Authored By: Momota Rakshit
Anglia Ruskin
Abstract
This Essay Explores The Fundamental Question “Does God Exist?” Using Mathematics As A Means To Navigate Toward A Logical Answer, While Fully Acknowledging That Modern Empirical Methods Cannot Fully Verify Such Claims. This Paper Examines Three Main Arguments: First, How Abstract Mathematical Concepts And Their Attributes Can Explain God’s Existence And Qualities; Second, A Brief Explanation Of Gödel’s Ontological Argument And Its Methodical Approach To Proving God’s Existence; And Third, How Mathematics Serves As The Intersectional Language Through Which We Understand Both The Natural Universe And Potentially Divine Design. This Essay Aims To Spark Philosophical And Mathematical Conversation Rather Than Convince Readers Of Any Particular Theological Position. The Phrases “Divine Higher Power” And “God” Are Used Interchangeably Throughout And Can Be Applied To Most Theological Beliefs.
Introduction
Why Is It That Among Natural Scientists, Mathematicians Appear More Inclined Toward Belief In God? Is It Possible That Mathematics Tends To Reveal Evidence Of A Divine Higher Power, Or Is This Merely Coincidence? Perhaps Approaches To The Sciences Differ From Those Applied To Mathematics, And Such Claims Represent Nothing But Misguided Reasoning. However, In This Essay, I Will Specifically Examine What It Means To Use Mathematics As A Tool To Explore God’s Existence And The Extent To Which Such Methods Can Substantiate Theological Claims.
Although This May Seem An Unusual Approach, Mathematics And Philosophy Have Long Been Intertwined Through Abstract Thinking And Concerns For Absolute Truth. Many Mathematicians Engage In Philosophy And Vice Versa, With Numerous Famous Thinkers Contributing To Both Disciplines. Whereas A Posteriori And Modern Scientific Methods Can Only Reveal Truths About Things Existing In The Natural World, Mathematics Can Be Understood As A Language For Comprehending All Universal Things, Both Within And Beyond The Natural World. I Aim To Demonstrate How The Logical And Abstract Components Of Mathematics Can Create An Approach Allowing Us To Understand God And His Possible Existence, Even While Acknowledging That Empirical Proof Remains Physically Impossible.
Section 1: Attributing Mathematical Concepts To Ideas About God—Infinity And The Divine
The Mathematical Concept Of Infinity Shares Many Attributes That Can Help Us Understand God. Our Difficulty In Comprehending God’s Possible Existence Stems From Our Inability To Apply Finite Objects Of Experience To A Being That Must Be Infinite In Every Aspect—Infinite In Capacity And Capabilities, Exceeding The Restrictions Of Space, Time, And Power. However, In Mathematics, Even When We Cannot Visualize Infinity As A Physical Concept, We Can Still Understand It Conceptually, Use It In Discourse, And Apply It To Mathematical Problems. The Incomprehensibility Shared By Both Infinity And God Suggests Similar Essences.
God’s Very Existence Can Be Considered Paradoxical. One Might Pose This Logical Problem: If God Is Omnipotent, He Could Create A Mountain So Heavy That No Being Can Carry It, Yet If He Cannot Carry It Himself, How Does He Remain Conceptually Omnipotent? This Infinite Omnipotence Attributed To God Exceeds Our Understanding, Placing It Beyond Our Finite Comprehension Of Knowledge, Reality, And The Universe. However, This Limitation Of Understanding Does Not Negate God’s Infinite Properties; It Merely Demonstrates That We May Never Fully Comprehend Them.
A Similar Problem Occurs In Mathematics Through The Famous Zeno’s Paradox. This Paradox Posits That “A Moving Object Must Reach Halfway Before It Can Reach The End, And Because There Are An Infinite Number Of Halfway Points, It Is Impossible For It To Reach The End In A Finite Time.”[1] The Paradox Aims To Show That Motion Is Not Real And That Moving Objects Are Actually At Rest, Demonstrating That Even When We Can Comprehend Infinity Theoretically, Physically Grasping It Exceeds Our Cognitive Ability—Just As Understanding God Exceeds Our Cognitive Capacity.
This Parallel Provides A Basis For Accepting God’s Existence. Even If We Cannot Empirically Prove God’s Existence, We Accept The Concept Of Infinity Because Of Its Utility In Mathematics, Its Philosophical Implications, And Its Cultural And Historical Influence, Which Have Allowed It To Exist And Thrive. By The Same Reasoning, We Might Accept God As An Existing Being.
