Cresswell II 110
Paradox/liar/Cretans/Prior/Cresswell: thesis: the Cretan must, so that he can have expressed anything , have said more than one sentence. ((s) Otherwise the sentence refutes itself and thus logically expresses nothing).
Cresswell II 180ff
Paradox/Cohen/Prior/Cresswell: (Cohen 1957, p. 225)
(1), (Prior 1962)
(2).
Cohen: E.g. When the policeman testifies that everything that the prisoner says is wrong, and the prisoner explains that something that the policeman testified is true, then something that the police officer testified is wrong and something that the prisoner explains, true.
Notation: d1: "the policeman testified that:" d2:" the prisoner explains".
Logical form: (d1 p(d2p> ~ p) u d2Ep(d1 p up))> (Ep (d1P u ~ p) u Ep (d2p up))
Liar/Prior: d: "was told by a Cretan": dp (dp> ~ p)> (Ep (dp up) and Ep (dp u ~ p))
(ii) dp (dp> ~ p)> Ep Eq(p unequal q) u dp u dq).
(ii) states that the Cretans must have said at least two things.
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Prior I 81
Prior/(s): tautology p > pq.
Prior reads it like this: p E.g. Say, q: adverb.
E.g. CpAKpqKpNq: if it is the case that p, then either it is the case that p-and-q or it is the case that p-but-not-q.
Moore's paradox: the same device can be used for it, I believe that it is raining, but of course it does not rain.
Philosophers have found it remarkably difficult to explain what is wrong with it - but that happens all the time.
Prior I 2
Moore's Paradox/Prior: we only need normal truth and error (error or dishonesty as the only options).
>
Truth, >
Truthfulness, >
Error.
Prior I 85
Preface paradox/Prior: thesis that something is in the book, is not the case, can only be claimed outside of the book.
>
Levels/order, >
Description levels.
Variant: book with only one sentence: something in this book is wrong: sequence of theorems:
1. then something is wrong
2. the say that something is wrong in the book is true
3. which in turn is true
4. then something is wrong in the book and something is true. ((s) But only a statement).
Prior: But then at least two different things are said in the book - by contraposition: if nothing is wrong in the book, except that it is said that something is wrong in the book, then this is not said in the book.
Prior I 88
Preface paradox/Prior: in the book there is something wrong just cannot be the only assertion - but self-reference is not the problem.
>
Self-reference.
Prior I 96f
Preface Paradox/Prior: Parallel/Cohen E.g. If John has a brown cow which is then and only then pregnant if any animal of John is not pregnant, then any animal of John is not pregnant - Proof: e.g. hypothesi : when an animal of John is not pregnant, the cow is pregnant so if the cow is not pregnant, the other animal is pregnant - and therefore (because the cow is only pregnant, when another animal is not, then an animal of John is not pregnant. - He must have at least two animals - Prior: oddly enough, not essential that the pregnant animal must be a brown cow, just so:
for x, x means that the sky is blue and x is true, iff grass is green.
Both elements are quite irrelevant for each other - Even for the preface paradox.
Prior I 98
Preface paradox/PriorVsTarski: my concept of truth here non-Tarski: truth is not property of sentences, but of propositions. - That means, Quasi properties of quasi-objects. - Rather adverbs than adjectives. - E.g. truthfully and incorrectly.
>
Sentences, >
Propositions, >
Truth/Tarski, >
Truth Definition/Tarski.
1. L.J. Cohen (1957). The Diversity of Meaning. London, 1962.
2. Arthur Prior (1960). On a family of paradoxes. Notre Dame Journal of Formal Logic 2 (1):16-32
