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I've noticed it is often nontrivial to transcribe informal arguments into formal logic, but most introductory texts on formal logic make a show of it. Is this for pedagogical reasons only, or is there more advanced literature on this topic?

The paradoxes of implication, for me so far, have been the largest hidden trap in logic. Perhaps it is because texts strongly associate implication with if-then statements, but now I nearly want to remove implication from any logic that I would want to rely on. Negation, conjunction, and disjunction could be sufficient on their own.

I also worry about other potential hidden traps in logic, as well as the plurality of logical systems. The existence of intentional contexts seems like another hidden trap for someone who isn't aware of it. It also isn't altogether clear into which logical system one should transcribe an argument into. It is hard to see much similarity between a logic that allows "It is possible that I could be making more money than I am" and "It is possible that I'm a paper spoon." It is hard to make use of modal logic when it becomes too difficult to reign these possibilities in. Sometimes I feel lost in possible worlds just trying to articulate a mundane concept.

Is there advanced work on how to deal with these problems and others that I might not be aware of?

  • Can you give an example? Most people don't find it very difficult. All men are mortal. "For all x if x is a man then x is mortal." – user4894 Sep 7 '14 at 20:22
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    Concerning your first question: If you're looking for some kind of algorithm for translating natural language arguments into formal languages have a look at Richard Montague's work on formal semantics. Montague's target language is a higher-order modal logic, that is capable of dealing with a variety of 'intensional contexts'. For an introduction see Dowty et al.: Introduction to Montague Semantics. – sequitur Sep 7 '14 at 20:26
  • @user4894 Sure. Lets say for a particular photoelectric device, as solar input increases, electric output also increases. Therefore, as solar input decreases, electric output also decreases. Is this valid or not? At the moment, I'm not even sure. – Kevin Holmes Sep 7 '14 at 20:40
  • Thinking about it, I would use some kind of modal logic: In every situation in which the input is greater than the current input, the output is greater than the current output. Therefore, in every situation in which the input is less than the current input, the output is less than the current output. But is this logically valid? In any case, I wouldn't call this transcription trivial. – Kevin Holmes Sep 7 '14 at 20:51
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    I can only comment in saying that I share your concern. Some statements can be tricky. For starters...Here are some good tips for common English notions. legacy.earlham.edu/~peters/courses/log/transtip.htm – Casey Sep 7 '14 at 22:38
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In simple answer, no, there is no contemporary group involved in informal logic that thinks it should all be a question of formalization.

Historically, there were those including Quine who believed all statements in normal languages could be transcribed into formal logic. This claim is by and large the central thesis of logical positivism. The idea has largely passed ...

  • Nope, the project of formalization defines a very vital branch of linguistics and philosophy: (formal) semantics, whose aim it has always been to provide algorithms for formalization based on various kinds of logics stronger than classical first-order. So the idea has not passed. What has passed is Quine's ludicrous idea that classical first-order logic is the ideal target of the translation process. – sequitur Sep 9 '14 at 21:56
  • @sequitur I've never met someone in philosophy who is still writing who believes what you state above. And I know plenty of analytic philosophers. Moreover, Quine didn't believe it needed to be classical first-order logic. He did believe he didn't need the question mark or so the apocryphal story goes. – virmaior Sep 9 '14 at 21:59

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