Word of the Month: Proto-Indo-European ‘Four’

As promised in a comment to my previous blog post, I’m going to discuss an etymological question: the origin and structure of the numeral ‘4’ in the Indo-European languages.

The Proto-Indo-European numeral ‘four’ had several intriguing properties. It was the largest non-complex cardinal number that agreed grammatically with a noun it modified. Consequently, it was inflected for gender and case, like any ordinary adjective. It shared that property with the words for ‘one’, ‘two’ and ‘three’. For obvious semantic reasons, their declension was defective: ‘one’ was normally singular, ‘two’ was declined only in the dual number, and ‘three’ and ‘four’ only in the plural.

The fourth is for luck.

The basic forms of the numeral ‘4’ (as reconstructed in handbooks) were the animate “count plural” *kʷetwores and the inanimate (neuter) “collective plural” *kʷetwōr (from earlier *kʷetwor-h₂). There is some uncertainty about the accentuation of these forms: some reconstruct them with PIE stress on the first syllable, others on the second (the comparative evidence is not unambiguous).

Proto-Indo-European probably had no feminine gender as a formal category, but it had ways to express femininity in derivatives. Curiously, the numerals ‘three’ and ‘four’ seem to have had feminine forms, preserved only in Celtic and Indo-Iranian. They are reconstructed as *tisres ‘3’ and *kʷetesres ‘4’. The final *-es is the familiar nom.pl. ending of animate stems ending in a consonant, but the rest looks baffling. The suffix *-sr-, known also from the Anatolian languages, where it forms nouns denoting human females, probably reflects an archaic, almost completely abandoned word for ‘woman’ (*ser-), although the zero grade (absence of a vowel) in the nom.pl. is aberrant; the initial part (*ti-, *kʷete-) looks in either case like the badly mangled residue of an actual numeral stem. Given the normal rules of IE word-formation, we would expect something like *trí-sor-es and *kʷétwr̥-sor-es. The characteristic “defects” of the attested forms are nevertheless shared between Celtic and Indo-Iranian; they must therefore go back at least to their most recent common ancestor. Such distortions are not quite unexpected in compound words, which commonly lose their transparency through irregular simplification.

Let’s ask a stupid question: what is *kʷetwores/*kʷetwōr the plural of? I mean, if it’s really an adjective, perhaps it had an older “etymological” meaning before it became part of the numeral system? If we strip off the inflections, what remains is the stem *kʷetwor-/*kʷetwr- (the second vowel is lost in so-called “weak” case-forms like loc.pl. *kʷetwr̥sú). This “bare” stem also occurs as a compositional variant of ‘four’, sometimes with  the final segments reversed (*kʷetwr̥- ~ *kʷetru-).

An Indo-European stem with four consonants and two vowel slots must have been morphologically complex at some point. The most likely division into morphemes would be *kʷet-w(o)r-. The *-w(o)r- part looks familiar. A suffix of this form is found in a number of Indo-European nouns, typically inanimate abstracts derived from verb roots. We also find it e.g. in the PIE word for ‘fire’, *páh₂wr̥, which is not obviously deverbal (though a connection with *pah₂- ‘guard’ is thinkable). We also have at least one evidently archaic example od an adjective built in the same manner. Beside the inanimate noun *p(e)iH-wr̥ ‘fat’ (Greek pĩar) we find an adjective meaning ‘fat, fertile’ whose masculine form was *p(e)iH-won-; its neuter must have been originally identical with the noun, and a suffixed feminine *piH-wer-ih₂ was added to the paradigm as the IE gender system developed a three-way contrast (I use the cover symbol *H here for a laryngeal whose “index” is hard to determine). Note the consonant alternation in the suffix: it’s characteristic of an entire class of neuters, so-called r/n-stems. They show *-r in the nom./acc. singular and collective (e.g. *páh₂-wōr, the collective of the ‘fire’ word), but *-n- in the remaining cases (like the gen.sg. *ph₂-wén-s). The variant *-n- is also expected in related animate forms, with the strange exception of *-r- occurring before the femininising suffix *-ih₂, as illustrated by the preserved forms of the adjective ‘fat’. The striking agreement between Greek píōn (m.), píeira (f.) and Vedic pī́van- (m.), pī́varī (f.) shows that this unusual alternation is inherited.

To continue our Gedankenexperiment: so far we haven’t identified the underlying root *kʷet-. Still, if we tentatively assume that it was indeed a verb root, some predictions can be made: beside the hypothetical abstract noun *kʷét-wr̥, possible derivatives include an adjective of exactly the same form in the inanimate gender. Its expected animate form would be *kʷét-won- (nom.sg. *kʷétwō, nom.pl. *kʷétwones). The neuter noun/adjective would form the collective plural *kʷétwōr. Of these forms, two can be regarded as attested: *kʷétwōr is a possible reconstruction of the neuter numeral, and *kʷétwr̥ is its uninflected compositional variant. Conspicuous by their absence are any forms with *n instead of *r. Why, for example, is the animate (masculine) plural *kʷetwores rather than *kʷetwones? The most natural explanation is that this particular plural isn’t old enough to participate in the *-n/r- alternation.

Let’s imagine that *kʷétwr̥ was originally a neuter noun (without an accompanying adjective). Whatever its etymological meaning (let’s symbolise it ‘X’), the collective plural *kʷétwōr (meaning ‘a set of instances of X’) came to be employed as a cardinal number, at first uninflected (like ‘five’, ‘six’, etc.), but eventually attracted into the adjective system, presumably on the analogy of the already adjectival numerals ‘two’ and ‘three’. In the early history of Indo-European the accent was often shifted to the second syllable in such collectives; hence the by-form *kʷ(e)twṓr, in which the first vowel could be phonetically reduced (*kʷətwṓr) or lost altogether. Non-initial stress is reflected in Germanic (cf. Gothic fidwor, displaying the voicing effect of Verner’s Law), and vowel reduction accounts for Latin quattuor (with Lat. /a/ from *ə).

When *kʷétwōr ~ *kʷ(e)twṓr came to be interpreted (and declined) as a neuter plural adjective, an animate counterpart was analogically supplied by adding appropriate inflectional endings to the stem *kʷétwor- or *kʷ(e)twór-. Since its origin as an n/r-noun had been forgotten by that time, PIE-speakers had no reason to make their life more difficult by reviving an ancient alternation. The only case-forms requiring distinctly animate inflections (different from neuter ones) were the nom.pl. (*-es) and acc.pl. (*-n̥s from earlier *-m̥-s). The unsettled stress pattern (*kʷétwores ~ *kʷ(e)twóres) may well be an old feature of the numeral ‘four’.

Some details require more attention, but first I would like to address the question left unanswered above: what exactly was *kʷet-, the root supposedly underlying the derivation of the numeral ‘four’? I will try to suggest an answer in the next post (later this week, I hope), so please stay tuned.

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