Stephen said

Whether Q exists is very important is determining how much of the material is authentic. As I understand it, the “Q hypothesis” was created to give credibility to the material in Matthew after scholars agree that Mark was written first. If Q never existed, then Matthew either wrote down oral tradition that wasn’t known to the author of Mark (or he didn’t want to use) or invented it himself. The same goes for the “L” parts of Luke. 

I don’t think that follows. I think the “Q” hypothesis was formulated in large part to hold on to Matthean and Lukan independence.  Whether a source was shared or not has little to do with its provenance.  And of course “Q” could have existed as a document and Matthew the only one who knew about it.       

  

That’s not my understanding. Herbert Marsh came up with the hypothetical “sayings” source to deal with how Matthew and Luke got their similar stories that aren’t in Mark. Schleiermacher later believed that Papias (“a man of exceedingly small intelligence”, according to Eusebius) referred to a source that could have been the “sayings” source used by Matthew and Luke. This appears to have lost favor among scholars so Marsh’s beth (ב) source, and Holtzmann’s Lambda (Λ) source, was changed to the “Q” source. 

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The next person to advance the “sayings” hypothesis was the German ** you do not have permission to see this link **

In 1838 another German, ** you do not have permission to see this link ** in 1863, and the two-source hypothesis has dominated ever since.

At this time, the second source was usually called the ** you do not have permission to see this link ** to denote Quelle, meaning ‘source’) adopted instead to remain neutral about the connection of Papias to the collection of sayings.

This ** you do not have permission to see this link **