Logic. (System of phil., 1). (Google eBook)

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Contents

CHAPTER I
10
Which may be called an act of objectification
11
In the specific forms of the parts of speech
12
Relation of substantive verb adjective to substance event property
13
Relation of thought to its linguistic expression
14
The other parts of speech Prepositions and conjunctions
15
Judgment not rightly treated in pure logic before conception
17
B Position distinction and comparison of the matter of simple ideas 9 Further reaction of thought in positing distinguishing and comparing ideas
18
Position practically inseparable fromobjectification 3
19
lisation
20
Such a view ignores the tme logical import of the act
21
Comparison implies a universal this not a universalconcept
22
Like all universals it is not strictly an idea
23
Distinction of instances of a universal implies idea of more and less
24
Also those of unity and multiplicity and greatness and smallness
25
In the operations of B as compared with those of A thought may be called receptive
26
its various forms
28
The form of conception implies the idea of a ground iar the synthesis 2y 22 Comparison of different instances and observation of the same instance u...
30
Abstraction involved in comparison does not mean mere omission of differences
31
The formation of the second universal logical concept implies the first 5 14
34
Marks not merely coordinated but also mutually determined in a concept
35
Subordination of species to genus and subsumption of species and genus under a mark
36
Species a universal which can be imaged genus one which can only be formulated
37
Inverse ratio of content and extent how far true or important
38
differentia property accident
40
Idea of a complete system of concepts
41
Transition to the Form of the Judgment 34 Change makes such an idea unrealisable and leads from conception to judgment
42
CHAPTER II
44
This is indicated in the terms Subject Predicate and Copula
45
The logical sense of the copula is not affected by the quantity of the judgment
46
Nor by its quality
47
Nor by its modality as ordinarily understood
48
Tree apodeictic modality is found in the three forms of rtlation
49
Not of course that any form of judgment can guarantee its material truth
50
Socalled problematic judgments are not truly problematic nor are questions or prayers
51
The only true problematic modality is expressed by particular and singular judgments
52
The ordinary classification omits or confuses many modal distinctions
53
THE SERIES OF THE FORMS OF JUDGMENT A The impersonal judgment The categorical judgment The principle of identity 47 The categorical j...
54
Relating a present perception to a permanent though unexpressed subject
55
Difficulty as to the logical import of the categorical judgment
56
Nor is it explained by saying that the one is predicated of the other 5 7
58
In fact the judgment is indefensible against the principle of identity
59
B The particular judgment the hypothetical judgment the principle of sufficient reason 56 The difficulty applies to analytical as well as to synthetical j...
61
The justification of categorical judgments is that they are really identical
62
But in that case they are not judgments at all in the real sense
65
This dilemma is met in the hypothetical judgment by making the identity conditional
66
cause and reason
67
True formulation of the principle of sufficient reason
68
The principle of identity alone is no source of knowledge
69
The princ rat suff not a necessity of thought but a fact of all mental experience
70
The general judgment the disjunctive judgment the dictum ce omni et nullo and the principium exclusi medii 67 The connexion between reason and ...
72
This universality is expressed in the general judgment
73
Further determination of the predicate in the disjunctive judgment
74
True formulation of dictum de omni et nullo
75
Its true logical formulation
76
Incompatibility of contrary and compatibility of disparate predicates
77
The disjunctive judgment leads on to inference
79
Inference ad subalternatam
80
Ad contradictoriam
81
Inference by conversion
83
Conversion by contraposition
84
CHAPTER III
85
General conditions of valid inference in them
86
The second figure
87
The third figure when both premises are affirmative
88
The third figure when both premises are negative
89
The fourth figure is superfluous
90
Reduction of the other figures to the first
91
Syllogisms with hypothetical premises involve no new principle 9a 94 Difference of the relation between reason and consequence from that between ...
93
Syllogisms with disjunctive copulative or remotive premises
94
Chains of inference
95
A Syllogistic inferences inference by subsumption inference by induction inference by analogy 97 The Aristotelian or subsumptive syllogisms merel...
96
Snch inference by subsumption involves a double circle
97
It must be possible to establish 1 major and 2 minor premises with out full knowledge
99
Inductive inference as solution of the first requirement
100
The defect of induction as of subsumption lies in the practice not the principle of it
101
Inference by analogy as solution of the second requirement
102
Defect and justification of analogical inference
103
B Mathematical inferences inference by substitution inference by proportion constitutive equation pac b 105 The previous forms of inference deal on...
104
Thus do not satisfy the needs of real thinking which requires them to be specific
105
They are in fact inferences from the extent instead of from the content of concepts
106
It implies substitution of an analysed for an unanalysed middle term
107
Remarks on the symbolisation of logical relationships
108
Inference by substitution is only strictly applicable to pure quantities
109
Still as an ideal of thought in general it has its place in logic
110
Extension of it to incommensurable objects in the form of proportion m
113
Proportion between marks is modified by the constitution of the whole subject
114
Inference by proportion thus leads to the idea of constitutive concepts
115
Which however are only fruitful in Mathematics where all is com mensurable
117
