Arithmetic

by sheer force of character conscience inspired abraham lincoln rose from abject depths of squalid environment to become the most august figure in american history and perhaps the most significant and lovable personality in the annals of mankind in his amazing emergence to greatness from poverty and ignorance is to be found a supreme demonstration and justification of american institutions it was the common people who recognized the nobility and majesty of this singular man he understood that always and even in his days of power when great battles were fought at the nod of his head and a whisk of his pen set a whole race free it kept him humble perhaps the profoundly tender love which the american people have for his memory is to be explained by the fact that in the secret recesses where every man communes with the highest bravest and most unselfish elements of his own nature the average american is an abraham lincoln to himself the power to recognize is not so far removed from the power to be recognized and is thrillingly significant after all these dreary years of babble about the omnipotence of money that the same people who raised lincoln from penniless obscurity to his place of power and martyrdom still cherish his name and example with a depth of devotion that increases with each year of national growth confusing and confounding the learned foreign cities of the republic who miss the finest thing in American civilization when they fail to learn why we love Lincoln.

why we love lincoln chapter two if daniel boone the mighty hunter and indian fighter had not roused the imagination of virginians and carolinians by his wonderful and romantic deeds in the exploration of the kentucky wilderness the grandfather of abraham lincoln would not have left rockingham county virginia and entered seventeen hundred acres of land in kentucky where he was presently slain on his forest farm by a savage in the presence of his three sons the youngest of these sons thomas lincoln was the father of the future president of the united states in spite of an educated well-to-do american ancestry of pure english quaker stock one was a member of the boston tea party another was a revolutionary minuteman served in the continental congress and was attorney-general of the united states under jefferson this frontier boy who was only six years old when his father was murdered before his eyes grew up without education to be a wandering workboy who gradually picked up odd jobs of carpenting he became a powerfully built square-set young man somewhat indolent and improvident who occasionally showed his temper and courage by knocking down a frontier rowdy the rough young carpenter in eighteen o six married nancy hanks a niece of joseph hanks in whose shop he worked at his trade nancy who was the mother of abraham lincoln was the daughter of a supposedly illiterate and superstitious family but she was calmly intelligent knew how to read and write and taught her husband to scrawl his name the great lincoln always believed that he got his intellectual powers from his mother for a time this pair who were to bring forth the saviour of america dwelt in a log hut fourteen feet square at elizabethtown kentucky where they were married then a daughter was born a year later the carpenter bought a small farm on the big south fork of norland creek in harding county here on wretched soil overgrown with stunted brush thomas lincoln and nancy hanks lived with their infant daughter in a rude log cabin enduring profound poverty it was in this mere wooden hutch which had an earth floor one door and one window that abraham lincoln was born on february twelfth eighteen o nine what american however poor ignorant unlettered or discouraged can look upon the rude timbers of the home which sheltered the birth of the greatest man of the western hemisphere without a thrill of hope and a new realization of the opportunities that are co-eternal with conscience courage and persistence what man of any race or country can stand before that cabin and be a coward moses the waif peter the fisherman mahomet the shepherd columbus the sailor-boy each age has its separate message of the humanity of god and the divinity of man the gray-eyed boy lincoln played alone in the forest near knob creek where his father had secured a better farm it was a solitary and cheerless life for a child sometimes he sat among the shavings of his father's carpenter's shanty a silent lean little boy with long black hair and grave deep-set eyes dressed in deer-skin breeches and moccasins without toys and almost without companions for a few months he attended log-cabin schools with his sister sarah but he learned little more than his letters it is amazing to think that this man whose gettysburg address is accepted as one of the noblest classics of english literature did not have much more than six months of schooling in his whole life in eighteen sixteen thomas lincoln decided to move from kentucky to indiana he built a raft loaded it with a kit of carpenter's tools and four hundred gallons of whiskey and depending on his rifle for food floated down into the ohio river in search of a new home having picked out a place in the indiana forest he walked home and with a borrowed wagon and two horses he took his wife and children into the wilderness actually cutting a way through the woods for them near little pigeon creek the carpenter and his wife assisted by young abraham now seven years old built a shed of logs and poles partly open to the weather and here the family lived for a year meanwhile a patch of land was cleared corn was planted and as soon as a log cabin without windows could be built the lincolns moved into it the forest swarmed with game and the carpenter's