Section 2: Using Mathematical Logic To Prove God’s Existence—Gödel’s Ontological Argument
Gödel’s Ontological Argument, Typically Considered A Deductive Argument, Uses Modal Logic To Demonstrate How God Must Exist. To Understand Modal Logic, We Must Recognize That It Concerns Expressions Of Existence In A Large Conceptual Space Rather Than Simply Determining Whether Something Is Discretely True Or False. Modal Logic Considers “What Might Be, What Might Have Been, What Should Be, Or What Should Have Been, Or What Can Come To Be.”[2]
Before Proceeding, I Must Explain Two Concepts Essential To Understanding This Argument:
Vacuous Truths: These Are Conditional Or Universal Statements That Are True Because The Logically Preceding Proposition Cannot Be Satisfied, And The Negation Of Such Truths Is Always Obviously False. For Example, The Implication “If P, Then Q” Shows That When P Is True, Q Is Also True. However, P Can Be False While Q Remains True. In This Case, The Premise P Is False, But Q, Which We Take As The Conclusion, Still Holds True—Vacuously True, Since It Actually Tells Us Nothing At All. Consider The Statement “All Cows In The Sky Are Purple.”[3] Upon First Reading, This May Seem False, But It Actually Holds True Because There Are No Cows In The Sky. I Could Claim These Non-Existent Sky Cows Are Any Color Or Shape, And The Statement Would Remain Correct—Though It Provides No Meaningful Information. Conversely, The Negation Of This Statement—”There Exists A Cow In The Sky That Is Not Purple”—Is Unmistakably False, As There Are Definitively No Cows In The Sky.
Entailment (Logical Consequence): This Occurs When A Succeeding Statement Must Be True Because The First Statement Is True; It “Logically Follows” From The First One.[4] For Example, If “X” Entails “Y,” Then In Every Possible World (Defined As Worlds Where The Laws Of Logic Apply), When “X” Is True, “Y” Will Also Be True. If “Ice” Entails “Water,” Then Every World In Which Ice Exists Will Also Contain Water, And No World Will Exist Where This Is Not The Case[5]—Except An Illogical One. However, Impossible Things Entail Everything, As No Possible World Will Ever Contain An Impossible Thing. Therefore, If “X” Being True Means “Y” Is True, But “X” Is Impossible, Then “Y” Could Be Absolutely Anything. This Is Because No Possible World Exists In Which “X” Is True, Yet The Conclusion That “Y” Is True Would Remain True—Existing Only In An Impossible World Where Logic Fails.[6]
Gödel Operates With Modal Logic—Statements Concerning Necessity And Possibility[7]—To Develop God’s Existence As A Necessary Truth. His Argument Builds On Six Axioms, Self-Evidently Truthful Propositions Based On Definitionally True Statements Regarding God, Referred To As “Positive Properties.” For Example, One Axiom States That God Possesses The Property Of Perfection. We Can Say That The Property Of Perfection Does Not Entail Imperfection, Which Is Undeniably True, And This Can Demonstrate God’s Existence.
To Expand: Perfection Is Either Possible Or Impossible. If We Start With The Idea That Perfection Is Possible, Then God May Exist. If God Might Exist, Then God Must Exist, As This World Could Be One Containing Perfection (And In A Perfect World, The Most Perfect Being—God—Would Exist).
Conversely, If We Take The Route That Perfection Is Impossible, One Might Immediately Think God’s Existence Is Also Impossible. However, If Imperfection Is Impossible, We Can Say That No Possible World Contains Perfection. From This, It Would Naturally Follow That All Worlds With Perfection Also Have Imperfections. This Statement Is Vacuously True: Since We Started With The Premise That Perfection Is Impossible, There Are No Possible Worlds (Realistically Zero Worlds) Where Perfection Exists. We Would Conclude That Perfection “Entails” Imperfection.
Nevertheless, Since Our Original Premise Claims That Perfection Does Not Entail Imperfection, We Must Reject The Idea That Perfection Can Entail Imperfection, Meaning All Premises Following From The Impossibility Of Perfection Are Incorrect. This Naturally Leads Us To Accept That Perfection Is Possible. Because Perfection Is Possible, It Is Possible For God To Exist. Because God Can Exist, God Must Exist In Versions Of The World That Are Perfect. Therefore, God Exists—At Least According To Our Rational Comprehension Of Logic.
