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The Negative Inference Fallacy: The Error of Adding ‘Only’

I briefly explain the negative inference fallacy. After an initial introduction, I go into more detail to explain how to recognize and prevent the error. After doing that, I present two axioms to support the ideas I discuss. These axioms have interpretative, as well as apologetic value. I also included two appendices that show how a negative inference may be true, and I provide a basic foundation for understanding what a sound argument is.

An inference is defined as “the act of passing from one proposition, statement, or judgment considered as true to another whose truth is believed to follow from that of the former”(1). Therefore, a negative inference is one that moves from one statement that has a positive truth claim and then–from that statement–makes a claim that some other statement is not true. The negative inference fallacy is a type of logical error that is wide-spread and can be hard to spot. D.A. Carson describes a negative inference as a common but “improper syllogism”. He states, “It does not necessarily follow that if a proposition is true, a negative inference from that proposition is also true” (2). Consistent with how Carson describes the error, it can be categorized as a specific type of non-sequitur fallacy (when somebody reaches a conclusion from a statement does not follow from that statement). The negative inference fallacy can be described as drawing a negative conclusion from an affirmative premise. If that still sounds complicated and technical, don’t worry I will explain it further and give examples. I describe the negative inference fallacy with the phrase:

“Examples do not prove exclusions.”

Suppose I say, “Carl likes chicken.”

From that sentence alone, it would be illogical for a person to reach the conclusion and say, “Carl does not like beef.”

The statement, “Carl likes chicken” is a positive (affirmative) claim. Logically, it does not follow to make a negative claim from that (i.e., “Carl does not like beef”). Chicken is an example of one type of food that Carl likes. However, it may be true that he does not like beef– but nobody should use the statement that he likes chicken to reach the conclusion that he does not like beef. However, there are types of affirmative statements than can be made where a negative conclusion can be reached from the affirmative statement (See Appendix A).

How to Recognize the Error

One way to recognize the negative inference fallacy is by paying attention to words and phrases that are added to interpretations of Scripture, such as: only, exclusively, alone, no one else, and not [insert name, group, or idea that is not mentioned] etc.… These words are red-flags that can serve as a warning that a negative inference has been made.  Adding these words to passages that do not have them can cause problems. Here are three examples:

Example 1:

We can say: Andrew followed Jesus (John 1:40).

We cannot say:

Only Andrew followed Jesus.

Andrew exclusively followed Jesus.

Andrew alone followed Jesus.

Andrew and no one else followed Jesus.

Andrew followed Jesus, not Peter.

Reading the rest of the chapter (and the rest of the Bible) will quickly reveal the error of the five negatively inferred statements above.

Example 2:

An obvious misunderstanding of the following passage can be used to demonstrate the error:

“I have been crucified with Christ. It is no longer I who live, but Christ who lives in me. And the life I now live in the flesh I live by faith in the Son of God, who loved me and gave himself for me” (Galatians 2:20).

If we understood this passage using the negative inference fallacy, we would have to say that Christ only lives in Paul and only loved and gave himself for Paul. Clearly, this would be erroneous because examples do not prove exclusions. Paul is an example (one person) for whom Christ loved and gave Himself for. We cannot say:

Christ only gave Himself for Paul.

Jesus loved Paul exclusively.

Christ loved Paul alone.

Christ loved Paul, and no one else.

Christ loved Paul, not Peter.

Example 3:

“Jesus answered them, ‘Destroy this temple, and in three days I will raise it up.’ The Jews then said, ‘It has taken forty-six years to build this temple, and will you raise it up in three days?’ But he was speaking about the temple of his body” (John 2:19-21).

We cannot say that Jesus only was the only one that raised His body because other passages indicate that the God, the Father, (Acts 4:10) and the Spirit (Romans 8:11) did as well.

All three of these examples demonstrate the error of adding ‘only’ to the text. By adding this, or similar words, the meaning of passages get distorted into meaning less than originally stated in Scripture. Fortunately, preventing the error is rather straightforward and does not require any special training.  

