  The role of probability appears unchallenged as the key measure of
uncertainty, used among other things for practical induction in the empirical
sciences. Yet, Popper was emphatic in his rejection of inductive probability
and of the logical probability of hypotheses; furthermore, for him, the degree
of corroboration cannot be a probability. Instead he proposed a deductive
method of testing. In many ways this dialectic tension has many parallels in
statistics, with the Bayesians on logico-inductive side vs the non-Bayesians or
the frequentists on the other side. Simplistically Popper seems to be on the
frequentist side, but recent synthesis on the non-Bayesian side might direct
the Popperian views to a more nuanced destination. Logical probability seems
perfectly suited to measure partial evidence or support, so what can we use if
we are to reject it? For the past 100 years, statisticians have also developed
a related concept called likelihood, which has played a central role in
statistical modelling and inference. Remarkably, this Fisherian concept of
uncertainty is largely unknown or at least severely under-appreciated in
non-statistical literature. As a measure of corroboration, the likelihood
satisfies the Popperian requirement that it is not a probability. Our aim is to
introduce the likelihood and its recent extension via a discussion of two
well-known logical fallacies in order to highlight that its lack of recognition
may have led to unnecessary confusion in our discourse about falsification and
corroboration of hypotheses. We highlight the 100 years of development of
likelihood concepts. The year 2021 will mark the 100-year anniversary of the
likelihood, so with this paper we wish it a long life and increased
appreciation in non-statistical literature.
