"The poet only asks to get his head into the heavens. It is the logician who seeks to get the heavens into his head. And it is his head that splits." G.K. Chesterton

Monday, March 31, 2008

But, it’s the same ship!

In the following essay I will give reasons supporting the view that an object exposed to gradual change over time does not loose its identity. To further strengthen that view I will illustrate in the context of the ancient puzzle of Theseus’s ship, by means of discounting claims contrary to mine, how continuous persistence in space and over time is a necessary condition for maintaining identity. In the context of the presented puzzle (see the Annex enclosed at the end, to familiarize yourself with it) the above will be carried out by defending the soundness of the argument claiming that ship A, at the end of the day remains the one and only ship of Theseus, namely The Spirit of Athens.

Object such as trees or rivers are contained in the conceptual repertoire of our reality. Furthermore each of such objects is agreed to possess an identity, which means that although imbedded in the continuous flux of apparent existence it remains the one and the same object over time (numerical identity). A tree may shed its leaves in autumn, so obviously some part of its material constituency is carried away by the wind, that is to say some physical part of the tree at an earlier moment in time is not a part of the tree anymore at some later time (qualitative identity requires exact resemblance, so in this case it is violated). Conversely, a tree grows new branches, a phenomenon which introduces new parts which have not been part of the plant at some earlier stage. One should also note that it is the tree that is undergoing change, and although it is not similar to its earlier self, it does not cease to be the self – the object undergoing change. The point is that the above described changes do not alter the numerical identity of the part of reality we agreed to label a tree. By definition, trees are objects which among many other things grow and shed leafage seasonally.
The phenomenon of a river, serves as another example of that which retains its identity in spite of not possessing identical parts from one moment to the next. It is the same river at any moment, due to its nature. This is what we define as a river – a flowing and meandering trail of water guided by gravity, prone to evaporation, erosion of the banks and occasional flooding which changes its shape significantly. To be sure it varies along its length even at a single moment in time. Arguably if it didn’t flow, and possessed neither a spring at a higher altitude nor a mouth spilling into the sea it would be labeled a lake, albeit an oddly elongated one.

The case of the ship of Theseus can be placed in the same category of phenomena as the above examples. Ships are prone to damage, and consequently to the replacement of parts. Such repairs do not alter the numerical identity of the ship. Although its qualitative identity has changed (teak planks instead of oak planks) from some earlier moment in time, nevertheless it remains the same ship. The Key Premise (KP) here is the gradual replacement of one plank at a time not altering the numerical identity of the ship. Since replacing one plank does not alter the numerical identity of the ship, I conclude that the ship in Dock A, that is ship A, at the end of the entire replacement process (at t-1000 minutes) is still Theseus’s ship, namely The Spirit of Athens. The argument follows the valid form of Modus Ponens.

(1) At minute 0t the ship in Dock A is clearly The Spirit of Athens.
(2) The gradual replacement of one plank at a time does not alter the identity (numerical) of the ship.
(3) Changes applied to the ship in Dock A, between 0t minutes and 1000t minutes were such that only one plank at a time has been replaced.
(Hence) The ship in Dock A at minute 1000t is the same ship as that in Dock A at minute 0t, namely The Spirit of Athens.

Suppose one was to question the truth of (KP) and deny persistence of ship’s numerical identity if any of the intrinsic parts, which constituted The Spirit of Athens at time t-0 minutes, were to be removed or shifted (that is, if its qualitative identity were in any way altered). Furthermore, one could claim contrary to (KP) that “a complex whole object such a ship is nothing more than the sum of its parts in a determinate arrangement” which would consequently imply that in fact it is ship B in Dock B at time t-1000 which is the actual and only ship of Theseus since it consists of no more or less than precisely the 1000 oak planks which made up the Spirit of Athens at time t-0. Suppose further, that one would argue by interpreting that what has actually taken place in Dock A was not the repair of the original ship, but in fact the building of a teak replica of it, which had to be disassembled temporarily in order to facilitate the replication process. To be sure, the original boat was to be only momentarily disassembled, only to be reassembled again (in Dock B) upon the replica’s completion (in Dock A).

It seems perfectly natural to inquire where would the actual ship in question, namely The Spirit of Athens, be between the beginning and the end of the repair, or if some may wish replication process. That would be also the first step in the inquiry how did The Spirit of Athens get from dock A to dock B? (I suppose the answer would be more substantial then the soul of the ship literally leaping between docks, which would amount to an unjustified metaphysical claim.) Clearly at t-0 it’s in Dock A, and according to the above reasoning it would be in Dock B at t-1000. As far as the above definition is concerned, once a single original oak plank has been taken away the identity would in fact perish. This would be equivalent to saying that there is no ship with the identity of the original ship, which amounts to saying that the original ship ceases to exist. This would imply that if Theseus during one of his voyages were to lose a plank from The Spirit of Athens he would literally at one moment be sailing The Spirit of Athens, and in the next he would not be sailing The Spirit of Athens, but supposedly some other ship, or what’s worse no ship at all!

