A group of verbs that are preterite (past tense) in form but present tense in meaning. They are mainly the modal verbs of English and related languages, such as shall ~ should, can ~ could, may ~ might. Their hybrid nature partly explains why these are grammatically unusual even in modern English, though it is clearer if you look at them in Old English.

The name is ungainly. You may also see variants like perfect-present or praeterito-present.

Modal verbs

A normal verb in the present tense has an -s ending in the third person singular: I eat, you eat, we eat, they eat, but she, he, or it eats. In the past tense there is no such marking: I ate, she ate.

The modal verbs of English are those that stand in front of another and modify its meaning: I eat, I can eat, I would eat, I might eat. They have several peculiarities. First, their third singular has no -s: she would eat, he can eat.

Second, they mostly come in pairs, present and past: today I can eat, yesterday I could eat. But the supposedly past-tense forms (could, would, should, might) usually have distinct modal meanings of their own: I could do with another cup of tea, you would like that, they should listen more, we might do it tomorrow.

Thirdly, the past tense forms are irregular: we don't use *canned, willed, shalled in this modal context.

They can be negated by themselves, and precede the negative: I will not go, compared with a normal verb like go that has to take do-support in the negative, which it follows: I did not go.

Old English strong verbs

In Old English, as in modern English, there were strong and weak verbs. Simplifying slightly, the strong verbs form their past tense by ablaut (vowel change), such as bind ~ bound, while the weak verbs just add an ending -(e)d, as in walk ~ walked.

Here are the forms of a normal strong verb in its present and preterite (past) tenses:

present:
   ic binde        I bind
   þú bindest      thou bindest
   hé bindeþ       he binds (or bindeth)
   wé bindaþ       we bind
past:
   ic band         I bound
   þú bunde        thou boundest
   hé band         he bound
   wé bundon       we bound
In Old English the plural forms for ye and they were the same as for we. The past tense had two different ablaut vowels. Generally the ending vowels all disappeared in Middle English. In early modern English the thou forms began to disappear and the -eth ending was replaced by -s.

Here are the corresponding past forms of a weak verb:

   ic híerde       I heard
   þú híerdest     thou heardest
   hé híerde       he heard
   wé híerdon      we heard

Old English preterite-presents

The preterite-present verbs of Old English were a hybrid between strong and weak. The second person singular (thou form) had -est and the same vowel as the rest of the singular, like a weak verb. But the first and third singular had zero endings, and singular and plural had different ablaut vowels, like a strong verb. Here is cunnan 'know, ken, can':
   ic cann         I can
   þú canst        thou canst
   hé cann         he can
   wé cunnon       we can
This is a mix of weak and strong past forms, but is present in meaning. This is why there is a zero ending on the he form in modern English he can, and so on for the rest of the modals.

Since the meaning was present, these needed a new past tense, so a weak past was created, cúþe. This doesn't look completely regular (why -þ- instead of -d-?), but the essential thing is it inflected regularly as a weak past tense.

Similarly, the other modals that had present tense meaning by virtue of being preterite-present also developed new weak forms to supply the past tense. I'll now briefly go through details of each one. They were in some cases rather churned up in Middle English, and I won't give every variant.

Also, in many cases the actual meanings have changed since the Old English period.

can, could, ken, cunning, couth

Can had the past tense cúþe, which became coud in Middle English. The letter L crept into the spelling and gave could by false association with would and should.

In Old English cunnan meant 'to know', so ic cann was 'I know'. Via the sense 'I know how to' it became the modern 'I am able to'. A newer sense (from the nineteenth century on) is 'I am allowed to': you can go now. Also, the past tense could has taken on an extra new meaning 'it is possible that'. The old sense survives as the dialectal ken and in the participial cunning.

There was also an Old English adjectival form cúþ 'known'. This gives rise to the rare modern couth, and its much more common negative uncouth: 'not known, outlandish, not the done thing round these parts'.

may, might

The Old English for 'can, be able to' was magan. The changed vowel in the present singular is illustrated by ic mæg and the new weak past was mihte or meahte. These give us our modern forms may and might.

Also, the meaning of may has changed from 'be able to' to 'be allowed to', and might has additionally acquired the new senses 'it is possible that' and 'it is uncertain whether'.

mote, must

The sense of 'may, be allowed to' was conveyed in Old English by a verb with present singular mót, which survives today only in the archaic form mote said to be used by witckhes to end their spells: So mote it be.

