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- Roger Wertheimer (2008). The Paradox of Translation. In B. . Lewandowska-Tomaszczyk & M. Thelen (eds.), Translation and Meaning. Hogeschool Zuyd.
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This commentary attempts to show that the inverted Turing Test (Watt 1996) could be simulated by a standard Turing test and, most importantly, claims that a very simple program with no intelligence whatsoever could be written that would pass the inverted Turing test. For this reason, the inverted Turing test in its present form must be rejected.
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The translation of Schleiermacher's key phrase ‘das schlechthinnige Abhängigkeitsgefühl’ is a matter of some contention. It has been suggested that the traditional translation (‘feeling of absolute dependence’) is in fact inaccurate and that it should be replaced with the accurate ‘absolute feeling of dependence’. This change would have serious implications for our understanding of Schleiermacher's theology. This essay examines the case for and against a change of translation. It concedes that the change is demanded if one strictly adheres to the rules of grammar but that there are several reasons for putting those rules to one side and holding firm to the traditional translation.
In Part V of his Discourse on the Method, Descartes introduces a test for distinguishing people from machines that is similar to the one proposed much later by Alan Turing. The Cartesian test combines two distinct elements that Keith Gunderson has labeled the language test and the action test. Though traditional interpretation holds that the action test attempts to determine whether an agent is acting upon principles, I argue that the action test is best understood as a test of common sense. I also maintain that this interpretation yields a stronger test than Turing's, and that contemporary artificial intelligence should consider using it as a guide for future research.
A teacher announced to his pupils that on exactly one of the days of the following school week (Monday through Friday) he would give them a test. But it would be a surprise test; on the evening before the test they would not know that the test would take place the next day. One of the brighter students in the class then argued that the teacher could never give them the test. It can't be Friday, she said, since in that case we'll expect it on Thurday evening. But then it can't be Thursday, since having already eliminated Friday we'll know Wednesday evening that it has to be Thursday. And by similar reasoning we can also eliminate Wednesday, Tuesday, and Monday. So there can't be a test!The students were somewhat baffled by the situation. The teacher was well-known to be truthful, so if he said there would be a test, then it was safe to assume that there would be one. On the other hand, he also said that the test would be a surprise. But it seemed that whenever he gave the test, it wouldn't be a surprise.
Resolution of Frege's Puzzle by denying that synonym substitution in logical truths preserves sentence sense and explaining how logical form has semantic import. Intensional context substitutions needn't preserve truth, because intercepting doesn't preserve sentence meaning. Intercepting is nonuniformly substituting a pivotal term in syntactically secured truth. Logical sentences (GG: Greeks are Greeks; gg: Greece is Greece) and their synonym interceptions (GH: Greeks are Hellenes; gh: Greece is Hellas) share factual content (extrasentential reality asserted). Semantic (cognitive) content is (identifiable with) factual content in synthetic predications, but not logical sentences and interceptions. Putnam's Postulate (Logical form has semantic import) entails interception nonsynonymy. Syntax and vocabulary explain only the factual content of synthetic predications; extrasentential reality explains their truth. Construction of logical factual content explains logical necessity. Terms retain objectual reference, but logical syntax preempts their function (and thereby function of extrasentential reality) in explaining truth. Grasping the facts GG/gg assert entails understanding this. Understanding what GH states requires some recognition that GH must be true just because GmH ("Greeks" means Hellenes), and GmH ("Greeks" means what "Hellenes" means) state an empirical fact. GH (but not GG) is standardly used to express that fact. Church's Test exposes puzzles. QMi sentences ("Ex" means Ex), and QTi sentences (p≡it is true p≡"p" is true) are metalogical necessities, true by syntax. Intercepting QMi creates empirical QM contingencies ("Ex" means Ey). Synonymy turns semantic contingencies (GmH/GmH) into metalogical (GmG/GmG) and lexical (GH) necessities. That transformation is syntactic, via the syntactic duality of definite descriptions. GmH is a contingent copredication, and a lexically necessary referential identity with rigidly codesignating indexicals. Metalogical sentences may be about expressional matter or what it expresses (meaning, proposition). GG (Griechen sind Griechen) has GG's semantic content, but the referent expression switches. Metalogical syntax secures truth by self-referential quotational indexing. Metalogically, referents are identified with intrasentential replica. Extrasentential identifications are metalogically irrelevant.
Although it was traditionally thought that self-reference is a crucial ingredient of semantic paradoxes, Yablo (1993, 2004) showed that this was not so by displaying an infinite series of sentences none of which is self-referential but which, taken together, are paradoxical. Yablo’s paradox consists of a countable series of linearly ordered sentences s(0), s(1), s(2),... , where each s(i) says: For each k > i, s(k) is false (or equivalently: For no k > i is s(k) true). We generalize Yablo’s results along two dimensions. First, we study the behavior of generalized Yablo-series in which each sentence s(i) has the form: For Q k > i, s(k) is true, where Q is a generalized quantifier (e.g., no, every, infinitely many, etc). We show that under broad conditions all the sentences in the series must have the same truth value, and we derive a characterization of those values of Q for which the series is paradoxical. Second, we show that in the Strong Kleene trivalent logic Yablo’s results are a special case of a more general fact: under certain conditions, any semantic phenomenon that involves self-reference can be emulated without self-reference. Various translation procedures that eliminate self-reference from a non-quantificational language are defined and characterized. An Appendix sketches an extension to quantificational languages, as well as a new argument that Yablo’s paradox and the translations we offer do not involve self-reference.
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