Aquinas’ Five Ways

Original response · editorial edition; model unspecified

1. The Argument from Motion (First Way)

Natural Language Explanation — In Summa Theologiae I.2.3, motion includes change from potentiality to actuality, not merely movement through space. The following reconstruction isolates the premises needed for a limited conclusion.

• Premise 1: Change occurs. On the act–potency account, what is merely potential in a given respect cannot, precisely as potential, actualize itself; the relevant actualization comes from something already actual.
• Premise 2: The actualizing power in the relevant dependence order cannot be wholly derivative without any nonderivative source. This is the contested foundation premise; a beginning in time is not its meaning.
• Conclusion: The changing thing depends on at least one source not actualized by another within that order. Identifying it as universally unmoved, unique, or divine requires further argument.

Syllogistic Form

• P1: A particular thing a is undergoing change.
• P2: Whatever undergoes that kind of change has an actualizer distinct in the relevant respect.
• P3: The ancestral dependence order of a has a member with no further actualizer in that order. Aquinas motivates this by treating intermediate actualizing power as borrowed rather than independent.
• C1: At least one nonderivative actualizer belongs to the dependence order of a.
• C2, limited: This provides a candidate for further theological argument, not yet a proof that one being directly causes every change.

Symbolic Logic — Here and below, these are explicit conditional reconstructions. Stating a foundation principle in symbols does not prove that principle.

1. Define M(x): x undergoes change; A(y,x): y actualizes x in the relevant order. Quantifiers range over the things involved in that order.
2. Define A⁺(y,x): a finite nonempty path of actualizing dependence connects y to x; RootA(y): ¬∃z A(z,y).
3. Local premise: ∀x[M(x) → ∃y A(y,x)]. Actuality and potentiality must be distinguished in the same respect; A is not just “earlier than.”
4. Foundation premise: for each changing x, its ancestral A-order is well-founded—every nonempty subset has a member with no A-predecessor in that subset. This rules out endlessly derivative ancestry; it is a substantive assumption, not a theorem of ordinary predicate logic.
5. Existence premise: ∃x M(x). For a witness a, the nonempty ancestor set supplied by the local premise has an A-minimal member r; any predecessor of r would also be in that ancestor set.
6. Limited conclusion: ∃a∃r[M(a) ∧ A⁺(r,a) ∧ RootA(r)]. The original formula’s claim that a single unmoved being directly moves every changing thing does not follow from these premises.

2. The Argument from Causation (Second Way)

Natural Language Explanation

• Premise 1: There are effects within an order of efficient causes; a thing cannot be its own efficient cause in the same respect, since that would require the relevant causal priority over itself.
• Premise 2: In the relevant order, derivative causes require a nonderivative source. An endless sequence of merely borrowed causal power is excluded by a premise needing defense.
• Conclusion: At least one cause is not derivative within that order. No temporal first event, universal direct cause, or full set of divine attributes has yet been established.

Syllogistic Form

• P1: At least one effect e has an efficient cause.
• P2: No thing is its own efficient cause in the same respect.
• P3: The efficient-causal ancestry relevant to e is well-founded; this is the disputed requirement that borrowed efficacy has a nonderivative source.
• P4: Causes in this ancestry are related by dependence, not merely by being earlier events in time.
• C1: There is a nonderivative cause in e’s ancestry.
• C2, limited: Calling that source God introduces an identification project; the causal conclusion alone does not establish the full identification.

Symbolic Logic

1. Define E(x): x is an effect in the order considered.
2. Define C(y,x): y efficiently causes x; C⁺ is finite nonempty causal ancestry; RootC(y): ¬∃z C(z,y).
3. Causal premise: ∀x[E(x) → ∃y C(y,x)]. This is not the premise that absolutely everything, including a proposed root, is caused.
4. No self-causation: ∀x ¬C(x,x), for the same causal respect. This condition alone would not exclude longer cycles.
5. Foundation premise: the ancestral C-order of each effect under consideration is well-founded. It excludes cycles and endless dependence; its application to reality is disputed.
6. Existence premise: ∃x E(x). Choose a witness e and apply the foundation premise to its nonempty ancestor set.
7. Conclusion: ∃e∃r[E(e) ∧ C⁺(r,e) ∧ RootC(r)]. Neither one common root for all effects nor direct causation of everything follows without additional premises.

