# What is the logical form of a question?

A common thread in Analytic philosophy, starting with Frege, and through Russell, Wittgenstein and the Logical Positivists, is that there is an ideal and purely logical language, with which we can solve philosophical problems.

1. Can a question be put into a purely logical form in such an ideal language?
2. Are there any extensions of classical logic (in the way that modal logic and temporal logic are extensions of classical logic) that allow for formally stating questions?
• Isn't any logical proposition a formally stated question? May 7, 2015 at 2:55
• @DanBron Not really. Propositions are typically thought of as having truth values, but there isn't any meaningful way to describe questions as being either true or false. May 7, 2015 at 6:32
• You can see Jaakko Hintikka, Interrogative Logic and M.J.Cresswell, The Logic of Interrogatives. May 7, 2015 at 8:54
• In the "Handbook of Logic and Language" (edited by Johan van van Benthem & Alice G.B. ter Meulen) there is a long chapter on questions. It explains the formal semantics of questions. May 7, 2015 at 11:29
• Here is nice looking introduction, it goes through the basic proposals for the semantics of questions in chapter 2: Introduction to the semantics of questions Some familiarity with formal semantics (like Montague semantics) is probably useful, but that paper even includes a short introduction to the basics. May 7, 2015 at 23:50

I think the standard response here is to call upon two particular parts of the Frege/Russell tradition - the first being the concept of a Proposition (SEP) and the second being the concept of Logical Form (another SEP).

Consider a simple question like "Is it raining outside?". One way to go about working out what it is that this question is asking is to try to determine under what conditions would this question receive an affirmative answer, and what would receive a negative answer. Naturally, we would say that it would be answered affirmatively if, and only if, it is raining outside, and negatively if, and only if, it is not raining outside.

Now in one interpretation of the analytic philosophical project, what we're doing is constructing a theory of propositions (that we take to represent the bearers of semantic value) in a formal framework, and then using this theory to further interpret assertion more generally by saying that the logical form of a statement or argument reduces to the expression of either propositions or of relations featuring at least propositions and speakers as constitutive elements.

The logical form of my question then will feature the proposition "It is raining outside" as a proper part. Is there something else that might be necessary here? Well, perhaps we might also add that in asking a question, I (the speaker) am addressing this question to you (a prospective answerer), in a manner which suggests that I do not know the answer but hope/believe that you do and want you to tell me if you do.

So. Let's suppose we have a proposition-forming operator '`k`' to form a proposition `[k]` from the sentence `k`. Perhaps a candidate for a correct logical form of "Is it raining outside?" asked by A to B would be something like this:

``````¬knowsThat(A,'it is raining outside') ^ ¬knowsThat(A,¬'it is raining outside')
^ believesThat(A,knowsThat(B,'it is raining outside') v knowsThat(B,¬'it is raining outside'))
^ (desiresThat(A,
knowsThat(B,'it is raining outside') -> asserts(B,'it is raining outside')
^ knowsThat(B,¬'it is raining outside') -> asserts(B,¬'it is raining outside')
)
``````

A bit unwieldy perhaps, but then that's why we have natural language to simplify all of this!

• To add a comment that I think would just gum up the answer, the idea here is that you're specifically including this stuff into the theory of logical form rather than into the logic. You don't specifically need any extension to the predicate logic that we take to form the basis of the theory of propositions in order to apply that logic to a theory of the logical form of expressions. May 7, 2015 at 10:40
• This make sense, but then this means that question has no status without the person asking it. On one hand I am inclined to agree with you (and the implications for philosophy of mind and intentionality are interesting). On the other hand, I still feel that some questions should be able to have a status independent of the asker? "Does P=NP ?" , "Is there life on other planets?" seems to be meaningful enough to have a status independent of the individual asker. May 8, 2015 at 13:10
• @AlexanderSKing I see what you mean, but I might respond by saying that although there's a distinction between asking whether P=NP and asserting that P=NP, independently of being asked or asserted, the underlying content of both is the same in terms of propositional meaning; namely, the proposition that P=NP. May 9, 2015 at 9:16

I'm not at all capable of answering your second question, but could we not formulate the questions by means of equations and unknowns? Such frugal formulation will, however, deprive our question of all the nigh-infinite gamut of subtle connotations, given that we don't always ask questions for the sole purpose of finding an answer to them.

I'm not sure that this is possible to solve philosophical questions by such a method; first it is true that to formulate a question correctly is important; but one might be asking the wrong question; and even if the right question is asked there still remains the hard and difficult task of solving it; it may simply be insoluble.

• See my comment to the other answer: Some open questions in math and science are valid and should have some sort of status independent of the asker. Why can't we have an interrogation quantifier along with the existential and universal ones? May 9, 2015 at 14:17
• Well you were asking about philosophical questions being put into a logical form; if you're asking about questions per se - then I think you can so long as it's about extracting formal facts from a formal world; ie asking questions about what we know already; or can be deduced from it. May 9, 2015 at 14:39
• But for the analytic crowd (see the names I mentioned), there's no real difference between philosophical questions and the examples I gave later in the comments. You know all that jazz about being the handmaiden of science. May 9, 2015 at 14:42
• I think what you say is true for some but not all; certainly Russell didn't judging from what he wrote in the introduction to Wittgensteins Tractatus; I'd say that a question like does P=NP turns into a proposition if it has a settled answer, one way or the other; but that doesn't tell me the why. May 9, 2015 at 14:55
• Ok, I think I see what you mean; philosophical questions in the sense that the analytic crowd considers them. May 9, 2015 at 14:57