ellauri096.html on line 155: In the twentieth century, suspicions about conceptual pathology were strongest for the liar paradox: Is ‘This sentence is false’ true? Philosophers who thought that there was something deeply defective with the surprise test paradox assimilated it to the liar paradox. Let us review the assimilation process.
ellauri096.html on line 182: Is (K) true? On the one hand, if (K) is true, then what it says is true, so no one knows it. On the other hand, that very reasoning seems to be a proof of (K). Proving a proposition is sufficient for knowledge of it, so someone must know (K). But then (K) is false! Since no one can know a proposition that is false, (K) is not known.
ellauri096.html on line 189: Trivially, false propositions cannot be proved true. Are there any true propositions that cannot be proved true?
ellauri096.html on line 199: Several commentators on the surprise test paradox object that interpreting surprise as unprovability changes the topic. Instead of posing the surprise test paradox, it poses a variation of the liar paradox. Other concepts can be blended with the liar. For instance, mixing in alethic notions generates the possible liar: Is ‘This statement is possibly false’ true? (Post 1970) (If it is false, then it is false that it is possibly false. What cannot possibly be false is necessarily true. But if it is necessarily true, then it cannot be possibly false.) Since the semantic concept of validity involves the notion of possibility, one can also derive validity liars such as Pseudo-Scotus’ paradox: ‘Squares are squares, therefore, this argument is invalid’ (Read 1979). Suppose Pseudo-Scotus’ argument is valid. Since the premise is necessarily true, the conclusion would be necessarily true. But the conclusion contradicts the supposition that argument is valid. Therefore, by reductio, the argument is necessarily invalid. Wait! The argument can be invalid only if it is possible for the premise to be true and the conclusion to be false. But we have already proved that the conclusion of ‘Squares are squares, therefore, this argument is invalid’ is necessarily true. There is no consistent judgment of the argument’s validity. A similar predicament follows from ‘The test is on Friday but this prediction cannot be soundly deduced from this announcement’.
xxx/ellauri186.html on line 636: Which one is true? We simply do not know for sure. The facts about his death have not been historically proven, beyond a reasonable doubt. In fact, there is no historical consensus on the person of Matthew. There are several conflicting accounts, and the Greek text does not state anywhere he was an eyewitness (and therefore a disciple). Maybe he was a fake. The problem is the gospel of Matthew is anonymous: the author is not named within the oldest surviving text, and the superscription "according to Matthew" was added some time in the second century, although the gospel doesn't state it's an eyewitness account. The historically very likely incorrect tradition that the author was the disciple Matthew begins with the early Christian bishop Papias of Hierapolis.
xxx/ellauri202.html on line 352: But was Frank’s account true? Let's have closer look at a controversial claim!
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