Alethic modality is a linguistic modality

Linguistic modality

In linguistics, modality is what allows speakers to evaluate a proposition relative to a set of other propositions.In standard formal approaches to modality, an utterance expressing modality can always roughly be paraphrased to fit the following template:...

 which indicates logical necessity, possibility or impossibility.

Alethic modality is often associated with epistemic modality in research. However, it has been questioned whether this modality should be considered distinct from epistemic modality

Epistemic modality

Epistemic modality is a sub-type of linguistic modality that deals with a speaker's evaluation/judgment of, degree of confidence in, or belief of the knowledge upon which a proposition is based. In other words, epistemic modality refers to the way speakers communicate their doubts, certainties, and...

 which denotes the speaker's evaluation or judgment of the truth. The criticism states that there is no real difference between "the truth in the world" (alethic) and "the truth in an individual's mind" (epistemic). An investigation has not found a single language in which alethic and epistemic modalities are formally distinguished, as by the means of a grammatical mood

Grammatical mood

In linguistics, grammatical mood is a grammatical feature of verbs, used to signal modality. That is, it is the use of verbal inflections that allow speakers to express their attitude toward what they are saying...

. In such a language, "A circle can't be square", "can't be" would be expressed by an alethic mood, whereas for "He can't be that wealthy", "can't be" would not be expressed by an alethic mood. As we can see, this is not a distinction drawn in English grammar.