rifle kept his family supplied with venison and deer hides for clothing they relied on the rifle and the corn patch for life little lincoln climbed at night to his bed of leaves in the loft by a ladder of wooden pins driven into the logs not only were the means of life hard to get but it was a malarial country and in eighteen eighteen the small group of pioneers who came to dwell at pigeon creek near the lincolns were attacked by a pestilence known as the milk sickness in october the mother of abraham lincoln died her husband sought a coffin out of the forest trees and buried her in a little clearing several months later a wandering frontier clergyman preached a sermon over her lonely snow-covered grave no wonder the countenance of the great emancipator moved all who beheld it by its deep melancholy he knew what sorrow was forty-five years before he paced his office in the white house all night with white face and bowed head sorrowing over the bloody defeat of chancellorsville wondering whether he was to be the last president of the united states and praying for the victory that came at gettysburg all that year the sensitive boy grieved for the mother who had gone out of his life but in time his father went back to elizabethtown kentucky where he married the widow of the town jailer and presently a four-horse raggin creaked up to the door of the lincoln cabin in the indiana forest with the bride her son and two daughters and a load of comfortable household goods including a feather bed and a walnut burrow valued at fifty dollars sarah bush lincoln the stepmother of abraham lincoln was a woman of thrift and energy tall straight fair and a kind-hearted motherly christian the american people owe a debt to this noble matron who did so much to influence and develop the character of the boy who was yet to save the nation from destruction she was good to the lincoln orphans whose mother lay out in the wild forest grave she gave them warm clothes she threw away the mat of corn husks and leaves on which they slept and replaced it with a soft feathered tick she loved little abe and the lonely boy returned her kindness and affection in a primitive cabin set in the midst of a savage country she created that noblest and best result of a good woman's heart and brain a happy home o pale woman of the twentieth century sighing for a mission in the great world's affairs perhaps there may be a suggestion for you in the simple story of what sarah bush did for abraham lincoln and through him for the ages did not the two malaria racked and care-driven mothers who lived in the rough-hewn lincoln cabin do more to influence the political institutions of mankind than all speeches and votes of women since voting was first invented chapter two CHAPTER III even at the age of ten years the frontier lad was a hard worker when he was not wielding the axe in the forest he was driving the horses threshing ploughing assisting his father as a carpenter he also hired out to the neighbors as a ploughboy water carrier baby minder or doer of odd chores at twenty-five cents a day he suddenly began to grow tall and there was no stronger youth in the community than the lank loose-limbed boy in deerskin's linsey woolsey and coolskin cap who could make an axe bite so deep into a tree his stepmother sent him to school again for several months in eighteen twenty six two he walked nine miles a day to attend a log school house he had new companions at home now a step-brother two step-sisters and his cousins john and denise hanks as young lincoln grew taller his skill and strength as a wood-chopper and rail-splitter and his willingness to do any kind of work however drudging or menial in spite of a natural meditative indolence made him widely known his kindly helpful disposition and simple honesty gave him a distinct popularity and he was much sought after as a companion notwithstanding his ungainly figure and rough ways but it was his extraordinary thirst for knowledge his effort to raise himself out of the depths of ignorance that showed the inner power struggling against adverse surroundings he grew to a height of six feet and four inches by the time he was seventeen years old his legs and arms were long his hands and feet big and his skin was dry and yellow his face was gaunt and his melancholy gray eyes were sunk in cavernous sockets above his prominent cheek-bones a girl schoolmate has described him his shoes when he had any were low he wore buckskin breeches linsey-woolsey shirt and a cap made of the skin of a squirrel or coon his breeches were baggy and lacked by several inches meeting the tops of his shoes thereby exposing his shin-bone sharp blue and narrow this is the real abraham lincoln who read and read and read whose constant spells of brooding abstraction eyes fixed dreaming face gave him a reputation for laziness among some of his shallow fellows who would crouch down in the forest or sit on a fence-rail for hours to study a book who would lie on his stomach at night in front of the fireplace and having no paper or slate would write and cipher with charcoal on the wooden shovel on boards and the hewn sides of logs shaving them clean when he wanted to write again here is his cousin's picture of him at the age of fourteen when abe and i returned to the house from work he would go to the cupboard snatch a piece of cornbread sit down take a book cock his legs up as high as his head and read we grubbed ploughed mowed and worked together barefooted in the field whenever abe had a chance in the field while at work or at the house he would stop and read His principal books were Arithmetic, the Bible, Aesop's Fables, Robinson Crusoe, Weems, Life of Washington, The Pilgrim's Progress, and A History of the United States.

