Proposition

Propositions are the meanings of declarative sentences, objects of beliefs, and bearers of truth values. They explain how different sentences, such as the English "Snow is white" and the German "Schnee ist weiß", can have identical meaning by expressing the same proposition. True propositions describe the world as it is, while false ones fail to do so.

Many theories about the nature and roles of propositions have been proposed. Realists argue that propositions form part of reality, while anti-realists reject this view. Some see propositions as sets of possible worlds, others as structured entities made of individuals and concepts, and still others as specific kinds of properties, relations, or states of affairs. Philosophers also debate whether propositions are abstract objects, psychological entities, or linguistic entities.

Propositions are important in many fields. Logicians study their logical form and inferential patterns. Linguists explore how natural language encodes propositional meaning, including issues of ambiguity and vagueness. In psychology and philosophy of mind, researchers look at how the mind handles propositions, examining propositional attitudes such as belief, desire, and intention.

Definition and roles

Propositions are like the ideas behind statements. They are what we mean when we say things like "The door is open." These ideas can be shared by people who speak different languages. For example, both "Snow is white" in English and "Schnee ist weiß" in German express the same proposition.

Propositions are also what we think about when we have beliefs, hopes, or fears. If someone believes the train will be delayed, they are thinking about the proposition that the train will be delayed. Different people can share the same proposition, even if they use different words.

Finally, propositions can be true or false. A true proposition matches how the world really is, while a false one does not. This helps us understand how our thoughts and statements relate to reality.

Types

Propositions are different depending on what they talk about and how they say it. Some say something is true, like "the tree is green," while others say it is not, like "the tree is not green." Others talk about everyone in a group, like "all humans are mortal," or just one person, like "Socrates is wise."

Propositions can also be about what if something happens, like "if it rains, then the ground gets wet." They can combine ideas with "and" or "or," such as "the tree is green and the sky is blue" or "it is windy or it is rainy." Some propositions are true just by the meaning of words, like "all bachelors are unmarried," while others depend on the real world, like "snow is white."

Others talk about what could or must be true, like "it is possible that I will win the lottery." There are also propositions about what should be done, like "you should not drink and drive." These help us understand different ways we can think and talk about the world.

Main article: classical logic

Theories

Several ideas about what propositions are and what they do have been suggested. These ideas try to explain how propositions exist, what jobs they have, and whether they have parts inside them. Other questions are about how propositions connect to language, thinking, truth, and the world.

Realism and anti-realism

Realism about propositions is the belief that propositions really exist as part of reality. Realism can mean many things. Some ways of thinking about realism explain propositions using other things. For example, some say propositions are groups of possible worlds, while others say they are built-up things, special features, types of actions, or states of things. Other theories say propositions are one-of-a-kind and can’t be explained using other things. They say only propositions can do the jobs we need them to do, like carrying truth values or showing what the world is like.

Realism is different from anti-realism, which says propositions do not exist. Anti-realists give other ways to explain things we usually think need propositions. For example, they might say other things can carry truth values or explain how different people can mean the same thing without needing propositions. Some anti-realists say propositions are just useful ideas that help us see patterns, but they are not really real.

Possible worlds

Possible worlds semantics is a way of thinking that explains propositions as groups of possible worlds. A possible world is one way things could be. For example, in our world, Paris is the capital of France, but in another possible world, Nairobi could be the capital of France. Possible worlds semantics says a proposition is the group of all possible worlds where it is true. It carries information that makes some ways of the world impossible.

Internal structure

The structured proposition view says propositions are made of parts put together in a certain way. This is because the meanings of sentences come from the meanings of their words and how they are put together. For example, the sentence “Tina is happy” has parts like “Tina”, “is”, and “happy”, and their meanings together make the whole meaning.

Ontological categories

Other theories ask what kind of thing propositions are. Some say they are like features of things. Others say they are special types of connections between things. Some think propositions are like abstract objects that exist outside of space and time, while others say they are part of our thinking or language.

Paradoxes

Studying propositions also looks at puzzles where certain ideas about propositions seem to give wrong or opposite answers. For example, the liar paradox is about a proposition that says “I am lying”. If it is true, then it must be false, and if it is false, then it must be true. This creates a loop that is hard to solve.

Other theories

Some theories say the truth of propositions can change over time. For example, “Richard Nixon is the US president” was true in 1971 but is false today. Other theories say the truth of a proposition never changes.

History

The idea of propositions started a long time ago with questions about belief, saying something is true, and puzzles about truth. Ancient Greek thinkers like Plato and Aristotle talked about what makes a belief true or false. Later, thinkers in different cultures also studied propositions. In more recent times, new ways of thinking about propositions have come up, like possible worlds semantics and ideas about their internal structure.

In various fields

Logic

Logic is the study of good thinking and strong arguments. Propositions are very important here because they are the starting points and ending points of arguments. They also show if something is true or false. Logicians look at how good reasons lead to good conclusions and how mistakes can happen in thinking. The best kind of argument is one where the conclusion has to be true if the starting points are true. To study this, logicians look at the basic patterns of propositions and arguments.

Formal systems are ways to study arguments in a very clear and organized manner. Propositional logic looks at simple ideas and how they connect using words like "not", "or", and "if ... then ...". For example, the idea "if P then Q" is made from the simpler ideas P and Q, joined by "if ... then ...". The logic in propositional logic depends only on whether the simpler ideas are true or false. Truth tables show all the ways these simpler ideas can be true or false and how that affects the whole idea.

Linguistics and philosophy of language

Linguistics and philosophy of language see propositions as the meanings of statements. They help explain how different sentences, like translations from another language, can mean the same thing. These areas study how the meaning of a sentence depends on the words used, how words fit together, and how the situation affects meaning.

Psychology, cognitive science, and philosophy of mind

Psychology, cognitive science, and philosophy of mind study propositions as what we think about when we have beliefs. For example, if someone believes that roses are red, they are thinking about the idea "roses are red". These beliefs can be things we think about on purpose or things we think without realizing it. These areas also study how we remember ideas and how computers can help us understand thinking.