Essays On Education And Kindred Subjects (Fiscle Part- 11) by Herbert Spencer (best mobile ebook reader TXT) 📖
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- Author: Herbert Spencer
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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.
Part 2 Chapter 3 (On The Genesis Of Science) Pg 108
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
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