Section 3: Mathematics As The Intersectional Language Of The Universe And God
The Universe, Often Described In Mystical Terms, Can Be Understood As Having A Language—One That Existed Long Before Our Human-Made Scientific Theories, Which Themselves Must Be Explained Through This “Natural Language.” Theists Can Additionally Claim This To Be “The Language Of God.” Throughout History, Many Have Claimed That Mathematics, Beyond Acting As A Relative Means To Understanding The Universe, Actually Is The Law And Language Of The Universe. It Provides Foundations For Various Disciplines Vital To Our Daily Lives—Physics, Computer Science, And Medicine—And Exists In Nature Through Hidden Patterns And Universality That Transcends Cultural And Geographical Boundaries.[8] Even Mathematics’ Most Abstract Fields, Such As Geometry, Number Theory, And Logic, Have Profound Importance.
In His Book The Assayer, Galileo Galilei Stated: “Philosophy Is Written In That Great Book Which Ever Lies Before Our Eyes—I Mean The Universe—But We Cannot Understand It If We Do Not First Learn The Language And Grasp The Symbols In Which It Is Written. This Book Is Written In The Mathematical Language, And The Symbols Are Triangles, Circles And Other Geometrical Figures, Without Whose Help It Is Impossible To Comprehend A Single Word Of It; Without Which One Wanders In Vain Through A Dark Labyrinth.”[9]
What Relevance Does This Hold For The Existence Of God? Many Theistic Arguments Claim That The Intricacy, Order, And Intelligent Design Of This Language And This Universe Cannot Be Mere Coincidence But Must Be Founded Upon A Creator Who Designed Both This Universe And The Language Used To Navigate Through It. Although Subject To Debate And Criticism, This Argument Has Endured For Numerous Years As A Means Of Arguing For The Existence Of An Omnipotent And Divine Higher Power, Supposedly The Only Credible Source For Such Design.
Conclusion
Mathematical Tools Should Not Be Underestimated As A Means Of Understanding Philosophical Questions. Even When Not Empirically Verifiable, Mathematics Can Serve As A Powerful Analytical Tool. The Arguments Presented Above Have Been Critically Discussed For Countless Generations, Demonstrating Their Plausibility And Ability To Withstand Numerous Criticisms.
The Ways In Which Mathematical Concepts Can Be Attributed To God Reveal Similarities Between Mathematical Ideas And Our Understanding Of A Divine Higher Power—An Argument Not To Be Disregarded In Its Attempt To Answer Fundamental Questions About Humankind’s Existence And Knowledge Beyond Our Feasible And Physical Understanding Of The Universe. Although The Ontological Argument Presents A Logical And Effective Case For God’s Existence, It Shares The Drawbacks Present In All Ontological Arguments, Particularly Regarding The Treatment Of Existence As A Predicate—Issues That Must Be Acknowledged And Discussed.
Ultimately, Mathematical Approaches To Philosophical Questions Have Proven Effective, Showing Evidence That Mathematics Can Be Used To Explore God’s Existence. Through Further Development Of Philosophical Debate And Argumentation, These Approaches Can Become Even More Perceptive And Convincing.
Reference(S):
[1] Britannica: “Paradoxes Of Zeno,” Https://Www.Britannica.Com/Topic/Paradoxes-Of-Zeno
[2] Johan Van Bentham, “Modal Logic: A Contemporary View,” Internet Encyclopedia Of Philosophy, Https://Iep.Utm.Edu/Modal-Lo/
[3] Bob Lou, “A Vacuous Truth,” Https://Boblou.Github.Io/2019/11/20/Vacuous-Truth.Html
[4] Wikipedia, “Logical Consequence,” Https://En.Wikipedia.Org/Wiki/Logical_Consequence
[5] Apologetics Squared, “Demystifying Gödelian Arguments,” Https://Www.Youtube.Com/Watch?V=Lk72mzvjdY
[6] Mark Jago And Francesco Berto, “Impossible Worlds,” Stanford Encyclopedia Of Philosophy
[7] Modal Logic Definition
[8] Arthur Jaffe, “Ordering The Universe: The Role Of Mathematics,” Https://Www.Jstor.Org/Stable/Pdf/2030976.Pdf
[9] Galileo Galilei, The Assayer (1623), Https://Www.Oxfordreference.Com/
