Can you log the instruction you are receiving from your CFI towards your Private as both dual received and PIC? At face value this seems to be a simple question and answer, but as you dig into it I can see arguments both ways. There is no FAA LOI on the topic that I can find.
Wanted to see what the opinions are out there on this.
If you instead trained in an LSA, then yes you could log it.
(e) Logging pilot-in-command flight time. (1) A sport, recreational, private, commercial, or airline transport pilot may log pilot in command flight time for flights-
(i) Except when logging flight time under §61.159(c), when the pilot is the sole manipulator of the controls of an aircraft for which the pilot is rated, or has sport pilot privileges for that category and class of aircraft, if the aircraft class rating is appropriate;Note that the regulation specifies only category and class, not necessarily PIC privileges. As such, the holder of a Sport Pilot certificate with ASEL privileges receiving training in a non-LSA ASEL can log both training and PIC time. It is much the same as a Private Pilot with ASEL but no complex or HP endorsement taking training in a complex or HP airplane. That PP gets to log both training and PIC time, and that is explicitly approved in a Chief Counsel interpretation letter. The logic is the same regarding Sport Pilots given the added language in 61.51(e)(1).