Essays On Education And Kindred Subjects (Fiscle Part- 11) by Herbert Spencer (best fiction novels to read TXT) 📕

Presenting Known Conceptions More Or Less _Like_ Them.

This View Is Further Confirmed, And The   Predominance Of    This Notion Of

Likeness In Primitive Times Further Illustrated, By The   Fact That Our

System Of    Presenting Ideas To The   Eye Originated After The   Same Fashion.

Writing And Printing Have Descended From Picture-Language. The   Earliest

Mode Of    Permanently Registering A Fact Was By Depicting It On A Wall;

That Is--By Exhibiting Something As _Like_ To The   Thing To Be Remembered

As It Could Be Made. Gradually As The   Practice Grew Habitual And

Extensive, The   Most Frequently Repeated Forms Became Fixed, And

Presently Abbreviated; And, Passing Through The   Hieroglyphic And

Ideographic Phases, The   Symbols Lost All Apparent Relations To The

Things Signified: Just As The   Majority Of    Our Spoken Words Have Done.

Observe Again, That The   Same Thing Is True Respecting The   Genesis Of

Reasoning. The   _Likeness_ That Is Perceived To Exist Between Cases, Is

The Essence Of    All Early Reasoning And Of    Much Of    Our Present Reasoning.

The Savage, Having By Experience Discovered A Relation Between A Certain

Object And A Certain Act, Infers That The   _Like_ Relation Will Be Found

In Future Cases. And The   Expressions We Constantly Use In Our

Arguments--"_Analogy_ Implies," "The Cases Are Not _Parallel_," "By

_Parity_ Of    Reasoning," "There Is No _Similarity_,"--Show How Constantly

The Idea Of    Likeness Underlies Our Ratiocinative Processes.

Still More Clearly Will This Be Seen On Recognising The   Fact That There

Is A Certain Parallelism Between Reasoning And Classification; That The

Two Have A Common Root; And That Neither Can Go On Without The   Other.

For On The   One Hand, It Is A Familiar Truth That The   Attributing To A

Body In Consequence Of    Some Of    Its Properties, All Those Other

Properties In Virtue Of    Which It Is Referred To A Particular Class, Is

An Act Of    Inference. And, On The   Other Hand, The   Forming Of    A

Generalisation Is The   Putting Together In One Class All Those Cases

Which Present Like Relations; While The   Drawing A Deduction Is

Essentially The   Perception That A Particular Case Belongs To A Certain

Class Of    Cases Previously Generalised. So That As Classification Is A

Grouping Together Of    _Like Things_; Reasoning Is A Grouping Together Of

_Like Relations_ Among Things. Add To Which, That While The   Perfection

Gradually Achieved In Classification Consists In The   Formation Of    Groups

Of _Objects_ Which Are _Completely Alike_; The   Perfection Gradually

Achieved In Reasoning Consists In The   Formation Of    Groups Of    _Cases_

Which Are _Completely Alike_.

Once More We May Contemplate This Dominant Idea Of    Likeness As Exhibited

In Art. All Art, Civilised As Well As Savage, Consists Almost Wholly In

The Making Of    Objects _Like_ Other Objects; Either As Found In Nature,

Or As Produced By Previous Art. If We Trace Back The   Varied Art-Products

Now Existing, We Find That At Each Stage The   Divergence From Previous

Patterns Is But Small When Compared With The   Agreement; And In The

Earliest Art The   Persistency Of    Imitation Is Yet More Conspicuous. The

Old Forms And Ornaments And Symbols Were Held Sacred, And Perpetually

Copied. Indeed, The   Strong Imitative Tendency Notoriously Displayed By

The Lowest Human Races, Ensures Among Them A Constant Reproducing Of

Likeness Of    Things, Forms, Signs, Sounds, Actions, And Whatever Else Is

Imitable; And We May Even Suspect That This Aboriginal Peculiarity Is In

Some Way Connected With The   Culture And Development Of    This General

Conception, Which We Have Found So Deep And Widespread In Its

Applications.

And Now Let Us Go On To Consider How, By A Further Unfolding Of    This

Same Fundamental Notion, There Is A Gradual Formation Of    The   First Germs

Of Science. This Idea Of    Likeness Which Underlies Classification,

Nomenclature, Language Spoken And Written, Reasoning, And Art; And Which

Plays So Important A Part Because All Acts Of    Intelligence Are Made

Possible Only By Distinguishing Among Surrounding Things, Or Grouping

Them Into Like And Unlike;--This Idea We Shall Find To Be The   One Of

Which Science Is The   Especial Product. Already During The   Stage We Have

Been Describing, There Has Existed _Qualitative_ Prevision In Respect To

The Commoner Phenomena With Which Savage Life Is Familiar; And We Have

Now To Inquire How The   Elements Of    _Quantitative_ Prevision Are Evolved.

