A priori and a posteriori facts for kids

A priori (pronounced "ah pree-OR-ee") and a posteriori (pronounced "ah pos-ter-ee-OR-ee") are Latin phrases used in philosophy. They help us talk about different kinds of knowledge, how we know things (called justification), or different ways of making an argument. The main difference is whether they rely on experience.

• A priori knowledge means knowing something before or without needing any experience. It comes from pure thought or reason. Think of things like mathematics, simple true statements (like "all bachelors are unmarried"), or figuring things out using logic.
• A posteriori knowledge means knowing something after or because of experience. It depends on what we observe or learn from the world around us. Most science is a posteriori, like knowing that water boils at 100 degrees Celsius, or knowing facts from history.

These ideas first came from the ancient Greek philosopher Aristotle. His works on logic, called Organon, talked about how we can reason. Prior analytics (a priori) was about deductive logic, which starts from general rules to reach specific conclusions. Posterior analytics (a posteriori) was about inductive logic, which uses observations to find general rules.

Later, these terms appeared in Euclid's famous book Elements about geometry. They became very well-known thanks to Immanuel Kant, an important German philosopher from the 1700s. He wrote a book called Critique of Pure Reason. Usually, these terms are used to describe "knowledge" (like "a priori knowledge"), but they can also describe other things, like "truth."

What are some examples?

A priori knowledge

Imagine someone tells you: "If George V was king for at least four days, then he was king for more than three days."

You don't need to look up history books or ask anyone to know this is true. You can figure it out just by thinking about what the words mean. If something is "at least four," it's definitely "more than three." This is an example of a priori knowledge because you know it through reason alone, without needing any experience.

A posteriori knowledge

Now, consider this statement: "George V was king from 1910 to 1936."

To know if this is true, you can't just think about it. You need to check a history book, look at a timeline, or ask someone who knows. This is a fact about the real world that you learn through experience (like reading or being told). So, this is an example of a posteriori knowledge.

How are these ideas connected?

Philosophers have thought a lot about how a priori knowledge connects to other ideas, like whether something is true by its meaning or if it's necessarily true.

True by meaning (Analytic) vs. True by fact (Synthetic)

Some philosophers, like Immanuel Kant, talked about two types of statements:

• Analytic statements are true just because of what their words mean. For example, "All bachelors are unmarried men." You know this is true because the definition of "bachelor" includes "unmarried man." You don't need to check the world to know this.
• Synthetic statements are true because of facts about the world. For example, "It is raining outside." To know if this is true, you have to look outside or check the weather.

Many philosophers used to think that all a priori knowledge was analytic. They believed that if you could know something without experience, it must be true just by its meaning.

Necessary truths vs. Contingent truths

Another way to think about truths is whether they are necessary or contingent.

• A necessarily true statement is one that must be true and couldn't possibly be false. It's true in every possible situation. For example, "2 + 2 = 4" is necessarily true. Its opposite ("2 + 2 does not equal 4") is impossible.
• A contingently true statement is one that happens to be true, but it could have been false. It's true in our world, but it might not be true in a different situation. For example, "The sky is blue" is contingently true. The sky could have been a different color.

It seems logical that all necessary truths would be known a priori, because our senses can only tell us about what is true in our world, not what must be true everywhere.

Are they all the same?

For a long time, many philosophers thought that a priori knowledge, analytic truths, and necessary truths were all basically the same thing. They believed that if something was known without experience (a priori), it was true by its meaning (analytic), and it had to be true (necessary).

However, a philosopher named Saul Kripke (in 1972) challenged this idea. He argued that there can be truths that are:

• Necessary but a posteriori: For example, "Water is H₂O." Kripke argued this is necessarily true because water and H₂O are the same thing. But you only know this through scientific investigation (experience), not just by thinking about the words. So, it's a posteriori.

Because of Kripke and others, most philosophers now agree that while these ideas (a priori/a posteriori, analytic/synthetic, necessary/contingent) are related and often overlap, they are not exactly the same.

• The a priori/a posteriori difference is about how we know something (through reason or experience).
• The analytic/synthetic difference is about what makes a statement true (its meaning or facts about the world).
• The necessary/contingent difference is about whether a statement must be true or just happens to be true.

History of these ideas

Early thoughts

The terms a priori (from what comes before) and a posteriori (from what comes later) are Latin. They were used in Latin versions of Euclid's Elements, which was a very important book for clear thinking in early modern Europe.

Even before these terms were used, the ancient Greek philosopher Plato had an idea similar to a priori knowledge. In his dialogue Meno, he suggested that some knowledge is already inside our minds, like a memory we just need to "recollect."

Later, in the 14th century, a logician named Albert of Saxony wrote about both a priori and a posteriori ways of thinking.

G. W. Leibniz, a German philosopher from the 1600s, also used these terms to talk about how we can know if an idea is possible. He even used a priori and a posteriori arguments to discuss the existence of God.

Immanuel Kant's ideas

The German philosopher Immanuel Kant (1781) brought together ideas from Rationalism (which emphasizes reason) and Empiricism (which emphasizes experience). Kant famously said: "Although all our cognition begins with experience, it does not follow that it arises from [is caused by] experience."

Kant believed that a priori knowledge is about the basic "form" of all possible experience. It's like the structure or rules our minds use to understand the world. A posteriori knowledge, on the other hand, is about the actual "content" of our experiences.

He argued that certain things, like space, time, and causality (cause and effect), are pure a priori ways our minds work. We don't learn about space or time from experience; instead, our minds use these concepts to organize all our experiences. Without these a priori forms, we wouldn't be able to experience the world in an orderly way. This big idea is a central part of his book, the Critique of Pure Reason.

Images for kids

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  A robot thinking, representing reason and knowledge.

See also

In Spanish: A priori y a posteriori para niños