Preterit present verbs

Preterit-present verbs
The so-called preterite-present verbs are a small group of anomalous verbs in the Germanic languages in which the present tense shows the form of the strong preterite.

Explanation
Some Germanic verbs underwent a shift whereby their strong preterite-tense forms became reinterpreted as their present-tense forms. New "weak" endings were then used to form the new preterite tense. The present tenses of these verbs therefore resemble the preterite tense forms of strong verbs, below.

Source
The perfect of Indo-European originally signified a current state of being rather than any particular tense; in the sense that the preterite-present verbs are non-past and still largely signify current states (temporalized as present tense), they constitute a partial retention of the originally non-past perfect of Indo-European.

For example
Proto-Indo-European *woida, "I have seen", which is attested in Latin vīdī (same meaning) became Gothic wait meaning "I know". The present tense thus has the form of a vocalic (strong) preterite, with vowel-alternation between singular and plural. A new weak preterite is formed with a dental suffix.

The known verbs in Proto-Germanic (PGmc):

Ablaut
The present tense has the form of a vocalic (strong) preterite, with vowel-alternation between singular and plural. A new weak preterite is formed with a dental suffix. The root shape of the preterite (in zero-grade) serves as the basis for the infinitive and past passive participle.

Personal endings
For the most part, the personal endings of the strong preterite are used for the present tense. In West Germanic the endings of the present tense of preterite-present verbs represent the original IE perfect endings better than that subgroup's strong preterite verbs do. The endings of the preterite (except for *kunnana) are the same as the endings of the first weak class.

Subsequent developments
In modern English, preterite-present verbs are identifiable by the absence of an -s suffix on the 3rd person singular present tense form, for instance, he can with he sings (pret. he sang); the present paradigm of can is thus parallel with the past tense of a strong verb.

Subsequent developments
In modern German there is also an ablaut shift between singular ich kann (I can) and plural wir können (we can). In the older stages of the Germanic languages (Old English, Middle High German) the past tense of strong verbs also showed different ablaut grades in singular and plural.

Subsequent developments
Many of the preterite-present verbs function as modal verbs (auxiliaries which are followed by a bare infinitive, without "to") and indeed most of the traditional modal verbs are preterite-presents. Examples are English must and shall/should, German dürfen (may), sollen (ought), mögen (like), and müssen (must).