2.3: Strength & Cogency

Previously, we’ve talked about validity
and soundness as important properties that a deductive argument can have. But what about inductive arguments? Let’s consider the following piece of inductive
reasoning: “Everyone in Bob’s office has the flu. Bob’s family has the flu. Bob’s friends have the flu. So, Bob has the flu as well.” Now, does this seem like a good inductive
argument or a bad one? Well, given the evidence presented in the
premises, it sure does seem likely that Bob would have the flu as well. So, it strikes me as a pretty good argument. But, of course, it’s not a valid argument,
since we can easily imagine a situation in which all of those people have the flu, but
by some miracle, Bob managed to not get it. So, it’s not a valid argument, but it does
seem to exhibit good reasoning, right? Remember that inductive arguments and deductive
arguments differ in the kind of support that they’re supposed to provide for the conclusion. Deductive arguments are supposed to provide
absolute proof, but an inductive argument can be perfectly rational even if it doesn’t
provide conclusive proof. So, instead of talking about validity, when
we are judging the reasoning in an inductive argument, we will say that it is either strong
or weak. A strong inductive argument is one that offers
really good evidence to support the conclusion. It means that the conclusion is very likely
to be true, on the assumption that the premises are true. Whereas, a weak inductive argument is one
that uses weak poor evidence. So, even if the premises are taken to be true,
it still doesn’t make the conclusion all that likely. Similarly to the notion of validity, when
judging the strength of an inductive argument, we take the premises for granted, and ignore
the question of whether they are true in reality. So, the following is a fairly strong inductive
argument, even though the premises are in fact false: “Poodles can fly. Golden retrievers can fly. Bulldogs can fly. Labradors can fly. Therefore, all dogs can fly.” Even though the premises are all patently
false, if we imagine that they’re true, then it seems like the conclusion is pretty
likely to be true as well. So, it’s a strong argument. On the other hand, contrast that with the
following: “Lions can talk. Cheetahs can talk. So, all animals can talk.” Let’s suppose the premises are true. Still, isn’t it kind of a leap to infer
that all animals can talk on the basis of just two examples? This argument does not provide much evidence
for the conclusion, even on the assumption that premises are true. So, it is definitely a weak inductive argument. In general, strong inductive arguments tend
to use a lot of data points to support the conclusion, while weak arguments use only
a few. So, strength is basically the inductive analog
of validity – they both pertain to the quality of the reasoning involved in the argument. What about soundness? Is there an inductive version of soundness? There is, and it’s known as cogency. Remember that soundness is essentially validity
plus true premises. So, similarly, cogency is strength plus true
premises. A cogent argument is one in which the conclusion
is most likely to be true, given the premises, and the premises are in fact true. So, just like with soundness, cogency does
care about whether the premises are true in reality. So, if we go back to this argument, we can
say that it is a strong inductive argument, but not a cogent one, since all of the premises
are false. Not that unlike with soundness, a cogent argument
does not have to have a true conclusion. Since strong a strong inductive argument only
means that the conclusion is very likely to be true, given the premises, an argument can
have true premises, and use good inductive reasoning, but still end up with a false conclusion. Finally, one more thing to note is that unlike
validity, inductive strength is a matter of degree. Inductive arguments provide more or less support
for the conclusion, but there isn’t a clear standard of what counts as enough evidence
to qualify as a strong argument. So, when it’s relevant, we’ll try to stick
with examples that are very obviously strong or very obviously weak. OK, so in this video we covered strong vs.
weak inductive arguments, and cogent vs. non-cogent inductive arguments. These concepts are analogs of the deductive
notions of validity and soundness, but differ in subtle ways.

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