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I started browsing through a proof copy of a Dent's Children's Illustrated Classic for some light relief.
It's a bit like watching a brilliant, mischievous mathematician at the blackboard, working through a proof: he's skipping the "obvious" steps and at some point he may start pulling your leg.
That is enough to refute claim (a), the claim that all diagrammatic thinking in thinking through a proof is superfluous.
That entire process would constitute thinking through a proof of the conclusion; and the diagrammatic thinking involved would not be superfluous.
This is done through a proof of stake mechanism, where a cryptographic message is signed by your private key and weighted by the amount of stake you have.
The idea behind (a) is that, because diagrammatic reasoning is unreliable, if a process of thinking through an argument contains some non-superfluous diagrammatic thinking, that process lacks the epistemic security to be a case of thinking through a proof.
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We also demonstrate the feasibility of our framework through a proof-of-concept implementation.
We demonstrate through a proof-of-principle study how the two sub-groups that display distinct patterns of disease progression may be compared on clinical attributes that correspond to the maximum difference in progression patterns.
We develop and demonstrate through a proof-of-concept case study, a new "query-driven" heuristics for database design that seeks to identify database structures that perform robustly in dynamic settings with dynamic queries.
This was done through a proof-of-concept evaluation of the risk of immune thrombocytopenic purpura (ITP) and aseptic meningitis (AM) following administration of the first dose of measles-mumps-containing vaccines using the self-controlled risk interval method in the primary analysis.
The models were evaluated through a proof-of-concept clinical study in healthy volunteers.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com