Consider these two arguments:
These arguments are of course not valid. Lee might be among the 7% of Chinese who can digest lactose.1 Snow might fall in Jakarta this winter due to unusual changes in global weather. But despite the fact that the arguments are invalid, their conclusions are more likely to be true than false given the information in the premises. If the premises are indeed true, it would be rational for us to be highly confident of the conclusion, even if we are not completely certain of their truth. In other words, it is possible for the premises of an invalid argument to provide strong support for its conclusion. Such arguments are known as inductively strong arguments. We might define an inductively strong argument as one that satisfies two conditions:
1. It is an invalid argument.
2. The conclusion is highly likely to be true given that the premises are true.
Let us elaborate on this definition a bit more:
- Recall that a valid argument can have false premises. The same applies to an inductively strong argument. The two arguments given earlier remain inductively strong, even if Lee is not Chinese, or it turns out that it snowed in Jakarta last year.
- When we say the conclusion is highly likely to be true given that the premises are true, it does not mean “it is highly likely for the conclusion and the premises to be true.” Consider ...