pg-xii
(2) Don't begin any fresh Chapter, or Section, until you are certain
that you _thoroughly_ understand the whole book _up to that point_, and
that you have worked, correctly, most if not all of the examples which
have been set. So long as you are conscious that all the land you have
passed through is absolutely _conquered_, and that you are leaving no
unsolved difficulties _behind_ you, which will be sure to turn up again
later on, your triumphal progress will be easy and delightful.
Otherwise, you will find your state of puzzlement get worse and worse as
you proceed, till you give up the whole thing in utter disgust.
(3) When you come to any passage you don't understand, _read it again_:
if you _still_ don't understand it, _read it again_: if you fail, even
after _three_ readings, very likely your brain is getting a little
tired. In that case, put the book away, and take to other occupations,
and next day, when you come to it fresh, you will very likely find that
it is _quite_ easy.
(4) If possible, find some genial friend, who will read the book along
with you, and will talk over the difficulties with you. _Talking_ is a
wonderful smoother-over of difficulties. When _I_ come upon
anything----in Logic or in any other hard subject----that entirely
puzzles me, I find it a capital plan to talk it over, _aloud_, even when
I am all alone. One can explain things so _clearly_ to one's self! And
then, you know, one is so _patient_ with one's self: one _never_ gets
irritated at one's own stupidity!
If, dear Reader, you will faithfully observe these Rules, and so give my
little book a really _fair_ trial, I promise you, most confidently, that
you will find Symbolic Logic to be one of the most, if not _the_ most,
fascinating of mental recreations! In this First Part, I have carefully
avoided all difficulties which seemed to me to be beyond the grasp of an
intelligent child of (say) twelve or fourteen years of age. I have
myself taught most of its contents, _vivâ voce_, to _many_ children, and
have found them take a real intelligent interest in the subject. For
those, who succeed in mastering Part I, and who begin, like Oliver,
"asking for more," I hope to provide, in Part II, some _tolerably_ hard
nuts to crack----nuts that will require all the nut-crackers they happen
to possess!
pg-xiii
Mental recreation is a thing that we all of us need for our mental
health; and you may get much healthy enjoyment, no doubt, from Games,
such as Back-gammon, Chess, and the new Game "Halma". But, after all,
when you have made yourself a first-rate player at any one of these
Games, you have nothing real to _show_ for it, as a _result!_ You
enjoyed the Game, and the victory, no doubt, _at the time_: but you have
no _result_ that you can treasure up and get real _good_ out of. And,
all the while, you have been leaving unexplored a perfect _mine_ of
wealth. Once master the machinery of Symbolic Logic, and you have a
mental occupation always at hand, of absorbing interest, and one that
will be of real _use_ to you in _any_ subject you may take up. It will
give you clearness of thought----the ability to _see your way_ through a
puzzle----the habit of arranging your ideas in an orderly and
get-at-able form----and, more valuable than all, the power to detect
_fallacies_, and to tear to pieces the flimsy illogical arguments, which
you will so continually encounter in books, in newspapers, in speeches,
and even in sermons, and which so easily delude those who have never
taken the trouble to master this fascinating Art. _Try it._ That is all
I ask of you!
L. C.
29, BEDFORD STREET, STRAND.
_February 21, 1896._
pg-xiv
pg-xv
CONTENTS.
=BOOK I.=
=THINGS AND THEIR ATTRIBUTES.=
CHAPTER I.
_INTRODUCTORY._
PAGE
'=Things=' 1
'=Attributes=' "
'=Adjuncts=' "
CHAPTER II.
_CLASSIFICATION._
'=Classification=' 1½
'=Class=' "
'=Peculiar=' Attributes "
'=Genus=' "
'=Species=' "
'=Differentia=' "
'=Real=' and '=Unreal=', or '=Imaginary=', Classes 2
'=Individual=' "
A Class regarded as a single Thing 2½
pg-xvi
CHAPTER III.
_DIVISION._
§ 1.
_Introductory._
'=Division=' 3
'=Codivisional=' Classes "
§ 2.
_Dichotomy._
'=Dichotomy=' 3½
Arbitrary limits of Classes "
Subdivision of Classes 4
CHAPTER IV.
_NAMES._
'=Name=' 4½
'=Real=' and '=Unreal=' Names "
Three ways of expressing a Name "
Two senses in which a plural Name may be used 5
CHAPTER V.
