User talk:Pterodaktilis

IMHO the original translation (as of 2020-04-05 10:37:51 UTC) for the formula:

   p⊃q:q⊃r.⊃.p⊃r

as

   ((p⊃q) ∧ (q⊃r))⊃(p⊃r)

was incorrect.

The rule, as stated in PM vol. I (2nd ed., 1963, https://ia800602.us.archive.org/35/items/PrincipiaMathematicaVolumeI/WhiteheadRussell-PrincipiaMathematicaVolumeI_text.pdf [viewed 2020-04-04]) reads:

"The scope of the bracket indicated by any collection of dots extends backwards or forwards beyond any smaller number of dots, or any equal number from a group of less force, until we reach either the end of the asserted proposition or a greater number of dots or an equal number belonging to a group of equal or superior force." (p. 9)

Thus, the scope of ":", even though if is in group III which has lower priority as group I single dots in the formula, still extends to the end of the formula over the smaller number of dots (single dots round the '⊃' symbol).

Also, the example on page 10 of PM is very thorough:

"“p⊃q:q⊃r.⊃.p⊃r“ will mean “if p implies q; and if q implies r then p implies r.“ (This is not true in general). Here the two dots indicate a logical product; since two dots do not occur anywhere else, _the scope of these two dots_ extends backwards to the beginning of the proposition, and _forwards to the end_." (emphasis mine)

I've fixed the formula. The text should probably also be amended, "having the same priority" -> "having higher priority".

Please double-check.

Pterodaktilis (talk) 16:50, 5 April 2020 (UTC)