4 ms·
It seems intuitively wrong that you can say "All X are Y" and yet that doesn't imply "At least one X exists".
by aftbit 2y ago
It seems intuitively wrong that you can say "All X are Y" and yet that doesn't imply "At least one X exists".
- titzer 2y agoIt also seems intuitively wrong that there are different sizes of infinity, yet Cantor discovered exactly that.
- deleted 2y ago[deleted]
- scotty79 2y agoThat's how math defined what "all" means. You can be talking about all elements of empty set without implying it must have some. Basically it disentangled two unrelated concepts, that English language unduly mixes. Concept of every item having some quality and concepts of at least one item existing.
- njtransit 2y agoThat how we define "all" logically but not linguistically. For instance, linguistically we would consider this inconsistent: "all 10-foot men have black hair AND all 10-foot men have blonde hair" yet it is true, logically, if there are no 10-foot tall men. The translation of the English word "all" should be something something like: |Q| > 0 ∧ ∀x∈Q, x is ...