Here are 14 a priori and a posteriori arguments for the existence of God including logic. A PRIORI ARGUMENTS 1. ONTOLOGICAL ARGUMENT (ANSELM) Idea: A maximally great being must exist necessarily. Definitions: G = God exists M(x) = x is the greatest conceivable being N(x) = x exists necessarily E(x) = x exists in reality Premises: God is the greatest conceivable being. M(G) A greatest conceivable being must possess necessary existence. M(x)→N(x) Whatever exists necessarily exists in reality. N(x)→E(x) Conclusion: E(G) Therefore: G ​ 2. MODAL ONTOLOGICAL ARGUMENT (PLANTINGA) Idea: If a maximally great being is possible, it exists necessarily. Definitions: □ = necessarily ◇ = possibly G = maximally great being exists Premises: It is possible that a maximally great being exists. ◊G If a maximally great being exists, it exists necessarily. G→□G Therefore, it is possible that a necessary being exists. ◊□G If something possibly exists necessarily, then it necessarily exists. ◊□G→□G Conclusion: □G Therefore: G ​ 3. ARGUMENT FROM NECESSARY EXISTENCE Idea: Contingent reality requires a necessary foundation. Definitions: C(x) = x is contingent N(x) = x is necessary E(y,x) = y explains x Premises: Contingent things exist. ∃x(C(x)) Every contingent thing requires an explanation. ∀x(C(x)→∃yE(y,x)) The explanation of contingent reality cannot consist only of contingent things. ¬∀x(C(x)→C(y)) Therefore, a necessary being exists. ∃x(N(x)) A necessary being is God. N(x)→G(x) Conclusion: G ​ 4. MORAL ARGUMENT Idea: Objective moral values require God. Definitions: O = objective moral values exist G = God exists Premises: Objective moral values exist. O If objective moral values exist, God exists. O→G Conclusion: G ​ 5. ARGUMENT FROM ABSTRACT OBJECTS Idea: Necessary truths require a necessary foundation. Definitions: A = abstract necessary truths exist M = necessary mind exists G = God exists Premises: Necessary truths exist. A Necessary truths require a necessary foundation. A→F The best necessary foundation is a necessary mind. F→M A necessary mind is God. M→G Conclusion: G ​ A POSTERIORI ARGUMENTS 6. KALAM COSMOLOGICAL ARGUMENT Idea: The universe began to exist, therefore it has a cause. Definitions: B(x) = x begins to exist C(x) = x has a cause Premises: Whatever begins to exist has a cause. ∀x(B(x)→C(x)) The universe began to exist. B(U) Conclusion: C(U) A cause of space-time cannot itself be inside space-time. C(U)→¬S∧¬T A timeless, spaceless, immaterial, powerful personal cause is God. X→G Conclusion: G ​ 7. LEIBNIZIAN CONTINGENCY ARGUMENT Idea: The universe requires an ultimate sufficient reason. Definitions: R(x) = x has a sufficient reason C(x) = x is contingent N(x) = x is necessary Premises: Everything that exists has a sufficient reason. ∀x(E(x)→R(x)) The universe exists. E(U) The universe is contingent. C(U) The sufficient reason for the universe cannot itself be contingent. R(U)→N(y) A necessary being is God. N(y)→G Conclusion: G ​ 8. TELEOLOGICAL / DESIGN ARGUMENT Idea: Order is better explained by intelligence than chance. (Abductive) Definitions: O= cosmic order D= design G=God Premises: The universe displays complex order. O Complex specified order is more probable under intelligence than non-intelligence. P(O∣D)>P(O∣¬D) Therefore design is the best explanation. D A cosmic designer is God. D→G Conclusion: G ​ 9. FINE-TUNING ARGUMENT (Abductive) Definitions: F= universe is fine-tuned D= design C= chance Premises: The universe is fine-tuned. F Fine-tuning is more expected under design than chance. P(F∣D)>P(F∣C) Therefore design is the best explanation. D Design implies God. D→G Conclusion: G ​ 10. ARGUMENT FROM CONSCIOUSNESS Definitions: C= consciousness exists P= physicalism R= consciousness reducible to physics G= God Premises: Consciousness exists. C If physicalism is true, consciousness should be physically explainable. P→R Consciousness is not physically reducible. ¬R Therefore physicalism is false. ¬P A non-physical foundation of consciousness exists. N God is the best explanation of this foundation. N→G Conclusion: G ​ 11. ARGUMENT FROM REASON Definitions: N= naturalism R= reason is reliable T= beliefs are true Premises: We trust reason. R Naturalism explains reasoning through survival. N→S Survival advantage does not guarantee truth. S→¬T Therefore naturalism gives a defeater for confidence in reason. N→¬R A rational source explains rational minds. G→R Conclusion: G ​ 12. RELIGIOUS EXPERIENCE ARGUMENT Definitions: E= religious experiences occur J(G)= belief in God is justified Premises: Many people experience God. E Experiences are generally rationally trustworthy unless defeated. E→J There is no defeater. ¬D Conclusion: J(G) Therefore: Belief in God is rationally justified ​ 13. MIRACLE ARGUMENT (Abductive) Definitions: M= miracle occurred G= God exists Premises: A miracle occurred. M Miracles are more probable given God than naturalism. P(M∣G)>P(M∣¬G) Therefore God is the best explanation. G Conclusion: G ​ 14. RESURRECTION ARGUMENT (Abductive) Definitions: C= Jesus was crucified A= disciples believed they saw Jesus alive R= resurrection occurred G= God exists Premises: Jesus was crucified. C The disciples sincerely believed they experienced appearances. A Resurrection best explains these facts. P(R∣C∧A)>P(H∣C∧A) Resurrection implies divine action. R→G Conclusion: G ​ #God #Aquinas #Anselm #Theism #Atheism

