The question asks why this mosaic has written “know thyself” as ΓΝΩΘΙ ϹΑΥΤΟΝ.
That Ϲ you see there is a capital letter, and it is not a final lowercase sigma ς. It is a lunate sigma. The Lunate Sigma predates the invention of lowercase, and was the form of the sigma used in the Roman and Byzantine eras; it is still used to allude to that period in modern fonts (e.g. in church contexts).
Both the medial and the final lowercase sigmas, σ ς, evolved out of the lunate sigma; and if you try writing lunate sigmas in cursive, you can work out why.
I have written more on the lunate sigma on my site on Unicode Greek.