If you give FontSize a number, it is ok.

Plot[Evaluate[{P[\[Xi]]}], {\[Xi], 0, 3 (2 \[Pi])}, PlotRange -> All, 
 PlotLabel -> "P(z-C t)", 
 LabelStyle -> Directive[FontSize -> 14, Black, Bold], 
 AxesStyle -> Black, AxesLabel -> {"z", "A"}, ImageSize -> Large, 
 PlotRange -> All]

Greetings!

I use 10.0.2.0 and get the same error for the following code:

Plot[
 Evaluate[{P[\[Xi]]}],
 {\[Xi], 0, 3 (2 \[Pi])},
 PlotRange -> All,

 PlotLabel -> "P(z-C t)",
 LabelStyle -> Directive[FontSize -> Medium, Black, Bold],
 AxesStyle -> Black,
 AxesLabel -> {"z", "A"},
 ImageSize -> Large,
 PlotRange -> All
 ]

If I remove LabelStyle option it works very fine!

What could be the issue?

If Mathematica had been fine and now has a strange behavior, I would suspect a damaged start-up file. These can be reset to default contents; see http://support.wolfram.com/kb/12464 .

If the cause is a corrupted style sheet, it might be easier to uninstall and re-install Mathematica than to try tracking down which line in which style in which stylesheet.

Have you checked in the Option Inspector (under the Global scope) for the value entered in the FontSize option?

If so, perhaps you have a problem with a corruption of your default StyleSheet (though I am not sure how that would happen, since those style sheets are generally protected from being overwritten).

One thing to try is to reset all preferences to defaults under the File>Preferences... menu item.

Craig, have you reported the bug you found with BaseStyle -> Large: it appears that it is associated with the PlotLabel.

Thanks WCC, but setting Style options in particular calls isn't the issue. (But, yes, your second option specification works in M10 but not in M9) My problem is that Mathematica seems to give the message "The specified setting for the option FontSize cannot be used." all of the time. Switching windows, start-up, closing windows, etc. I must have some sort of corrupted options file, but I don't know how to track it down and fix it.

Strange