Is falsification only applicable to deductive reasoning (as opposed to inductive, abductive and speculative deductive reasoning)?
Popper's concept of falsifiability is based on the assumption that
to prove any knowledge claim, we must use the same logic that mathematics uses for proving mathematical theorems.
The epistemology of mathematics calls for classical deductive logic for proving theorems. What is called Hume's problem of induction demonstrates that
observational generalizations are not provable ( = rationally justifiable ) through classical deductive logic.
In his days, any logic that was not classical deductive logic was called inductive logic. Hence, in Hume's terminology, probabilistic logic, defeasible logic, abductive logic, and what we call inductive logic ( = the logic needed for justifying observational generalisations on a population on the basis of a sample of observational reports) are all conflated as inductive logic.
Given Hume requirement that rationally justifying ( = proving) any knowledge claim calls for classical deductive logic, it follows that observational generalisations are not rationally justifiable. This is called Hume's problem of Induction in the philosophy literature.
Hume’s conclusion is true only if we accept Hume's concept of rational justification.
If we assume, contrary to Hume, that knowledge claims can be justified not only through classical deductive logic, but also through probabilistic deductive logic, defeasible logic, abductive logic and inductive logic, Hume's conclusion is false.
Like Hume, Popper assumed that to justify a knowledge claim, we need classical deductive logic. Hence he was forced to conclude that scientific claims are not provable. (e.g.. The scientific claim that all adult human beings have exactly one heart is not provable through classical deductive logic.
However, he pointed out that a single counterexample to an observational generalization constitutes a counterexample to the claim, and hence shows that the claim is false ( = is refuted.) A single adult human with no heart or two hearts is enough to show that the exactly one heart claim is false. This was the essence of Popper's concept of falsifiability in his Conjectures and Refutations. Popper's solution to 'Hume's Problem' was that
knowledge claims in science cannot be proved, but they can be refuted. Falsifiable means refutable with counterexamples.
But if we allow not only classical deductive logic, but also probabilistic deductive logic, defeasible deductive logic, inductive logics, and abductive logics as logics for proving scientific claims, it follows that scientific epistemology allows for both proving and refuting knowledge claims. So we need to replace the concept of falsifiability with the concept of testability.
A theory is testable if and only if its predictions ( =logical consequences) are provable or refutable on the basis of data.