The plural of English nouns is almost always formed with an S suffix. We can group deviations from this simple rule under three headings. Sometimes for illustration I'll mix up spelling and pronunciation, but this should be obvious.
  1. The S occasionally takes variant forms (as in buses, halves); there are some where the S has contracted in to form a new word (dice, pence).
  2. There is a small group of native English words that take other plurals, either zero (sheep, aircraft), or one with N (oxen, children, kine), or an internal vowel change (men, mice, kine).
  3. Foreign words sometimes retain foreign plurals. I shall not discuss these here: they need a node of their own.

Alterations of S

In most cases the S takes one of three pronunciations, which I shall write S, Z, and IZ: the third has some vowel, not necessarily that of "is" in your dialect, and in fact the schwa in most. The choice between these three is straightforwardly determined by the preceding sound.

Use IZ after a sibilant. For the purpose of this rule, English has six sibilants, S Z SH CH J and the ZH sound in sabotage. So bus ~ busIZ, maze ~ mazIZ, church ~ churchIZ, judge ~ judgIZ.

Use S (as in hiss) after any other voiceless sounds, namely P T K F and TH. So cap ~ capS, port ~ portS, plinth ~ plinthS.

Use Z after the remaining sounds, including vowels. So goad ~ goadZ, bag ~ bagZ, ball ~ ballZ, sofa ~ sofaZ.

The S and Z sounds are spelt with S, and the IZ sound is spelt with ES: catS = cats, dogZ = dogs, busIZ = buses. But IZ is spelt plain S if there is already a silent E at the end: horse ~ horsIZ = horses.

Most words ending in F or TH (as in thin) sounds change it to the voiced equivalent V or DH (= TH as in this): knife ~ kniVZ, bath ~ baDHZ. But this is not entirely automatic: you get words that don't make the change, e.g. giraffe, plinth. In general, common native words do change.

Uniquely, S changes to Z in house ~ houZIZ, though the spelling isn't affected.

Some compounds like "still lifes" and "Toronto Maple Leafs" resist the change even though they contain a word that undergoes it. This makes sense if you consider them as containing an extra inaudible compounding element, like brackets, and there being a rule FS -> VZ. Then life goes to lives, but (still life)s contains the phonetic string "f)s", not "fs", so the rule doesn't apply.

Then there are the respelling rules that have no phonetic effect: -y (but not -ey) becomes -ies, and -o becomes -oes in a few common words like zeroes, heroes, potatoes, tomatoes, goes.

Some things are plural to begin with: trousers, scissors, oats. If you need to make a plural of the countable things you add pairs of. (This class is called plurale tantum, 'plural only'.)

There are several odd words where the S has been fused into the word and respelt with C: die ~ dice, penny ~ pence. ('Dice' is also used in singular, and 'dies' and 'pennies' also occur depending on the meaning.) 'Mouse' has a change in pronunciation of its S as well as umlaut in 'mice'.

Native elements other than S

There is an N element in oxen, kine (from cow), brethren, and children. Formerly, hanging on into early modern English, you might also see eyen, shoon, hosen, and treen. This was one of the classes of Old English noun inflection; like German it had a number of different ways of forming plurals. The N suffix, had it survived in all the words it applied to in Old English, would also have given us namen, sunnen, moonen, starn, timen, churchen, hearten, tonguen, and ladyen.

There is no change in sheep. The word *sheeps does not exist and cannot be used in English. A number of other animal names, especially game animals and birds, often have zero plural, but they all have an alternative S plural: two fish(es), three partridge, four deer, five elk, six snipe (but six starlingS, seven rabbitS: they weren't hunted), and so on. It is also common with measurements (five foot, ten stone). Oddities: (i) fox is always pluralized foxes; (ii) aircraft (and hovercraft etc.) can't take a plural ending.

This semantic restriction is modern; in Old English the zero-ending class was just another word class: if it had survived intact we would speak of two bone, three house, four child, five bairn, six year, seven thing, eight word.

A class that left no survivors added U: we longer have shipu, weapnu, devlu, headu, or wondru. Other classes also disappeared entirely because of the loss of final vowels. In Middle English the S ending absorbed almost all the others. A small class added R: child could be one of these (or could stay unchanged); and so also lamber. The plural childer later acquired a second plural ending, N, to give modern children.

The words men, women, mice, geese, feet, teeth, kine, and brethren took the vowel change called umlaut. This was caused by a following vowel I or consonant J (Y) in the early Old English period, which disappeared after altering the previous vowel. (The vowel change in child/children is an unrelated more recent development.) Kine is cow with both umlaut and N; and brethren likewise has both.

The class of umlauting plurals was only slightly larger in Old English: if they had survived, we would say one book but two beech; one borough and two birry (or some such spelling).

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