PREFACE ...................................................... xiii
INTRODUCTION .................................................... 1
1 INTUITION .................................................... 9
1 Representation ............................................ 9
2 Understanding ............................................ 10
3 Thinking ................................................. 11
4 Semantics ................................................ 12
5 Syntax ................................................... 14
6 Syntactico-Semantic Integrity ............................ 16
7 Models ................................................... 17
8 Ampliation ............................................... 20
9 Empirical Reality ........................................ 21
10 Lebenswelt ............................................... 23
11 Time ..................................................... 24
12 Causation ................................................ 25
13 Subjectivity ............................................. 26
14 Hermeneutics ............................................. 28
15 Weltanschauung ........................................... 30
16 Occultism ................................................ 32
17 Scientism ................................................ 36
18 Summary .................................................. 41
2 INSIGHT ..................................................... 43
19 Geometry ................................................. 43
20 Experiment ............................................... 45
21 Articulation ............................................. 47
22 Exploration .............................................. 48
23 Necessity ................................................ 49
24 Model Types .............................................. 50
25 Certainty ................................................ 52
26 Bedrock .................................................. 56
27 Genius ................................................... 58
28 Summary .................................................. 60
3 REASON ...................................................... 63
29 Warranty ................................................. 63
30 Number ................................................... 64
31 Hypothesis ............................................... 68
32 Confirmation ............................................. 68
33 Critique ................................................. 70
34 Coherence ................................................ 71
35 Analogy .................................................. 72
36 Induction ................................................ 75
37 Deduction ................................................ 76
38 Absurdity ................................................ 80
39 Theorems ................................................. 83
40 Interpretation ........................................... 84
41 Axiomatization ........................................... 86
42 Formal Logic ............................................. 89
43 Paradox .................................................. 93
44 Undecidability ........................................... 94
45 Summary .................................................. 97
4 REPRESENTATION .............................................. 99
46 Models ................................................... 99
47 Spurious Models ......................................... 101
48 Space ................................................... 106
49 Antinomy ................................................ 108
50 Curved Space ............................................ 109
51 Hyperspace .............................................. 112
52 Space-Time .............................................. 114
53 Automation .............................................. 117
54 Simulation .............................................. 123
55 Summary ................................................. 127
5 SYMMETRY ................................................... 129
56 Pattern ................................................. 129
57 Randomness .............................................. 130
58 Normality ............................................... 132
59 Natural Form ............................................ 134
60 Sufficient Reason ....................................... 135
61 Symmetry Operations ..................................... 137
62 Limitation .............................................. 139
63 Invariance .............................................. 141
64 Nexus ................................................... 144
65 Heuristic ............................................... 145
66 Insight ................................................. 147
67 Particularity ........................................... 150
68 Atomic Structure ........................................ 152
69 Evolution ............................................... 154
70 Genetic Structure ....................................... 157
71 Decryption .............................................. 160
72 Algorism ................................................ 162
73 Summary ................................................. 169
6 SYMBOLIZATUON .............................................. 171
74 Calculation ............................................. 171
75 Algebra ................................................. 176
76 Unnatural Numbers ....................................... 178
77 Series .................................................. 180
78 Infinitesimals .......................................... 183
79 Numerical Geometry ...................................... 190
80 Perspective ............................................. 192
81 Complex Space ........................................... 194
82 Summary ................................................. 198
7 THEORY ..................................................... 201
83 The Euclidean Paradigm .................................. 201
84 Modernization ........................................... 207
85 The Newtonian Paradigm .................................. 210
86 The Syntactical Conception of Science ................... 223
87 Synchronic Critique of the Syntactical Conception ....... 226
88 Diachronic Critique of the Syntactical Conception ....... 227
89 Inadequacy of the Syntactical Conception of Science ..... 229
90 The Semantic Conception of Science ...................... 231
91 The Syntactico-Semantic Conception of Science ........... 235
92 Demarcation ............................................. 239
93 Engineering ............................................. 241
94 Creative Nexus .......................................... 243
95 Summary ................................................. 244
BIBLIOGRAPHY .................................................. 247
INDEX ......................................................... 249
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