We Shall Find That They Originate By The   Perfecting Of    This Same Idea Of

Likeness; That They Have Their Rise In That Conception Of    _Complete

Likeness_ Which, As We Have Seen, Necessarily Results From The   Continued

Process Of    Classification.

For When The   Process Of    Classification Has Been Carried As Far As It Is

Possible For The   Uncivilised To Carry It--When The   Animal Kingdom Has

Been Grouped Not Merely Into Quadrupeds, Birds, Fishes, And Insects, But

Each Of    These Divided Into Kinds--When There Come To Be Sub-Classes, In

Each Of    Which The   Members Differ Only As Individuals, And Not

Specifically; It Is Clear That There Must Occur A Frequent Observation

Of Objects Which Differ So Little As To Be Indistinguishable. Among

Several Creatures Which The   Savage Has Killed And Carried Home, It Must

Often Happen That Some One, Which He Wished To Identify, Is So Exactly

Like Another That He Cannot Tell Which Is Which. Thus, Then, There

Originates The   Notion Of    _Equality_. The   Things Which Among Ourselves

Are Called _Equal_--Whether Lines, Angles, Weights, Temperatures, Sounds

Or Colours--Are Things Which Produce In Us Sensations That Cannot Be

Distinguished From Each Other. It Is True We Now Apply The   Word _Equal_

Chiefly To The   Separate Phenomena Which Objects Exhibit, And Not To

Groups Of    Phenomena; But This Limitation Of    The   Idea Has Evidently

Arisen By Subsequent Analysis. And That The   Notion Of    Equality Did Thus

Originate, Will, We Think, Become Obvious On Remembering That As There

Were No Artificial Objects From Which It Could Have Been Abstracted, It

Must Have Been Abstracted From Natural Objects; And That The   Various

Families Of    The   Animal Kingdom Chiefly Furnish Those Natural Objects

Which Display The   Requisite Exactitude Of    Likeness.

The Same Order Of    Experiences Out Of    Which This General Idea Of    Equality

Is Evolved, Gives Birth At The   Same Time To A More Complex Idea Of

Equality; Or, Rather, The   Process Just Described Generates An Idea Of

Equality Which Further Experience Separates Into Two Ideas--_Equality Of

Things_ And _Equality Of    Relations_. While Organic, And More Especially

Animal Forms, Occasionally Exhibit This Perfection Of    Likeness Out Of

Which The   Notion Of    Simple Equality Arises, They More Frequently

Exhibit Only That Kind Of    Likeness Which We Call _Similarity_; And Which

Is Really Compound Equality. For The   Similarity Of    Two Creatures Of    The

Same Species But Of    Different Sizes, Is Of    The   Same Nature As The

Similarity Of    Two Geometrical Figures. In Either Case, Any Two Parts Of

The One Bear The   Same Ratio To One Another As The   Homologous Parts Of

The Other. Given In Any Species, The   Proportions Found To Exist Among

The Bones, And We May, And Zoologists Do, Predict From Any One, The

Dimensions Of    The   Rest; Just As, When Knowing The   Proportions Subsisting

Among The   Parts Of    A Geometrical Figure, We May, From The   Length Of    One,

Calculate The   Others. And If, In The   Case Of    Similar Geometrical

Figures, The   Similarity Can Be Established Only By Proving Exactness Of

Proportion Among The   Homologous Parts; If We Express This Relation

Between Two Parts In The   One, And The   Corresponding Parts In The   Other,

By The   Formula A Is To B As _A_ Is To _B_; If We Otherwise Write This, A

To B = _A_ To _B_; If, Consequently, The   Fact We Prove Is That The

Relation Of    A To B _Equals_ The   Relation Of    _A_ To _B_; Then It Is

Manifest That The   Fundamental Conception Of    Similarity Is _Equality Of

Relations_.

With This Explanation We Shall Be Understood When We Say That The   Notion

Of Equality Of    Relations Is The   Basis Of    All Exact Reasoning. Already It

Has Been Shown That Reasoning In General Is A Recognition Of    _Likeness_

Of Relations; And Here We Further Find That While The   Notion Of    Likeness

Of Things Ultimately Evolves The   Idea Of    Simple Equality, The   Notion Of

Likeness Of    Relations Evolves The   Idea Of    Equality Of    Relations: Of

Which The   One Is The   Concrete Germ Of    Exact Science, While The   Other Is

Its Abstract Germ.

