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The Axiom Of Choice Is Necessary To Select A Set From An Infinite Number Of Socks, But Not An Infinite Number Of Shoes.
-Bertrand Russell
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The Axiom Of Choice

Bertrand Russell
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The Axiom Of Choice Is Necessary To Select A Set From An Infinite Number Of Socks, But Not An Infinite Number Of Shoes.

Understanding the Quote: "the axiom of choice is necessary to select a set from an..."

This quote by Bertrand Russell reflects deeply on the theme of shoes. It connects to the universal human journey of purpose, motivation, and reflection. Often categorized under Shoes, Numbers, Choices, the quote offers insight, emotional clarity, and intellectual inspiration to readers worldwide.

Whether you’re a student exploring new ideas, a leader trying to motivate your team, or someone seeking direction in life — this quote provides value. It resonates because it’s more than words — it’s a bridge between experience and wisdom. It shows how Bertrand Russell interprets life's core challenges and triumphs.

Lessons From the Quote

This quote teaches resilience and focus. It reminds readers that no matter where they stand in life, reflection and self-awareness lead to growth. Each word has meaning, and when studied, it becomes clear how impactful thoughtful language can be.

About Bertrand Russell

Bertrand Russell is celebrated for insightful thoughts on shoes and numbers. Their legacy lives on through writings that guide, comfort, and inspire. Discover more on their profile page.

Actionable Takeaways

  • Reflect on how this quote applies to your current life path.
  • Share the message with someone who needs inspiration.
  • Write your thoughts on this quote in a journal or blog post.
  • Use it as a daily affirmation or reminder.

Closing Thoughts

Quotes like this endure because they capture universal truths. They comfort us in solitude and empower us in groups. Carry this quote forward — live by its wisdom, share its message, and keep its essence alive.

