What are a priori, a posteriori, and a fortiori arguments?

a priori, a posteriori, a fortiori
Question: "What are a priori, a posteriori, and a fortiori arguments?"

Answer:
In philosophy, knowledge is classified by whether it flows from universal, logical principles or is dependent on specific experiences and evidence. The difference between these, in broad strokes, draws the line between a priori and a posteriori knowledge. When a statement can be evaluated entirely via logic or universal truths, it is an a priori concept. When a statement requires specific observation or knowledge in order to be evaluated, it is an a posteriori concept. The same applies for philosophical “arguments” that are either supported entirely by reason or that require empirical data.

A priori means “from the earlier.” Knowledge is described as a priori when it can be validated independently of empirical evidence, experience, or observation. In simpler terms, a priori knowledge is that which is obtained entirely by logic. For example, “circles are not squares” and “bachelors are unmarried” are tautologies, known to be true because they are true by definition. They are considered a priori statements. The same applies to mathematical statements such as 2+2=4.

A posteriori means “from the latter.” Knowledge is described as a posteriori when it can only be obtained by experience or other empirical means. Simply put, a posteriori knowledge is that which could possibly be true or false, logically speaking, and so must be assessed using actual observations. The statement “John is a bachelor” cannot be verified using pure logic; we need to observe empirical facts about John to know whether or not that statement is true. Likewise, “I have five dollars in my pocket” is a statement that can possibly be true or false; it can only be proved or disproved through empirical means.

It’s important to note that a priori knowledge does not have to be derived entirely through logic, at least in terms of a particular discussion. The point in question simply needs to be verified or dismissed through reason alone. Once some fact or idea is considered “true,” for the sake of argument, then later ideas can be evaluated entirely according to logical outcomes of that idea. For instance, if both sides of a debate accept “John was in Kansas from March 1 through March 3” as a true statement, then the statement “John was not on the moon on March 2” would be considered true a priori, for the sake of that discussion.

Note that the second statement flows as an absolute logical necessity, given the first. This is why it can be called “true a priori.” If the first statement is true, the second is verified entirely on the basis of logic, not on any particular added fact. This is the literal meaning of a priori: “from the earlier.” Because we’ve accepted the earlier statement as true, we must, logically, accept the second.

The difference between a priori and a posteriori becomes important when attempting to confirm or refute certain ideas. The first step, generally, is to examine a claim for a priori confirmation—in short, is it self-referencing or logically necessary? If so, then it is “proved,” a priori, as true. This does not necessarily make such knowledge useful, but it does mean that the truth value of such a statement is not subject to debate. If it is not true a priori, the next step is to ask if the statement is self-contradictory or logically impossible. If so, then it can be dismissed, a priori, as false.

If a statement cannot be evaluated on an a priori basis, it must be examined using further evidence or observations: it is a posteriori knowledge. Most claims, in most cases, require some level of empirical information in order to be examined. If a statement has not been explicitly acknowledged as a priori, then it’s a posteriori, and the majority of human knowledge is a posteriori.

The term a priori is the more often-used term. In logic and debate, the ability to label something as a priori knowledge is an important distinction. At the same time, it’s uncommon to see an idea explicitly labelled a posteriori. When this does happen, it is usually meant to rebut a claim that the statement can be known a priori.

A much less-commonly used term, a fortiori, describes something related to a priori knowledge but not exactly the same. The term a fortiori means “from the stronger,” and it refers to arguments that seek to prove a “smaller” point by appealing to an already-proven “larger” point. For instance, if a man says he can afford to spend $100, we assume he can afford to spend $10. If drinking one sip of a liquid is fatal, we assume drinking an entire cup is also fatal. If a man can hold his breath underwater for three minutes, we assume he’s able to hold his breath for one minute. If it’s considered a sin to punch someone, we assume stabbing him would also be sinful.

When we argue a specific point based on some larger or broader established idea, we are using a fortiori arguments. In common dialogue, we often use phrases such as “even more so” or “all the more.” This is, in general terms, an appeal to a fortiori logic, and the examples given might all be framed using that kind of language.

Technically speaking, a fortiori arguments are not ironclad to the same extent as truly a priori statements. In the prior examples, if the man in question had been given a signed check for $100 by a friend, he might only be able to spend exactly $100. In other words, it’s logically possible that he can “afford” to spend $100, but not $10, since he has no other money. So, while a fortiori arguments are reasonable, they are not logically absolute, so they are not truly a priori.

As with all philosophical ideas, both Scripture and Christian experience reflect the ideas of a priori, a posteriori, and a fortiori knowledge. The book of Hebrews rhetorically asks, if animal sacrifice has a certain spiritual effect, “how much more” effective is the sacrifice of Christ (Hebrews 9:13–14)? This is an a fortiori argument. Jesus used an a fortiori argument when He said, “If you, then, though you are evil, know how to give good gifts to your children, how much more will your Father in heaven give good gifts to those who ask him!” (Matthew 7:11)—Jesus’ point hinges on the phrase how much more. Paul points out that Christianity is irrevocably tied to the idea of resurrection—if there is no resurrection, then our faith is false (1 Corinthians 15:12–19). This is an a priori statement. In contrast, Paul’s immediately following remark is that Christ is, in fact, raised from the dead (1 Corinthians 15:20), which is an a posteriori concept. Scripture invests significant importance in evidence and fact-checking (Luke 1:1–4; 2 Peter 1:16; Acts 17:11).

Christian evangelism and apologetics also involve these three ideas. Some arguments for the existence of God are a priori, based in pure logic, such as the ontological argument. Assuming the universe has a beginning, the cosmological argument becomes an a priori claim. Most conversations involving apologetics and evangelism rely primarily on a posteriori knowledge, especially those discussing the reliability of Scripture or utilizing the teleological argument. Discussions of how human justice and a need for morality echo God’s traits of love and holiness are a form of a fortiori argumentation. The same is true of comparisons showing the Bible to be factually, historically, and scientifically reliable: given that evidence, it “stands to reason” that claims contradicting the Bible are false, based on an a fortiori approach.

Knowing the difference between these ideas is useful both in matters of pure philosophy and in our interpretation of Scripture.

Recommended Resource: Philosophical Foundations for a Christian Worldview by William Lane Craig & J.P. Moreland

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