Horatio is represented as being a scholar. How does Shakespeare reveal this characteristic in Hamlet?

Hamlet is an allegorical hero.  He interacts with other characters who reflect his possible options in taking revenge:

1. Laertes reflects the limitations of instant revenge
2. Fortinbras reflects the limitations of political revenge
3. Ophelia reflects the limitations of madness
4. Horatio reflects the limitations of talk

From the very first scenes of the play, Horatio establishes himself as a talker.  When he first hears of the Ghost, he says:

Of that I shall have also cause to speak,
And from his mouth whose voice will draw on more;

• Horatio doubts the supernatural:

Tush, tush, (quiet, quiet) 'twill not appear.

And

Well, sit we down,
And let us hear Bernardo speak of this.

• Marcellus says this about Horatio:

Thou art a scholar; speak to it, Horatio.

And

Question it, Horatio.

• Horatio tells the Ghost:

by heaven I charge thee, speak!

And

stay! speak, speak! I charge thee, speak!

And

If thou hast any sound, or use of voice,
Speak to me:
If there be any good thing to be done,
That may to thee do ease and grace to me,
Speak to me:

Later, after Marcellus says, "We do it wrong, being so majestical, To offer it the show of violence;" Horatio knows that dialogue and not violence is the only way to deal with the world.

When Hamlet sees the Ghost, he follows it.  Horatio warns against this.  Thus, Horatio is a passive scholar and a doubter.  He is a man of books, a college student who only believes what he sees, and he can only engage is discourse, not action.  He is no soldier (like the Ghost), no general (like Fortinbras), and no passionate reactionary (like Laertes.  In this way, he only offers Hamlet his advice in words.

Hamlet, thus, makes the mistake throughout the play of engaging others in dialogue (Polonius, his mother).  Other times, he doesn't engage in dialogue at all (silent interview with Ophelia).  Certainly, words contribute to much of Hamlet's delay.