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Shoes
Numbers
Choices
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The Pursuit Of Knowledge Is, I Think, Mainly Actuated By Love Of Power. And So Are All Advances In Scientific Technique.
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It Is Only Through Imagination That Men Become Aware Of What The World Might Be; Without It, ‘progress’ Would Become Mechanical And Trivial.
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The World That I Should Wish To See Would Be One Freed From The Virulence Of Group Hostilities And Capable Of Realizing That Happiness For All Is To Be Derived Rather From Co-operation Than From Strife. I Should Wish To See A World In Which Education Aimed At Mental Freedom Rather Than Imprisoning The Minds Of The Young In Rigid Armor Of Dogma Calculated To Protect Them Through Life Against The Shafts Of Impartial Evidence.
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When The Journey From Means To End Is Not Too Long, The Means Themselves Are Enjoyed If The End Is Ardently Desired.
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Of All Evils Of War The Greatest Is The Purely Spiritual Evil: The Hatred, The Injustice, The Repudiation Of Truth, The Artificial Conflict.
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War
Evil
A Smile Happens In A Flash, But Its Memory Can Last A Lifetime.
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Memories
Lasts
Collective Wisdom, Alas, Is No Adequate Substitute For The Intelligence Of Individuals. Individuals Who Opposed Received Opinions Have Been The Source Of All Progress, Both Moral And Intellectual. They Have Been Unpopular, As Was Natural.
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Teachers Are More Than Any Other Group The Guardians Of Civilization.
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It Is The Things For Which There Is No Evidence That Are Believed With Passion.
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My Doctor Said To Me Afterwards, 'when You Were Ill You Behaved Like A True Philosopher. Every Time You Came To Yourself You Made A Joke.' I Never Had A Compliment That Pleased Me More.
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I Greatly Doubt Whether The Men Who Become Pirate Chiefs Are Those Who Are Filled With Retrospective Terror Of Their Fathers, Or Whether Napoleon , At Austerlitz, Really Felt That He Was Getting Even With Madame Mère. I Know Nothing Of The Mother Of Attila , But I Rather Suspect That She Spoilt The Little Darling, Who Subsequently Found The World Irritating Because It Sometimes Resisted His Whims.
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Never Let Yourself Be Diverted, Either By What You Wish To Believe, Or What You Think Could Have Beneficent Social Effects If It Were Believed; But Look Only And Solely At What Are The Facts.
Believe
Thinking
Wish
The Method Of "postulating" What We Want Has Many Advantages; They Are The Same As The Advantages Of Theft Over Honest Toil.
Honesty
Math
Toil
Life Is Nothing But A Competition To Be The Criminal Rather Than The Victim.
Funny
Life
Competition
To Expect A Personality To Survive The Disintegration Of The Brain Is Like Expecting A Cricket Club To Survive When All Of Its Members Are Dead.
Personality
Soul
Brain
Intelligence, It Might Be Said, Has Caused Our Troubles; But It Is Not Unintelligence That Will Cure Them. Only More And Wiser Intelligence Can Make A Happier World
World
Might
Trouble
I Believe That Communism Is Necessary To The World, And I Believe That The Heroism Of Russia Has Fired Men's Hopes In A Way Which Was Essential To The Realization Of Communism In The Future. Regarded As A Splendid Attempt, Without Which Ultimate Success Would Have Been Very Improbable, Bolshevism Deserves The Gratitude And Admiration Of All The Progressive Part Of Mankind.
Gratitude
Believe
Men
Very Few Men Can Be Genuinely Happy In A Life Involving Continual Self-assertion Against The Skepticism Of The Mass Of Mankind, Unless They Can Shut Themselves Up In A Coterie And Forget The Cold Outer World. The Man Of Science Has No Need Of A Coterie, Since He Is Thought Well Of By Everybody Except His Colleagues. The Artist, On The Contrary, Is In The Painful Situation Of Having To Choose Between Being Despised And Being Despicable.
Men
Artist
Self
So Far I Have Been Speaking Of Theoretical Science, Which Is An Attempt To Understand The World. Practical Science, Which Is An Attempt To Change The World, Has Been Important From The First, And Has Continually Increased In Importance, Until It Has Almost Ousted Theoretical Science From Men's Thoughts.
Men
Important
World
If The Ordinary Wage-earner Worked Four Hours A Day, There Would Be Enough For Everybody, And No Unemployment — Assuming A Certain Very Moderate Amount Of Sensible Organization. This Idea Shocks The Well-to-do, Because They Are Convinced That The Poor Would Not Know How To Use So Much Leisure.
