Tutorial Contents Tutorial Two: Propositional Calculus: Language - Truth Functors - The Propositional
Language
- "Implicate" -
Stand-alone sentences - Scope
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Stand-alone sentences

Notice that in the suggested translation of "I will wake up unless my alarm clock breaks" was "[My alarm clock will break I will wake up]"; it was not "[I will wake up my alarm clock breaks]. The latter would certainly be wrong. The reason is that, when "My alarm clock breaks" is used on its own it means something like my alarm clock is given to breaking. And this is the meaning it will bear in "[I will wake up my alarm clock breaks]". But this is not, of course, what it means in "I will wake up unless my alarm clock breaks", when that sentence is taken in its natural way. So, when translating using one of the new truth-functors, always consider what the proposed constituent sentences would mean on their own.

In fact the safest thing, to avoid mistakes, is to use as constituent sentences only stand-alone sentences: that is, sentences which can be understood (in the right way!) without reference to the linguistic context. So translate "John is English and so is Mary" as "[John is English Mary is English]". And translate "John likes David and David likes him" as "[John likes David David likes John]". That it is say, avoid cross-reference.

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