Latin <arbiter> 'witness, hearer, arbitrator, judge' is of obscure origin. Various unsatisfactory explanations have been proposed. The one reasonably certain relative which <arbiter> has outside Latin is the Umbrian ablative <ar^putrati>, corresponding in form and meaning to Latin <arbitra:tu:> 'by discretion'. It occurs in the following instruction of the Iguvine Tables, Va:10-13.
ar^fertur : pisi : pumpe : fust : erek : esunesku : vepurus : felsva : ar^putrati : fratru : atiier^iu : prehubia : et : nur^pener : prever : pusti : kastruvuf :
'Whoever shall be adfertor, he shall provide vegetables(?) with the unburnt sacrifices, by discretion of the Atiedian Brothers, and at the price of single new dupondii for (single) heads.'
The alphabet used in these instructions is based on the Etruscan, and it employs <t> for both /t/ and /d/, and <k> for both /k/ and /g/. However, it usually employs <b> for /b/, as in <prehubia> 'shall provide'; examples of <p> written for /b/ are few in those of the Tables which use this alphabet. Therefore, <ar^putrati> probably contains genuine /p/, as does <nur^pener> if we accept the most plausible derivation, ablative plural of the name of a coin, *nowo-dupendiyos.
As seen in <ar^fertur>, ar^- is the regular Umbrian reflex of the prefix identical to Latin ad-. The Etruscan-based alphabet uses <u> for both /u(:)/ and /o(:)/. If we had to deal only with <ar^putrati>, we might regard it as the abl. sg. of a verbal noun based on the stem *ad-potra:- 'to go to one or the other of two', 'to mediate between two disputants', 'to decide between two alternatives', etc., from the P-Italic pronominal root *pot(e)ro- 'which of two', Indo-European *kWoteró-, *kWótero- (Sanskrit <katarás>, Greek <póteros>, Old English <hwæðer>, Latin <uter>, etc.). This P-Italic root is otherwise attested in Umb. <putrespe> 'of each of two' = Lat. <utriusque> and Oscan <pútúrúspíd> 'each of both sides' = Lat. <utri:que>. Later Umb. <seipodruhpei> 'in either direction' (Lat. <se:dutra:que>), written in the Latin alphabet, shows the regular Umbrian voicing of -tr- to -dr- seen in other words, but not evident in the older alphabet. Oscan has anaptyxis between /t/ and /r/ in its forms.
Latin <bo:s> 'ox, cow, bull' and <lupus> 'wolf' are borrowed from a P-Italic language, usually identified as Sabine, as shown by /b/ and /p/ where Latin would have inherited /w/ and /kW/. If Umb. <ar^putrati> has been correctly explained above, perhaps Sabine had a parallel verbal noun, P-Italic *ad-potra:-tus 'a going to one side or the other, mediation, discretion', etc. becoming Sab. *ar^potora:tus with assibilation of /d/ and Oscan-like anaptyxis, preventing *-tr- > *-dr- later. The ad-hoc assumption *-r^p- > *-r^b- in a later stage of Sabine must be made, with Old Latin borrowing the resulting noun as *arbotora:tus, post-tonic weakening and syncope yielding <arbitra:tus> before the penultimate law established itself. As <magister> is to <magistra:tus>, <arbiter> could easily have been back-formed from <arbitra:tus> as 'official responsible for mediation'.
Like <arbiter>, Latin <arbor> 'tree' and <arbutus> 'wild strawberry-tree or shrub, Arbutus unedo' are of obscure origin. Usually <arbustum> 'vine-support, vineyard, plantation' is regarded as a collective of <arbor> (early nom. <arbos>, acc. <arbosem>), but the archaic meaning 'vine-support' ("arbustoque vitem copulari", Cato RR 7:1) cannot easily be derived from 'collection of trees'. More likely <arbustum> is etymologically independent of <arbor>. Possibly we can explain these three other words, like <arbiter>, as loanwords from Sabine showing *ad-p- > *ar^p- > *ar^b-.
In this view <arbutus> could represent Italic *ad-putos 'trimmed, pruned to size', with *putos the zero-grade participle of an obsolete verb (IE *peu- 'to cut' vel sim.) to which Lat. <puta:re> 'to trim, prune' is the frequentative. Its feminine gender in Latin, despite -us, follows other names of trees and shrubs. I have no evidence that the Sabines habitually pruned the arbutus to use it as an ornamental shrub, so this explanation is highly tentative.
For <arbustum>, the Italic participle *ad-pos(i)tom '(something) placed against' should have yielded, by hypothesis, Sab. *ar^bostom. Then Old Lat. *arbostom would be borrowed in a specialized vinicultural sense 'support placed against a vine'. Raising of */o/ to Lat. /u/ in closed medial syllables is regular (cf. <onustus>, <alumnus>). The plural <arbusta> would then commonly be applied to the contents of a vineyard where supports were used, or to a whole plantation of vineyards, leading to the extraction of an adjective <arbustus> 'pertaining to supported vineyards', and the usage of <arbustum> as 'single vineyard with supports'. Finally, folk-etymological association with <arbor> by non-specialists would readily shift the meaning of these, giving <arbustus> the sense 'abounding in trees' and making <arbustum> practically synonymous with <arbore:tum> 'collection of trees'.
