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Nicod's axiom

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178: 182: 203: 161:"Note (A) for Implications for Mathematics and Its Foundations: A New Kind of Science | Online by Stephen Wolfram [Page 1151]" 198: 47: 110: 82: 43: 77: 55: 51: 160: 192: 177: 73: 35: 32: 146: 132: 104: 25: 116:((φ | (ψ | χ)) | (((τ | χ) | ((φ | τ) | (φ | τ))) | (φ | (φ | ψ)))) 113:
discovered an equally powerful and easier-to-work-with alternative:
69:((φ | (χ | ψ)) | ((τ | (τ | τ)) | ((θ | χ) | ((φ | θ) | (φ | θ))))) 107: 90:
alone by using one inference rule, called "Nicod's modus ponens":
87: 63: 39: 28: 17: 183:
A Reduction in the number of the Primitive Propositions of Logic
54:used in the formulation of Nicod's axiom is the 8: 38:) is a formula that can be used as the sole 124: 7: 147:"Nic-mp - Metamath Proof Explorer" 133:"Nic-ax - Metamath Proof Explorer" 14: 176: 204:Theorems in propositional logic 1: 86:could be derived from this 220: 66:has the following form: 199:Propositional calculus 76:showed that the whole 48:propositional calculus 83:Principia Mathematica 44:semantically complete 78:propositional logic 111:Mordechaj Wajsberg 181:Works related to 96:2. (φ | (χ | ψ)) 24:(named after the 211: 180: 165: 164: 157: 151: 150: 143: 137: 136: 129: 56:Sheffer's stroke 219: 218: 214: 213: 212: 210: 209: 208: 189: 188: 173: 168: 159: 158: 154: 145: 144: 140: 131: 130: 126: 122: 102: 72: 61: 12: 11: 5: 217: 215: 207: 206: 201: 191: 190: 187: 186: 172: 171:External links 169: 167: 166: 152: 138: 123: 121: 118: 13: 10: 9: 6: 4: 3: 2: 216: 205: 202: 200: 197: 196: 194: 185:at Wikisource 184: 179: 175: 174: 170: 162: 156: 153: 148: 142: 139: 134: 128: 125: 119: 117: 114: 112: 109: 106: 103:In 1931, the 100: 97: 94: 91: 89: 85: 84: 79: 75: 70: 67: 65: 59: 57: 53: 49: 45: 41: 37: 34: 30: 27: 23: 22:Nicod's axiom 19: 155: 141: 127: 115: 101: 98: 95: 92: 81: 71: 68: 60: 21: 15: 50:. The only 33:philosopher 193:Categories 120:References 52:connective 46:system of 36:Jean Nicod 108:logician 29:logician 105:Polish 26:French 93:1. φ 88:axiom 74:Nicod 64:axiom 42:of a 40:axiom 18:logic 99:∴ ψ 62:The 31:and 80:of 16:In 195:: 58:. 20:, 163:. 149:. 135:.

Index

logic
French
logician
philosopher
Jean Nicod
axiom
semantically complete
propositional calculus
connective
Sheffer's stroke
axiom
Nicod
propositional logic
Principia Mathematica
axiom
Polish
logician
Mordechaj Wajsberg
"Nic-ax - Metamath Proof Explorer"
"Nic-mp - Metamath Proof Explorer"
"Note (A) for Implications for Mathematics and Its Foundations: A New Kind of Science | Online by Stephen Wolfram [Page 1151]"

A Reduction in the number of the Primitive Propositions of Logic
Categories
Propositional calculus
Theorems in propositional logic

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