(late edit: I have come to the conclusion that no words (or claims) have 'direct' reference to reality since all words are about people's conception. Words reference particular concepts in people's minds (i.e. the people who used or are using the words). People's conception can then directly (from memories of empirical experiences) or indirectly (though other conceptions) reference reality. By providing definitions of words we try to understand the same concept but in the light of words referencing concepts which are more familiar to us. Preferably concepts we have real life experience with i.e. those that have a more direct references to personal experiences for us. We often continue defining the definitions until our conceptions reference direct empirical experience i.e. some evidence that what we are trying to conceive have some effect in reality according to our past experiences. This is why we can never fully understand things until we have real life experience with it.) 

I just answered this question about 'Whether a definition is a proposition?' by arguing that it is. My argument is based on one of my most fundamental ideas. It is an argument inspired by Quine, which leads to the claim that there is no fundamental difference between a fact and a definition. 

"Like other Analytic philosophers before him, Quine accepted the definition of "analytic" as "true in virtue of meaning alone". Unlike them, however, he concluded that ultimately the definition was circular. In other words, Quine accepted that analytic statements are those that are true by definition, then argued that the notion of truth by definition was unsatisfactory. " (<http://en.wikipedia.org/wiki/Willard_Van_Orman_Quine#Rejection_of_the_analytic.E2.80.93synthetic_distinction>)

I will put my argument underneath so you know what I'm talking about, but my question is basically whether it is true or not that both definition claims and fact claims can (and therefore should) be verified and falsified against reality; does anyone know about any useful definitions (useful words) which have no direct or indirect reference to reality (i.e. the physical world); what words, that are not directly or indirectly verifiable against reality, not even hypothetically, do we find useful?

"... The way I understand the theory, or my spin on it, is that ultimately all definitions have to be verified and falsified in the physical world just like facts do, since they are ultimately about the same thing; they are about our experiences of reality. When you define words with other words you are at the same time making claims about what is true (i.e. propositions). (side note: a made up a story can have definitions which are not about reality, but they are still about our experiences of reality since they are about a story which exist in a book, online or memory etc.) When you claim that e=mc2 you are both saying that mc2 is a useful definition of energy and that it is true that the function of energy can be determined by these measurements. A more straight forward example; when you say that the earth is round you are at the same time saying that round is a good definition of the shape of the earth and that it is true that the earth is round (it is actually no way near round since we have high mountains and deep valleys). When you attack the argument it can be about definition or fact, but if you change one you will have to change the other in order to stay coherent. If you say that 'almost round' is a better definition of the shape of the earth, then it is also true to you that the earth is 'almost round' and not round anymore. If you conclude that it is true that the earth is round then you are also saying that the shape of the earth is a useful definition of round.

An interesting consequence of this is that 1+1 is not necessarily 2. In order to claim that 1+1 is a useful definition of 2 you have to prove it in the physical world. We have a lot of proof since we have added up a lot of apples and bananas throughout history, but there are cases when it is not true. If you add 1 pile of sand to 1 pile of sand you don't get 2 piles of sand, you only get 1. So 1x+1x is not always 2x and so it is not always true that 1+1 is 2 and so 2 is not always a useful definition of 1+1 in the same way that the shape of the earth is not always a useful definition of round (even though sometimes it is).

Summary: all definition are propositions because unless you can verify or falsify something which they are supposed to directly or indirectly be about they are not useful definitions because they ONLY try to describe something which does not exist i.e. something which does not have the slightest present or historical reference to reality. What use would 1+1=2 be if it had never been used to verify or falsify any real world events?"