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<blockquote data-quote="Hawkman" data-source="post: 444803" data-attributes="member: 23715"><p><strong>THE PARADOXICAL QUESTION</strong></p><p><strong></strong></p><p><strong>1 Markosian's Paradox ( paper author- Yunji Ellen Shi of the LSE)</strong></p><p>In the paper <em>The Paradox of the Question</em>, Ned Markosian told the following story: during an international conference of leading philosophers, an angel miraculously appeared. The angel claimed to be the messenger from God and granted philosophers with an opportunity to ask one question and he would then answer it truthfully. Philosophers immediately started discussing what they should ask – they wanted to ask the best question to ask. Finally they agreed on the proposal from one young logician:</p><p></p><p></p><p>This indeed seems to be a very good question, for, by asking (Q1), we can ask the best question indirectly and receive its answer, without violating the angel’s rule to ask only one question. So, when the angel appeared again, philosophers presented (Q1) to the angel. The angel replied:</p><p></p><p></p><p>Then the angel disappeared, leaving philosophers in frustration. The philosophers asked a seemingly very good question but received an answer which is totally useless. Markosian asked: What went wrong? This is the original paradox of the question. I shall call it Markosian’s paradox, following Wasserman and Whitcomb’s terms of use (Wasserman & Whitcomb, 2011).</p><p></p><p></p><p><strong>2. </strong>However, Markosian’s Paradox was shown to be ill-formulated by Theodore Sider (Sider, 1997). Sider showed that the angel is a cheater – on the one hand, (A1) is not a correct answer to (Q1). Because if it is, then (Q1) is indeed the best question to ask. And, as (A1) does not provide any useful information, (Q1) is a question whose answer is useless. A question with a useless answer can hardly be regarded as a good question. Then we arrive at a contradiction. Hence (A1) cannot be a correct answer to (Q1) – the angel did not answer the philosophers truthfully. On the other hand, (Q1) is not the best question to ask. For if it is, the answer to (Q1), whatever it may be, must take the form, "That Question, This Answer."</p><p></p><p></p><p>which is a useless answer. Hence (Q1) cannot be the best question. Thus, the philosophers in the conference have taken up the wrong belief that (Q1) is the best question to ask due to lack of the above reasoning. And they rely on the imposter angel to give them an answer. As a result, they end up with Markosian’s Paradox. Therefore, Markosian’s Paradox is not truly a paradox – the scenario is not properly-designed, for in fact the angel does not tell the truth at all and the philosophers have not actually come up with the best question to ask. In other words, the Markosian’s Paradox is ill-formulated, and we were led to the paradoxical situation because of our lack of crucial reasoning which can reveal the ill design of the situation.</p><p></p><p>If the answer given by the angel is wrong, what would the true answer to (Q1) be like? Let’s denote the best question, which is shown to be different from (Q1), by Q. Let’s also denote the answer to Q by Y. A truth-telling angel’s reply to (Q1) will be in the form</p><p></p><p></p><p>For example, Q may denote the question that what is the solution to the problem of world hunger and Y in turn denotes the solution to world hunger. However, Sider argues that (A2) generates further paradox. <span style="color: red">Since the answer (A2) to (Q1) contains both the information that Q is the best question to ask and the information in Y, which is more than the information that Y contains, which is what you get by asking Q , asking (Q1) is better than asking Q. Further, as Q is the best question by stipulation, (Q1) cannot be a better question than Q, so (Q1) must be as good as Q. </span>This means that there does not exist the unique best question to ask. Instead, there are some best questions to ask, which Q and (Q1) are two of. Hence, we should replace (Q1) which asks for the best question to ask and its answer by</p><p></p><p></p><p>Let’s consider whether (Q2) is one of the best questions to ask. Suppose it is, then one of the possible answers to (Q2), denote this answer by Z, takes the form Z=((Q2), Z), which is a useless answer, therefore (Q2) cannot be a good question, let alone one of the best questions. We arrive at a contradiction. Suppose (Q2) is not one of the best questions to ask, then the answer to (Q2) will take the form of (Q*, Y) where Q* is different from (Q2). By the same reasoning as above in red, (Q2) must be as good as Q*, then (Q2) is indeed one of the best questions, which leads us again to a contradiction. (Q2) must either be or not be one of the best questions to ask, but both cases end with a contradiction. Sider claimed that now we are confronted with the genuine paradox of the question. I shall call this paradox Sider’s paradox</p></blockquote><p></p>
