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The Dot Was Introduced As A Symbol For Multiplication By Leibniz. On July 29, 1698, He Wrote In A Letter To Johann Bernoulli: "i Do Not Like X As A Symbol For Multiplication, As It Is Easily Confounded With X.

-Gottfried Leibniz

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The Dot Was Introduced

Gottfried Leibniz

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The Dot Was Introduced As A Symbol For Multiplication By Leibniz. On July 29, 1698, He Wrote In A Letter To Johann Bernoulli: "i Do Not Like X As A Symbol For Multiplication, As It Is Easily Confounded With X.

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All The Different Classes Of Beings Which Taken Together Make Up The Universe Are, In The Ideas Of God Who Knows Distinctly Their Essential Gradations, Only So Many Ordinates Of A Single Curve So Closely United That It Would Be Impossible To Place Others Between Any Two Of Them, Since That Would Imply Disorder And Imperfection. Thus Men Are Linked With The Animals, These With The Plants And These With The Fossils Which In Turn Merge With Those Bodies Which Our Senses And Our Imagination Represent To Us As Absolutely Inanimate.

There Are Two Famous Labyrinths Where Our Reason Very Often Goes Astray. One Concerns The Great Question Of The Free And The Necessary, Above All In The Production And The Origin Of Evil. The Other Consists In The Discussion Of Continuity, And Of The Indivisibles Which Appear To Be The Elements Thereof, And Where The Consideration Of The Infinite Must Enter In.

The Art Of Discovering The Causes Of Phenomena, Or True Hypotheses, Is Like The Art Of Deciphering, In Which An Ingenious Conjecture Often Greatly Shortens The Road.

The Larger The Mass Of Collected Things, The Less Will Be Their Usefulness. Therefore, One Should Not Only Strive To Assemble New Goods From Everywhere, But One Must Endeavor To Put In The Right Order Those That One Already Possesses.

For, Above All, I Hold A Notion Of Possibility And Necessity According To Which There Are Some Things That Are Possible, But Yet Not Necessary, And Which Do Not Really Exist. From This It Follows That A Reason That Always Forces A Free Mind To Choose One Thing Over Another (whether That Reason Derives From The Perfection Of A Thing, As It Does In God, Or From Our Imperfection) Does Not Eliminate Our Freedom.

The Most Perfect Society Is That Whose Purpose Is The Universal And Supreme Happiness.

The Past Is Pregnant With The Present.

Indeed In General I Hold That There Is Nothing Truer Than Happiness, And Nothing Happier And Sweeter Than Truth.

Words Of Wisdom

We Should Like Nature To Go No Further; We Should Like It To Be Finite, Like Our Mind; But This Is To Ignore The Greatness And Majesty Of The Author Of Things.

For Since It Is Impossible For A Created Monad To Have A Physical Influence On The Inner Nature Of Another, This Is The Only Way In Which One Can Be Dependent On Another.

To Love Is To Place Happiness In The Heart Of Another.

We Live In The Best Of All Possible Worlds

Music Is The Pleasure The Human Mind Experiences From Counting Without Being Aware That It Is Counting.

Now This Connection Or Adaption Of All Created Things With Each, And Of Each With All The Rest, Means That Each Simple Substance Has Relations Which Express All The Others, And That Consequently It Is A Perpetual Living Mirror Of The Universe.

Nothing Is Necessitated Whose Opposite Is Possible.

One Cannot Explain Words Without Making Incursions Into The Sciences Themselves, As Is Evident From Dictionaries; And, Conversely, One Cannot Present A Science Without At The Same Time Defining Its Terms.

The Monad, Of Which We Shall Speak Here, Is Nothing But A Simple Substance Which Enters Into Compounds; Simple, That Is To Say, Without Parts.

Words Of Wisdom

The Words 'here You Can Find Perfect Peace' Can Be Written Only Over The Gates Of A Cemetery.

Reality Cannot Be Found Except In One Single Source, Because Of The Interconnection Of All Things With One Another. I Maintain Also That Substances, Whether Material Or Immaterial, Cannot Be Conceived In Their Bare Essence Without Any Activity, Activity Being Of The Essence Of Substance In General.

Words Of Wisdom

It Is Worth Noting That The Notation Facilitates Discovery. This, In A Most Wonderful Way, Reduces The Mind's Labour.

Philosophy Consists Mostly Of Kicking Up A Lot Of Dust And Then Complaining That You Can't See Anything.