He became the best speller and penman in his neighborhood, yet there was a vein of wagery in him which occasionally found a vent in such written verse as this, Abraham Lincoln, his hand and pen, he will be good, but God knows when.

All this has been told of him many times and in many ways, yet the nation he saved loves to dwell on the picture of the tall, tanned, awkward woodchopper and farm drudge, gawky, angular, iron-muscled with bare feet or moccasins, deer-hide breeches and coonskin cap battling out in the forest against his own ignorance and by sheer force of willpower conquering knowledge and commanding destiny.

In the Pure Mathematics of Geometrical Relationships we say that ‘if any Group of Entities enjoy any Relationships among its Members satisfying THIS SET OF ABSTRACT GEOMETRICAL CONDITIONS,’ Then SUCH AND SUCH ADDITIONAL ABSTRACT CONDITIONS MUST ALSO HOLD FOR SUCH RELATIONSHIPS.’ But when we come to Physical Space, we say that Some definitely OBSERVED GROUP OF PHYSICAL ENTITIES enjoys SOME DEFINITELY OBSERVED RELATIONSHIPS AMONG ITS MEMBERS WHICH DO SATISFY THIS ABOVE MENTIONED SET OF ABSTRACT GEOMETERICAL CONDITIONS.' We thence conclude that the Additional Relationships which we concluded to Hold IN ANY SUCH CASE Must therefore Hold in This PARTICULAR Case.The Certainty of Mathematics depends upon its complete Abstract Generality.But we can have no à priori Certainty that we are right in believing that the Observed Entities in the Concrete Universe form a Particular Instance of what falls under our General Reasoning.

To take another Example from Arithmetic.It is a General Abstract Truth of Pure Mathematics that any Group of Forty Entities can be subdivided into Two Groups of Twenty Entities.We are therefore justified in concluding that a particular group of Apples which we believe to contain forty Members can be subdivided into two groups of apples of which Each Contains twenty Members.But there Always remains the possibility that we have miscounted the big Group ;So that when we come in practice to subdivide itwe shall find that One of the two heaps Has an Apple Too Few Or An apple Too Many Accordinglyin Criticizing an Argument based Upon the application of Mathematics to particular Matters of FactThere Are Always Three Processes to Be Kept Perfectly Distinct in Our Minds.We Must First Scan the Purely Mathematical reasoningto Make sure that There Are No Mere slips in itNo Casual Illogicalities due to Mental Failure Any mathematician knows from bitter experience that, in first elaborating a train of reasoning, it is very easy to commit a slight error which yet makes all the difference.

But when a piece of mathematics has been revised and has been before the expert world for some time, the chance of a casual error is almost negligible.

The next process is to make quite certain of all the abstract conditions which have been presupposed to hold.