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authorp <grr@lo2.org>2024-11-29 22:18:45 -0500
committerp <grr@lo2.org>2024-11-29 22:18:45 -0500
commit958437abfc71342ac2b84a451c989e6eb20b7643 (patch)
treea442fcba060599f316a1ab6e21f4f7720e28769b /essays/post_formalism_memories.otx
parent9bdfeb8a204fbbce701fd75a19fc94b19ae06adb (diff)
downloadblueprint-958437abfc71342ac2b84a451c989e6eb20b7643.tar.gz
partially unbreak innperseqs diagram
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@@ -126,7 +126,7 @@ An \term{innperseq} is a sequence of sequences of sentences on one radius satisf
* The last sequence has one member.
\enditems}
-% \input innperseqs.diag.otx
+\input essays/innperseqs.diag.otx
In diagram \ref[innperdiag], different positions of the vague outer ring at different times are suggested by different shadings. The outer segment moves \dq{down the page.} The figure is by no means an innperseq, but is supposed to help explain the definition. In \sysname{Innperseqs,} a conventional proof would be redundant unless all the statements were on the same radius. And even if the weakest axiom were chosen (the initial outer endpoint), this axiom would imply the initial inner endpoint, and from there the theorem could be reached immediately. In other words, to use the standard definition of \dq{\term{proof}} in \sysname{Innperseqs} would result in an uninteresting derivation structure. Thus, a more interesting derivation structure is defined, the \dq{\term{innperseq.}} The interest of an \dq{\term{innperseq}} is to be as elaborate as the many restrictions in its definition will allow. Proofs are either disregarded in \sysname{Innperseqs}; or else they are identified with innperseqs, and lack Property 8. \sysname{Innperseqs} makes the break with the proof-theorem structure of formalist mathematics.