There Is No Argument So Cogent Not Only In Demonstrating, The Indestructibility Of The Soul, But Also In Showing That It Always Preserves In Its Nature Traces Of All Its Preceding States With A Practical Remembrance Which Can Always Be Aroused. Since It Has The Consciousness Of Or Knows In Itself What Each One Calls His Me. This Renders It Open To Moral Qualities, To Chastisement And To Recompense Even After This Life, For Immortality Without Remembrance Would Be Of No Value.

Taking Mathematics From The Beginning Of The World To The Time When Newton Lived, What He Had Done Was Much The Better Half.

What Is Is What Must Be.

I Have Said More Than Once, That I Hold Space To Be Something Purely Relative, As Time; An Order Of Coexistences, As Time Is An Order Of Successions.

The Present Is Big With The Future, The Future Might Be Read In The Past, The Distant Is Expressed In The Near.

I Am So In Favor Of The Actual Infinite That Instead Of Admitting That Nature Abhors It, As Is Commonly Said, I Hold That Nature Makes Frequent Use Of It Everywhere, In Order To Show More Effectively The Perfections Of Its Author.

Although The Whole Of This Life Were Said To Be Nothing But A Dream And The Physical World Nothing But A Phantasm, I Should Call This Dream Or Phantasm Real Enough, If, Using Reason Well, We Were Never Deceived By It.

Now Where There Are No Parts, There Neither Extension, Nor Shape, Nor Divisibility Is Possible. And These Monads Are The True Atoms Of Nature And, In A Word, The Elements Of Things.

Words Of Wisdom

In Symbols One Observes An Advantage In Discovery Which Is Greatest When They Express The Exact Nature Of A Thing Briefly And, As It Were, Picture It; Then Indeed The Labor Of Thought Is Wonderfully Diminished.

Every Substance Is As A World Apart, Independent Of Everything Else Except God.

I Don't Say That Bodies Like Flint, Which Are Commonly Called Inanimate, Have Perceptions And Appetition; Rather They Have Something Of That Sort In Them, As Worms Are In Cheese.

There Are Also Two Kinds Of Truths, Those Of Reasoning And Those Of Fact. Truths Of Reasoning Are Necessary And Their Opposite Is Impossible, And Those Of Fact Are Contingent And Their Opposite Is Possible. When A Truth Is Necessary Its Reason Can Be Found By Analysis, Resolving It Into More Simple Ideas And Truths Until We Reach Those Which Are Primitive.

If You Have A Clear Idea Of A Soul, You Will Have A Clear Idea Of A Form; For It Is Of The Same Genus, Though A Different Species.

The Knowledge Which We Have Acquired Ought Not To Resemble A Great Shop Without Order, And Without An Inventory; We Ought To Know What We Possess, And Be Able To Make It Serve Us In Need.

I Have Seen Something Of The Project Of M. De St. Pierre, For Maintaining A Perpetual Peace In Europe. I Am Reminded Of A Device In A Cemetery, With The Words: Pax Perpetua ; For The Dead Do Not Fight Any Longer: But The Living Are Of Another Humor; And The Most Powerful Do Not Respect Tribunals At All.

Why Is There Anything At All Rather Than Nothing Whatsoever?

God's Relation To Spirits Is Not Like That Of A Craftsman To His Work, But Also Like That Of A Prince To His Subjects.

Music Is Nothing But Unconscious Arithmetic.

In Whatever Manner God Created The World, It Would Always Have Been Regular And In A Certain General Order. God, However, Has Chosen The Most Perfect, That Is To Say, The One Which Is At The Same Time The Simplest In Hypothesis And The Richest In Phenomena.

According To Their [newton And His Followers] Doctrine, God Almighty Wants To Wind Up His Watch From Time To Time: Otherwise It Would Cease To Move. He Had Not, It Seems, Sufficient Foresight To Make It A Perpetual Motion. Nay, The Machine Of God's Making, So Imperfect, According To These Gentlemen; That He Is Obliged To Clean It Now And Then By An Extraordinary Concourse, And Even To Mend It, As Clockmaker Mends His Work.

It Has Long Seemed Ridiculous To Me To Suppose That The Nature Of Things Has Been So Poor And Stingy That It Provided Souls Only To Such A Trifling Mass Of Bodies On Our Globe, Like Human Bodies, When It Could Have Given Them To All, Without Interfering With Its Other Ends.

Music Is A Secret And Unconscious Mathematical Problem Of The Soul.

There Is Nothing Waste, Nothing Sterile, Nothing Dead In The Universe; No Chaos, No Confusions, Save In Appearance.