Those Who Cannot Understand How The   Recognition Of    Similarity In

Creatures Of    The   Same Kind Can Have Any Alliance With Reasoning, Will

Get Over The   Difficulty On Remembering That The   Phenomena Among Which

Equality Of    Relations Is Thus Perceived, Are Phenomena Of    The   Same Order

And Are Present To The   Senses At The   Same Time; While Those Among Which

Developed Reason Perceives Relations, Are Generally Neither Of    The   Same

Order, Nor Simultaneously Present. And If Further, They Will Call To

Mind How Cuvier And Owen, From A Single Part Of    A Creature, As A Tooth,

Construct The   Rest By A Process Of    Reasoning Based On This Equality Of

Relations, They Will See That The   Two Things Are Intimately Connected,

Remote As They At First Seem. But We Anticipate. What It Concerns Us

Here To Observe Is, That From Familiarity With Organic Forms There

Simultaneously Arose The   Ideas Of    _Simple Equality_, And _Equality Of

Relations_.

At The   Same Time, Too, And Out Of    The   Same Mental Processes, Came The

First Distinct Ideas Of    _Number_. In The   Earliest Stages, The

Presentation Of    Several Like Objects Produced Merely An Indefinite

Conception Of    Multiplicity; As It Still Does Among Australians, And

Bushmen, And Damaras, When The   Number Presented Exceeds Three Or Four.

With Such A Fact Before Us We May Safely Infer That The   First Clear

Numerical Conception Was That Of    Duality As Contrasted With Unity. And

This Notion Of    Duality Must Necessarily Have Grown Up Side By Side With

Those Of    Likeness And Equality; Seeing That It Is Impossible To

Recognise The   Likeness Of    Two Things Without Also Perceiving That There

Are Two. From The   Very Beginning The   Conception Of    Number Must Have Been

As It Is Still, Associated With The   Likeness Or Equality Of    The   Things

Numbered. If We Analyse It, We Find That Simple Enumeration Is A

Registration Of    Repeated Impressions Of    Any Kind. That These May Be

Capable Of    Enumeration It Is Needful That They Be More Or Less Alike;

And Before Any _Absolutely True_ Numerical Results Can Be Reached, It Is

Requisite That The   Units Be _Absolutely Equal_. The   Only Way In Which We

Can Establish A Numerical Relationship Between Things That Do Not Yield

Us Like Impressions, Is To Divide Them Into Parts That _Do_ Yield Us

Like Impressions. Two Unlike Magnitudes Of    Extension, Force, Time,

Weight, Or What Not, Can Have Their Relative Amounts Estimated Only By

Means Of    Some Small Unit That Is Contained Many Times In Both; And Even

If We Finally Write Down The   Greater One As A Unit And The   Other As A

Fraction Of    It, We State, In The   Denominator Of    The   Fraction, The   Number

Of Parts Into Which The   Unit Must Be Divided To Be Comparable With The

Fraction.

It Is, Indeed, True, That By An Evidently Modern Process Of    Abstraction,

We Occasionally Apply Numbers To Unequal Units, As The   Furniture At A

Sale Or The   Various Animals On A Farm, Simply As So Many Separate

Entities; But No True Result Can Be Brought Out By Calculation With

Units Of    This Order. And, Indeed, It Is The   Distinctive Peculiarity Of

The Calculus In General, That It Proceeds On The   Hypothesis Of    That

Absolute Equality Of    Its Abstract Units, Which No Real Units Possess;

And That The   Exactness Of    Its Results Holds Only In Virtue Of    This

Hypothesis. The   First Ideas Of    Number Must Necessarily Then Have Been

Derived From Like Or Equal Magnitudes As Seen Chiefly In Organic

Objects; And As The   Like Magnitudes Most Frequently Observed Magnitudes

Of Extension, It Follows That Geometry And Arithmetic Had A

Simultaneous Origin.

Not Only Are The   First Distinct Ideas Of    Number Co-Ordinate With Ideas

Of Likeness And Equality, But The   First Efforts At Numeration Displayed

The Same Relationship. On Reading The   Accounts Of    Various Savage Tribes,

We Find That The   Method Of    Counting By The   Fingers, Still Followed By

Many Children, Is The   Aboriginal Method. Neglecting The   Several Cases In

Which The   Ability To Enumerate Does Not Reach Even To The   Number Of

Fingers On One Hand, There Are