Philosophy
Son
Men
[industrialism's Soon Diminishing] Capacity To Supply Human Needs Could Be Prevented If Men Exercised Any Restraint Or Foresight In Their Present Frenzied Exploitation.
Men
Needs
Capacity
A Good Social System Is Not To Be Secured By Making People Unselfish, But, By Making Their Own Vital Impulses Fit In With Other Peoples. This Is Feasible. Those Who Have Produced Stoic Philosophies Have All Had Enough To Eat And Drink. I Feel I Shall Find The Truth On My Deathbed And Be Surrounded By People Too Stupid To Understand—fussing About Medicines Instead Of Searching For Wisdom. I Hate Being All Tidy Like A Book In A Library Where Nobody Reads – Prison Is Horribly Like That.
Hate
Philosophy
Stupid
To Be Happy In This World, Especially When Youth Is Past, It Is Necessary To Feel Oneself Not Merely An Isolated Individual Whose Day Will Soon Be Over, But Part Of The Stream Of Life Flowing On From The First Germ To The Remote And Unknown Future.
Funny
Happiness
Laughter
Three Passions, Simple But Overwhelmingly Strong, Have Governed My Life: The Longing For Love, The Search For Knowledge, And Unbearable Pity For The Suffering Of Mankind.
Life
Strong
Fear
Man Is A Rational Animal – So At Least I Have Been Told. Throughout A Long Life, I Have Looked Diligently For Evidence In Favour Of This Statement, But So Far I Have Not Had The Good Fortune To Come Across It, Though I Have Searched In Many Countries Spread Over Three Continents.
Animal
Men
Long
A Man's Acts Are Partly Determined By Spontaneous Impulse, Partly By The Conscious And Unconscious Effects Of The Various Groups To Which He Belongs.
Men
Groups
Determined
When You Are Studying Any Matter Or Considering Any Philosophy, Ask Yourself Only: What Are The Facts, And What Is The Truth That The Facts Bear Out. Never Let Yourself Be Diverted By What You Wish To Believe, But Look Only And Surely At What Are The Facts.
Philosophy
Believe
Wish
Americans Need Rest, But Do Not Know It.
Needs
Knows
It Is A Curious And Painful Fact That Almost All The Completely Futile Treatments That Have Been Believed In During The Long History Of Medical Folly Have Been Such As Caused Acute Suffering To The Patient. When Anesthetics Were Discovered, Pious People Considered Them An Attempt To Evade The Will Of God. It Was Pointed Out, However, That When God Extracted Adam's Rib He Put Him Into A Deep Sleep. This Proved That Anesthetics Are All Right For Men; Women, However, Ought To Suffer, Because Of The Curse Of Eve.
Pain
Sleep
Science
At All Times, Except When A Monarch Could Enforce His Will, War Has Been Facilitated By The Fact That Vigorous Males, Confident Of Victory, Enjoyed It, While Their Females Admired Them For Their Prowess.
War
Victory
Facts
Right Conduct Can Never, Except By Some Rare Accident, Be Promoted By Ignorance Or Hindered By Knowledge.
Ignorance
Knowledge
Right Conduct
Boys And Young Men Acquire Readily The Moral Sentiments Of Their Social Milieu, Whatever These Sentiments May Be.
Boys
Men
May
Patriotism Which Has The Quality Of Intoxication Is A Danger Not Only To Its Native Land But To The World, And "my Country Never Wrong" Is An Even More Dangerous Maxim Than "my Country, Right Or Wrong."
Country
Land
Quality
Aristotle Is The Last Greek Philosopher Who Faces The World Cheerfully; After Him, All Have, In One Form Or Another, A Philosophy Of Retreat.
Philosophy
Greek
World
The Search For Something Permanent Is One Of The Deepest Of The Instincts Leading Men To Philosophy.
Philosophy
Men
Instinct
It Is Entirely Clear That There Is Only One Way In Which Great Wars Can Be Permanently Prevented, And That Is The Establishment Of An International Government With A Monopoly Of Serious Armed Force.
War
Government
Serious
To Acquire Immunity To Eloquence Is Of The Utmost Importance To The Citizens Of A Democracy.
Democracy
Citizens
Importance
Fear Is The Parent Of Cruelty, And Therefore It Is No Wonder If Cruelty And Religion Have Gone Hand-in-hand. It Is Because Fear Is At The Basis Of Those Two Things. In This World We Can Now Begin A Little To Understand Things, And A Little To Master Them By The Help Of Science, Which Has Forced Its Way Step By Step Against The Christian Religion, Against The Churches, And Against The Opposition Of All The Old Precepts.
Christian
Hands
Two
The Fact That A Belief Has A Good Moral Effect Upon A Man Is No Evidence Whatsoever In Favor Of Its Truth.
Men
Favors
Facts
It Is Preoccupation With Possessions, More Than Anything Else, That Prevents Us From Living Freely And Nobly.
Life
Money
Freedom
I Do Not Believe That Science Per Se Is An Adequate Source Of Happiness, Nor Do I Think That My Own Scientific Outlook Has Contributed Very Greatly To My Own Happiness, Which I Attribute To Defecating Twice A Day With Unfailing Regularity.