There Are Also Two Kinds Of Truths: Truth Of Reasoning And Truths Of Fact.

Now, As There Is An Infinity Of Possible Universes In The Ideas Of God, And As Only One Of Them Can Exist, There Must Be A Sufficient Reason For God's Choice, Which Determines Him Toward One Rather Than Another. And This Reason Can Be Found Only In The Fitness, Or The Degrees Of Perfection, That These Worlds Contain, Since Each Possible Thing Has The Right To Claim Existence In Proportion To The Perfection It Involves.

There Is Nothing Without Reason.

If We Could Sufficiently Understand The Order Of The Universe, We Should Find That It Exceeds All The Desires Of The Wisest Men, And That It Is Impossible To Make It Better Than It Is, Not Only As A Whole And In General But Also For Ourselves In Particular, If We Are Attached, As We Ought To Be, To The Author Of All, Not Only As To The Architect And Efficient Cause Of Our Being, But As To Our Master And To The Final Cause, Which Ought To Be The Whole Aim Of Our Will, And Which Can Alone Make Our Happiness.

Justice Is Charity In Accordance With Wisdom.

[alternate Translation:] The Divine Spirit Found A Sublime Outlet In That Wonder Of Analysis, That Portent Of The Ideal World, That Amphibian Between Being And Not-being, Which We Call The Imaginary Root Of Negative Unity.

It Is Unworthy Of Excellent Men To Lose Hours Like Slaves In The Labor Of Calculation Which Could Be Relegated To Anyone Else If Machines Were Used.

I Agree With You That It Is Important To Examine Our Presuppositions, Throughly And Once For All, In Order To Establish Something Solid. For I Hold That It Is Only When We Can Prove All That We Bring Forward That We Perfectly Understand The Thing Under Consideration. I Know That The Common Herd Takes Little Pleasure In These Researches, But I Know Also That The Common Herd Take Little Pains Thoroughly To Understand Things.

Words Of Wisdom

I Am Convinced That The Unwritten Knowledge Scattered Among Men Of Different Callings Surpasses In Quantity And In Importance Anything We Find In Books, And That The Greater Part Of Our Wealth Has Yet To Be Recorded.

It's Easier To Be Original And Foolish Than Original And Wise.

There Is A Certain Destiny Of Everything, Regulated By The Foreknowledge And Providence Of God In His Works.

To Love Is To Take Delight In Happiness Of Another, Or, What Amounts To The Same Thing, It Is To Account Another's Happiness As One's Own.

Happiness And Love

The Present Is Great With The Future.

Virtue Is The Habit Of Acting According To Wisdom.

There Is A World Of Created Beings - Living Things, Animals, Entelechies, And Souls - In The Least Part Of Matter.... Thus There Is Nothing Waste, Nothing Sterile, Nothing Dead In The Universe; No Chaos, No Confusions, Save In Appearance.

He Who Understands Archimedes And Apollonius Will Admire Less The Achievements Of The Foremost Men Of Later Times.

Every Present State Of A Simple Substance Is The Natural Consequence Of Its Preceding State, In Such A Way That Its Present Is Big With Its Future.

I Do Not Believe That A World Without Evil, Preferable In Order To Ours, Is Possible; Otherwise It Would Have Been Preferred. It Is Necessary To Believe That The Mixture Of Evil Has Produced The Greatest Possible Good: Otherwise The Evil Would Not Have Been Permitted. The Combination Of All The Tendencies To The Good Has Produced The Best; But As There Are Goods That Are Incompatible Together, This Combination And This Result Can Introduce The Destruction Of Some Good, And As A Result Some Evil.

A Great Doctor Kills More People Than A Great General.

Nihil Est Sine Ratione. There Is Nothing Without A Reason.

The Present Is Saturated With The Past And Pregnant With The Future.

The Dot Was Introduced As A Symbol For Multiplication By Leibniz. On July 29, 1698, He Wrote In A Letter To Johann Bernoulli: "i Do Not Like X As A Symbol For Multiplication, As It Is Easily Confounded With X.

Natural Religion Itself, Seems To Decay Very Much. Many Will Have Human Souls To Be Material: Others Make God Himself A Corporeal Being.

Take What You Need, Do What You Should, You Will Get What You Want.

The World Is Not A Machine. Everything In It Is Force, Life, Thought.

Imaginary Numbers Are A Fine And Wonderful Refuge Of The Divine Spirit Almost An Amphibian Between Being And Non-being.

To Love Is To Be Delighted By The Happiness Of Someone, Or To Experience Pleasure Upon The Happiness Of Another. I Define This As True Love.