It is sometimes claimed that <arbor> formerly showed root-syllable gradation like <pe:s> 'foot', gen. <pedis>, <Cere:s> 'Ceres', gen. <Cereris>. That is, Old Latin supposedly had nom. *arbo:s, gen. *arbosis. The nom. sg. <arbor> gives no information since *-o:r was regularly shortened to -or. And the poets are in the peculiar habit of placing the archaic form <arbos> only at the end of a line, where its final quantity is opaque. Thus, while we have no direct evidence, we should not assume that <arbor> did originally have gradation in its declension.
One ancient occurrence of <arbos> is in a mutilated augurial formula cited by Varro (LL 7:8). The unintelligible sequence "templum tescumquem festo" of the manuscript was corrected by E. Norden (Aus altrömischen Priesterbüchern 52-68, 1939) to "templum tescumque m. f. esto" where the abbreviation is for "mea finis", 'my limit'. The relevant section of the formula is thus restored:
... [o]llaber arbos quirquir est qu[od] me sentio dixisse
templum tescumque m(ea) f(inis) esto [laevom]
ollaner arbos quirquir est quod me sentio dixisse
templum tescumque m(ea) f(inis) esto dextrum ...
'The upper(?) tree, wherever it is, for I am aware that I have declared a bounded and sacred space, shall be my limit to the left. The lower(?) tree, wherever it is, for I am aware that I have declared a bounded and sacred space, shall be my limit to the right.'
To an augur, then, the <arbos> marked the limit of a sacred plot of ground for observing birds, and it is conceivable that its ancient sense was not 'tree' as such, but '(object) next to a plot' or the like. The base could then be Italic *podos 'ground, plot of ground' (cognate with Lithuanian <pâdas> 'sole of a foot or boot' and Russian <pod> 'bottom, hearth, floor'), with derived adjective *ad-podyos 'next to a plot'. In the evolution of Sabine augural practice, the original technical sense might have been a grammatically masculine object, such as a stake or pole, used to mark the corners of the observational plot. Later this sense could have been extended to any such markers, in particular standing trees when it became customary to use them to delimit the plot. Now, the original Appius Claudius was the Sabine Attus Clausus ("cui postea Appio Claudio fuit Romae nomen", Livy 2:16), showing that Italic */dy/ in intervocalic position was assibilated to /s/ in Sabine. (The substitution of <Appius> for <Attus> cannot be explained on phonetic grounds. Probably Clausus, as the patron of a large number of Sabine clients, was addressed with a title colloquially meaning 'Father'. But in Rome ca. 500 BCE, which still had an Etruscan presence, <Attus> would have sounded ludicrously close to Etr. <ati> 'mother', and so a new title based on Etr. <apa> 'father' was substituted. This title <Appius> then became Claudius's Roman praenomen, and in fact the hereditary praenomen of first-born sons in his line.)
Determining the Sabine reflex of Italic *ad-podyos is complicated by the fact that samprasa:ran.a occurs with /yo/-stems in Oscan and Umbrian (the /o/ being syncopated before final /s/ or /m/ and the /y/ vocalized to /i/), so we expect it in Sabine as well. In Umbrian, assibilation of the preceding consonant does not absorb the /y/ before samprasa:ran.a can take place. Thus Lat. <Lu:cius> nom. sg. corresponds to Osc. <Lúvkis> and Umb. <Vuvçis>, and Lat. <Fidium> acc. sg. apparently corresponds to Umb. <Fisim> (also <Fisi> and once <Fisei>, but these are mere orthographic variants). With /o/-stems, Oscan and Umbrian have substituted the gen. sg. in *-eis from /i/-stems. Following this behavior, and applying assibilation of */dy/ along with the hypothesis about */dp/, we expect *adpodyos to yield in the singular the Sabine nom. *ar^bosis, gen. *ar^boseis, and acc. *ar^bosim. Old Latin would very likely remodel these into an /i/-stem *arbosis. In order to get the observed early Latin <arbos>, one possibility is back-formation from the plural *arbose:s (OL *arboseies) on the model of other consonant-stems. Another is that the Sabine nom. sg. may conceivably have been *ar^boss, either through secondary syncope or through a combination of assibilation and samprasa:ran.a not exactly parallel to that in Umbrian. Such a pronunciation, if it was still reflected by conservative augural usage in classical times, might explain the unwillingness of poets to place <arbos> in the middle of a line. But further speculation is unwarranted by such paltry evidence.
The final problem is that <arbor> is almost always feminine (an exception being "inter duos arbores" in an inscription of Gaul), while the proposed derivation requires a masculine adjective which has been substantivized (after 'stake, pole' or the like) in Sabine. My guess is that after <arbor> became established in Latin as the generic term for 'tree', its gender as used by most speakers followed that of the feminine majority of Latin tree-names.
DGK