How to Prevent the Error

The easiest way to prevent the negative inference fallacy from making its way into your interpretive process is to make sure you know the scriptural background of the subject you are dealing with. This is done by reading all the passages that deal with the issue you are studying. If you want to know who followed Jesus, go to the passages that say who followed Jesus. If you want to know where Paul went on missionary journeys, go to those passages. There is no secret to preventing the negative inference fallacy, but reading all the relevant passages (and reading them in context) that deal with the subject at hand can help you determine if you have made or observed the negative inference fallacy. There is no substitute for reading passages in context. Not every occurrence of the negative inference fallacy will be easy to spot with red-flag language (e.g., ‘only’, ‘exclusively’, & ‘alone’ ‘no one else’ etc…). The error may occur simply by not reading far enough ahead or far enough back from the passage you are looking at. More extreme forms reading out of context can include cherry-picking (when a person isolates a verse out of a chapter or even out of a whole book and ignores other passages that do not help their favored view).

Cherry-picking

Interpretations that rely on the negative inference fallacy can be the result of cherry-picking. The skewed view that cherry-picking can create is the false conclusion that if a teaching is not found in one passage, then the teaching is not in the Bible. Not every aspect of every doctrine can be taught in every passage–that is why it is important to do a survey of a given doctrine before drawing rigid conclusions about a single passage. Even passages that are read in context can still be misinterpreted if a negative inference is relied on. The following section will help explain this.

One Error, Two Axioms

The negative inference fallacy can also take the form of ‘using the lesser to disprove the greater’. There are two principles to observe:

1)     The lesser does not disprove the greater.

2)     The greater necessitates the lesser.

These principles are axiomatic –they are self-evidently true. However, I will still go into some detail to show their truth. For example, some critics of the Bible will say there is a contradiction in the empty tomb accounts because Matthew says there was an angel at the tomb, but Luke and John mention or imply more than one angel at the tomb. The problem can be easily shown when the critic realizes Matthew did not say there was only one angel at the tomb (3). Again, the error of adding ‘only’ is demonstrated. There are two ideas to take away from this:

1)     The lesser never disproves the greater.

If someone on the street asks if you have a dollar– and you have twenty dollars, you can truthfully answer, “yes”. However you cannot truthfully say you only have one dollar.  Having one dollar does not disprove that you have any amount greater than a dollar. The lesser never disproves the greater (4).

2)     The greater necessitates the lesser.

If you go to a concert and say there are 1,000 people in attendance. You can also truthfully say that you sat in a section of 100 people or a row of 10 people. The greater amount (1,000 people) necessitates that there will be every number less than 1,000 people in certain areas or sub-groups of the entire concert venue. The greater necessitates the lesser.

So, returning to the empty tomb. If there were two angels, it is necessary that there was one angel at the tomb– the greater necessitates the lesser. Likewise, if there was an angel, this would not disprove there were more than one angel–the lesser never disproves the greater.

This discussion is not limited to quantitative aspects of passages (i.e., “how many”?) but deals with qualitative passages as well (i.e. “who?” and “what?” questions). To give one example: Who is Jesus Christ a light to?

Israel (Isaiah 42 49)

The Gentiles (Luke 2:32)

Israel and Gentiles (Acts 26:23)

Everyone (John 1:9)

The World (John 8:12)

None of these examples should be read in competition with each other. Just because the Messiah is a light to Israel in one passage does not mean that he is not a light to Gentiles in another passage. When read in context, the purpose of Israel having the light is to take the gospel to the Gentiles. Likewise, a passage that says Jesus is a light to the Gentiles in one passage does not mean he is not a light for Israel. As it can be seen, Jesus is a light to everyone. Romans 15:1-21 provides a summary of the passages referenced above. 

Summary

I have introduced the negative inference fallacy, given an everyday illustration of it, and have presented three verses and illustrated how the negative inference fallacy, if applied to them, would distort the meaning of the text. I have pointed out the type of language, which, if added to the text, can be identified to help recognize the error. Absent any red-flag language (e.g., “only”) being added to an interpretation of a passage, I have mentioned that negative inferences may occur simply from reading verses without their immediate or larger context. Finally, I have shown two principles that are relevant for making sense of negative inferences. Being able to recognize and prevent the negative inference fallacy has great interpretive value– which in turn, has great apologetic value. 

