Exercise 2.1 - Answers

1

(i)

This is. If j and y are replaced by declarative sentences, the result will be a declarative sentence.

 

 
(ii)

This isn't. Replacing j and y with declarative sentences will result in ungrammatical nonsense; for instance:

            John is a man and Mary is a woman will both be there.

 

 
(iii)

This isn't. The result of replacing j by a declarative sentence will be a sentence, but not a declarative sentence. ("Please make sure that the door is shut" is not the sort of thing that can be true or false.)


 
(iv)

This is.

 

 
(v)

This isn't. The result of replacing j by a declarative sentence will be a question.

 

 
(vi)

This is. (It is, of course, similar to the previous example, and they could often be used interchangeably. But that just shows that a declarative sentence and a question can sometimes be used interchangeably.)

 

 
(vii)

Surely this isn't.  Consider, for example, "John stands up whenever Mary sits down". This does not consist of "j whenever y" together with the declarative sentences, "John stands up" and "Mary sits down". (Think of the various things that these sentences can mean if used on their own, and ask yourself whether that is what they mean in the original sentence.) Try some other examples. In fact "whenever" plays the same sort of role as, for instance, "whoever" in, "Whoever is knocking at the door is angry". And clearly "whoever j, y" is not a sentence-functor. (We could paraphrase"John stands up whenever Mary sits down" as "At whatever time John stands up, Mary sits down".)

 

 
(viii)

It isn't. Replacing  j and y with declarative sentences will not result in a single sentence. However, it must be said that Descartes sometimes talks as if "I think, therefore I am" expresses a single proposition. Nonetheless, it is surely not correct to ask, "Is it true that I think, therefore I am?" And this suggests that "I think, therefore I am" is not a single declarative sentence.

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