fossilesque@mander.xyzM to Science Memes@mander.xyzEnglish · 5 months agoGeometrymander.xyzimagemessage-square54fedilinkarrow-up1578arrow-down113
arrow-up1565arrow-down1imageGeometrymander.xyzfossilesque@mander.xyzM to Science Memes@mander.xyzEnglish · 5 months agomessage-square54fedilink
minus-squareweker01@feddit.delinkfedilinkEnglisharrow-up2·5 months agoI think the statement “this system is consistent” is a practical statement that is unprovable in a sufficiently powerful consistent system. Can you help me understand the tone of your text? To me it sounds kinda hostile as if what you said is some kind of gotcha.
minus-squareKogasa@programming.devlinkfedilinkEnglisharrow-up1·5 months agoJust explaining that the limitations of Gödel’s theorems are mostly formal in nature. If they are applicable, the more likely case of incompleteness (as opposed to inconsistency) is not really a problem.
I think the statement “this system is consistent” is a practical statement that is unprovable in a sufficiently powerful consistent system.
Can you help me understand the tone of your text? To me it sounds kinda hostile as if what you said is some kind of gotcha.
Just explaining that the limitations of Gödel’s theorems are mostly formal in nature. If they are applicable, the more likely case of incompleteness (as opposed to inconsistency) is not really a problem.