# Propositions

A proposition is a statement of fact. It is a claim about the way the world is, or the way some part of the world is. The following are examples of propositions:

• “The sky is blue”
• “I don’t like cheese”
• “2+2=4”
• “Paris is the capital of Germany”

Propositions are abstractions. This means that a proposition is not the same as the sentence used to express the proposition. Indeed, the same proposition can generally be expressed in many different ways. For instance, all of the following sentences express the same proposition:

• “Two plus two is equal to four”
• “Two added to two yields a total of four”
• “2 + 2 = 4”
• “zwei plus zwei gleich vier“
• “二加二等於四”

A proposition is also not the same as the state of affairs (or fact) to which it refers. Thus, the proposition “grass is green” is distinct from the fact that grass actually is green. A proposition has a truth value (usually either true or false), while a fact or state of affairs does not – it simply exists. To put it another way, to refer to the sentence “the grass is green”, I could point at the computer screen displaying these words, while to refer to the fact of grass being green, I would point to the grass in question. I cannot, however, point to the proposition ‘grass is green’, because propositions are abstractions and so do not have physical existence. Philosophers typically say that sentences express propositions, which in turn refer to facts or states of affairs in the real world.

While propositions are very common in speech, there are still many things people say that are not propositions. Other types of speech include:

• Questions: “why is the sky blue?”
• Injunctions: “don’t look at the sky.”
• Exclamations: “oh my gosh, the sky!”

Propositions are unique in that they make factual assertions about the way things are, or the way the world is. As such, they are the most common object of study in philosophical logic.

Propositions possess what are called ‘truth values’. Usually there are taken to be two possible truth values: true and false. Exactly what it means for a proposition to be ‘true’ is subject to some debate. For our purposes here, however, we shall take it to mean ‘corresponds to the way things really are’. We may not know whether a proposition is true or false, but (if it is a meaningful proposition and not merely gibberish) it is always either one or the other. Questions, injunctions, and exclamations do not have truth values, since it does not make sense to ask, for example, whether the utterance “what is the capital of France?” is true or false.

In real life, people very often make assertions that are vague, and so can be true in one sense or context, but not in another. For example, the claim ‘politicians are usually intelligent’ is vague because its truth value will likely depend upon what exactly we mean by ‘intelligent’, and who counts as a ‘politician’. Exactly how to deal with vague propositions is subject to dispute, though generally it is thought that vague propositions can still have a truth value, even if we aren’t sure exactly what it is.