_DEFINITIONS._
'=Definition=' 6
Examples worked as models "
pg-xvii
=BOOK II.=
=PROPOSITIONS.=
CHAPTER I.
_PROPOSITIONS GENERALLY._
§ 1.
_Introductory._
Technical meaning of "some" 8
'=Proposition=' "
'=Normal form=' of a Proposition "
'=Subject=', '=Predicate=', and '=Terms=' 9
§ 2.
_Normal form of a Proposition._
Its four parts:--
(1) '=Sign of Quantity=' 9
(2) Name of Subject "
(3) '=Copula=' "
(4) Name of Predicate "
§ 3.
_Various kinds of Propositions._
Three kinds of Propositions:--
(1) Begins with "Some". Called a '=Particular=' Proposition:
also a Proposition '=in I=' 10
(2) Begins with "No". Called a '=Universal Negative='
Proposition: also a Proposition '=in E=' "
(3) Begins with "All". Called a '=Universal Affirmative='
Proposition: also a Proposition '=in A=' "
pg-xviii
A Proposition, whose Subject is an Individual, is to be
regarded as Universal "
Two kinds of Propositions, 'Propositions of Existence',
and 'Propositions of Relation' "
CHAPTER II.
_PROPOSITIONS OF EXISTENCE._
'=Proposition of Existence =' 11
CHAPTER III.
_PROPOSITIONS OF RELATION._
§ 1.
_Introductory._
'=Proposition of Relation=' 12
'=Universe of Discourse=,' or '=Univ.=' "
§ 2.
_Reduction of a Proposition of Relation
to Normal form._
Rules 13
Examples worked "
§ 3.
_A Proposition of Relation, beginning with "All",
is a Double Proposition._
Its equivalence to _two_ Propositions 17
pg-xix
§ 4.
_What is implied, in a Proposition of Relation,
as to the Reality of its Terms?_
Propositions beginning with "Some" 19
" " "No" "
" " "All" "
§ 5.
_Translation of a Proposition of Relation into
one or more Propositions of Existence._
Rules 20
Examples worked "
=BOOK III.=
=THE BILITERAL DIAGRAM.=
CHAPTER I.
_SYMBOLS AND CELLS._
The Diagram assigned to a certain Set of Things, viz. our
Univ. 22
Univ. divided into 'the x-Class' and 'the x'-Class' 23
The North and South Halves assigned to these two Classes "
The x-Class subdivided into 'the xy-Class' and 'the xy'-Class' "
The North-West and North-East Cells assigned to these
two Classes "
The x'-Class similarly divided "
The South-West and South-East Cells similarly assigned "
The West and East Halves have thus been assigned to
'the y-Class' and 'the y'-Class' 24
=Table I.= Attributes of Classes, and Compartments, or
Cells, assigned to them 25
pg-xx
CHAPTER II.
_COUNTERS._
Meaning of a Red Counter placed in a Cell 26
" " " " on a Partition "
American phrase "=sitting on the fence=" "
Meaning of a Grey Counter placed in a Cell "
CHAPTER III.
_REPRESENTATION OF PROPOSITIONS._
§ 1.
_Introductory._
The word "Things" to be henceforwards omitted 27
'=Uniliteral=' Proposition "
'=Biliteral=' do. "
Proposition '=in terms of=' certain Letters "
§ 2.
_Representation of Propositions of Existence._
The Proposition "Some x exist" 28
Three other similar Propositions "
The Proposition "No x exist" "
Three other similar Propositions 29
The Proposition "Some xy exist" "
Three other similar Propositions "
The Proposition "No xy exist" "
Three other similar Propositions "
The Proposition "No x exist" is _Double_, and is equivalent
to the two Propositions "No xy exist" and "No xy' exist" 30
pg-xxi
§ 3.
_Representation of Propositions of Relations._
The Proposition "Some x are y" "
Three other similar Propositions "
The Proposition "Some y are x" 31
Three other similar Propositions "
Trio of equivalent Propositions, viz.
"Some xy exist" = "Some x are y" = "Some y are x" "
'=Converse=' Propositions, and '=Conversion=' "
Three other similar Trios 32
The Proposition "No x are y" "
Three other similar Propositions "
The Proposition "No y are x" "
Three other similar Propositions "
Trio of equivalent Propositions,
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