ABSTRACT
The rule of modus ponens, which tells us that from an indicative conditional ┌ If ϕ then ψ ┐ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429495687/ec6ae4cf-7647-4c24-8bcc-da916afd1ed3/content/eq9.tif"/> 2 together with its antecedent ϕ, one can infer ψ, is one of the fundamental principles of logic. 3 Yet, as the following examples show, it is not strictly valid; there are occasions on which one has good grounds for believing the premises of an application of modus ponens but yet one is not justified in accepting the conclusion. Later on, we shall see how these examples can be modified to give counterexamples to Stalnaker’s semantics for the conditional:
Opinion polls taken just before the 1980 election showed the Republican Ronald Reagan decisively ahead of the Democrat Jimmy Carter, with the other Republican in the race, John Anderson, a distant third. Those apprised of the poll results believed, with good reason:
If a Republican wins the election, then if it’s not Reagan who wins it will be Anderson.
A Republican will win the election.
Yet they did not have reason to believe
64If it’s not Reagan who wins, it will be Anderson.
I see what looks like a large fish writhing in a fisherman’s net a ways off. I believe
If that creature is a fish, then if it has lungs, it’s a lungfish.
That, after all, is what one means by “lungfish.” Yet, even though I believe the antecedent of this conditional, I do not conclude
If that creature has lungs, it’s a lungfish.
Lungfishes are rare, oddly shaped, and, to my knowledge, appear only in fresh water. It is more likely that, even though it does not look like one, the animal in the net is a porpoise.
Having learned that gold and silver were both once mined in his region, Uncle Otto has dug a mine in his backyard. Unfortunately, it is virtually certain that he will find neither gold nor silver, and it is entirely certain that he will find nothing else of value. There is ample reason to believe
If Uncle Otto doesn’t find gold, then if he strikes it rich, it will be by finding silver.
Uncle Otto won’t find gold.
Since, however, his chances of finding gold, though slim, are no slimmer than his chances of finding silver, there is no reason to suppose that
If Uncle Otto strikes it rich, it will be by finding silver.
