The boat that took Theseus to Crete as well as the tribute of seven young men and seven young women whom Theseus saved by killing the Minotaur was kept by the Athenians in thanks for their safe return. Later it prolonged Socrates time in prison, giving Plato the opportunity to set a couple of dialogues in the prison while Socrates was waiting for his death including my favourite, Phaedo, and became an example to later philosophers on the question of identity. Was it the same ship when all the timbers had been replaced?
First Phaedo explains by Socrates was not executed immediately.
τοῦτ᾽ ἔστι τὸ πλοῖον, ὥς φασιν Ἀθηναῖοι, ἐν ᾧ Θησεύς ποτε εἰς Κρήτην τοὺς ‘δὶς ἑπτὰ’ ἐκείνους ᾤχετο ἄγων καὶ ἔσωσέ τε καὶ αὐτὸς ἐσώθη. τῷ οὖν Ἀπόλλωνι ηὔξαντο ὡς λέγεται τότε, εἰ σωθεῖεν, ἑκάστου ἔτους θεωρίαν ἀπάξειν εἰς Δῆλον: ἣν δὴ ἀεὶ καὶ νῦν ἔτι ἐξ ἐκείνου κατ᾽ ἐνιαυτὸν τῷ θεῷ πέμπουσιν. ἐπειδὰν οὖν ἄρξωνται τῆς θεωρίας, νόμος ἐστὶν αὐτοῖς ἐν τῷ χρόνῳ τούτῳ καθαρεύειν τὴν πόλιν καὶ δημοσίᾳ μηδένα ἀποκτεινύναι, πρὶν ἂν εἰς Δῆλόν τε ἀφίκηται τὸ πλοῖον καὶ πάλιν δεῦρο: τοῦτο δ᾽ ἐνίοτε ἐν πολλῷ χρόνῳ γίγνεται, ὅταν τύχωσιν ἄνεμοι ἀπολαβόντες αὐτούς. ἀρχὴ δ᾽ ἐστὶ τῆς θεωρίας ἐπειδὰν ὁ ἱερεὺς τοῦ Ἀπόλλωνος στέψῃ τὴν πρύμναν τοῦ πλοίου: τοῦτο δ᾽ ἔτυχεν, ὥσπερ λέγω, τῇ προτεραίᾳ τῆς δίκης γεγονός. διὰ ταῦτα καὶ πολὺς χρόνος ἐγένετο τῷ Σωκράτει ἐν τῷ δεσμωτηρίῳ ὁ μεταξὺ τῆς δίκης τε καὶ τοῦ θανάτου.
This is the boat, so say the Athenians, in which Theseus once went to Crete with the “two sevens” (seven youths and girls) and saved them and himself. They made a vow to Apollo at that time that if they came back safe they would send an embassy every year to Delos. Ever since then even nowadays they still send it every year to the God. When they begin the mission, there is a law to keep the city pure and not to execute anyone by public decree before the boat has arrived at Delos and come back again. This can take a long time when the winds happen to take them off course. The beginning of the mission is when the priest of Apollo puts a garland on the stern of the ship. This happened, as I said, on the day before the trial. That is why Socrates spent so much time in the prison between his trial and death.
Plato Phaedo 57b
Next Plutarch mentions the philosophical question. This was called the growing argument – as something grows or diminishes does it retain its identity? Was it really the same boat once all the timbers had been replaced?
τὸ δὲ πλοῖον ἐν ᾧ μετὰ τῶν ἠϊθέων ἔπλευσε καὶ πάλιν ἐσώθη, τὴν τριακόντορον, ἄχρι τῶν Δημητρίου τοῦ Φαληρέως χρόνων διεφύλαττον οἱ Ἀθηναῖοι, τὰ μὲν παλαιὰ τῶν ξύλων ὑφαιροῦντες, ἄλλα δὲ ἐμβάλλοντες ἰσχυρὰ καὶ συμπηγνύντες οὕτως ὥστε καὶ τοῖς: φιλοσόφοις εἰς τὸν αὐξόμενον λόγον ἀμφιδοξούμενον παράδειγμα τὸ πλοῖον εἶναι, τῶν μὲν ὡς τὸ αὐτό, τῶν δὲ ὡς οὐ τὸ αὐτὸ διαμένοι λεγόντων.
The boat in which he sailed with the youths and maidens and got him back safe was preserved by the Athenians up to the time of Demetrios Phalereus by taking away the old timbers and putting different sound ones in their place, fitting it out in a way that led to the the boat becoming an example to philosophers of the disputed growing argument, some maintaining it was the same boat and others saying it did not stay the same.
Plut. Thes. 23.1