3. The Argument from Contingency (Third Way)

Natural Language Explanation — Aquinas’s Third Way starts from generation and corruption, argues against everything being able not to exist, and then distinguishes borrowed from unborrowed necessity. The original WordPress response instead gives a dependence-based reformulation. That reformulation is retained below with its missing assumptions exposed; it is not a literal transcription of the historical argument.

• Premise 1: At least one contingent being exists: its existence is not necessary in the sense under discussion.
• Premise 2: Each contingent being has an explanatory ancestry reaching a nonderivative existent, and every nonderivative existent is necessary. Both the foundation requirement and the contingency/necessity bridge require defense.
• Conclusion: At least one necessary existent grounds the contingent witness. This does not establish one common ground, a person, or the biblical God.

Syllogistic Form

• P1: Some contingent being a exists.
• P2: Every contingent being has a nonderivative explanatory ground, perhaps through intermediate dependence.
• P3: Any nonderivative existent is necessary. This excludes brute contingent roots and must not be smuggled in as a definition of “nonderivative.”
• C1: A necessary ground exists for a. The conclusion is conditional on P2 and P3, not merely on the existence of contingency.
• C2, limited: Further arguments must establish uniqueness, scope, and divine attributes; “necessary” here also needs an explicitly defended modal interpretation.

Symbolic Logic

1. Define C(x): x is contingent; N(x): x is necessary. Quantifiers in this schema range over existing things.
2. Define R(x): x is a nonderivative existent. R(x) and N(x) are distinct predicates, not synonyms.
3. Define G(y,x): y ultimately grounds x, allowing intermediate dependence.
4. Existence premise: ∃x C(x).
5. Foundation premise: ∀x[C(x) → ∃y(R(y) ∧ G(y,x))].
6. Necessity bridge: ∀y[R(y) → N(y)]. A critic can reject this while accepting some nonderivative reality.
7. Conclusion: ∃x∃y[C(x) ∧ N(y) ∧ G(y,x)], hence ∃y N(y). The conclusion that one necessary being grounds every contingent thing is stronger and has not been derived.

4. The Argument from Degrees (Fourth Way)

Natural Language Explanation

• Premise 1: Things display gradations of being, truth, or goodness as understood in Aquinas’s metaphysics. These are not simply all measurable properties indiscriminately.
• Bridge and conclusion: If those gradations require a maximal source that causes their finite instances, such a source exists. The bridge from comparison to maximal causal source is the substantive metaphysical claim, not a logical consequence of comparison alone.

Syllogistic Form

• P1: Instances of a relevant perfection P exist in differing degrees.
• P2: Such limited instances require a source maximally possessing P. This is a participation premise: limited possession depends on a fuller source.
• P3: The source explains the perfection in its instances. This causal claim goes beyond the existence of a highest point on a scale.
• C: A maximal source of the relevant perfection exists, conditional on P2–P3. Unifying all such sources as one God requires another argument.

Symbolic Logic

1. Define P(x): x possesses the relevant perfection; V(x,y): x has more of it than y.
2. Define S(y,x): y is a source of x’s possession of P.
3. Define MaxP(y): y maximally possesses P. Its possibility and interpretation must be established within the metaphysical account.
4. Gradation premise: ∃x∃z[P(x) ∧ P(z) ∧ V(x,z)]. This supplies instances, not a maximum by itself.
5. Source bridge: ∀x[P(x) → ∃y(MaxP(y) ∧ S(y,x))]. This expresses the required extra premise rather than proving it from a comparative scale.
6. Conclusion: ∃y MaxP(y). One common maximal source of every perfection does not follow simply by exchanging “for each instance, some source” with “some source for every instance.”

5. The Argument from Governance (Fifth Way)

Natural Language Explanation

• Premise 1: Non-intelligent natural things regularly produce characteristic outcomes. Aquinas interprets this regularity as acting for ends, not merely as biological complexity.
• Bridge and conclusion: If such directedness requires intelligent governance, at least one intelligence directs it. The need for intelligence is the contested bridge; empirical regularity alone does not supply it.