Some of my notes on math/physics/quantum for anyone who may benefit. Unified mathematical view of reality (clean + complete): Spacetime: ∫ₛ 1 dx > 0 = space exists ∫ₜ 1 dt > 0 = time exists ∫ₛ∫ₜ 1 dx dt > 0 = spacetime exists dim(S) > 0 → S ≠ ∅ → ∃x ∈ S Objects: ∃x : O(x) > 0 = an object exists Σ O(xᵢ) ≥ 1 = discrete objects exist ∫ₛ O(x) dx > 0 = objects exist in space ∫ₜ∫ₛ O(x,t) dx dt > 0 = objects exist in spacetime Properties: ∃x : p(x) > 0 ∫ₛ p(x) dx > 0 = properties exist over space Relations: R(x,y) → ∃x ∧ ∃y R(x,y) ∧ p(x)>0 → S ≠ ∅ Classical chain: dim(S) > 0 → S ≠ ∅ → ∃x → O(x) → ∫ₜ 1 dt > 0 Probability (discrete): Σᵢ Pᵢ = 1 → ∃i : Pᵢ > 0 P(A ∪ B) = P(A)+P(B)-P(A∧B) Probability (continuous): ∫ p(x) dx = 1 → p(x) ≥ 0 ∫ₐ p(x) dx = P(A) ∫∫ p(x,t) dx dt = 1 Conditional: P(A|B) = P(A∧B)/P(B) P(A∧B) = P(A|B)P(B) Bayes: P(A|B) = (P(B|A)P(A))/P(B) P(B) = Σᵢ P(B|Aᵢ)P(Aᵢ) P(B) = ∫ P(B|x)p(x) dx Information: Σᵢ Pᵢ = 1 → H(X) ≥ 0 H(X) = -Σᵢ Pᵢ log Pᵢ H(X) = -∫ p(x) log p(x) dx I(A;B) = H(A) - H(A|B) Quantum states: Σₙ |ψₙ|² = 1 → ∃n : |ψₙ|² > 0 ∫ |ψ(x)|² dx = 1 → ∃x : |ψ(x)|² > 0 ∫ |ψ(p)|² dp = 1 Operators: H|n⟩ = Eₙ|n⟩ Σₙ Eₙ|n⟩⟨n| = H Entanglement: Σₙₘ |cₙₘ|² ≥ 0 → ∃n,m ∫∫ |Ψ(x₁,x₂)|² dx₁ dx₂ > 0 Quantum → classical: Pᵢ = |ψᵢ|² Σᵢ |ψᵢ|² = 1 → Σᵢ Pᵢ = 1 Superposition: ψ = Σᵢ cᵢ ψᵢ |ψ₁ + ψ₂|² ≠ |ψ₁|² + |ψ₂|² Graphs (relations): G = (V,E) R(x,y) → x,y ∈ V Σⱼ Aᵢⱼ ≥ 1 Calculus bridge: Σ f(xᵢ)Δx → ∫ f(x) dx dx/dt ∫ v dt Grand unified chain: dim(S) > 0 → S ≠ ∅ → ∃x : O(x) > 0 → R(x,y) → Σᵢ Pᵢ = 1 → H(X) ≥ 0 → Σᵢ |ψᵢ|² = 1 → ∫ |ψ(x)|² dx = 1 Core idea: Existence → structure → relations → probability → information → quantum reality Discrete (Σ) and continuous (∫) are two views of the same underlying system.

