I think Lakatos, Proofs and Refutations is a fun book, but the chief thing I learned from it is that mathematical proofs aren’t absolutely true, even when there is no error in reasoning. It’s about mathematics, not science. It’s also quite short, particularly if you skip the second, much more mathematically-involved dialogue.
I learned the opposite: that mathematical proofs can be and should be absolutely true. When they fall short, it is a sign that some confusion still remains in the concepts.
I said mathematical proofs aren’t absolute because mathematical proofs and refutations are subject to philosophical, linguistic debate—argument about whether the proof fits the concept being played with, argument which can result in (for example) proof-constructed definitions. During this process, one might say that the original proof or refutation is correct, but no longer appropriate, or that the original proof is incorrect. Neither statement implies different behavior.
I think Lakatos, Proofs and Refutations is a fun book, but the chief thing I learned from it is that mathematical proofs aren’t absolutely true, even when there is no error in reasoning. It’s about mathematics, not science. It’s also quite short, particularly if you skip the second, much more mathematically-involved dialogue.
I learned the opposite: that mathematical proofs can be and should be absolutely true. When they fall short, it is a sign that some confusion still remains in the concepts.
I see no contradiction between these interpretations. :P
If they’re never absolutely true (your interpretation), how can they ever be absolutely true (my interpretation)?
I said mathematical proofs aren’t absolute because mathematical proofs and refutations are subject to philosophical, linguistic debate—argument about whether the proof fits the concept being played with, argument which can result in (for example) proof-constructed definitions. During this process, one might say that the original proof or refutation is correct, but no longer appropriate, or that the original proof is incorrect. Neither statement implies different behavior.