Believe
Thinking
Adequate
When One Admits That Nothing Is Certain One Must, I Think, Also Admit That Some Things Are Much More Nearly Certain Than Others. It Is Much More Nearly Certain That We Are Assembled Here Tonight Than It Is That This Or That Political Party Is In The Right. Certainly There Are Degrees Of Certainty, And One Should Be Very Careful To Emphasize That Fact, Because Otherwise One Is Landed In An Utter Skepticism, And Complete Skepticism Would, Of Course, Be Totally Barren And Completely Useless.
Party
Thinking
Political
Every Increase In Knowledge Requires An Increase In Wisdom
Increase
The Fundamental Defect Of Christian Ethics Consists In The Fact That It Labels Certain Classes Of Acts 'sins' And Others 'virtue' On Grounds That Have Nothing To Do With Their Social Consequences.
Christian
Class
Labels
There Are Two Ways Of Avoiding Fear: One Is By Persuading Ourselves That We Are Immune From Disaster, And The Other Is By The Practice Of Sheer Courage. The Latter Is Difficult, And To Everybody Becomes Impossible At A Certain Point. The Former Has Therefore Always Been More Popular. Primitive Magic Has The Purpose Of Securing Safety, Either By Injuring Enemies, Or By Protecting Oneself By Talismans, Spells, Or Incantations.
Practice
Two
Safety
Inferences Of Science And Common Sense Differ From Those Of Deductive Logic And Mathematics In A Very Important Respect, Namely, When The Premises Are True And The Reasoning Correct, The Conclusion Is Only Probable.
Common Sense
Important
Logic
The Social Psychologist Of The Future Will Have A Number Of Classes Of School Children On Whom They Will Try Different Methods Of Producing An Unshakable Conviction That Snow Is Black. When The Technique Has Been Perfected, Every Government That Has Been In Charge Of Education For More Than One Generation Will Be Able To Control Its Subjects Securely Without The Need Of Armies Or Policemen.
Children
School
Army
The Very Best Proof That Something Can Be Done Is That Someone Has Already Done It.
Done
Proof
I Like Mathematics Because It Is Not Human And Has Nothing Particular To Do With This Planet Or With The Whole Accidental Universe - Because, Like Spinoza's God, It Won't Love Us In Return.
Math
Science
Return
Ideas And Principles That Do Harm Are As A Rule, Though Not Always, Cloaks For Evil Passions.
Passion
Ideas
Evil
Thinking You Know When In Fact You Don't Is A Fatal Mistake, To Which We Are All Prone
Mistake
Thinking
Facts
In Action, In Desire, We Must Submit Perpetually To The Tyranny Of Outside Forces; But In Thought, In Aspiration, We Are Free, Free From Our Fellowmen, Free From The Petty Planet On Which Our Bodies Impotently Crawl, Free Even, While We Live, From The Tyranny Of Death.
Desire
Body
Action
Of All Forms Of Caution, Caution In Love Is Perhaps The Most Fatal To True Happiness.
Love
Happiness
Marriage
When Considering Marriage One Should Ask Oneself This Question; 'will I Be Able To Talk With This Person Into Old Age?' Everything Else Is Transitory, The Most Time Is Spent In Conversation.
Age
Able
Should
It Will Be Found, As Men Grow More Tolerant In Their Instincts, That Many Uniformities Now Insisted Upon Are Useless And Even Harmful.
Men
Useless
Instinct
If The West Can Claim Superiority In Anything, It Is . . . In Science And Scientific Technique.
Technique
West
Claims
No People Anywhere In The World Would Accept Being Expelled En Masse From Their Own Country; How Can Anyone Require The People Of Palestine To Accept A Punishment Which Nobody Else Would Tolerate?
Country
Punishment
People
By Self-interest, Man Has Become Gregarious, But In Instinct He Has Remained To A Great Extent Solitary; Hence The Need Of Religion And Morality To Reinforce Self-interest.
Men
Self
Needs
We Are ... Led To A Somewhat Vague Distinction Between What We May Call "hard" Data And "soft" Data. This Distinction Is A Matter Of Degree, And Must Not Be Pressed; But If Not Taken Too Seriously It May Help To Make The Situation Clear. I Mean By "hard" Data Those Which Resist The Solvent Influence Of Critical Reflection, And By "soft" Data Those Which, Under The Operation Of This Process, Become To Our Minds More Or Less Doubtful.
Taken
Mean
Science
The Essence Of Good Manners Consists In Making It Clear That One Has No Wish To Hurt. When It Is Clearly Necessary To Hurt, It Must Be Done In Such A Way As To Make It Evident That The Necessity Is Felt To Be Regrettable.
Hurt
Essence
Good Man
I Did Not, However, Commit Suicide, Because I Wished To Know More Of Mathematics.
Suicide
Math
Commit
We Must Be Skeptical Even Of Our Skepticism.
Skepticism
Skeptical
A Man Of Seville Is Shaved By The Barber Of Seville If And Only If The Man Does Not Shave Himself. Does The Barber Shave Himself?
Men
Ifs And
Doe
The Only Thing That Will Redeem Mankind Is Cooperation.
