fossilesque@mander.xyzM to Science Memes@mander.xyzEnglish · 6 days agoTheories on Theoriesmander.xyzimagemessage-square133fedilinkarrow-up1633arrow-down118
arrow-up1615arrow-down1imageTheories on Theoriesmander.xyzfossilesque@mander.xyzM to Science Memes@mander.xyzEnglish · 6 days agomessage-square133fedilink
minus-squareyetAnotherUser@discuss.tchncs.delinkfedilinkEnglisharrow-up3·6 days agoWorse: If the chosen axioms are contradictory, then the theorem is effectively worthless. And it is impossible to know whether axioms are consistent. You can only prove that they are not.
minus-squareYTG123@sopuli.xyzlinkfedilinkEnglisharrow-up3·5 days agoYou can go deeper. To prove anything, including the consistency or inconsistency of a theory, you need to work within a different system of axioms, and assume that it is consistent, etc.
Worse: If the chosen axioms are contradictory, then the theorem is effectively worthless.
And it is impossible to know whether axioms are consistent. You can only prove that they are not.
You can go deeper. To prove anything, including the consistency or inconsistency of a theory, you need to work within a different system of axioms, and assume that it is consistent, etc.