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 							An Accessible Introduction to Serious Mathematical Logic
  Tony Roy
  version 7.1
  pages -
1003
  March 19, 2016
  
  ---------------------------
  
 
Preface.................................................. i
  Contents
.................................................v
  Named Definitions
........................................ix
  Quick Reference Guides ..................................xvii
  I
The Elements: Four Notions of Validity ...................1
  1 Logical Validity and Soundness
............................4
  1.1 Consistent Stories . . . . . . . . . . . . . . . . . . . 5
  1.2 The
Definitions . . . . . . . . . . . . . . . . . . . . 10
  1.3 Some Consequences . . . . . . . . . . . . . . . . . .
. 22
  2 Formal Languages......................................... 30
  2.1 Sentential Languages . . . .. . .
. . . . . . . . . . . 31
  2.2 Quantificational Languages . . . . . . . . . . . . . . 46
  3 Axiomatic
Deduction...................................... 67
  3.1 General . . . . . . . . . . . . . . . . . . . . . . . .
68
  3.2 Sentential . . . . . . . . . . . . . . . . . . . . . . 72
  3.3 Quantificational . . . . . . . . . .
. . . . . . . . . 80
  4 Semantics ................................................96
  4.1 Sentential . . . .
. . . .. . . . . . . . . . . . . . . 96
  4.2 Quantificational . . . . . . . . . .... . . . . . . . .113
  5
Translation .............................................138
  
  5.1 General . . . . . . . . . . . . . . . .
. . . . . . . 138
  5.2 Sentential . . . . . . . . . . . . . . . . . . . . . . 140
  5.3 Quantificational . .
. . . . . . . . . . . . . . . . . 170
  6 Natural Deduction....................................... 208
  6.1
General . . . . . . .... . . . . . . . . . . . . . . . 208
  6.2 Sentential . . . . . . . . . . . . . . . . . . . .
. . 218
  6.3 Quantificational . . . . . ..... . . . . . . . . . . . 270
  6.4 The system ND+ . . . . . . . .
. ... . . . . . . . . . 318
  II Transition: Reasoning About Logic ......................329
  7 Direct
Semantic Reasoning ...............................331
  7.1 General . . . . . . . . . . . . . . . . . . . . . . .
332
  7.2 Sentential . . . . . . . . . . . . . . . . . . . . . . 335
  7.3 Quantificational . . . . . . . . .
. . . . . . . . . . 350
  8 Mathematical Induction ..................................378
  8.1 General
Characterization . . . . . . . . . . . . . . . 378
  8.2 Preliminary Examples . . . . . . . . . . . . . . . . .
384
  8.3 Further Examples (for Part III) . . .. . . . . . . . . 397
  8.4 Additional Examples (for Part IV) .
. . . . . . . . . 407
  III Classical Metalogic: Soundness and Adequacy ...........423
  9 Preliminary Results
.....................................426
  9.1 Semantic Validity Implies Logical Validity . . . . . . 426
 
9.2 Validity in AD Implies Validity in ND .. . . . . . . . 431
  9.3 Validity in ND Implies Validity in AD . . . .
. . . . 438
  9.4 Extending to ND+ . . . . . . ... . . . . . . . . . . . 459
  10 Main
Results........................................... 464
  10.1 Soundness . . . . . . . . . . . . . . . . . . . . .
.465
  10.2 Sentential Adequacy . . . . . . . . . . . . . . . . . 472
  10.3 Quantificational Adequacy: Basic
Version . . . . . . 483
  10.4 Quantificational Adequacy: Full Version . . . . . . . 498
  11 More Main
Results ......................................514 						

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