Knowledge of Mathematics without Proof

@article{Paseau2015KnowledgeOM,
  title={Knowledge of Mathematics without Proof},
  author={Alexander Paseau},
  journal={The British Journal for the Philosophy of Science},
  year={2015},
  volume={66},
  pages={775 - 799}
}
  • Alexander Paseau
  • Published 2015
  • Mathematics
  • The British Journal for the Philosophy of Science
  • Mathematicians do not claim to know a proposition unless they think they possess a proof of it. For all their confidence in the truth of a proposition with weighty non-deductive support (for example, the Riemann hypothesis), they maintain that, strictly speaking, the proposition remains unknown until such time as someone has proved it. This article challenges this conception of knowledge, which is quasi-universal within mathematics. We present four arguments to the effect that non-deductive… CONTINUE READING
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