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(In linguistics, modality sometimes also refers to the means of transfer, which helps remind us that it's often multi-modal, e.g spoken languages are acoustic and visual, sign languages are manual and visual, that there are variations like manual-somatic, that there is behaviour (expressions, shrugging, hand gestures) that typically also assists, and more[1]. But more usually...)

In linguistics and philosophy, modality[2] usually refers to expressing things like permissibility, desirability, likeliness, truthfulness.

Modal language, then, is any utterance that expresses such things.

Modal language is frequently also normative - which refers to the permissibility part. For example, laws are largely normative, that tend to be exporessed in modal language.

In philosophy, and teaching, modality helps being clearer about what you know, what you think is likely, why, and helps to encoding some of that into your phrasing.

To paraphrase a quote from wikipedia, the difference between "unicorns never existed" and "it seems unlikely that unicorns could ever have existed" is largely a modal one.

In most langauges, expressions have clear signals that they are modal in this sense, including

modal auxiliaries like "can", "could", "should", or "must", "might", "will"
modal adverbs such as "possibly" or "necessarily"
modal adjectives such as "conceivable" or "probable"

...though may also be more embedded in grammatical expressions, as direct as saying whether you know or believe something, or phrases like "they say" or "rumour has it", but also more complex structures.

It also helps certain language learning, in that some languages may have specific ways of expressing modality, may have specific modal forms others do not, and such.

If you life subtypes:

Epistemic modality - evaluates potentials, often via observations and reason

"You must be right"
"Agatha must be the murderer"
Not necessarily objectively true, but
Tends to have an unspoken "with what we know, ...", i.e. relative to the information the speaker(s) have

Deontic modality - speaker's attitude of what should happen

"You must go now"
"Agatha must go to jail"
See also deontology

Intrinsic modality - often about options that inherently come from a things or situation

"The meeting can be canceled"

Disposition modality - intrinsic ability

"I can play the guitar" - mostly suggesting I will potentially do so

The last three are also grouped under 'root modality' (J Benjamins (2007) "Cognitive English Grammar")

People have argued for marginal modality (sometimes semi-modal), e.g. pointing out that English auxiliary verbs such as need, used to, ought to, dare, are also expressing potential situations, but ones that are often semantically fuzzier.

(The distinction in English is then between modal auxiliaries and marginal auxiliary verbs, marginal modals)

See also: