Fallacy Files #3: Confused Conditionals

One common logical fallacy is known as ‘affirming the consequent’. Arguments that commit this fallacy have this general form:

If P then Q.


Therefore P.

(In technical terminology, P is the antecedent of the first, conditional premise and Q is the consequent of that premise. The second premise of the argument affirms the consequent of the first premise rather than its antecedent; hence the fallacy of ‘affirming the consequent’.)

It isn’t difficult to see that such arguments are fallacious, as this example makes plain:

If Bob lives in Chicago then Bob lives in America.

Bob lives in America.

Therefore Bob lives in Chicago.

One unfortunate example of this fallacy can be found in the book of Job (although it’s not committed by the author of Job). Throughout the book, Job’s ‘friends’ exhort him to repent of whatever sin it is that has resulted in his suffering. They see his distress and deduce from it that God must be punishing Job for some evil act or ungodly attitude. They believe, correctly, that God is just and therefore He must punish those guilty of sin (and punishment, of course, entails some kind of suffering). But their reasoning commits the fallacy of affirming the consequent:

If Job had committed a sin then Job would suffer.

Job suffers.

Therefore Job committed a sin.

One of the morals of the story, then, is that while suffering can be the consequence of sin, it needn’t be the consequence of sin. There may be other reasons why a person suffers (cf. John 9:1-3). Sad to say, the philosophical descendants of Eliphaz et al live on in every generation, always ready to add illogic to injury.

A closely related fallacy to ‘affirming the consequent’ is that of ‘denying the antecedent’. Arguments of this second type have the following form:

If P then Q.

Not P.

Therefore not Q.

One real-life example of this fallacy comes from my undergraduate days. In the early 90s I had several encounters with members of a local cult at large in Edinburgh whose proselytizing efforts were concentrated mainly on students. The group was an offshoot of the Boston Church of Christ, and one of their distinctive teachings was that believer’s baptism by immersion is necessary for salvation. (Indeed, only baptisms performed by this group would cut the mustard, for they alone were the One True Church.) One of the verses wielded in support of this teaching was Mark 16:16:

Whoever believes and is baptized will be saved, but whoever does not believe will be condemned. (ESV)

Now, the vast majority of scholars (conservative ones included) agree that Mark 16:9-20 is not part of the original text of Mark’s Gospel. But leave that aside for the moment and assume for the sake of argument that verse 16 is divinely inspired and therefore authoritative for Christian doctrine. (One might add that Acts 2:38, whose authenticity isn’t in doubt, expresses a very similar theological proposition.) Would it follow that baptism is necessary for salvation? Not at all.

Consider how the argument is suppose to run:

If you believe and are baptized then you’ll be saved.

You haven’t believed and been baptized.

Therefore you won’t be saved.

(In this example, the antecedent of the first premise is true only if you have both believed and been baptized. If you’re a believer who hasn’t been baptized — or, for that matter, a non-believer who has been baptized — the antecedent is false.)

Clearly the cultists’ argument was an instance of ‘denying the antecedent’, and thus its conclusion doesn’t logically follow from its premises (i.e., the conclusion can be false even if the premises are true). Indeed, they ought to have been tipped off by the second half of Mark 16:16. If the author had thought baptism necessary for salvation, one would have expected him to write “whoever does not believe or is not baptized will be condemned” rather than merely “whoever does not believe will be condemned“. As it is, verse 16 taken as a whole comports nicely with the evangelical doctrine that faith in Christ is both necessary and sufficient for salvation, whilst also indicating that baptism is the norm for believers.

Both of the fallacies discussed above commit the same underlying mistake, that of confusing the antecedent and the consequent of a conditional premise. In other words, both treat “If P then Q” as if it were “If Q then P”.

I recently encountered another example of this confusion in an exchange with a fellow Christian about the biblical arguments for and against infant baptism. (In the interests of full disclosure: I’m a Reformed Baptist by conviction, but I’m much more sympathetic toward paedobaptism than most Baptists.)

At one point in our exchange, my friend laid out what he took to be a near irrefutable case for believer’s baptism from the New Testament. One of his arguments was that Matthew 28:19 clearly teaches that the proper subjects of baptism are disciples (and disciples must be believers):

Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit…

But note carefully what this verse does and doesn’t teach. It does teach that new disciples should be baptized; but it doesn’t teach that only new disciples should be baptized. This verse, at least, is silent on the latter question.

It appears that my friend was reasoning like this:

(1) If S is a disciple then S is a proper subject of baptism.

(2) Infants are not disciples.

(3) Therefore infants are not proper subjects of baptism.

Yet this argument is invalid, for the reasons already discussed. What the argument needs instead of (1) is the following premise:

(1*) If S is a proper subject of baptism then S is a disciple.

The argument would then be valid as an instance of modus tollens. But as I’ve pointed out, (1*) isn’t stated or implied by Matthew 28:19. So the Great Commission doesn’t offer the support for believer’s baptism that my friend supposed.

In fact, there’s some irony here in that the original premise (1) suggests an argument for infant baptism. As I noted above, my friend made the assumption that disciples must be believers (and thus infants cannot be disciples). However, the Greek verb translated here as “make disciples” can simply mean “to make someone a follower through teaching and instruction”. It doesn’t require that a ‘disciple’ be able to give a “credible profession of faith” — the usual criterion of believer’s baptism. One might therefore argue from Matthew 28:19 as follows:

(1) If S is a disciple then S is a proper subject of baptism.

(2*) Children of Christian parents are disciples.

(3*) Therefore children of Christian parents are proper subjects of baptism.

The idea behind (2*) is that when Christian parents teach their children to believe and obey the teachings of Jesus (as they certainly ought to do), that amounts to “making disciples” of them. So the children of faithful Christian parents are ‘disciples’ in the Great Commission sense (so the argument goes) and since the disciple-making process involves baptizing as well as teaching, those children ought to be baptized.

I hasten to add that I don’t endorse this argument for paedobaptism, but at least it illustrates the importance of getting one’s conditional premises straight in the first place!