Rules that govern the (T) predicate are: ‘truth’ T-introduction: p -- T<p> T-elimination: T<p> -- p Now, let be a sentence that is equivalent to K the Pope a) T(<K>) I’m That is, the sentence is equivalent to the sentence that in ordinary K this sentence is true then I am the language reads: “If Pope”. To illustrate when someone might utter or conceive a sentence that corresponds to our above, Field gives the following scenario: K in passing a department store window I might see a TV (…) display, showing what I take to be my least favorite politician, leading me to say what that guy is now saying is true then “If the If in fact the display is of those passing the I’m Pope”. window, then my utterance is the empirical “equivalent given to the claim that if it itself is true then the Pope. facts” I’m The paradoxical result is that from this sentence we can prove any sentence whatsoever or in this case that I am indeed the Pope. Here is the formal derivation: 1. T(<K>) supposition 2. K 1.T-elimination 3. T(<K>) the pope 2. equivalence to a) I’m 4. the pope 1., 3. elimination I’m 5. T(<K>) the pope 1., 4. introduction I’m 6. K 5. equivalence 7. T(<K>) 6. T-introduction 8. the pope 5., 7., elimination I’m This instance of the paradox is plausibly taken to show that Curry’s logical rules are not truth-preserving. In the derivation of the necessarily false sentence, one only needs to use four rules: truth introduction, truth elimination, conditional (<>) elimination and conditional introduction. Since the only premise of the argument was discharged in the derivation of
Rules that govern the ‘truth’ (T) predicate are: T-introduction: p -- T<p> T-elimination: T<p> -- p Now, let K be a sentence that is equivalent to a) T(<K>) I’m the Pope That is, the sentence K is equivalent to the sentence that in ordinary language reads: “If this sentence is true then I am the Pope”. To illustrate when someone might utter or conceive a sentence that corresponds to our K above, Field gives the following scenario: (…) in passing a department store window I might see a TV display, showing what I take to be my least favorite politician, leading me to say “If what that guy is now saying is true then I’m the Pope”. If in fact the display is of those passing the window, then my utterance is “equivalent given the empirical facts” to the claim that if it itself is true then I’m the Pope. The paradoxical result is that from this sentence we can prove any sentence whatsoever or in this case that I am indeed the Pope. Here is the formal derivation: 1. T(<K>) supposition 2. K 1.T-elimination 3. T(<K>) I’m the pope 2. equivalence to a) 4. I’m the pope 1., 3. elimination 5. T(<K>) I’m the pope 1., 4. introduction 6. K 5. equivalence 7. T(<K>) 6. T-introduction 8. I’m the pope 5., 7., elimination This instance of the Curry’s paradox is plausibly taken to show that logical rules are not necessarily truth-preserving. In the derivation of the false sentence, one only needs to use four rules: truth introduction, truth elimination, conditional (<>) elimination and conditional introduction. Since the only premise of the argument was discharged in the derivation of
823242.2016_06_23_Jurjako_-_Do_philosophical_intuitions_need_calibration_M.docx