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Proof and Refutations
Lakatos' "Proof and Refutations" is a series of four articles that were published between 1963 and 1964 and gathered into a collection after his death. In this work Lakatos argues that mathematics is not perfect and that the proofs and refutations are not so in the full sense of the words. This brings into question the fact that currently students of mathematics are taught the latest definitions without ever truly understanding what they are learning. -
Popper on demarcation and induction
Lakatos published this paper in 1970 criticizing Poppers views on demarcation. Lakatos argues that based on Poppers criteria, some of the most significant scientific discoveries broke the rules set about by Popper and do not count as scientific, but would be considered unscientific. Despite praising Popper at the beginning of this work, the criticism brought forth in this paper caused the relationship between Lakatos and Popper to deteriorate. -
Science and Pseudoscience
Lakatos Speech was broadcast late June of 1973. This was his last major work before his passing in February 1974. In this lecture Lakatos argues that distigushing between science and pseudoscience is not only important for the fields of philosophy and history of science but for all other facets of life as well. The linked video talks more about Lakatos views on the subject. https://www.youtube.com/watch?v=YD4HlJ9xikM -
Methodology of Scientific Research Programmes
Lakatos incorporated ideas from both Kuhn and Popper in to his proposed research programs. In these programs he stated that a hypothesis should be protected by several falsifiable supplementary hypotheses whose core is shared with the main theory. This ensures when a hypothesis is refuted, the supplementary hypotheses are blamed instead. The main theory is intended to be unfalsifiable and this is important because it a change to Poppers criteria that a theory must be falsifiable to be science.