No, you're wrong. 1 is about the cause of motion. 2 is about the cause of existence.

Can you prove a priori and a posteriori that magic exists using logic?

SAINT THOMAS AQUINAS' FIVE WAYS 1. THE ARGUMENT FROM MOTION (FIRST WAY) Idea: Things undergo change from potentiality to actuality. Whatever is changed is changed by another. An essentially ordered series of movers cannot regress infinitely. Therefore, there must be a first unmoved mover. Definitions: M(x) = x is moved/changed A(x,y) = x actualises the potential of y U(x) = x is an unmoved mover G = God Logic: Some things are changed: ∃x(M(x)) Whatever is changed is changed by another: ∀x(M(x)→∃y(A(y,x))) Nothing can actualise itself: ∀x(¬A(x,x)) An essentially ordered chain of movers cannot regress infinitely: ¬Infinite(A) Therefore, there exists a first unmoved mover: ∃x(U(x)) The unmoved mover is God: ∀x(U(x)→G) Therefore: G ​ 2. THE ARGUMENT FROM EFFICIENT CAUSES (SECOND WAY) Idea: Things depend on efficient causes. Nothing can be the cause of itself. An essentially ordered causal series cannot regress infinitely. Therefore, there must be a first efficient cause. Definitions: E(x) = x exists C(x,y) = x efficiently causes y FC(x) = x is the first efficient cause G = God Logic: Existing things have efficient causes: ∀x(E(x)→∃y(C(y,x))) Nothing can cause itself: ∀x(¬C(x,x)) An essentially ordered series of causes cannot regress infinitely: ¬Infinite(C) Therefore, a first efficient cause exists: ∃x(FC(x)) The first efficient cause is God: ∀x(FC(x)→G) Therefore: G ​ 3. THE ARGUMENT FROM CONTINGENCY (THIRD WAY) Idea: Some things are contingent; they do not have to exist. A purely contingent reality cannot explain why anything exists rather than nothing. Therefore, a necessary being must exist. Definitions: C(x) = x is contingent N(x) = x is necessary E(x) = x exists R(x) = x contains the sufficient reason for its own existence G = God Logic: Some things are contingent: ∃x(C(x)) A contingent thing does not contain the sufficient reason for its own existence: ∀x(C(x)→¬R(x)) If everything were contingent: ∀x(C(x)) then there would be no necessary explanation for existence: ¬∃x(N(x))→¬∃x(E(x)) But something exists: ∃x(E(x)) Therefore, not everything is contingent: ¬∀x(C(x)) Therefore, a necessary being exists: ∃x(N(x)) The necessary being is God: ∀x(N(x)→G) Therefore: G ​ 4. THE ARGUMENT FROM DEGREES OF PERFECTION (FOURTH WAY) Idea: Things possess qualities such as goodness, truth, and nobility in different degrees. Degrees of perfection imply a maximum standard. The maximum perfection is the source of all lesser instances of perfection. Definitions: P(x) = x possesses a perfection D(x,y) = x possesses more perfection than y Max(P) = the maximum perfection Cause(x,y) = x causes y G = God Logic: Things possess different degrees of perfection: ∃x∃y(D(x,y)) Degrees of perfection imply a maximum: Degrees(P)→Max(P) The maximum perfection is the cause of perfection in other things: Max(P)→Cause(Max(P),P) The maximum perfection is God: Max(P)→G Therefore: G ​ 5. THE ARGUMENT FROM GOVERNANCE / DESIGN (FIFTH WAY) Idea: Non-intelligent things act regularly toward ends. Regular directedness toward ends requires guidance by intelligence. Therefore, there must be an ultimate ordering intelligence. Definitions: O(x) = x acts toward an ordered end I(x) = x possesses intelligence Guides(x,y) = x guides y toward an end UI(x) = x is the ultimate intelligence G = God Logic: Natural things act toward ordered ends: ∃x(O(x)) Non-intelligent things acting toward ends require guidance: ∀x((¬I(x)∧O(x))→∃y(Guides(y,x))) A guide toward an end must possess intelligence: ∀x∀y(Guides(y,x)→I(y)) Therefore, an intelligent ordering cause exists: ∃x(I(x)) The ultimate ordering intelligence is God: ∀x(UI(x)→G) Therefore: G

