In "The Cask of Amontillado," what is the significance of Fortunato being a Mason? How does he determine Montresor isn't?

At this point in the story, Montresor has lured Fortunato into the catacombs below his family residence, and intends to do him some type of harm (as yet undisclosed) in retaliation for Fortunato's "many insults." Montresor is also attempting to keep Fortunato drunk in order to dull his wits. 

Fortunato gives an indecipherable sign with his hands, a form of signaling that would be recognized had Montresor been a Mason, and taught how to recognize it. Montresor's lack of response, or of recognition, is how Fortunato determines that Montresor is not a member. 

The Masons are a fraternal order, something like a club or social group, with a series of traditions and practices that distinguish them, such as giving signals and handshakes which would only be recognized by other Masons. One of these traditions is the requirement that Masons may not lie to each other. If one is versed in Masonic culture, they may begin to understand how endangered Fortunato is at this point.

We might also question why Fortunato gave the sign in the first place - perhaps he was suspicious of Montresor's intentions, and was subtly asking "are you lying to me?" - however, we would presume that Fortunato would address this directly when Montresor fails the test. Instead, it may have simply been a mark of Fortunato's ever-present hubris, and he was simply making a show of his status.

Is Fortunato a mason in "The Cask of Amontillado"?

Although the short story "The Cask of Amontillado" is not typically thought of as being humorous, it certainly has moments of dark humor. This issue concerning the masons is one of them.

When Fortunado makes the "grotesque" movement that Mostresor does not comprehend, he was showing the sign of "the brotherhood" of the Free Masons, an old secret society. So the irony is that Fortunado is referring to the secret society and Montresor pulls out "a trowel" showing that he too is a mason. The mason that Montresor refers to is the straight definition of someone who builds and works with masonry. 

What is the significance of Fortunato being a Mason in "The Cask of Amontillado", and how does he discern that Montresor is not a member?

The short story "The Cask of Amontillado" by Edgar Allan Poe is a tale of revenge. The narrator, a man named Montresor, lures his victim Fortunato deep into the family catacombs beneath his palazzo, chains him there, and bricks up the entrance to the chamber, effectively burying him alive. On the way through the vaults, Fortunato makes a "gesticulation," or gesture, that Montresor does not understand. Fortunato therefore assumes that Montresor is not a member of the brotherhood of the Masons. When Montresor insists that he is, he offers as proof the trowel that he carries.

The organization that Poe refers to in this passage is the brotherhood of the Freemasons or Masons. The Masons trace their origins back to the Middle Age guilds that regulated stonemasons who assisted in constructing cathedrals and other buildings. Freemasonry consists of progressive levels into which members are initiated or raised, and there are various signs, words, gestures, and grips that accompany each level. To become a Mason, men must be free, of good moral character, believe in a higher power, and be devoted to the brotherhood of men. Among the symbols used in Freemasonry are the traditional tools of stonemasons, which would include trowels.

The fact that Fortunato is a Mason tells readers something about his character. His acceptance into the order is indicative of his belief in God and generally good moral character, although his drunkenness is somewhat of a lapse. The fact that Montresor is not a real Mason may be one of the insults he refers to at the beginning of the story as motivation for his crime. His immorality may be responsible for the Masons rejecting him.

Fortunato knows that Montresor is not a real Mason because he does not respond to the "gesticulation" or "movement" that Fortunato makes, a secret signal that one member would give to another. In fact, Montresor calls the gesticulation "grotesque," which may be a bitter reaction to his exclusion from the order. Montresor insists that he is a Mason, and as proof he produces a trowel. In response, Fortunato says, "You jest," which means, "You are joking." Concerning Montresor, at least, Fortunato does not take the symbol of the trowel seriously. If he were not so drunk, he should have realized at that point that something was wrong, and he should have tried to escape.

What is the significance of Fortunato being a mason in "The Cask of Amontillado"?

Yes, but only to a point is the mention that Fortunato is a Mason a significant detail. Masons have secret handshakes and codes of conduct relating to other Masons.  It is against the Masonic code to harm or lie to a brother Mason.  When the Montressor failed the "mason test" by producing a trowel, Fortunato should have figured out that he was being lied to and made good his escape.

Fortunato made the secret sign to "ask" if Montressor were a Mason, and he seemed not to understand rather than make the corresponding "reply" sign that yes he was a Mason. Fortunato made the sign because he felt uncomfortable going into the damp and underground catacombs with Montressor.  If Montressor were a true Mason, Fortunato could trust his life in the hands of his "brother Mason".

I think Poe uses an interesting play on words in that the Masonic organization and the brick masons use the same symbols and tools.  Masons meet in secret, and the narrator has Fortunato in a secret place in the catacombs.  Montressor uses brick and mortar to seal up Fortunato because of an insult. Many Masonic symbols deal with stone or brick work.

Poe mainly chooses the word to stress its double meaning, but the reader could also infer that Montresor uses it because it has some connection to the wrong that Fortunato supposedly did to Montresor.  Perhaps Montresor desired to be a member of the secret society, and Fortunato helped block his admission to the "club."  It could also be that Montresor is so jealous of Fortunato that he uses this opportunity to demonstrate that he can do something that Fortunato is good at (masonry).  These are all speculations, but they could be supported by other parts of the story.

In "The Cask of Amontillado," what does Fortunato's reaction to "mason" reveal about him?

As they proceed through the catacombs, Fortunato throws his arms up with a movement that Montresor finds "grotesque." Asking Montresor, "You do not comprehend?" he is given the reply, "Not I." Then, Fortuanto observes, " You are not of the masons." To this remark, Montresor counters, "Yes,yes,...yes, yes." Fortunato asks for a sign, and Montresor produces a trowel, causing Fortunato to fall back.

"You jest," he exclaimed, recoiling a few paces. "But let us proceed to the Amontillado."

Fortunato may be worried about the repercussions of his having identified himself as a mason because in Italy the Freemasons would not be looked upon favorably since the Catholic Church prohibits membership because this naturalistic, deistic organization does not accept revelation or Church authority as a source of religious knowledge. Further, as a man who lacks independence of thought, by making the sign, Fortunato admits to his willingness to belong to a group that dictates his beliefs and behavior.