[QUOTE="Hawkman, post: 444803, member: 23715"] [B]THE PARADOXICAL QUESTION 1 Markosian's Paradox ( paper author- Yunji Ellen Shi of the LSE)[/B] In the paper [I]The Paradox of the Question[/I], Ned Markosian told the following story: during an international conference of leading philosophers, an angel miraculously appeared. The angel claimed to be the messenger from God and granted philosophers with an opportunity to ask one question and he would then answer it truthfully. Philosophers immediately started discussing what they should ask – they wanted to ask the best question to ask. Finally they agreed on the proposal from one young logician: This indeed seems to be a very good question, for, by asking (Q1), we can ask the best question indirectly and receive its answer, without violating the angel’s rule to ask only one question. So, when the angel appeared again, philosophers presented (Q1) to the angel. The angel replied: Then the angel disappeared, leaving philosophers in frustration. The philosophers asked a seemingly very good question but received an answer which is totally useless. Markosian asked: What went wrong? This is the original paradox of the question. I shall call it Markosian’s paradox, following Wasserman and Whitcomb’s terms of use (Wasserman & Whitcomb, 2011). [B]2. [/B]However, Markosian’s Paradox was shown to be ill-formulated by Theodore Sider (Sider, 1997). Sider showed that the angel is a cheater – on the one hand, (A1) is not a correct answer to (Q1). Because if it is, then (Q1) is indeed the best question to ask. And, as (A1) does not provide any useful information, (Q1) is a question whose answer is useless. A question with a useless answer can hardly be regarded as a good question. Then we arrive at a contradiction. Hence (A1) cannot be a correct answer to (Q1) – the angel did not answer the philosophers truthfully. On the other hand, (Q1) is not the best question to ask. For if it is, the answer to (Q1), whatever it may be, must take the form, "That Question, This Answer." which is a useless answer. Hence (Q1) cannot be the best question. Thus, the philosophers in the conference have taken up the wrong belief that (Q1) is the best question to ask due to lack of the above reasoning. And they rely on the imposter angel to give them an answer. As a result, they end up with Markosian’s Paradox. Therefore, Markosian’s Paradox is not truly a paradox – the scenario is not properly-designed, for in fact the angel does not tell the truth at all and the philosophers have not actually come up with the best question to ask. In other words, the Markosian’s Paradox is ill-formulated, and we were led to the paradoxical situation because of our lack of crucial reasoning which can reveal the ill design of the situation. If the answer given by the angel is wrong, what would the true answer to (Q1) be like? Let’s denote the best question, which is shown to be different from (Q1), by Q. Let’s also denote the answer to Q by Y. A truth-telling angel’s reply to (Q1) will be in the form For example, Q may denote the question that what is the solution to the problem of world hunger and Y in turn denotes the solution to world hunger. However, Sider argues that (A2) generates further paradox. [COLOR=red]Since the answer (A2) to (Q1) contains both the information that Q is the best question to ask and the information in Y, which is more than the information that Y contains, which is what you get by asking Q , asking (Q1) is better than asking Q. Further, as Q is the best question by stipulation, (Q1) cannot be a better question than Q, so (Q1) must be as good as Q. [/COLOR]This means that there does not exist the unique best question to ask. Instead, there are some best questions to ask, which Q and (Q1) are two of. Hence, we should replace (Q1) which asks for the best question to ask and its answer by Let’s consider whether (Q2) is one of the best questions to ask. Suppose it is, then one of the possible answers to (Q2), denote this answer by Z, takes the form Z=((Q2), Z), which is a useless answer, therefore (Q2) cannot be a good question, let alone one of the best questions. We arrive at a contradiction. Suppose (Q2) is not one of the best questions to ask, then the answer to (Q2) will take the form of (Q*, Y) where Q* is different from (Q2). By the same reasoning as above in red, (Q2) must be as good as Q*, then (Q2) is indeed one of the best questions, which leads us again to a contradiction. (Q2) must either be or not be one of the best questions to ask, but both cases end with a contradiction. Sider claimed that now we are confronted with the genuine paradox of the question. I shall call this paradox Sider’s paradox [/QUOTE]
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