fossilesque@mander.xyzM to Science Memes@mander.xyzEnglish · 1 month agoTheories on Theoriesmander.xyzimagemessage-square135fedilinkarrow-up1631
arrow-up1631imageTheories on Theoriesmander.xyzfossilesque@mander.xyzM to Science Memes@mander.xyzEnglish · 1 month agomessage-square135fedilink
minus-squareyetAnotherUser@discuss.tchncs.delinkfedilinkEnglisharrow-up3·1 month 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-up3·1 month 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.