LOGICAL TYPES 1. Ontological - Deductive 2. Modal Ontological - Deductive (S5) 3. Necessary Existence - Deductive 4. Moral - Deductive 5. Abstract Objects - Deductive 6. Kalam - Deductive + Metaphysical 7. Leibnizian Contingency - Deductive 8. Design - Abductive 9. Fine-Tuning - Bayesian Abductive 10. Consciousness - Conditional Deductive 11. Reason - Epistemic Abductive 12. Religious Experience - Epistemic 13. Miracle - Abductive 14. Resurrection - Abductive

RESURRECTION ARGUMENT Idea: Historical facts surrounding Jesus' death and appearances support resurrection. Premises: Jesus was crucified. C His followers sincerely believed they saw him alive afterward. A The resurrection hypothesis best explains these facts. R > H Resurrection implies divine action. R -> G Conclusion: G

MIRACLE ARGUMENT Idea: Certain events are best explained by divine intervention. Premises: A miracle occurred. M A miracle is more probable given God than naturalism. P(M∣G) > P(M∣¬G) Therefore, God is the best explanation. G

RELIGIOUS EXPERIENCE ARGUMENT Idea: Experiences of God provide evidence for God. Premises: Many people report experiences of God. E Unless there is a defeater, people are generally justified in trusting experiences. E -> J Religious experiences are not defeated. ¬D Therefore, belief in God is justified. J(G) Conclusion: G

ARGUMENT FROM REASON Idea: Rational thought requires a rational foundation. Premises: We trust reason. R If naturalism is true, human reasoning is only the product of survival pressures. N -> S Survival does not guarantee truth. S !-> T Therefore, naturalism undermines confidence in reason. N -> ¬R A rational source of reason explains reason. G -> R Conclusion: G

To your point, motion does not require a mover. Then it follows as a corollary that an object can be the mover of itself. May I prevail upon your good favour for an object that is the mover of itself? You have my ear.

The uncertainty principle doesn't state that an object does not require a mover, it merely states that the location of the object is difficult to predict, i.e., uncertain.

Yours truly went by steam train to visit an old foundry from the 1700s.