Many such concepts are formed unconsciously by psychical mechanism
118
Hence the idea that any group of common marks forms a concept
119
The distinction of essential from unessential leads to comparison and classification
120
Artificial or combinatory classification
121
Its defects It may include more than the facts
122
Or less than the facts
123
Logical classification aims at constitutive concepts or ideas
125
Which naturally connect with the notions of active tendency and purpose
126
And so with that of more and less perfect species
127
Illustrations from Mathematics of the gradation of species
128
The logically most perfect species is that in which all the marks are at the highest value allowed by the genus
130
But each genus may itself have its standard of perfection in a higher genus
131
And so lead ultimately to a highest genus which governs the develop ment of all the rest
132
Antagonism between aesthetic and scientific view of things Possible reconciliation
143
Laws are not external to reality but constitute its very nature
144
Form of the ultimate ideal of thought
145
Supposed analogy of the living organism Hegelianism Speculation
146
Value of the speculative ideal It belongs to logic but points beyond it
147
1523 Prefatory Remarks
149
CHAPTER I
152
Poetry and rhetoric 15a 156 Uncertainty of communication
153
Explanation by abstraction
154
This the only method for simple ideas
155
Explanation by construction Description
156
1601 Description and definition
157
Nominal and real definitions
160
Three faults to avoid
161
Elegance and brevity
162
Evil of superfluity
164
Popular definitions 105
165
Genetic definition
167
CHAPTER II
169
Popular language justified
173
PAGE
174
Scale of sounds
175
Heatsensations
176
Arbitrariness of scale
177
Illustrations from practical life
178
Moral and aesthetic distinctions
179
Transition from concave to convex
180
to another
181
And though there be a term in the series that satisfies both conceptions
182
Illustrations
183
Development
185
SCHEMES AND SYMBOLS 184 The notion of a universal scheme or system of conceptions
187
Pythagoreanism
189
Poverty of the particular form in which it is expressed
191
Numbers and things
192
Other kindred speculations
193
Demand for symmetry
195
1915 The Hegelian dialectic
197
The scheme of Leibnitz
204
Is such a scheme possible?
205
What it would require
207
Note on the Logical Calculus
208
CHAPTER IV
224
Proof rests on axioms Axioms how distinguished
225
Before starting to prove a proposition we must know that it is worth proving i e that a the ideas are def1nite
227
b their combination possible
228
r the proposition true in fact
229
Eight forms of proof distinguished
230
2056 1 First direct progressive proof from the conditions of 7 to T
231
2 Second direct progressive proof from 7 to its consequences
233
3 First direct regressive proof from T to its conditions
234
20910 4 Second direct regressive proof from the consequences of 70 T
236
5 First indirect progressive proof
239
Indirect regressive proofs
241
The mathematicians proof by strict analogy is also proof by subsumption
245
Illustrations from Geometry
251
The universality of a pure connexion or its character as a law
253
A line without mass cannot be moved
264
Facts as they appear are not only relative to one another but to
268
Difficulty of analysis
273
CHAPTER VI
282
Fallacies of too wide or too narrow definition
288
CHAPTER VII
298
The raw matter of Inductions consists not of passive impressions
300
The truths of Geometry are universal because the diagram is used as
306
Typical cases of the relation in which two phenomena C and E
312
Whether the phenomenon C is or only contains the cause of E can only
320
The exact nature of the causal nexus inferred from any of the above
326
CHAPTER VIII
332
Laws based on statistics are mostly partial truths
344
Rules for framing of hypotheses not to be laid down beforehand
352
An hypothesis must limit itself to asserting what is possible i e what
358
The mathematical determination of chances assumes that they are
364
as compared with the sum of its alternatives not as compared with
368
Calculus of chances not only presupposes the laws of all calculation
377
Success of attempts made to test by experiment the calculus of chances
381
Use of the calculus in determining the probable accuracy of our observa
388
The weight of votes A majority of majorities may be a minority
394
Election by elimination
400
BOOK III
406
Methodology however as treatment of Knowledge is enquiry into
413
But any decision postulates the competence of thought
420
That Things may not be what they seem as a mere general doubt
426
CHAPTER II
433
Confusion of Existence and Validity in case of the Ideas
440
Ideas impart no motion criticised importance of Judgments
446
only an ideal 134
452
This doubt involves the assumption of a world of things which
455
Both in simple Perception and in such ideas as that of causal connexion
458
There may be spurious selfevidence which is tested by thinking
465
CHAPTER IV
472
Only as independent of individual min d The case of Things
478
The Reality of general notions is only validity
484
Subjective character of Syllogism and Induction
490
Actual Reality adequacy of Judgments to it
497
And 3 synthetic judgments a priori as basis of knowledge of parti
503
And by his geometrical instance
509
Intuition is opposed to discursive thoughtmeans immediate appre
516
Mechanical principles like those of Arithmetic and Geometry at once
523
A synthetic yet necessary development the supreme goal of science
529
Disparate groups of sensations 170
537
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Page 59 - I will state the conclusion to which we are driven : this absolute connexion of two concepts S and P, in which the one is unconditionally the other and yet both stand over against each other as different, is a relation quite impracticable in thought ; by means of this copula, the simple ' is ' of the categorical judgment, two different contents cannot be connected at all; they must either fall entirely within one another, or they must remain entirely separate, and the impossible judgment 'S is P'...

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