Syllogistic Form

• P1: At least one non-intelligent natural thing acts toward characteristic ends.
• P2: Every such non-intelligent end-directed thing is directed by an intelligence. This is Aquinas’s governing analogy developed as a premise, not a result of the quantifiers.
• P3: The natural regularities cited actually satisfy the kind of directedness meant in P1–P2; this interpretation also needs defense.
• C1: At least one intelligence directs at least one such natural thing.
• C2, limited: Additional premises are needed for a single director of all nature and for identification with the biblical God.

Symbolic Logic

1. Define T(x): x acts toward characteristic ends.
2. Define I(x): x is intelligent.
3. Define D(y,x): y intelligently directs x.
4. Governance premise: ∀x[(T(x) ∧ ¬I(x)) → ∃y(I(y) ∧ D(y,x))].
5. Existence premise: ∃x[T(x) ∧ ¬I(x)].
6. Conclusion: ∃x∃y[T(x) ∧ ¬I(x) ∧ I(y) ∧ D(y,x)]. This establishes an intelligent director conditional on the premises. It does not entail ∃y∀x D(y,x): different things could have different directors.

General Critiques of the Five Arguments

1. The immediate conclusions do not identify a common source or establish the entire Christian doctrine of God. Aquinas’s wider project supplies further arguments; each must be assessed on its own merits.
2. Historical physical examples and metaphysical principles should be evaluated separately. Refuting a medieval physical illustration does not automatically refute every reconstruction of dependence.
3. Branching causal networks are compatible with having roots. The relevant question is whether the kind of dependence invoked can be ungrounded, cyclic, or endlessly derivative.
4. The Ways use distinct causal, modal, participation, and governance premises. They should not all be reduced to one unrestricted principle of sufficient reason.

Original response · editorial edition; model unspecified

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

Critique: The strong objection targets the foundation premise: why must an order of actualizing dependence reach something nonderivative? Calling the series “borrowed power” offers a motivation, but the premise needs justification rather than repetition. An infinite past and an infinite dependence order are different claims.

1. Infinite Regress: A directed order can be nonempty and have a predecessor for every member. This is a logical countermodel to deriving a root from dependence alone; it is not an established cosmological model.
   • Countermodel: Let the domain be all integers and let A(n+1,n) hold for every integer n. Every node has a predecessor and there is no root. The model satisfies the local dependence condition while denying well-foundedness. A defender must explain why real actualizing dependence cannot have this structure.
2. Inertia: Uniform motion without a sustaining force challenges a crude equation of motion with continual pushing. Aquinas’s act–potency notion is broader, so inertia alone does not refute the reconstructed argument.
   • Scope Test: “Uniform velocity requires no net force” and “every relevant actualization requires an actualizer” use different predicates. An objection must connect the physical result to the metaphysical premise rather than treating the statements as direct contradictories.
3. Quantum Indeterminacy: Probabilistic predictions do not by themselves establish complete absence of causes or dependence. Interpretations differ. A rigorous objection would identify a specific process and show that the relevant actualizer requirement fails.
   • Logical Negation: A counterexample to ∀x[M(x) → ∃y A(y,x)] would satisfy ∃x[M(x) ∧ ¬∃y A(y,x)]. Writing that formula states the needed counterexample; it does not show quantum physics supplies one.

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

Critique: Neither “effects have causes” nor “nothing causes itself” entails a first cause. The second Way needs the additional claim that the relevant order cannot be wholly derivative. The challenge is to that claim, not merely to deterministic or linear physics.

