must be true without any doubt whatsoever. To say that a conclusion follows from a premise means that we are justified in having reasoned appropriately from one claim (the premise) to another claim (the conclusion). Cartman puts forward a deductive argument in “The Tooth Fairy Tats 2000” episode that goes something like this:
Premise 1: If the boys combine their lost teeth, then they'll get money from the Tooth Fairy
Premise 2: If they get money from the Tooth Fairy, then they can buy a Sega Dreamcast
Conclusion: Hence, if the boys combine their lost teeth, then they can buy a Sega Dreamcast
We can see that, provided that the two premises are true, the conclusion absolutely must be true. We can also see that there is no other conclusion that could correctly be drawn from these premises. In fact, from looking at the premises alone you know the conclusion before even seeing it. The previous argument about Jews apologizing for Jesus's death is also a deductive argument. Just like with the Tooth Fairy argument, if all the premises are true then the conclusion must be true, there is no other conclusion that possibly could be drawn from the premises, and you know exactly what the conclusion is without even seeing it.
In inductive arguments, the speaker intends the conclusion to follow from the premises with a degree of probability or likelihood such that, if all of the premises are true, then the conclusion probably or likely is true, but it is still possible that the conclusion is false. In the “Towelie” episode, the boys notice that when they speak about anything having to do with towels, Towelie shows up, and so they reason like this:
Premise 1: Because in the past, when we mentioned towel‐related things, Towelie showed up
Premise 2: And because we will mention something towel‐related now
Conclusion: We can conclude that Towelie will show up
We can see that, provided the premises are true, the conclusion is probably or likely true, but not definitely true. It makes sense to conclude that Towelie will show up, given past experience. But the truth of Towelie showing up in the past does not guarantee that, with absolute certainty or without a doubt, Towelie will show up. It is still possible that Towelie will not show up, so the conclusion is merely probable or likely. In the episode, Towelie does show up, but he need not necessarily have shown up.
Consider Stan's reasoning at the end of the episode “Scott Tenorman Must Die” after it has been revealed that Cartman orchestrated the death of Scott's parents, the subsequent addition of their bodies to the chili, and Radiohead's witnessing the entire event so as to make fun of Scott for being a woosie.
Premise 1: Since Cartman does horrible things to people for minor offenses (like being cheated out of $16.12)
Premise 2: And since we (the boys) commit, at least, minor offenses against Cartman frequently, and he may retaliate like he did with Scott
Conclusion: Therefore, we had better not piss Cartman off in the future, for fear of retaliation
Again, even if both of the premises are true, it does not follow with absolute certainty that the boys had better not piss off Cartman in the future. In fact, as it turns out, the boys piss off Cartman numerous times without receiving the kind of retaliation given poor Scott Tenorman. So, the conclusion is false.
The Good, the Bad, and … Well, That's it Really
Our goal is not just to form arguments. We need to form good arguments, and we need to evaluate the arguments of others. There are good arguments and there are bad arguments in both the deductive and inductive realms. A good argument, in either realm, is one in which the conclusion logically follows from the premises and all of the premises are true. If either one of these conditions is absent, then the argument is bad and should be rejected.
In the deductive realm, that a conclusion follows from premises means that the argument is valid (or invalid if the conclusion does not follow). When an argument is valid and all the premises are true, the argument is said to be a good, sound argument. The conclusion absolutely, positively, without a doubt, is true, and this is a good thing! In the inductive realm, that a conclusion likely will follow from premises means that the argument is strong (or weak if the conclusion likely does not follow). When an argument is strong and all the premises are true, the argument is said to be a good, cogent argument. The conclusion is most likely or probably true, and this is a good thing too!
So, as rational, adult critical thinkers we must always go through this two‐step procedure of checking our own arguments and the arguments of others to see if (A) the conclusion follows from the premises (is the argument deductively valid or inductively strong?) and (B) all of the premises are true. If the argument fails to meet either (A) or (B) or both, then we should reject it, thereby rejecting the person's conclusion as either absolutely false or probably false. For example, Cartman's argument for pooling together the boys' teeth is probably a bad one because Premise 2 seems false, given the information. It is not true that if they get money from the Tooth Fairy then they will be able to buy a Sega Dreamcast, because the Tooth Fairy only gave Cartman $2.00. The sum of $2.00 × 4 boys is $8.00 and, provided we are talking about a new one from the store, that is not enough to buy a Sega Dreamcast. So in the case of this particular deductive argument, the conclusion “If the boys combine their teeth, then they can get a Sega Dreamcast” is false. On the other hand, the Towelie argument was a good one. It was true that the few times they mentioned towel‐related things, Towelie showed up. And given this fact, they had a strong case for drawing the conclusion that he would show up again asking, of course, “Wanna get high?”
“If Chewbacca Lives on Endor, You Must Acquit”
At times, checking to see if conclusions follow from premises and if premises are true can be very difficult. Some words have multilevel meanings. And some people will try to convince us of the truth of claims in order to deceive us, or sell us something, or get us to vote for them, or become part of their group, or share their ideology. Often, people will try to convince us that a conclusion follows from a premise or premises when, in fact, it does not, kind of like what the cartoon Cochran does with the Chewbacca defense in the episode, “Chef Aid,” a satire of Cochran's actual closing arguments in the O.J. Simpson case.
In the episode, Alanis Morissette comes out with a hit song “Stinky Britches,” which, it turns out, Chef had written some 20 years ago. Chef produces a tape of himself performing the song, and takes the record company to court, asking only that he be credited for writing the hit. The record company executives then hire Cochran. In his defense of the record company, Cochran shows the jury a picture of Chewbacca and claims that, because Chewbacca is from Kashyyyk and lives on Endor with the Ewoks, “It does not make sense.” Cochran continues: “Why would a Wookie, an eight‐foot‐tall Wookie, want to live on Endor with a bunch of two‐foot‐tall Ewoks? That does not make sense … If Chewbacca lives on Endor, you must acquit! The defense rests.” The jury is so convinced by Cochran's “argument,” that not only do they apparently deny Chef's request for credit recognition but they also find Chef guilty of harassing a major record label, fining him $2 million to be paid within 24 hours. Friends of Chef then organize “Chef Aid” to pay his fine.
We laugh at Cochran's defense because it has absolutely nothing to do with the actual case. We laugh all the more at the absurdity when the Chewbacca defense is also used to find Chef guilty of harassing the very record company that had produced a stolen song. The issue of Chewbacca living on Endor has absolutely nothing to do with, and is in no way logically related to, the issues of whether Chef should receive credit for the song, or whether he has harassed the record company. As rational thinkers, we recognize this, laugh at the absurdities, and wonder why anyone in their right mind would be convinced that the Chewbacca defense and the other issues are related.
As we have seen in Section 2.1, logicians have a special term for these bad arguments in which the conclusion