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Is Yes the Same as No?


Tristan L
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They are interchangeable in some languages in some cases, but even then they mean different things. Here is one analysis:

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But first, let’s look at what such little words as yes and no (linguists call them “polarity particles”) really mean. In English, one can answer a positive yes/no question, such as Did Mary pass the exam? with either Yes, she did or No, she didn’t. But if the question itself contains negation, things get a bit more complicated: Did Mary not pass the exam? can be answered in one of four ways: (i) Yes, she didn’t, (ii) No, she didn’t, (iii) No, she did, and (iv) Yes, she did. Note that (i) and (ii) mean the same thing, as do (iii) and (iv); yet, one response in each pair contains yes and the other no. What is going on here? It turns out that yes and no can each mean one of two things. In (i) Yes, she didn’t, yes means ‘I agree’ (let’s call it simply “Agree”), and in (iv) Yes, she did, it means roughly ‘that which you talk about actually happened’ (in this case, Mary’s passing the exam; let’s notate it as “+”). Similarly, in (iii) No, she did, no means ‘I disagree’ (let’s call it “Disagree”), and in (ii) No, she didn’t, it means ‘that which you talk about didn’t happen’ (let’s mark it as “−”). If we think of these as two features with two values each, we get four possible combinations of these features’ values, two in response to a positive question and two in response to a negative question: 
[Agree, +] Did Mary pass the exam? Yes, she did.
[Disagree, −] Did Mary pass the exam? No, she didn’t. 
[Agree, −] Did Mary not pass the exam? Yes, she didn’t. or No, she didn’t. 
[Disagree, +] Did Mary not pass the exam? Yes, she did. or No, she did
Some languages have a special particle for the latter combination, [Disagree, +]. For example, in French si is used exactly for this situation: Est-ce que Marie n’a pas passé l’examen? – Si, elle l’a passé. Let’s now turn to polarity particles in Russian. As in English, with positive questions all is simple: you can answer the Russian counterpart of ‘Did Mary pass the exam?’ with either Da ‘yes’ or Net ‘no’, accompanied by sdala (literally, ‘passed’) or ne sdala (‘not passed’), respectively. In negated questions, however, things are once again more complicated. Unlike in English, where Did Mary not pass the exam? can be answered in one of four ways, in Russian only three responses are possible: (i) Da, ne sdala (‘yes, she didn’t’), (ii) Net, ne sdala (‘no, she didn’t’), and (iii) Net, sdala (‘no, she did’). The option corresponding to the English (iv) above, ‘yes, she did’, is not possible in Russian in an answer to a negative question: *Da, sdala. To use the features defined above, net – like English no – can mean “Disagree” or “−”, but da – unlike English yes – can only mean “Agree”, but not “+.” Therefore, it cannot be used when the French would say si, to mean [Disagree, +]. 

Pereltsvaig, Asya. Languages of the World (pp. 428-429). 

 

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  • 2 weeks later...

There are three distinct problems under discussion here.

Problem 1: There exists a set of questions for whom the answers cannot be uniquely ascribed the value of true or false. (ie: They violate Aristotle's excluded middle.) There is no requirement that those answers to any given question of this type be both true and false, they can be neither.

This cannot be generalized. Nor can it be used to prove that true is false.

Problem 2: In order to assume that true is always false, we must have a universal set of questions such that each question maps to the universal set of answers, and a universal set of answers such that each answer maps to the universal set of questions. Because all results are equal, it also necessitates that the universal set is the empty set.

If we were to argue that the set of all questions for which all possible answers to any possible question are both true and false answers to that question is the empty set, then this would at least make some sort of sense.

Problem 3: The original proposition requires that, for all questions, the power set of all possible answers is a strict subset of itself.

It isn't enough for there to be a special case where this would be true, it would need to be true for every question. It would be true for the empty question and the empty answer, if we allow the empty set to be a strict subset of itself, but it would not be true of any other.

 

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In paraconsistent logic, one feature is that yes and no are not contradictory i.e. the logical operand "not" (~) doesn't mean negation as understood in classical logic (categorical, sentential, and predicate).

As pertains to the OP, no doesn't mean not yes

Suppose an issue pops up between persons X and Y, God's existence.

A question is asked: Does God exist? 

X: Yes! [nothing to see here]

Y: No! [since no doesn't mean not yes, God's existence hasn't been negated completely i.e. no is (partially) yes or, to be precise, may be (yes/no)]

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