Does the existence of subjective properties (such as goodness and beauty) weaken the Argument from Degrees, which assumes an objective standard for all qualities?
How does the analogy of “gold and a spherical cube of gold” help clarify the limitations of Aquinas’ Five Ways when applied to the Christian God?
Does the idea of omniscience inherently conflict with the concept of human free will? How might proponents of free will defend it against this conflict?
How might the Problem of Evil challenge the coherence of a God who is both omnipotent and omnibenevolent?
Does the doctrine of the Trinity, where God is both one and three, logically conflict with the principle of non-contradiction? Why or why not?
How does evolutionary biology provide a naturalistic counter to Aquinas’ Argument from Governance, which suggests that natural order implies an intelligent designer?
Can the concept of a “brute fact” (a fact without explanation) be a reasonable alternative to the Principle of Sufficient Reason in explaining the existence of the universe?
How do modern scientific understandings of causation, such as networked or circular causation, differ from Aquinas’ linear causative chain, and what implications does this have for his arguments?
Should arguments for God’s existence be expected to prove the specific qualities of the Christian God, or is a more general concept of God sufficient? Why?

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