1. Uncaused Versus Self-Caused: An event lacking a cause is not therefore its own cause. Treating those claims as equivalent makes the proposed objection invalid.
   • Distinct Formulas: ¬∃y C(y,x) means x has no cause; C(x,x) means x causes itself. The former entails ¬C(x,x), not C(x,x). A proposed exception must specify which causal premise it challenges.
2. Circular and Networked Causation: Feedback across time does not automatically provide a cycle of simultaneous explanatory dependence. A network can also be grounded. Its structure alone does not settle the metaphysical question.
   • Countermodel: On a two-node domain, C(a,b) and C(b,a), with a ≠ b and no self-loops, satisfy the prohibition of self-causation while lacking a root. This demonstrates that irreflexivity is insufficient; it does not show such a dependence cycle is physically or metaphysically possible.
3. Sufficient Reason: The requirement that every fact have an adequate explanation is stronger than many local causal claims. A probabilistic law may still explain why an outcome had a given chance. Indeterminism is not simply absence of every explanation.
   • Targeted Challenge: To reject universal explanation, a critic may propose a brute fact. To reject the Second Way, the critic must show how that proposal bears on its efficient-causal foundation premise. Neither rejection follows merely from probabilities.

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

Critique: The historical Third Way and the dependence reconstruction face different tests. For the historical temporal step, individual perishability does not alone imply a time when nothing exists. For the reconstruction, a critic can deny either ultimate grounding or the claim that a nonderivative ground must be necessary.

1. Contingency Without a Common Empty Time: Different beings could have overlapping finite lifetimes. A collection in which each member is absent at some time need not have a time when every member is absent. No speculative multiverse is needed to expose that inference.
   • Quantifier Test: ∀x∃t ¬E(x,t) does not entail ∃t∀x ¬E(x,t), where E means existence at a time. As a countermodel, let beings indexed by integers n exist during [n,n+2). Each is absent at some times, yet at every real time at least one exists. This tests the temporal inference, not every possible defense of the Third Way.
2. Brute Contingent Ground: A critic can allow a nonderivative reality while denying that it exists necessarily. “Unexplained” and “self-explanatory” are different claims; the former supplies no positive explanation.
   • Countermodel to the Necessity Bridge: Let a be contingent and grounded in r, with R(r) true and N(r) false. Then the foundation premise can hold while ∀y[R(y) → N(y)] fails. Defending that bridge is indispensable to the stated conclusion.
3. Unending Contingent Dependence: A chain of contingent members can challenge the requirement of a nonderivative ground. Its mathematical describability does not prove explanatory adequacy; the parties must argue about the relevant standard of explanation.
   • Dependency Schema: ∀x[C(x) → ∃y(C(y) ∧ D(x,y))] is consistent with a predecessor structure containing no necessary member. It provides a rival structure, not proof that contingent reality sustains itself or explains its own existence.

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

Critique: Comparative judgments alone entail neither a realized maximum nor a cause of all lesser instances. A critic need not first prove moral subjectivism to expose those missing bridges.

1. Standards of Perfection: Evaluations can depend on criteria and context; even an objective ordering does not by itself establish a maximal being. The relevant metaphysical account of goodness must be defended.
   • Logical Separation: “x is better than y by criterion K” does not entail “there exists a being maximal under every criterion.” The latter adds existence, maximality, and a relation among distinct standards.
2. Degrees Without a Maximum: The positive integers are ordered but have no greatest member. The real interval (0,1) is bounded above but contains no maximum. These mathematical examples avoid speculative claims about physically unlimited temperature.
   • Countermodel: Take P(x) to mean x ∈ (0,1) and V(x,y) to mean x > y. Gradations exist, but every member has a larger member, such as (x+1)/2. Thus gradation does not entail an attained maximum.
3. Maximum Versus Source: Even if a maximum exists, it need not cause the lesser instances. The tallest member of a group is not thereby the cause of everyone else’s height.
   • Remaining Burden: MaxP(m) alone does not entail ∀x[P(x) → S(m,x)]. A defender must justify the participation/source premise and explain why it applies to the perfections used in the Fourth Way.

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

Critique: Natural regularity does not logically entail intention. The Fifth Way needs its bridge from non-intelligent directedness to intelligent governance. Explaining a mechanism can weaken a design inference, but a defender may still ask why the mechanism has its characteristic powers.

