Hypothesized pre-Celtic language substrate
The Goidelic substrate hypothesis refers to the hypothesized language or languages spoken in Ireland before the arrival of the Goidelic languages.
Hypothesis of non-Indo-European languages.
Ireland was settled, like the rest of northern Europe, after the retreat of the ice sheets c. 10,500 BC. Indo-European languages are usually thought to have been a much later arrival. Some scholars hypothesize that the Goidelic languages may have been brought by the Bell Beaker culture circa 2500 BC. This dating is supported by DNA analysis indicating large-scale Indo-European migration to Britain about that time. In contrast, other scholars argue for a much later date of arrival of Goidelic languages to Ireland based on linguistic evidence. Peter Schrijver has suggested that Irish was perhaps preceded by an earlier wave of Celtic-speaking colonists (based on population names attested in Ptolemy's "Geography") who were displaced by a later wave of proto-Irish speakers only in the 1st century AD, following a migration in the wake of the Roman conquest of Britain, with Irish and British Celtic languages only branching off from a common Insular Celtic language around that time.
Scholars have suggested:
Suggested non-Indo-European words in Irish.
Gearóid Mac Eoin proposes the following words, some of which are found only in Early Irish literature, as deriving from the substrate
He also puts forward the following place names, also from old Irish literature: 
Gerry Smyth, in "Space and the Irish Cultural Imagination", suggested that "Dothar", the Old Irish name for the River Dodder, could be a substrate word.
Peter Schrijver submits the following words as deriving from the substrate: 
Schrijver noted the numerousness of words relating to fishing. He suggested that the presence of unlenited stops among these fishing words may indicate that these words entered Irish as late as 500AD. In a further study he gives counter-arguments against some criticisms by Graham Isaac.
Ranko Matasović lists the following words
He also points out that there are words of possibly or probably non-Indo-European origin in other Celtic languages as well; therefore, the substrate may not have been in contact with Primitive Irish but rather with Proto-Celtic. Examples of words found in more than one branch of Celtic but with no obvious cognates outside Celtic include:
The Old Irish word for "horn", "adarc", is also listed as a potential Basque loanword; in Basque the word is "adar".
References.
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