A chaotic (inconsistent) world in which the definiendum no longer entails the definiens and vice versa? — Pippen
What prevents us from imagining that we all wake up tomorrow and a circle is no longer round, because we find ourselves in a chaotic (inconsistent) world in which the definiendum no longer entails the definiens and vice versa? — Pippen
I really do not get it, why Hume judged at his time, it was possible at any time, the sun could not rise tomorrow (experience as an unreliable source of knowledge) — Pippen
that from p and p -> q from tomorrow no more q follows (logic as an unreliable source of knowledge) — Pippen
What prevents us from imagining that we all wake up tomorrow and apply other logical rules? — Pippen
What are these destructive conclusions of which you speak? — A Seagull
But if not experience, then - it's not clear what it could even mean to extend the problem of induction to logic and math. — StreetlightX
For example, deduction might be considered to be special case of induction in which there is believed to exist perfect certainty for a conclusion with respect to a given premise. — sime
As long as P does not change, then Q will keep necessarily following. — alcontali
Why? P, P -> Q | Q is just right because it follow from some rules. But these rules can change overnight, can they? — Pippen
So MP could be true today but false tomorrow. Imagine - overnight - our world becomes weird in the way that it becomes impossible to construct any implication P -> Q (~P v Q). I know it's hard to imagine, but I can just write it down and say: so be it from henceforward. — Pippen
Why? P, P -> Q | Q is just right because it follow from some rules. But these rules can change overnight, can they? — Pippen
Hume clearly differentiated between what he called 'matters of fact', ie facts about the real world, and what he called 'relations of ideas' ie abstract logical systems such as mathematics. — A Seagull
Suppose the world changes overnight so that it becomes impossible to model an implication (per se and of course especially for our human minds). — Pippen
Which gives logic and math a kind of atemporal, aspatial quality. Which is odd, given that we inhabit temporal, spatial universe of change. — Marchesk
What prevents us from imagining that we all wake up tomorrow and apply other logical rules? What prevents us from imagining that we all wake up tomorrow and a circle is no longer round, because we find ourselves in a chaotic (inconsistent) world in which the definiendum no longer entails the definiens and vice versa? — Pippen
Again, I don't understand why the induction problem is never seen as problem for logic and math as well, — Pippen
Which gives logic and math a kind of atemporal, aspatial quality. Which is odd, given that we inhabit temporal, spatial universe of change. — Marchesk
abstract ideas are not about anything, so they don't answer to the challenge of observation, which is what the problem of induction is all about. — SophistiCat
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