1. Evolution and Self-Organization: Natural selection explains the emergence of many functional adaptations without adding a conscious selector to the biological mechanism. This challenges some design arguments, while the Fifth Way’s broader question about natural powers remains a separate issue.
   • Scope of the Objection: A mechanism explaining a function removes the need to insert intention into that mechanism. It does not logically establish the nonexistence of every possible directing intelligence. The critic should demand evidence for the extra governance claim.
2. Law-Governed Behavior: Regular outcomes can be described through powers, conditions, and laws without attributing deliberation to the objects. Whether such regularities require an ultimate mind is exactly what must be argued.
   • Countermodel: Let one natural thing a satisfy T(a), let no thing satisfy I, and let D be empty. This satisfies the observed-directedness premise while falsifying the governance premise. Its philosophical admissibility is disputed, but it shows regularity alone does not entail intelligence.
3. Analogy and Identification: Human tools often have designers, but extending that relationship to all natural directedness requires justification. Even the governance premise as written allows different directors for different things.
   • Quantifier Limit: ∀x∃y D(y,x) does not entail ∃y∀x D(y,x). Two things with distinct directors and no shared director form a countermodel. Unity and specifically divine attributes therefore remain further burdens.

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General Critiques of All Five Arguments

1. Identification Gap: A causal or explanatory conclusion does not by itself establish every divine attribute, scripture, incarnation, or revelation. The Fifth Way explicitly aims at intelligence, so it is also inaccurate to say all five yield only an impersonal cause.
2. Historical Framework: Distinguish objections to physical illustrations from objections to act–potency, dependence, participation, and governance. Merely calling a premise medieval does not assess whether it is true.
3. Causal Structure: Networks may be rooted or rootless; feedback may be sequential rather than a same-respect dependence cycle. A useful counterargument specifies the relation and the disputed foundation claim.
4. Explanatory Demands: The five arguments do not share one identical premise. The strongest criticism identifies which extra requirement is doing the work in each and tests it without treating scientific uncertainty as a proof of its negation.

Original response · editorial edition; model unspecified

The Conceptual Gulf between a Metaphysical Source and the Biblical God

Granting a cosmological conclusion does not grant Christianity as a package. That is the central challenge in the prompt, and it survives a needed correction to its wording: validity alone is not soundness, and the Five Ways do not entail that their proposed source is a detached, nonintervening deistic god. They aim at features of the God of classical theism, including intelligent governance in the Fifth Way. The question is what has actually been established, and which additional attributes and historical claims still require support.

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What the Five Ways Would Establish, If Successful

A conclusion about a first actualizer, cause, or necessary ground is initially an explanatory claim. It does not yet identify that source with a speaker in scripture or validate an account of salvation. Aquinas pursues further arguments elsewhere; he does not present the Five Ways as the whole of Christian theology. Nor must a cause be merely an initiator at a first moment: in Summa Theologiae I.46.2, he distinguishes belief in a temporal beginning from what can be demonstrated. The immediate limits of each Way can be stated separately:

1. Motion: A nonderivative actualizer in an order of change does not by itself establish revelation, moral commands, or interventions in human history.
2. Causation: A causal ground need not be merely an event at the beginning of time. Neither ongoing dependence nor a first cause alone establishes the identity of a biblical agent.
3. Contingency: A necessary existent, if established, still requires arguments connecting necessity with knowledge, agency, moral perfection, and a particular religious history.
4. Degrees: A maximal source of goodness in a metaphysical account does not immediately establish every claim about moral character or action made in Christian theology.
5. Governance: The intended conclusion includes intelligence, so reducing it to impersonal laws misstates the argument. Yet intelligence alone does not identify a single biblical deity or establish incarnation, covenant, or salvation.

The evidential gap concerns attributes not established, not attributes disproved. Failure to derive personality is not a derivation of impersonality; failure to derive intervention is not a proof of nonintervention. This distinction strengthens the curator’s objection by locating the missing support precisely.

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Specific Christian Claims and Their Further Burdens

Christian theology combines claims about divine knowledge, power, goodness, and personal action with interpretations of particular texts and events. Those claims create questions that a bare cosmological conclusion cannot answer. Aquinas himself denies that natural reasoning establishes the Trinity in Summa Theologiae I.32.1. Testing the additional claims requires both coherent definitions and independent reasons for accepting them.