Of What Use Would It Be To You, Sir, To Become King Of China On Condition That You Forgot What You Have Been? Would It Not Be The Same As If God, At The Same Time He Destroyed You, Created A King In China?

..this Is Why The Ultimate Reason Of Things Must Lie In A Necessary Substance, In Which The Differentiation Of The Changes Only Exists Eminently As In Their Source; And This Is What We Call God.

Words Of Wisdom

Differentiation

There Is No Way In Which A Simple Substance Could Begin In The Course Of Nature, Since It Cannot Be Formed By Means Of Compounding.

Words Of Wisdom

Either There Are No Corporeal Substances, And Bodies Are Merely Phenomena Which Are True Or Consistent With Each Other, Such As A Rainbow Or A Perfectly Coherent Dream, Or There Is In All Corporeal Substances Something Analogous To The Soul.

I Also Readily Admit That There Are Animals, Taken In The Ordinary Sense, That Are Incomparably Larger Than Those We Know Of, And I Have Sometimes Said In Jest That There Might Be A System Like Ours Which Is The Pocketwatch Of Some Enormous Giant.

God Makes Nothing Without Order, And Everything That Forms Itself Develops Imperceptibly Out Of Small Parts.

Each Portion Of Matter May Be Conceived Of As A Garden Full Of Plants, And As A Pond Full Of Fishes. But Each Branch Of The Plant, Each Member Of The Animal, Each Drop Of Its Humors, Is Also Such A Garden Or Such A Pond.

In My Judgment An Organic Machine New To Nature Never Arises, Since It Always Contains An Infinity Of Organs So That It Can Express, In Its Own Way, The Whole Universe; Indeed, It Always Contains All Past And Present Times.

Men Act Like Brutes In So Far As The Sequences Of Their Perceptions Arise Through The Principle Of Memory Only, Like Those Empirical Physicians Who Have Mere Practice Without Theory.

It Is A Good Thing To Proceed In Order And To Establish Propositions. This Is The Way To Gain Ground And To Progress With Certainty.

Words Of Wisdom

When A Truth Is Necessary, The Reason For It Can Be Found By Analysis, That Is, By Resolving It Into Simpler Ideas And Truths Until The Primary Ones Are Reached. It Is This Way That In Mathematics Speculative Theorems And Practical Canons Are Reduced By Analysis To Definitions, Axioms And Postulates.

Words Of Wisdom

It Is God Who Is The Ultimate Reason Things, And The Knowledge Of God Is No Less The Beginning Of Science Than His Essence And Will Are The Beginning Of Things.

Let There Be Two Possible Things, A And B, One Of Which Is Such That It Is Necessary That It Exists, And Let Us Assume That There Is More Perfection In A Than In B. Then, At Least, We Can Explain Why A Should Exist Rather Than B And Can Foresee Which Of Them Will Exist; Indeed, This Can Be Demonstrated, That Is, Rendered Certain From The Nature Of The Thing.

Therefore, I Have Attacted [the Problem Of The Catenary] Which I Had Hitherto Not Attempted, And With My Key [the Differential Calculus] Happily Opened Its Secret. Acta Eruditorum

To Love Is To Find Pleasure In The Happiness Of Others.

But It Is The Knowledge Of Necessary And Eternal Truths Which Distinguishes Us From Mere Animals, And Gives Us Reason And The Sciences, Raising Us To Knowledge Of Ourselves And God. It Is This In Us Which We Call The Rational Soul Or Mind.

When God Works Miracles, He Does Not Do It In Order To Supply The Wants Of Nature, But Those Of Grace. Whoever Thinks Otherwise, Must Needs Have A Very Mean Notion Of The Wisdom And Power Of God.

Nothing Is More Important Than To See The Sources Of Invention Which Are, In My Opinion More Interesting Than The Inventions Themselves.

If We Were Magically Shrunk And Put Into Someone's Brain While She Was Thinking, We Would See All The Pumps, Pistons, Gears And Levers Working Away And We Would Be Able To Describe The Workings Completely, In Mechanical Terms, Thereby Completely Describing The Thought Processes Of The Brain. But That Description Would Not Contain Any Mention Of Thought! It Would Contain Nothing But Descriptions Of Pumps, Pistons, Levers!

Everything That Is Possible Demands To Exist.

The Greatness Of A Life Can Only Be Estimated By The Multitude Of Its Actions. We Should Not Count The Years, It Is Our Actions Which Constitute Our Life.

