According to Matthew 13:55:
Isn't this the carpenter's son? Isn't his mother named Mary? And aren't his brothers James, Joseph, Simon, and Judas? (NET)
οὐχ οὗτός ἐστιν ὁ τοῦ τέκτονος υἱός; οὐχ ἡ μήτηρ αὐτοῦ λέγεται Μαριὰμ καὶ οἱ ἀδελφοὶ αὐτοῦ Ἰάκωβος καὶ Ἰωσὴφ καὶ Σίμων καὶ Ἰούδας; (NA28)
Can it be said that there was only one carpenter in the village and that he was still alive?
In early days people from a villages knew almost everybody from their village. As the pervious verse state that He was in His hometown, so they must have known His parents and family. I dont know about the 'ONLY carpenter in the village' but regarding the joseph life span this link might be helpful. According to this joseph passed away before Jesus started His ministry.
At first glance it seems like Joseph had just recently passed away or was still alive when Jesus's neighbors wondered about his intelligence, healing abilities and oratory skills(Mathew 13:55). But first. when a man is called "son of...." this only indicates this man is a young person, probably younger than 30 and/or probably the oldest of his siblings(Levi son of Alphaus Mark 2:14; Simon son of Jonas-Matthew 16:17).
Jesus being called "son of the Carpenter" indicates Joseph was a prominent laborer in the town but not necessary the only one. Levi was sitting on the table when Jesus called him but he was not the only one sitting there and because he is called "son of Alphaus" indicates that Levi was a young man and his father was a prominent figure, probably a senior publican tax collector himself.
Matthew 13:55:
Isn't this the carpenter's son? Isn't his mother named Mary? And aren't his brothers James, Joseph, Simon, and Judas?
There is a parallel account in Mark 6:3
Isn't this the carpenter? Isn't this Mary's son and the brother of James, Joseph, Judas and Simon? Aren't his sisters here with us?" And they took offense at him.
Mark seems to suggest that Jesus has replaced his father as the carpenter.
In both accounts, Jesus is known by the villagers as a carpenter, and not as a rabbi. A carpenter works with his hands. A rabbi works with his brain.
Can it be said that there was only one carpenter in the village?
No, at least not with certainty. It is not justified simply by the use of the Greek definite article.
