The Hangman and the Surprise Test_ Dealing with a Paradox

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					        The Hangman and the Surprise Test, Dealing with a Paradox –

Alexander P. (1950) Pragmatic Paradoxes (in Mind, vol.59(236), p536-538)

Ande rson A.C. (1983) The Paradox of the Knower (in Journal of Philosophy, vol.80, p338-
Abstract: The paradox of the knower is a formalized version of the hangman paradox. It uses
     Gödel numbering to produce self reference and results in an inconsistency between
     apparently evident principles about knowledge and inference and Robinson’s arithmetic
     Q. The author examines a number of possible solutions and concludes that the predicates
     expressing the knowing and inference relations must be sorted into hierarchies
     analogous to Tarsi’s hierarchy for the truth predicate.

Blau U. (1983) Vom Henker, vom Lügner und von ihrem Ende (in Erkenntnis, vol.19, p27-
Abstract: The hangman paradox has a simple solution. The amazing refutation of the judge’s
     decree rests on the axiom of ‘knowledge conservation’. This axiom is false under
     unfavourable conditions. You can have a perfect piece of knowledge in the ordinary
     sense, i.e., a true justified conviction, and yet be unable to conserve it. More interesting
     than its solution is the element of self-reference connecting the hangman via Moore’s
     paradox and Buridan’s epistemic paradox with the liar. This one, I think, has also a
     natural solution, but less simple. The basic idea is given here, but the technical treatment
     goes far beyond this paper. It requires a strong, but conservative extension of classical
     and three-valued logic to a six- valued logic with infinitely many ‘levels of reflection’

Blau U. & Blau J. (1995) Epistemische Paradoxien, Teil 1 (in Dialectica, vol. 49(2-4), p169-
Abstract: A satisfactory analysis of the well-known Hangman Paradox is not known to us.
     Two theses: 1) The logical solution of the Hangman Paradox(es) is easy and
     disappointing. 2) The origins of the(se) paradox(es) are manyfold and inexhaustible. We
     analyse particularly perspicuous timeless version of the paradox due to Hollis (1986). In
     a sequel which is to appear in Dialectica we analyse two version of the original
     Hangman Paradox.

Cargile J. (1967) The Surprise Test Paradox (in Journal of Philosophy, vol.64, p550-563)

Chapman J.M. & Butler R.J. (1965) On Quine’s ‘So-called Paradox’ (in Mind, vol.74(295),

Cohen L.J. (1950) Mr O’Connor’s ‘Pragmatic Paradoxes’ (in Mind, vol.59(233), p85-87)

Galle P. (1981) More on the Surprise Test Puzzle (in Informal Logic, vol.3, p21-22)
Abstract: In Informal Logic vol.2(2), H. Nielsen outlined a version of the surprise test puzzle
     and presented his analysis. In this note, it is argued that in Nielsen’s version of the
     puzzle, the students’ argument that no test can occur involves a variation of ‘begging the
Halpern J. & Moses Y. (1986) Taken by Surprise: the Paradox of the Surprise Test Revisited
     (in Journal of Philosophical Logic, vol.15, p281-304)
Abstract: We re-examine the surprise test paradox (also called the hangman paradox) and
     translate it into formal logic with a fixed-point operator and a provability operator. We
     consider four possible translations. The first is contradictory, the second is consistent
     with the test being given any day of the week, the third rules out the last day (but no
     other), while the fourth is paradoxical in that it is consistent if and only it is inconsistent!

Jongeling B. & Koetsier T. (1993) A Reappraisal of the Hangman Paradox (in Philosophia,
     vol.22(3-4), p299-311)
Abstract: The hangman paradox or unexpected examination paradox is usually solved by
     construing it as a form of Liar's paradox. A different solution is proposed, based on the
     idea that a reference shift occurs. The proposed solution is claimed to do more justice to
     the spirit of the original. The relationship between informal and formalized versions of
     logical paradoxes is discussed.

Kiefer J. & Ellison J. (1965) The Prediction Paradox Again (in Mind, vol.74, p426-427)

Lyon A. (1959) The Prediction Paradox (in Mind, vol.68, p510-517)

Meltzer B. & Good I.J. (1965) Two Forms of the Prediction Paradox (in British Journal for
     the Philosophy of Science, vol.16, p50)
Abstract: Two forms of the prediction paradox are here resolved and thus correcting a
     previous article by Meltzer in Mind (vol.73, 1974).

Meschl U. (1989) Ein klein Uberraschung für Gehirne im Tank: eine skeptische Notiz zu
     einem antiskeptischen Argument (in Zeitschrift für philosophische Forschung, vol.43,
Abstract: The paper is concerned with Pr. Putnam’s recent argument that ‘we’ cannot be
     brains in a vat. It is argued that brains in a vat are in a situation parallel to that of the
     prisoner of the Hangman Paradox. In addition, some remarks are made concerning
     metaphysical realism and the idea of consistency.

Nielsen H.A. (1979) A Note on the Surprise Test Puzzle (in Informal Logic, vol.2, p6-7)
Abstract: A promised surprise test is one whose date a student could not reasonably predict
     on his way to class. Friday seems to be out, for if no test came in by Thursday, Friday
     would be no surprise, and the same reasoning seems to hold for Thursday, Wednesday
     and so forth. The fallacy: a human cannot reason himself forward to the end of the week,
     but must live through the intervening days one by one.

