A Dichotomic Analysis of the Surprise Examination Paradox
نویسنده
چکیده
This paper proposes a new framework to solve the surprise examination paradox. I survey preliminary the main contributions to the literature related to the paradox. I introduce then a distinction between a monist and a dichotomic analysis of the paradox. With the help of a matrix notation, I also present a dichotomy that leads to distinguish two basically and structurally different notions of surprise, which are respectively based on a conjoint and a disjoint structure. I describe then how Quine's solution and Hall's reduction apply to the version of the paradox corresponding to the conjoint structure. Lastly, I expose a solution to the version of the paradox based on the disjoint structure.
منابع مشابه
Examination or Unexpected Hanging Paradox
Many mathematicians have a dismissive attitude towards paradoxes. This is unfortunate , because many paradoxes are rich in content, having connections with serious mathematical ideas as well as having pedagogical value in teaching elementary logical reasoning. An excellent example is the so-called " surprise examination paradox " (described below), which is an argument that seems at first to be...
متن کاملThe surprise examination
We examine a version of the surprise examination paradox using dynamic epistemic logic. We claim that the difficulties in the puzzle arise from the assumption that announcements are in general successful: the hearer will come to believe that they are true. This principle fails in certain specific cases, and we show that the announcement in the surprise exam paradox is an example. In dynamic epi...
متن کاملThe Surprise Examination Paradox and the Second Incompleteness Theorem
Few theorems in the history of mathematics have inspired mathematicians and philosophers as much as Gödel’s incompleteness theorems. The first incompleteness theorem states that, for any rich enough consistent mathematical theory, there exists a statement that cannot be proved or disproved within the theory. The second incompleteness theorem states that for any rich enough consistent mathematic...
متن کاملThe Paradox of the Surprise Examination
1.1. A STATEMENT OF THE PARADOX ...................................................................................................... 2 1.2. THE NATURE OF PAST APPROACHES TO THE PARADOX ...................................................................... 2 1.3. KEY POINTS TO THE ‘EPISTEMOLOGICAL NOTATION’ SOLUTION ....................................................... 3 1.4. OVERVIEW .........
متن کاملKnowledge, Time, and Paradox
Epistemic logic in the tradition of Hintikka provides, as one of its many applications, a toolkit for the precise analysis of certain epistemological problems. In recent years, dynamic epistemic logic has expanded this toolkit. Dynamic epistemic logic has been used in analyses of well-known epistemic “paradoxes”, such as the Paradox of the Surprise Examination and Fitch’s Paradox of Knowability...
متن کامل