In logic it is common to speak of propositions, since they are the basic units of the arguments that logic analyzes. So, what is a proposition?
In english, there are a number of types of sentences:
- interrogative sentences: when we ask a question;
- imperative sentences: when we give an order;
- declarative sentences: when we state a statement about the world.
Where does the concept of “proposition” come into this story? A proposition is that which is expressed through declarative sentences and which is true or false.
These are some examples of propositions:
- the cat has hair;
- the car is fast;
- Brazil is over five hundred years old and has a green, yellow and blue flag;
- all people are mortal.
What you might be asking yourself is why one more word (proposition) that basically indicates the same as “declarative sentence”?
What is a proposition?
Logic values clarity and conceptual distinctions are fundamental to this. Consider the same declarative sentence spoken by two different people, one fat and one thin:
- I am fat.
Is this sentence true or false? If we think that sentences are true or false, we will have to conclude that the phrase “I am fat” is both true and false: when spoken by the thin person, false; by the real, fat person. Which would be a contradiction. So, there is something expressed by the sentence, its content, which is not equivalent to the sentence, which is true or false.
So, for the sake of clarity, there is this distinction:
- Declarative sentences are phrases in a given language, grammatically correct, with a meaning.
- Propositions are the content expressed by declarative sentences and which can be true or false.
Thus, different sentences can express the same proposition:
- o carro é vermelho;
- the car is red;
- el coche es rojo;
although they are different sentences, including in another language, they express the same proposition – if one is true, all are.
And the same declarative sentence can express different propositions:
- I live in a house far from the city center.
When stated by different people, that same sentence expresses different propositions.
Walton, Douglas. Informal Logic: A Pragmatic Approach. Cambridge: Cambridge University Press, 2008.