| 6006 | If you say truly that you are lying, you are lying [Eubulides, by Dancy,R] |
| Full Idea: The liar paradox of Eubulides says 'if you state that you are lying, and state the truth, then you are lying'. | |
| From: report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School | |
| A reaction: (also Cic. Acad. 2.95) Don't say it, then. These kind of paradoxes of self-reference eventually lead to Russell's 'barber' paradox and his Theory of Types. |
| 9464 | One of their own prophets said that Cretans are always liars [Anon (Titus)] |
| Full Idea: One of themselves, even a prophet of their own, said, the Cretians are always liars, evil beasts, slow bellies. This witness is true. | |
| From: Anon (Titus) (17: Epistle to Titus [c.115], I.12) | |
| A reaction: The classic statement of the paradox, the word 'always' being the source of the problem. |
| 21564 | Vicious Circle: what involves ALL must not be one of those ALL [Russell] |
| Full Idea: The 'vicious-circle principle' says 'whatever involves an apparent variable must not be among the possible values of that variable', or (less exactly) 'whatever involves ALL must not be one of ALL which it involves. | |
| From: Bertrand Russell (On 'Insolubilia' and their solution [1906], p.204) | |
| A reaction: He offers this as a parallel to his 'no classes' principle. That referred to classes, but this refers to propositions, and specifically the Liar Paradox (which he calls the 'Epimenedes'). |
| 21567 | 'All judgements made by Epimenedes are true' needs the judgements to be of the same type [Russell] |
| Full Idea: Such a proposition as 'all the judgements made by Epimenedes are true' will only be prima facie capable of truth if all his judgements are of the same order. | |
| From: Bertrand Russell (The Theory of Logical Types [1910], p.227) | |
| A reaction: This is an attempt to use his theory of types to solve the Liar. Tarski's invocation of a meta-language is clearly in the same territory. |
| 19187 | The Liar makes us assert a false sentence, so it must be taken seriously [Tarski] |
| Full Idea: In my judgement, it would be quite wrong and dangerous from the point of view of scientific progress to depreciate the importance of nhtinomies like the Liar Paradox, and treat them as jokes. The fact is we have been compelled to assert a false sentence. | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 07) | |
| A reaction: This is the heartfelt cry of the perfectionist, who wants everything under control. It was the dream of the age of Frege to Hilbert, which gradually eroded after Gödel's Incompleteness proof. Short ordinary folk panic about the Liar? |
| 8940 | Tarski avoids the Liar Paradox, because truth cannot be asserted within the object language [Tarski, by Fisher] |
| Full Idea: In Tarski's account of truth, self-reference (as found in the Liar Paradox) is prevented because the truth predicate for any given object language is never a part of that object language, and so a sentence can never predicate truth of itself. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Jennifer Fisher - On the Philosophy of Logic 03.I | |
| A reaction: Thus we solve the Liar Paradox by ruling that 'you are not allowed to say that'. Hm. The slightly odd result is that in any conversation about whether p is true, we end up using (logically speaking) two different languages simultaneously. Hm. |
| 6569 | 'This sentence is false' sends us in a looping search for its proposition [Wittgenstein, by Fogelin] |
| Full Idea: According to Wittgenstein, 'this sentence is false' sends us off on an endless, looping search for the proposition to be evaluated. | |
| From: report of Ludwig Wittgenstein (Zettel [1950], §691) by Robert Fogelin - Walking the Tightrope of Reason Ch.2 | |
| A reaction: Fogelin quotes this as one possible strategy for dealing with the Liar Paradox. It doesn't sound like much of a solution to the paradox, merely an account of why it is so annoying. Wittgenstein's challenge is that the Cretan can't state his problem. |
| 21692 | If we write it as '"this sentence is false" is false', there is no paradox [Quine] |
| Full Idea: If we supplant the sentence 'this sentence is false' with one saying what it refers to, we get '"this sentence is false" is false'. But then the whole outside sentence attributes falsity no longer to itself but to something else, so there is no paradox. | |
| From: Willard Quine (The Ways of Paradox [1961], p.07) | |
| A reaction: Quine is pointing us towards type theory and meta-languages to solve the problem. We now have the Revenge Liar, and the problem has not been fully settled. |
| 14964 | The Liar reappears, even if one insists on propositions instead of sentences [Gupta] |
| Full Idea: There is the idea that the Liar paradox is solved simply by noting that truth is a property of propositions (not of sentences), and the Liar sentence does not express a proposition. But we then say 'I am not now expressing a true proposition'! | |
| From: Anil Gupta (Truth [2001], 5.1) | |
