Part II: Examples

1. Take the sentence, “All trees are shorter than 10,000 feet”, and think about why this is a proposition based on our definition above. This sentence turns out to be false if there is at least one tree taller than 10,000 feet or it turns out to be true if there are no trees taller than 10,000 feet. The former happens to be the case, but the point is that this sentence is a proposition because it could in principle be true or false. 
2. Next, let’s take the proposition, “They write quickly.” We might rephrase this as, “They are things that write quickly.” Now it is clear that we are comparing whatever are members of the category designated by “They” (it depends on the intension) and the category “things that write quickly”. 
3. Thirdly, let’s take a look at the proposition, “dogs get crazy easily.” We can reformulate the proposition in a similar way to the last one. We can say “dogs are things that get crazy easily”. 
4. Finally, take the example, “Logic makes me love philosophy.” We can rephrase this to say “Logic is a thing that makes me love philosophy”. Now it is clear that we are comparing the categories “Logic” and “things that make me love philosophy”.

[Activity] Think of some propositions and share them with the class. Once every student has shared, get in small groups and try to identify the subject, predicate, and copula of each proposition shared. If any of them are not yet explicit, reformulate them so that they are explicit. 

It should be noted that two propositions could mean the same thing while taking differing surface forms ( i.e. different words could be used to express the same underlying idea). For example, take these two assertions: 

1. There are leafless trees. 
2. Not all trees have leaves. 

Looking at these two propositions, we can see that they mean the same thing. Namely, they both are equivalent to the proposition, “Some trees are leafless”.

 [Activity] In the same groups as before, take the propositions mentioned in the first activity and try to come up with alternative propositions that mean the same thing.