Endnotes:

(1) Inference. https://www.merriam-webster.com/dictionary/inference.

(2) D.A. Carson, Exegetical Fallacies (2nd Edition; Grand Rapids, MI: Baker Academic, 1996), 101-102.

(3) For a more detailed discussion, see J. Warner Wallace “How Many Angels were Present at Jesus’ Tomb?”Accessed from http://coldcasechristianity.com/2015/how-many-angels-were-present-at-jesus-tomb/.

(4) Similarly, a lesser amount cannot prove a greater amount.

(5) D.A. Carson, Exegetical Fallacies (2nd Edition; Grand Rapids, MI: Baker Academic, 1996), 101-102.

(6)  Evidence used to support a premise is called data. Additionally, warrants are used to connect the data to the conclusion. In our case, a warrant would be a reasonable interpretive process. 

Appendix A

There is one way a negative inference can be true. Again, it won’t be true because it is a negative inference. The one way a negative inference can be show to be true is with background information. This will either occur through use of definitions (which can take the form of a tautology; a necessarily true statement) or by demonstrating some form of exclusivity:

Definitions

1)     Tautology

Example 1: Mike is a vegan. Because the definition of a vegan is somebody who does not eat meat– without any other information– it can be said, “Mike does not eat meat.”

Example 2: If you see the vacancy sign at the hotel is lit up– you can say the hotel is not fully booked because vacant means empty.

Exclusivity

2)     Through a Strict Binary:

Example: Suppose you are in a classroom. Everyone gets one marble and one marble only. Everybody must keep their marble. Nobody can trade their marble. Each person either gets a red marble or a black marble. Each marble is a solid color; red or black. There are nor swirled or mixed-color marbles.

Carl got a black marble.

Given the background information and that statement, we can say that Carl did not get a red marble.

So, we have an affirmative statement, “Carl got a black marble.”

And we have a negative conclusion, “Carl did not get a red marble.”

This can be known because there is a strict binary.

3)     Exclusive Language

Example 1: Pismo Beach is the only place I go on vacation.

With that information alone, the following conclusion can be reached: “I do not go on vacation in San Diego.”

Example 2: The Arizona Cardinals are Kevin’s favorite football team.

With that information only, the following conclusion can be reached: “The Seattle Seahawks are not Kevin’s favorite football team.

4)     Superlative Language

Example 1: “Mt. Everest is the tallest mountain in the world.”

With that information only, a person can say, [name of any other mountain] is not the tallest in the world.”

5)     Expectation for Exactness

Example: The Dr. asks the nurse how much the patient weighs (to determine the proper amount of anesthesia before surgery). The nurse says 100 kilograms.

With that information, it can be said the patient does not weigh any other amount.

6)     Unique Office

Example: Donald Trump was elected President of the United Stated for the 2016 term.

Therefore, Hillary Clinton was not.

7)     Known Limited Number

Example: There are 30 students registered for the Philosophy 100 class (& knowing that there are only 30 available spots based on the class registration page); a student who has not yet enrolled will know that they cannot enroll in that class (unless an opening becomes available). 

Appendix B

Here, I provide a ‘Syllogism Starter Kit’ to explain what a sound syllogism is– to help you understand the fallacy more thoroughly. Since Carson calls a negative inference an “improper syllogism”; it needs to be established what a proper (i.e., sound) syllogism is (5).  If you are already familiar with argumentation (i.e., you can at least explain the difference between a valid, good, and sound argument– this will only be an ultra-brief review).

The negative inference fallacy is a type of non sequitur fallacy (an error where someone reaches a conclusion that does not follow from the statement given).  Before we get into a more technical discussion, just think in common-sense terms: If you wanted to communicate you have not been to certain places; it would not make any sense to only mention the places that you have been to. Instead, it would make sense to tell people the places you have not been to (or to say the places that you have only been to). This would help prevent negative inferences from being made. Similarly, if you were trying to communicate that something was provided only for a certain group of people, it would make sense to communicate that fact.