The weak past móste gives our modern must. This is a present meaning with the strange property of having no past form. To say 'must' in the past we must use a different verb: yesterday I had to use a different verb.

shall, should

The preterite-present sceal with new weak past scolde meant 'to be obliged to' in Old English. These survive as shall and should.

From an early period the present was co-opted to form a future tense: first as a commanding 'You shall obey me', then a definite resolution 'You shall go to the ball', and subsequently as a plain future 'I shall be there tomorrow, I think' in the first person. In recent years this has dropped out to a large extent and most of us probably say 'I will' for simple future.

As with the others, its past should grew its own secondary meanings: two more in this case, 'is probably, is likely to be' and 'ought to, be under some obligation to'.

ought

The verb 'to own' had present singular áh and weak past áhte, giving modern owe and ought. Only the latter has kept a modal sense in modern English, and is also different from the others by having an attached to: I ought to go.

dare, durst

There are numerous other helping verbs in modern English, usually connected with a to: I tried to go, wanted to eat, went and looked, dared to question. But grammatically these are quite normal, and don't show any irregularity.

Dare, however, in rather archaic language still shows traces of the fact that it was once a preterite-present. The weak past of dearr was dorste, and we still find durst in Tolkien: I durst not do it. The third person singular may even stand without the regular -s: he dare not go. In less archaic style we wouldn't say he dares not go, we'd say he doesn't dare to go.

The verb need has gravitated into modality too, though it's not preterite-present: like dare it can now take an s-less present tense: she need not do it. (The OED dates this usage to 1470.) More commonly perhaps that's said as a non-modal verb with do-support: she doesn't need to do it.

will, would

Obviously will and would belong here, but strictly speaking they aren't preterite-present, because their conjugation was different in Old English. The present had an ending: ic wille; and the plural also used the present plural ending: wé willaþ. The weak past was wolde. But of course this pair has gravitated into the orbit of the other modal verbs.

The original meaning 'want to' has become a future tense, and the past has become a conditional, as well as other idiomatic uses: well, you would say that; the baby would cry just at that moment.

German and Germanic

This peculiar nature of preterite-present modals was not an invention of Old English, but occurred in its ancestor Proto-Germanic, because all the descendant Germanic languages such as Gothic, Old Norse, and German also show them.

Several Old English preterite-presents have not survived to the present day. They are deah ~ dohte 'avail', man ~ munde 'remember', and þearf ~ þorfte 'need'.

This last however still exists in German, as darf ~ dürfen, but meaning 'may'. The German senses are often a little different from the corresponding English ones. The preterite-presents are often recognizable by the fact that the singular and plural have different vowels, a feature that might puzzle those who know a little German grammar. Others include kann ~ können 'can', mag ~ mögen 'is probably; like to', muss ~ müssen 'must', weiss ~ wissen 'know', and will ~ wollen 'want to'. However soll ~ sollen 'ought to', the etymological equivalent of English shall, is regular.

to wit, Proto-Indo-European

It's mainly the Germanic branch of the Indo-European family that shows this preterite-present behaviour, and it's the only branch where all the modals exhibit it. There are several verbs in Latin that have prefect tense endings but are present in meaning: odi 'I hate', memini 'I remember' (showing the reduplication also characteristic of the perfect), and novi an uncommon word for 'I know'.

But one verb has this behaviour in multiple branches, so must have had it in the original Proto-Indo-European. That is the verb *wid- 'to see' (cf. video, vision from Latin), with a perfect tense form whose meaning is the present tense of 'know'. This makes sense semantically: the transfer from having seen a thing to knowing it. In Sanskrit veda 'know' comes from the root vid- 'see'. In Greek likewise oîda 'know' comes from ideîn 'see' (the initial w- was lost in early Greek).

The English cognate of this is wit. In Old English witan meant just 'know' and was a preterite-present with present singular wát and new weak past wiste or wisse. This survived with its vowel alternation into Middle English: I wot, thou wost, he wot, we wit, and infinitive to wit. Apart from to wit, which is no longer a living verb, these have dropped out of modern English, but may still be found in archaizing language: God wot! I wot not, my liege. The waters were muddied in Middle English as new regular forms developed in the present: thou wottest; he, she, or God wotteth; but these did not survive long.

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