Q:

Did Jesus write on stone in John 8:6?

In John 8 (KJV), Jesus stoops down to write something. We are not told what he wrote, but one line of thinking is that he wrote the Ten Commandments with "his finger" on solid stone, just as God had written the Ten Commandments "on stone" and "with his finger", as recorded in Deuteronomy 9:10.
The verses in John say: 

8:6 ...and with his finger wrote on the ground.
8:8 ...and wrote on the ground.

Now the story takes place in the temple. Would the ground have been stone, sand, dust, or mud? My thinking is that the ground would have been solid stone, would it not? Or are there reasons to think otherwise?

A:

The short answer: No
This answer is supported by two facts that tend to indicate that Jesus wrote in soil: location and word usage. First, in John 8:2-3, the text states:

Early in the morning he came to the temple courts again. All the people came to him, and he sat down and began to teach them. The experts in the law and the Pharisees brought a woman who had been caught committing adultery. They made her stand in front of them

This tends to indicate that Jesus was probably teaching in the court of the Gentiles. In the temple there were several major courts: The court of the Gentiles, the Court of the Women, The Court of Israel, the Court of the Priests, and several others:

Because women were not allowed into the Court of Israel and it would have been atypical for Rabbis to be teaching in the Women's court, it seems most likely that the setting to this scene was in the Gentile's court. While the temple itself did have stone foundations, the Gentile's court did not. This can be seen from pictures of the Wailing Wall today. The trees just behind the wailing wall would have been part of the Gentile's court and these can only grow in soil:

This is also consistent with the text itself which uses the word γῆν (ghen) when referring to the medium in which Jesus wrote. This is perhaps best illustrated by the parable of the Sower. In the parable of the Sower, some seeds fall on the good soil. The word for soil used in Luke 8 is this same word, γῆν (ghen), which is then contrasted with the seeds that fall on the πέτραν (petran; rock). This word, πέτραν (petran) is the same word used in the parable of wise and foolish builders in Matthew 7. In this parable, the wise man selects the πέτραν (petran) for the foundation of his home. Were Jesus writing in the foundation of the temple, we would expect him to be writing on πέτραν (petran), not in γῆν (ghen).

