falsifying an argument, scientists will inevitably verify its negation. Thus, verification and falsification are perfectly symmetrical. It seems, in the philosophy of logic, that neither syllogisms nor polysyllogisms will save underdetermination and overdetermination from the perils of infinite regress. Furthermore, Popper defended his critical rationalism as a normative and methodological theory, that explains how objective, and thus mind-independent, knowledge ought to work. Hungarian philosopher Imre Lakatos built upon the theory by rephrasing the problem of demarcation as the problem of normative appraisal. Lakatos' and Popper's aims were alike, that is finding rules that could justify falsifications. However, Lakatos pointed out that critical rationalism only shows how theories can be falsified, but it omits how our belief in critical rationalism can itself be justified. The belief would require an inductively verified principle. When Lakatos urged Popper to admit that the falsification principle cannot be justified without embracing induction, Popper did not succumb. Lakatos' critical attitude towards rationalism has become emblematic for his so called critical fallibilism. While critical fallibilism strictly opposes dogmatism, critical rationalism is said to require a limited amount of dogmatism. Though, even Lakatos himself had been a critical rationalist in the past, when he took it upon himself to argue against the inductivist illusion that axioms can be justified by the truth of their consequences. In summary, despite Lakatos and Popper picking one stance over the other, both have oscillated between holding a critical attitude towards rationalism as well as fallibilism. Fallibilism has also been employed by philosopher Willard V. O. Quine to attack, among other things, the distinction between analytic and synthetic statements. British philosopher Susan Haack, following Quine, has argued that the nature of fallibilism is often misunderstood, because people tend to confuse fallible propositions with fallible agents. She claims that logic is revisable, which means that analyticity does not exist and necessity (or a priority) does not extend to logical truths. She hereby opposes the conviction that propositions in logic are infallible, while agents can be fallible. Critical rationalist Hans Albert argues that it is impossible to prove any truth with certainty, not only in logic, but also in mathematics. Mathematical fallibilism In Proofs and Refutations: The Logic of Mathematical Discovery (1976), philosopher Imre Lakatos implemented mathematical proofs into what he called Popperian "critical fallibilism". Lakatos's mathematical fallibilism is the general view that all mathematical theorems are falsifiable. Mathematical fallibilism deviates from traditional views held