Change
Teamwork
Collaboration
Literature Is Inexhaustible, With Every Book A Homage To Infinity
Book
Literature
Infinity
I Do Not Believe That I Am Now Dreaming, But I Cannot Prove That I Am Not. I Am, However, Quite Certain That I Am Having Certain Experiences, Whether They Be Those Of A Dream Or Those Of Waking Life.
Dream
Believe
Waking Life
Philosophy, Though Unable To Tell Us With Certainty What Is The True Answer To The Doubts Which It Raises, Is Able To Suggest Many Possibilities Which Enlarge Our Thoughts And Free Them From The Tyranny Of Custom.
Philosophy
Doubt
Answers
Curious Learning Not Only Makes Unpleasant Things Less Unpleasant But Also Makes Pleasant Things More Pleasant.
Inspirational
Curious
Pleasant
Liberty Is The Right To Do What I Like; Licence, The Right To Do What You Like.
Liberty
License
Thought Is Subversive And Revolutionary, Destructive And Terrible, Thought Is Merciless To Privilege, Established Institutions, And Comfortable Habit. Thought Is Great And Swift And Free.
Privilege
Revolutionary
Habit
Envy ... Is One Form Of A Vice, Partly Moral, Partly Intellectual, Which Consists In Seeing Things Never In Themselves But Only In Their Relations.
Envy
Intellectual
Vices
We Know Too Much And Feel Too Little.
Littles
Too Much
Emotion
All Serious Innovation Is Only Rendered Possible By Some Accident Enabling Unpopular Persons To Survive.
Innovation
Enabling
Serious
What Was Exciting In The Victorian Age, Would Leave A Man Of Franker Epoch Quite Unmoved. The More Prudes Restrict The Permissible Degree Of Sexual Appeal, The Less Is Required To Make Such An Appeal Effective.
Men
Age
Prudes
Zeno Was Concerned With Three Problems... These Are The Problem Of The Infinitesimal, The Infinite, And Continuity.
Education
Three
Statistics
The Average Man's Opinions Are Much Less Foolish Than They Would Be If He Thought For Himself.
Inspirational
Men
Average
Philosophy Is That Part Of Science Which At Present People Chose To Have Opinions About, But Which They Have No Knowledge About. Therefore Every Advance In Knowledge Robs Philosophy Of Some Problems Which Formerly It Had ...and Will Belong To Science.
Philosophy
Knowledge
Science
Morality In Sexual Relations, When It Is Free From Superstition, Consists Essentially In Respect For The Other Person, And Unwillingness To Use That Person Solely As A Means Of Personal Gratification, Without Regard To His Or Her Desires.
Mean
Desire
Use
The Reason Is, And By Rights Ought To Be, Slave To The Emotions.
Rights
Emotion
Slave
From The Height Of Their Disillusionment They Look Down Upon Those Whom They Despise As Simple Souls. For My Part I Have No Sympathy With This Outlook. All Disenchantment Is To Me A Malady, Which, It Is True, Certain Circumstances May Render Inevitable, But Which None The Less, When It Occurs, Is To Be Cured As Soon As Possible, Not To Be Regarded As A Higher Form Of Wisdom.
Simple
Soul
May
Beggars Do Not Envy Millionaires, Though Of Course They Will Envy Other Beggars Who Are More Successful.
Successful
Envy
Millionaire
It Is Not Known Why The Lord Made The Human Body As He Did, Since One Might Suppose That Omnipotence Could Have Made It Such As Would Not Have Shocked The Nice People.
Nice
Omnipotence
People
There Is Exactly The Same Degree Of Possibility And Likelihood Of The Existence Of The Christian God As There Is Of The Existence Of The Homeric God. I Cannot Prove That Either The Christian God Or The Homeric Gods Do Not Exist, But I Do Not Think That Their Existence Is An Alternative That Is Sufficiently Probable To Be Worth Serious Consideration.
Christian
Thinking
Religion
The First Dogma Which I Came To Disbelieve Was That Of Free Will. It Seemed To Me That All Notions Of Matter Were Determined By The Laws Of Dynamics And Could Not Therefore Be Influenced By Human Wills.
Law
Dynamics
Matter
I Am Looking Forward Very Much To Getting Back To Cambridge, And Being Able To Say What I Think And Not To Mean What I Say: Two Things Which At Home Are Impossible. Cambridge Is One Of The Few Places Where One Can Talk Unlimited Nonsense And Generalities Without Anyone Pulling One Up Or Confronting One With Them When One Says Just The Opposite The Next Day.
Home
Mean
Thinking
The Satisfaction To Be Derived From Success In A Great Constructive Enterprise Is One Of The Most Massive That Life Has To Offer.
Happiness
Satisfaction
Enterprise
It [is] Possible To Suppose That, If Russia Is Allowed To Have Peace, An Amazing Industrial Development May Take Place, Making Russia A Rival Of The United States.
Russia
United States
Development
Democracy Has At Least One Merit, Namely That A Member Of Parliament Cannot Be Stupider Than His Constituents, For The More Stupid He Is, The More Stupid They Were To Elect Him.
Stupid
Democracies Have
Democracy
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