So, to recap: the ' ship of Theseus' paradox is a thought experiment that raises the question of whether an object which has had all of its components replaced remains fundamentally the same object. The paradox is most notably recorded by Plutarch in Life of Theseus from the late first century. Plutarch asked whether a ship which was restored by replacing each and every one of its wooden parts remained the same ship. He writes:
"The ship wherein Theseus and the youth of Athens returned had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place, insomuch that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same."
The Hellenic philosopher Heraclitus (535 – c. 475 BC) attempted to solve the paradox by introducing the idea of a river where water replenishes it. Arius Didymus quoted him as saying:
"On those stepping into rivers staying the same other and other waters flow." (DK22B12)
Heraclitus holds the 'Flux Doctrine': everything is constantly changing; no object retains all of its component parts from one moment to the next. In other words, though the waters are always changing, the rivers stay the same. He thus believed that while the material of Theseus' ship was replaced, the greater whole--this thing called 'a ship'--remained the same. That ship was the ship of Theseus, thus the ship of Theseus remained, even if all parts were replaced. This is option 'A' in the video example.
Aristotle also spent a lot of time on this paradox, and he discussed it with his followers. They came up with four causes, or reasons, that describe an object: the 'Formal Cause' (the design of an object), the 'Material Cause' (the matter that the object is made of), the 'Final Cause' (the intended purpose), and the 'Efficiency Cause' (how, and by whom, an object was made). Aristotle then goes on to say that an object is its formal cause; so the Ship of Theseus is the same ship, because the formal cause, or design, does not change, even though the matter (Material Cause) used to construct it may vary with time. Furthermore, the renewed ship of Theseus would have the same end (final cause)--transporting Theseus--even though its material cause would change with time. If the workers who replaced the planks of the ship could have used the same techniques and made the ship as it was before--thus preserving all previous causes as well.
So, is there an answer to the paradox? No, not really. The proper response is that the definition we have for the ship is not clear enough to provide an answer to that question. The ship of Theseus does not really exist as the ship of Theseus. There is no exact definition of what is meant by the ship of Theseus. The atoms are not tagged as the ship’s atoms. Rather, it is we who make those atoms into a whole entity called a ship. It is we who further demarcate this ship as somehow belonging to Theseus. In short, this whole discussion is in our minds only. The ancient Hellenes took a ship said to have sailed Theseus to Krete and back. They kept it in the harbour and maintained it for centuries because it was an ideal, a reminder, and a trophy. It had a function: no longer to carry Theseus but to be the ship that carried Theseus. For this purpose, it does not matter if the boards are the same as those on the original ship. It's the lore we--and the ancient Hellenes--connected to it that matters.
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