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I need a logic book in the German language, preferably introductory rather than a focus on symbolic logic. The book should show how one constructs different sentence structures and how one expresses logical ideas in the German language (of course, remember that what is needed is a logic book, rather than a language learning book). For example, the difference between the propositions:

  • Alice knows who Bob is.
  • Alice does not know who Bob is.
  • Alice knows who Bob is not.(i.e ,she knows that Bob is not a square.)
  • Alice does not know who Bob is not.

And similar uses in which one can see how logically strict expressions can be constructed. I know I will never learn that in German language classes, since their concern is common communication (where there is no difference between 'Alice does not want to go to XYZ' and 'Alice wants not to go to XYZ').

Thank you for your answers.

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    So you are interested in logic as a part of classical philosophy, not in mathematical logic? – Carsten S Feb 23 '15 at 8:05
  • Is there such a book for, say, English? – Emanuel Feb 23 '15 at 15:21
  • To Garsten: rather than classical logic now, I want to be able to express logically in German, then I will go for classical logic and mathematical logic (and for that I must enrich my German math vocabulary) – Luis Vásquez Feb 24 '15 at 14:48
  • To Emanuel: 'Introduction to Logic' from Irving M. Copi and Carl Cohen will serve you extremely well. It has now become kind of a classic for the teaching of introductory logic. – Luis Vásquez Feb 24 '15 at 14:50
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I would be surprised if there is such a book, because every German book on logic very likely will assume that the reader knows how to construct sentences, and only explain how to express them in symbols. So the best you can hope for is that they use example sentences in natural language from which you can infer the construction. But I can explain to you how negation in German sentences work, if that is what you want to know.

The principle is that adverbs that can modify parts of the sentence (like nicht, but also auch and others) are put directly in front of the part of the sentence they modify. However, there are two problems:

In a main clause, the verb must be in second position, so you can't put nicht in front of it, and if there's no auxiliary, you have to find some other place where to put it. English solves this by introducing an extra auxiliary if necessary. In German, you either look for a different part of the sentence you can negate if it doesn't change the meaning too much, or you put it at the very end if you can't find such a part. This rule is somewhat vague, because "does not change too much" depends on experience what is acceptable and what is not.

The second problem is that sometimes expressions are perceived as a whole, so they are negated as a whole, and not just the verb. Again, this needs experience.

Your first examples don't really touch on these difficulties, because the logical propositions are in different sentences:

  • Alice weiß, wer Bob ist.
  • Alice weiß nicht, wer Bob ist.
  • Alice weiß, wer Bob nicht ist.
  • Alice weiß nicht, wer Bob nicht ist.

The last example is ambigous when phrased naturally ("Alice möchte nicht nach XYZ gehen"), so you can make it unambigous by using a sublause (which has the disadvantage that it sounds a bit unnatural):

  • Alice möchte nicht, dass sie nach XYZ geht. = (Alice möchte nicht) nach XYZ gehen.
  • Alice möchte, dass sie nicht nach XYZ geht. = Alice möchte (nicht nach XYZ gehen).

A third grouping ("Alice möchte (nicht nach XYZ) gehen" = It's not XYZ that Alice wants to go to) is also possible. In spoken German, you can distinguish the grouping.

In case you need to know as well, quantifiers are read "für alle/für jedes" (∀) and "es gibt" (∃), in combination "∀x.∃y" also "für alle/zu jedem x gibt es ein y", e.g.

∀x. ∀𝜀>0. ∃𝛿>0. ∀x'. |x'-x|<𝛿 => |f(x')-f(x)|<𝜀

Read as: "Für alle x gilt: Zu jedem Epsilon größer Null gibt es ein Delta größer Null, so dass für alle x Strich der Betrag der Differenz der Funktionswerte f von x Strich und f von x kleiner als Epsilon ist, wenn der Betrag der Differenz von x Strich und x kleiner als Delta ist."

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  • There is no delta in your statement. – Martin Peters Feb 23 '15 at 11:40
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    @MartinPeters: There's a perfectly fine unicode "U+1D6FF MATHEMATICAL ITALIC SMALL DELTA" in the formula. It looks like this: 𝛿. If you can't see it, maybe something is wrong with your fonts? – dirkt Feb 23 '15 at 19:45
  • How about using LaTeX? It gets the job done in a competent way. – Martin Peters Feb 24 '15 at 8:12
  • @MartinPeters: I'm fine with using LaTeX encoding, but I wasn't aware this is enabled on german.stackexchange, and I don't know how the markdown for it is supposed to look like. So if you can point my to the relevant documentation ... – dirkt Feb 24 '15 at 11:32
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    LaTeX is not enabled in GLU, as far as I know. Unicode is the best you can do. – c.p. Feb 24 '15 at 11:52
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I'm pretty sure there's no book about that in German, because I've never seen such a book in another language. The topic is just not broad enough to write a book, unless you mean mathematical logic. If that's the case, there is even online wiki-material:

For instance, Mathe für Nicht-Freaks (in German obviously) is addressed to non-experts who speak German and want to learn logic. But you (as I did) can use it the other way around: if you know some logic, i.e. the symbols there, you can read off the German expressions there.

That said, I remember we did cover in a course the diverse places where nicht can be put in the sentence.

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As an introductory book to mathematical logic you could try Mathematische Logik von Martin Ziegler, ISBN 978-3-0346-0652-3.

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