Nothing Is Accomplished All At Once, And It Is One Of My Great Maxims, And One Of The Most Completely Verified, That Nature Makes No Leaps: A Maxim Which I Have Called The Law Of Continuity.

Our Reasonings Are Grounded Upon Two Great Principles, That Of Contradiction, In Virtue Of Which We Judge False That Which Involves A Contradiction, And True That Which Is Opposed Or Contradictory To The False.

I Hold That It Is Only When We Can Prove Everything We Assert That We Understand Perfectly The Thing Under Consideration.

All Things In God Are Spontaneous.

But In Simple Substances The Influence Of One Monad Over Another Is Ideal Only.

Every Mind Has A Horizon In Respect To Its Present Intellectual Capacity But Not In Respect To Its Future Intellectual Capacity.

And There Must Be Simple Substances, Because There Are Compounds; For The Compound Is Nothing But A Collection Or Aggregatum Of Simples.

Words Of Wisdom

Nature Does Not Make Leaps.

I Also Take It As Granted That Every Created Thing, And Consequently The Created Monad Also, Is Subject To Change, And Indeed That This Change Is Continual In Each One.

Words Of Wisdom

There Never Is Absolute Birth Nor Complete Death, In The Strict Sense, Consisting In The Separation Of The Soul From The Body. What We Call Births Are Developments And Growths, While What We Call Deaths Are Envelopments And Diminutions.

For Things Remain Possible, Even If God Does Not Choose Them. Indeed, Even If God Does Not Will Something To Exist, It Is Possible For It To Exist, Since, By Its Nature, It Could Exist If God Were To Will It To Exist.

Music Is A Hidden Arithmetic Exercise Of The Soul, Which Does Not Know That It Is Counting.

I Hold That The Mark Of A Genuine Idea Is That Its Possibility Can Be Proved, Either A Priori By Conceiving Its Cause Or Reason, Or A Posteriori When Experience Teaches Us That It Is In Fact In Nature.

Words Of Wisdom

We May Say, That Not Only The Soul (the Mirror Of An Indestructible Universe) Is Indestructible, But Also The Animal Itself Is, Although Its Mechanism Is Frequently Destroyed In Parts.

The Pleasure We Obtain From Music Comes From Counting, But Counting Unconsciously. Music Is Nothing But Unconscious Arithmetic.

I Do Not Conceive Of Any Reality At All As Without Genuine Unity.

Words Of Wisdom

Reality Cannot Be Found Except In One Single Source, Because Of The Interconnection Of All Things With One Another.

Whence It Follows That God Is Absolutely Perfect, Since Perfection Is Nothing But Magnitude Of Positive Reality, In The Strict Sense, Setting Aside The Limits Or Bounds In Things Which Are Limited.

These Principles Have Given Me A Way Of Explaining Naturally The Union Or Rather The Mutual Agreement [conformité] Of The Soul And The Organic Body. The Soul Follows Its Own Laws, And The Body Likewise Follows Its Own Laws; And They Agree With Each Other In Virtue Of The Pre-established Harmony Between All Substances, Since They Are All Representations Of One And The Same Universe.

Thus God Alone Is The Primary Unity, Or Original Simple Substance, From Which All Monads, Created And Derived, Are Produced.

Words Of Wisdom

Make Me The The Master Of Education, And I Will Undertake To Change The World.

Changing The World

It Is Necessary To Believe That The Mixture Of Evil Has Produced The Greatest Possible Good: Otherwise The Evil Would Not Have Been Permitted.

We Never Have A Full Demonstration, Although There Is Always An Underlying Reason For The Truth, Even If It Is Only Perfectly Understood By God, Who Alone Penetrated The Infinite Series In One Stroke Of The Mind.

...a Distinction Must Be Made Between True And False Ideas, And That Too Much Rein Must Not Be Given To A Man's Imagination Under Pretext Of Its Being A Clear And Distinct Intellection.

Indeed Every Monad Must Be Different From Every Other. For There Are Never In Nature Two Beings, Which Are Precisely Alike, And In Which It Is Not Possible To Find Some Difference Which Is Internal, Or Based On Some Intrinsic Quality.

Words Of Wisdom

He Who Hasn't Tasted Bitter Things Hasn't Earned Sweet Things.

God, Possessing Supreme And Infinite Wisdom, Acts In The Most Perfect Manner, Not Only Metaphysically, But Also Morally Speaking, And ... With Respect To Ourselves, We Can Say That The More Enlightened And Informed We Are About God's Works, The More We Will Be Disposed To Find Them Excellent And In Complete Conformity With What We Might Have Desired.

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