1. Omniscience and Freedom: If infallible foreknowledge is fixed, a critic can ask in what sense the known action could be otherwise. But knowledge does not by itself cause the action, and “necessarily, if God knows p, then p” does not alone imply “if God knows p, then necessarily p.” A rigorous incompatibility argument must explain the relevant necessity and the account of freedom being excluded. The first-cause argument settles none of those questions.
2. Power, Goodness, and Suffering: Suffering that a perfectly good and capable being would have no adequate reason to permit conflicts with that being’s existence. The challenge is to establish the relevant absence of justification, not simply to define every unexplained case as justified or pointless. The scale and distribution of suffering can also count as evidence against a proposed benevolent governor without furnishing a strict logical contradiction. Free-will and greater-good replies therefore remain arguments to assess, not automatic exemptions.
3. Trinity and Incarnation: “Three persons and one essence” is not formally “three persons and one person in the same respect.” A critic must examine whether the proposed distinction can be made coherent and whether the associated identity claims are consistent. Incarnation adds questions about divine and human natures and their predicates. Calling these mysteries does not discharge the burden, but merely counting one and three does not prove inconsistency either.
4. Moral Character: Narratives of commanded killing, slavery, and collective punishment place serious pressure on claims of perfect benevolence and justice. A defender must address the actual texts, interpretations, and moral principles rather than borrowing credibility from cosmology. Showing that reality has a cause would not justify any particular command attributed to that cause.

These difficulties remain independent of the cosmological starting point. An identification argument needs support for the additional attributes and an answer to any established inconsistency; success at one stage cannot simply be transferred to all later stages.

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Analogy: Evidence of Gold and the Spherical Cube of Gold

The source’s gold analogy usefully separates a general existence claim from an incoherent specification. Finding gold does not establish a solid that is, in exactly the same geometric respect, both a sphere and a cube. If those requirements contradict one another, more evidence for gold cannot make the specified object possible. This is stronger than the ordinary point that gold does not establish every imaginable golden artifact.

The analogy applies to a proposed deity only after an actual contradiction in that proposal has been demonstrated. An identification gap alone is not enough: evidence for a general category can sometimes support a coherent specific hypothesis without entailing it. The curator’s central criticism remains that evidence for a cause neither proves the biblical specification nor repairs a contradiction if one is established. The arguments about foreknowledge, suffering, and divine identity must therefore do their own work.

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Conclusion

Even granting sound versions of the Ways would leave the specifically Christian identification unfinished. The five conclusions need to be connected to one another, further attributes defended, and historical and revelatory claims independently supported. Neither the word “God” at the end of an argument nor an appeal to mystery supplies those missing steps. The gold analogy preserves the sharpest logical point: a general existence claim cannot rescue an independently contradictory specification. It does not remove the responsibility to demonstrate that contradiction.

Original response · editorial edition; model unspecified

Original response · editorial edition; model unspecified

1. Which attributes and historical claims about the biblical God remain unestablished by the immediate conclusions of the Five Ways?
2. Could the Five Ways provide partial support for a cumulative religious argument without establishing either Christianity or nonintervening deism?
3. What distinguishes change understood through act and potency from uniform motion in mechanics, and how should a physical objection connect the two?
4. What would be required to turn an indeterministic physical process into a counterexample to a specified causal principle?
5. What are the strengths and weaknesses of using the Principle of Sufficient Reason (PSR) as a basis for proving the existence of God?
6. How does the Argument from Contingency rely on a “necessary being,” and are there alternative ways to account for existence without this concept?
7. Why do an ordered scale, an attained maximum, and a causal source constitute different claims? Does the Fourth Way justify the transitions?
8. How does the gold and spherical-cube analogy distinguish insufficient identification from an independently established contradiction?
9. 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?
10. How might the Problem of Evil challenge the coherence of a God who is both omnipotent and omnibenevolent?
11. Can the distinction between persons and essence be formulated consistently, and which additional identity claims would a logical criticism need to examine?
12. Which design inferences are weakened by evolutionary mechanisms, and which broader claims about natural directedness would require a separate reply?
13. 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?
14. How does a feedback loop across time differ from a same-respect dependence cycle, and can either provide an adequate rootless explanation?
15. 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?