The difference between epistemic & deontic, necessity & possibility, in an overlapping diagram

This is a handy reference diagram I made way back in grad school for remembering the difference between epistemic necessity, deontic possibility, and other basic types of modality, and I’ve finally put it online. 

Here’s how it works: 

In linguistics, modals (aka modal verbs, modal auxiliaries) refer to words like can, could, shall, should, will, would, may, might, must which indicate likelihood, permission, obligation, and ability. The concept of modality includes both modal auxiliaries as well as longer constructions, like ought, have to, be obliged to, be able to, be capable of, it’s possible that, it’s necessary for __ to, it’s obligatory to, it’s permissible that, possibly, necessarily, maybe, perhaps, and so on.   

In the diagram, the blue areas are epistemic modality (according to evidence, reasoning, or beliefs), the red areas are deontic modality (according to a set of rules or desires), the dark areas are necessity (in all possible worlds), the light areas are possibility (in at least one possible world). Every area has both a colour (blue/red) and a shade (light/dark) because modality is made up of a modal base (according to what, on the basis of what) and a modal force (how strong is the result). 

Here are some examples for each of the regions.  

Dark blue is epistemic necessity

  1. “It must be raining outside (I can hear the rain).” In all worlds consistent with my beliefs, it is raining outside. 
  2. “When you add vinegar to baking soda, it should fizz.” In all worlds consistent with my reasoning about chemical properties, vinegar added to baking soda fizzes. 

Light blue is epistemic possibility

  1. “It may be raining outside (I heard that it was going to rain today)” In at least one world consistent with my beliefs, it is raining outside. 
  2. “The doctor has said, they can go to the bathroom.” In at least one world consistent with the doctor’s assessment of their physical capabilities, they go to the bathroom. 

Dark red is deontic necessity

  1. “It must rain this week (in order for the crops not to spoil)” In all worlds consistent with my desires, it rains this week. 
  2. “You should drive under the speed limit.” In all worlds consistent with the rules for proper driving, you drive under the speed limit. 

Light red is deontic possibility

  1. “It may rain this week (as far as I’m concerned, I’m not planning any activities that would be spoiled by the rain so I don’t care).” In at least one world consistent with my desires, it rains this week. 
  2. “The teacher has said, they can go to the bathroom.” In at least one world consistent with the teacher’s rules for the classroom, they go to the bathroom.  

Notice that English is generally good at making distinctions between necessity and possibility but bad at making distinctions between epistemic and deontic, which must be cleared up via context. Some languages do make straightforward lexical distinctions between various flavours of modality like epistemic and deontic. 

Also note that more advanced theories of modality distinguish between more types of modality than epistemic and deontic (such as circumstantial, dynamic, logical, metaphysical, ability, teleological, bouletic, etc) but this is a basic introduction to making these distinctions at all, so I’m not going to get into them here. If you want to expand the diagram yourself, however, you could assign these other types of modality other colours, as long as you give them each two shades. (And in case anyone reading this already knows a lot about modality, I’d also like to point out that the Wikipedia article on linguistic modality is in dire need of improvement.)