Is there any truth to the idea that you shouldn't multiply seasonings when multiplying a recipe?
The notion that salt or spices specifically don't scale linearly sounds like nonsense to me.  In any recipe involving salt and water, the salt is dissolved, so all that matters is the concentration, and that concentration is going to be the same with linear scaling.

Scaling in general is problematic when scaling more than 2x or 4x.  When you take into account that:


Recipes targeted at home cooks are imprecise to begin with and often use volumetric measurements that are sensitive to heat, humidity, and other environmental conditions, so the imprecision is magnified at larger scale;
Larger portions of food may get cooked less evenly and/or at less consistent temperatures due to the volume/surface area ratio; that part is correct, but it has nothing to do with salt, it has to do with your equipment.  On the stovetop, most of the heat is coming from the bottom of the pan unless you use induction, and even in an oven you've got one or two heat sources radiating heat in a specific pattern.
Cooking times are also going to vary due to changes in things like rates of evaporation.  The total amount of heat you're able to deliver at any given time generally does not increase as quickly as the amount of heat you need to deliver, so very often you need to increase cooking times.


I'm sure you probably already know all this, but the reason I'm pointing it all out is that I'm pretty sure that this odd-sounding assertion about non-linear salt/spice scaling is due to some mutation or misunderstanding of general scaling issues.

Probably, salt and spices are typically present in very small quantities in most recipes, and those quantities are already wild guesses much of the time, so the effect of compounding all this wild inaccuracy, especially with volumetric measurements, is actually pretty noticeable at large scale.  Scaling sucks with these ingredients because the initial quantities and scaling method are both nonsense.

Assuming you have a precise recipe that gives weight measurements, and you scale by weight, then you're not going to have any problems as long as you either cook it in batches or adjust your cooking time/temp accordingly.

I suppose I could be wrong, but I spent 20 minutes digging for some evidence to contradict my claims above and came up dry; you'd think that somebody would have presented some evidence if the claim were true.