Elements of Symbolic Logic |
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Page 32
... false or ' a ' is false and ' b ' is true ' a v b ' is false = Df ' a ' is false and ' b ' is false Ꭰ f ( 1 ) ( 2 ) This is a definition in use , given in semantic language ; it contains , not in quotes , the words ' or ' and ' and ...
... false or ' a ' is false and ' b ' is true ' a v b ' is false = Df ' a ' is false and ' b ' is false Ꭰ f ( 1 ) ( 2 ) This is a definition in use , given in semantic language ; it contains , not in quotes , the words ' or ' and ' and ...
Page 46
... false , the first two lines show that both ' b.c ' and ' a.c ' must be false ; therefore ' c ' is false , and thus ' c ' is true . This is the implication from right to left in the third line . Furthermore , when ' c ' is true , the ...
... false , the first two lines show that both ' b.c ' and ' a.c ' must be false ; therefore ' c ' is false , and thus ' c ' is true . This is the implication from right to left in the third line . Furthermore , when ' c ' is true , the ...
Page 68
... false ; the first is also false when the implication is interpreted in the connective sense . But the con- clusion is true . Whereas the propositions occurring in an inference are either true or false , the inference itself is not ...
... false ; the first is also false when the implication is interpreted in the connective sense . But the con- clusion is true . Whereas the propositions occurring in an inference are either true or false , the inference itself is not ...
Contents
Logic and language | 1 |
Different levels of language | 9 |
Continued PAGE | 14 |
Copyright | |
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Common terms and phrases
adjunctive implication all-operators all-statement analysis apply argument variables asserted bound variable calculus of functions calculus of propositions called combination conception connective implication connective operations constructed contradiction conversational language corresponding defined definition denote derivation disjunction disjunctive normal form elementary propositions equisignificance example existence existential operators false follows formula free variables func function f(x given higher calculus holds implicans instance interpretation introduced kind left-hand side meaning ment metalanguage metatheorem modalities negation line nomological statements notation object language operand ɔ g(x Peter possible predicate premises proof of consistency propositional expression propositional function propositional operations propositional variables reference regarded relation represents result right-hand side rule for free rule of inference rule of substitution schema sentence simple calculus square of opposition synthetic formulas T-cases tautology theorem things tion token transformed transition truth tables truth-values two-place function usage word