If the premises are true, the conclusion cannot be false (Carnap, p. 17). Carnap believes that if one can formalize a valid deductive argument from induction that one can begin to solve the "problem of induction".
The heart of Carnap's argument lies in logical/inductive probability. Carnap believes if the evidence is so strong that the hypothesis follows logically from it-is logically implied by it-we have one extreme case in which the probability is 1. Similarly, if the negation of the hypothesis is logically implied by the evidence, the logical probability of the hypothesis is 0 (Carnap, p. 19-20). The previous two states show the Carnap is using confirmationism as the heart of his argument.
Confirmationism lies in confirming laws through finding positive instances and having no negative instances. This is where he believes induction plays a role. He believes this because there is a continuum of probabilities between zero and one and nothing can be deduced about the hypothesis from the evidence. The solution to using confirmation as a basis of Carnap's argument lies in proper testing. In order for testing to be proper, Carnap believes that the sample must be random, diversified, and wide. This means that one must look at every possibility when testing and not just those that are guaranteed to produce positive instances. By testing in this manner, each positive instance adds strength to the law. If one can then show that there are only positive instances and never negative ones, the probability would be 1. This then leads to a universal law, which in turn shows how logical/inductive probability can be used to show 100% confirmation with no negative instances.
Through the logic used above, Carnap was able to show why he believed the "problem of induction" could be solved. Though Carnap's argument is deductively valid, there are still downfalls in using induction. The first lies in the circularity of the argument.