O’Connor D.J. (1948) Pragmatic Paradoxes (in Mind, vol.57(227), p358-359)

O’Connor D.J. (1948) Pragmatic Paradoxes and Fugitive Propositions (in Mind, vol.60(240),

Olin D. (1986) On a Paradoxical Train of Thought (in Analysis, vol.46, p18-20)
Abstract: A paradox presented by Martin Hollis (Analysis 44.4) is shown to be a new version
     of the familiar prediction paradox. What chiefly distinguishes Hollis’ version from the
     standard ones is that it is based on an arithmetic example and involves infinitely many
Olin D. (1988) Predictions, Intentions and the Prisoner’s Dilemma (in Philosophical
     Quarterly, vol.38, p111-116)
Abstract: It has recently been argued by Roy Sorensen that Kavka’s intentional puzzle is a
     new version of the prediction paradox (the paradox of the surprise test). The first stage
     of this paper discredits Sorensen’s argument by showing that it can be extended to the
     prisoner’s dilemma, thereby reaching the conclusio n that the prisoner’s dilemma and the
     prediction paradox are, at the core, one and the same. The second stage analyses the
     flaws in the argument.

Pitioni V. (1983) Das Vorhersageparadoxon (in Conceptus, Zeitschrift für Philosophie,
      vol.17, p88-92)
Abstract: The prediction paradox is shown to bet the consequence of two simple mistakes.
      First: concepts like ‘unexpected’ refer to at least binary relations and not to unary
      properties of events. Second, even if the meaning of a concept remains unchanging, its
      extension may change. At last it is shown that certain forms of self- reference cannot be
      excluded by logical means.

Scriven M. (1951) Paradoxical Announcements (in Mind, vol.60(239), p403-407)

Sorensen R. (1993) The Earliest Unexpected Class Inspection (in Analysis, vol.53(4), p252)
Abstract: This is a reverse version of the surprise test paradox--though one that goes
     "forward" in time. Suppose everybody knows that university regulations require the
     chairman to evaluate the performance of new faculty. The basis must be a surprise
     inspection and must be done as soon as possible. Here is an argument for its
     infeasibility. The inspection cannot take place on the first day because the teacher would
     know it was the first available day. Once this day is eliminated, we must also rule out
     the second day because it is now the first available day. This reasoning can be repeated
     for all the alternatives--apparently demonstrating that the earliest unexpected inspection
     is impossible.

Sorensen R. (1999) Infinite "Backward" Induction Arguments (in Pacific Philosophical
     Quarterly, vol.80(3), p278, 283)
Abstract: A large family of paradoxical arguments have been subsumed under the label
     "backward induction arguments". These include the iterated prisoner's dilemma, the
     centipede game, and the surprise test paradox. They are described as backward because
     they begin by considering a future hypothetical alternative, rule it out, and then rule out
     each predecessor. Thus, they go backward in time ruling out finitely many alternatives. I
     present examples that go forward in time and eliminate infinitely many alternatives.
     These pose problems for solutions that focus on common knowledge assumptions.

Sorensen R. (2002) Formal Problems about Knowledge (in The Oxford Handbook of
     Epistemology, Moser, Paul K (ed), p539-568)
Abstract: The hopes of the modal logicians who developed epistemic logic are illustrated
     with Fitch's proof for unknowables and the surprise test paradox. The epistemology of
     proof is covered with the help of the knower paradox. One of the solutions to this
     paradox is that knowledge is not closed under deduction. The broader history of this
     manoeuvre is reviewed along with the relevant alternatives model of knowledge. This
     model assumes that 'know' is an absolute term like 'flat'. I argue that epistemic absolute
     terms differ from extensional absolute terms by virtue of their sensitivity to the
     completeness of the alternatives. This asymmetry undermines recent claims that there is
     a structural parallel between the supervaluational and epistemicist theories of vagueness.

Sorensen R. (2004) Paradoxes of Rationality (in The Oxford Handbook of Rationality, Mele
     A.R.(ed), p257-275)
Abstract: This survey provides a bird's eye view of trouble spots for the theory of rational
     choice and rational belief. The troubles take the form of apparent counterexamples to
     attractive generalizations, such as the principle of charity, the transitivity of preferences,
     and the principle that utility should be maximized. The following paradoxes are
     discussed: fearing fiction, the surprise test paradox, Pascal's wager, Pollock's 'ever better
     wine', Newcomb's problem, the iterated prisoner's dilemma, Kavka's paradoxes of
     deterrence, backward inductions, the bottle imp, Moore's problem, weakness of will, the
     Ellsberg paradox, Allais's paradox, and Peter Cave's puzzle of self- fulling belief.

Weiss P. (1952) The Prediction Paradox (in Mind, vol.61(242), p265-269)

Windt P.Y. (1973) The Liar in the Prediction Paradox (in American Philosophical Quarterly,
     vol.10, p65-68)
Abstract: An argument schema is introduced which seems to offer a way to disprove any
     proposition whatever. It is shown to owe its apparent power to a self referential
     proposition of the sort involved in the liar paradox. It is argued that the prediction
     (surprise examination) paradox is a special version of this schema, and does not require
     different treatment than does the liar. Ways are suggested to make non paradoxical
     announcements about unpredictable future events.

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