A Sound Syllogism

A syllogism is a form of deductive reasoning where there are two (or more) premises and a conclusion drawn from those premises (I will use the terms syllogism and argument interchangeably). A standard, deductive syllogism moves from the general to the specific. There are two criteria an argument needs to be considered sound. An argument needs to have 1) good premises and 2) a valid structure. An argument is good when all premises are true. An argument is valid when the conclusion logically follows from them. In other words, an argument being good refers to the content of the premises; an argument being valid refers to the structure, or form, of the argument. Conversely, an argument can be bad (have a false premise) and be invalid (have a conclusion does not logically result from the premises). An argument does not need to be bad and invalid to be considered unsound. If the argument is either bad or invalid then the whole argument is unsound.

Creating a sound argument is the goal. When all the premises are good (true) and the form is valid (when the conclusion follows from the truth of the premises); the argument is considered sound. In a sound syllogism, the truth of the premises will guarantee the truth of the conclusion– this is important and I will discuss it later. If an argument is not sound– it should be discarded or re-worked until it meets the necessary criteria. There are other concerns as well, but this will get us started (6). I will start with a labeled, easy-to-understand example to show the concept:

Sound Argument #1

People who live in Fresno live in California (Premise 1)

Don lives in Fresno (Premise 2)

Therefore, Don lives in California (Conclusion)

Notice that premise 1 is a tautology– a statement that is necessarily true. People who live in Fresno live in California because Fresno is in California. Therefore, if I can prove that Don lives in Fresno, I can prove that Don lives in California. Notice also that premise 1 is not the same as the conclusion. When the first premise is the same as the conclusion, it is called circular reasoning– an invalid form of reasoning.

When constructing a syllogism, it is important to define the terms being used. So, when I say, “live”–I mean “has primary residence”. This would prevent objections to the argument and would take account for Don going on business or taking vacations outside California. Similarly, we are talking about a particular Don with a certain last name and social security number. This will prevent me from equivocating (using the same word with different meanings) the term Don and will prevent an objector from defeating the argument by finding some other Don who lives outside California.

Evidence (referred to as data) needs to be is used to establish the truth of the premises. For premise 1, I can demonstrate that premise 1 is true with a map. For premise 2, I can use Don’s driver’s license, tax forms, utility bills and similar documents to establish that he lives in Fresno. With the truth of both premises and the logical connection between the premises and the conclusion, I have constructed a sound argument. With a baseline for a sound argument established, I will now contrast it with an unsound syllogism:

Unsound Argument #1

People who live in Fresno live in California (Premise 1)

Carl does not live in Fresno (Premise 2)

Therefore, Carl does not live in California (Conclusion)

Premise 1 is true (it is a tautology). For premise 2, all his documentation shows he lives in Sacramento. With all premises being true, the argument above is good, but invalid because the conclusion does not follow from the two statements above. That is to say, there are many other counties Carl can live in, like Sacramento, and still live in California. Even if both premises are true– the conclusion does not follow (it relies on a negative inference). The person making the argument presupposes: people who live in Fresno and only people who live in Fresno live in California. Again, we see the error of adding ‘only’.

Some negative inferences are harder to spot than others. If my first premise was, “People who live in Kansas City live in California”– this error would be easier to demonstrate because it can be easily shown that there is not a Kansas City in California. It would be a bad argument and the syllogism would not be sound. However, the argument is valid because it would be true if the premises were true.

Invalid arguments can be harder to spot than bad arguments because both premises may, in fact, be true. Additionally, if a person already believes the conclusion of a good, but invalid argument, this can make the error almost impossible to recognize. A person who already believes a conclusion and also sees two true statements that seem to support it will have much difficulty recognizing the unsound argument in front of them. If the conclusion really is true, there will be a way to create a sound argument that demonstrates the truth of the conclusion.