| A reaction: Disappointed to learn this, since I think focusing on propositions (which are unambiguous) rather than sentences solves a huge number of philosophical problems. |
| 14969 | Strengthened Liar: either this sentence is neither-true-nor-false, or it is not true [Gupta] |
| Full Idea: An example of the Strengthened Liar is the following statement SL: 'Either SL is neither-true-nor-false or it is not true'. This raises a serious problem for any theory that assesses the paradoxes to be neither true nor false. | |
| From: Anil Gupta (Truth [2001], 5.4.2) | |
| A reaction: If the sentence is either true or false it reduces to the ordinary Liar. If it is neither true nor false, then it is true. |
| 13507 | The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD] |
| Full Idea: In effect, the machinery introduced to solve the liar can always be rejigged to yield another version the liar. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: [He cites Hans Herzberger 1980-81] The machinery is Tarski's device of only talking about sentences of a language by using a 'metalanguage'. |
| 9138 | An infinite series of sentences asserting falsehood produces the paradox without self-reference [Yablo, by Sorensen] |
| Full Idea: Banning self-reference is too narrow to avoid the liar paradox. With 1) all the subsequent sentences are false, 2) all the subsequent sentences are false, 3) all the subsequent... the paradox still arises. Self-reference is a special case of this. | |
| From: report of Stephen Yablo (Paradox without Self-Reference [1993]) by Roy Sorensen - Vagueness and Contradiction 11.1 | |
| A reaction: [Idea 9137 pointed out that the ban was too narrow. Sorensen p.168 explains why this one is paradoxical] This is a nice example of progress in philosophy, since the Greeks would have been thrilled with this idea (unless they knew it, but it was lost). |
| 15428 | The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut' [Burgess] |
| Full Idea: It is a common view that the liar sentence ('This very sentence is not true') is an instance of a truth-value gap (neither true nor false), but some dialethists cite it as an example of a truth-value glut (both true and false). | |
| From: John P. Burgess (Philosophical Logic [2009], 5.7) | |
| A reaction: The defence of the glut view must be that it is true, then it is false, then it is true... Could it manage both at once? |
| 13372 | There are Liar Pairs, and Liar Chains, which fit the same pattern as the basic Liar [Priest,G] |
| Full Idea: There are liar chains which fit the pattern of Transcendence and Closure, as can be seen with the simplest case of the Liar Pair. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §4) | |
| A reaction: [Priest gives full details] Priest's idea is that Closure is when a set is announced as complete, and Transcendence is when the set is forced to expand. He claims that the two keep coming into conflict. |
| 13371 | If you know that a sentence is not one of the known sentences, you know its truth [Priest,G] |
| Full Idea: In the family of the Liar is the Knower Paradox, where φ(x) is 'x is known to be true', and there is a set of known things, Kn. By knowing a sentence is not in the known sentences, you know its truth. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §4) | |
| A reaction: [mostly my wording] |
| 11014 | Self-reference paradoxes seem to arise only when falsity is involved [Read] |
| Full Idea: It cannot be self-reference alone that is at fault. Rather, what seems to cause the problems in the paradoxes is the combination of self-reference with falsity. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.6) |
| 9137 | Banning self-reference would outlaw 'This very sentence is in English' [Sorensen] |
| Full Idea: The old objection to the ban on self-reference is that it is too broad; it bans innocent sentences such as 'This very sentence is in English'. | |
| From: Roy Sorensen (Vagueness and Contradiction [2001], 11.1) | |
| A reaction: Tricky. What is the sigificant difference between 'this sentence is in English' and 'this sentence is a lie'? The first concerns context and is partly metalinguistic. The second concerns semantics and truth. Concept and content.. |
| 15355 | Strengthened Liar: 'this sentence is not true in any context' - in no context can this be evaluated [Horsten] |
| Full Idea: The Strengthened Liar sentence says 'this sentence is not true in any context'. It is not hard to figure out that there is no context in which the sentence can be coherently evaluated. | |
| From: Leon Horsten (The Tarskian Turn [2011], 04.6) |
| 16336 | The liar paradox applies truth to a negated truth (but the conditional will serve equally) [Halbach] |
| Full Idea: An essential feature of the liar paradox is the application of the truth predicate to a sentence with a negated occurrence of the truth predicate, though the negation can be avoided by using the conditional. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 19.3) |