I see two possibilities of defending the denial of (KP) against the above absurdity. The first would be where one may argue that the ship does not cease to exist, but enters a potential state of being. This means that the object in question potentially exists, awaiting its reassembly in the same manner as a watch does on a watchmakers table after being disassembled for repair. Surely one wouldn’t question that it is the same watch once it has been fixed! The first line of defense of the objection to (KP) would then rely on justifying the possibility of intermittent existence.
The concept of intermittent existence is unfortunately a problematic one and weakens the position of the objection to (KP). Firstly, when something does not exist (arguably ceases to exist only temporarily) one cannot refer to it because one would be referring to nothing. If one was to ask where is The Spirit of Athens at say time t-20 one could only say that (1) it is not known, since both its existential status and thus position have only potential values and thus both are undetermined (2) The Spirit of Athens does not exist, consisting of a negative existential claim would have to be meaningless if true. For if it indeed does not exist, then what are we referring to?
Now, a defense resorting to intermittent existence would thus permit a scenario where Theseus is once again sailing the Aegean, and the ship upon loosing one plank causes its own location to become undetermined. Where, would then Theseus be? Well I hope that no one would hold that he shares the ship’s undetermined location, and what’s worse its existential status! If not, then where would he be? He’s clearly not walking on water. In fact he would be still aboard a ship the location of which is determined after all, namely under Theseus’s own feet. I cannot accept such support of the objection to (KP) which implies the possibility of an object possessing a determined and undetermined location at the same time.

The second line of defense of the denial of the truth of (KP) would be as follows. Alternatively one may claim that Theseus’s ship identity vanishes once and for all upon replacing the first plank, and thus avoid the difficulties of explaining the original ship’s whereabouts at any given moment. Would one hold such a view if the ship was made up of a million planks? How about a trillion? I understand that the thrust of the denial of (KP) is not concerned with the number of constituent parts, but merely their sum in a determinate arrangement.
To consistently embrace such a view would require the denial of anything maintaining its numerical identity with the slightest alternation of its qualitative identity. Since as far as empirical evidence shows everything is in a state of continuous flux, at least on the fundamental level, the two categories could not mutually persist over time, except within some infinitesimal intervals where change does not take place. But the shortest intervals that we can speak of in any meaningful way refer to the oscillation cycles of radiation in atoms which by definition are undergoing a constant exchange of energy quanta (exchange of “parts”). So it would follow that numerical identity could not, in any meaningful way be applied to any physical object. In other words identity would be rendered meaningless when applied to the reality which unfolds itself before us. Consequently the tree in my backyard would not be the same tree it was in the previous minute, and the ephemeral phenomenon labeled at one particular moment in time as The Brisbane River would be some other river at the very next moment or maybe not even a river at all! As far as I acknowledge this line of reasoning, I’m not prepared to accept it and consistently follow it through because I fear it would lead me to hypocrisy.

As the argument for ship A is valid, the only way to undermine its soundness would be to show the falsehood of one of the premises. I have provided serious objections to the premise on which the entire argument depends. Since my refutations have shown these objections to contain serious problems I declare the argument as successfully defended within the scope of this paper.

The Problem of Theseus's Ship
Suppose that the seafaring Theseus arrives in a shipyard near Athens with his ship The Spirit of Athens that is made of nothing but 1000 oak planks. It requires repair so he sails it into Dock A. At this time, minute 0t, the ship in Dock A is clearly The Spirit of Athens — Theseus's ship. The shipwright begins repairs by replacing one of its oak planks with a matching teak plank, putting the teak plank in exactly the same position as the original oak one and putting the oak plank to one side. This is completed at minute 1t. At minute 2t the ship in Dock A again has another oak plank removed and replaced by a teak one of the same size and shape in the same position, the oak plank being put to one side. Proceeding in this way the shipwright eventually replaces all the oak planks on the ship in Dock A with matching teak planks put together in the same way as the original — thus constructing Ship A. The ship in Dock A at minute 1000t — Ship A — is made completely of teak planks, the original 1000 oak planks having all been put to one side.
Meanwhile another shipwright decides to build a ship in Dock B. Finding an oak plank now lying around he begins to assemble Ship B. At minute 1t the ship in Dock B consists of nothing but the one oak plank in the same position as it was in the original ship before being removed. At minute 2t another discarded plank is found and put into the very same position it occupied in the original ship. After 1000t minutes Dock B contains a ship — Ship B — which is made out of all and only the oak planks from Theseus's original ship put together in exactly the same way as they were in Dock A at minute 0t.
Now, regardless of which ship Theseus now claims as his own and sails away in, there appear to be good arguments for each ship, Ship A and Ship B, being counted as Theseus's ship The Spirit of Athens.

ARGUMENT IN SUPPORT OF SHIP A: Consider Ship A. At minute 0t the ship in Dock A is clearly The Spirit of Athens. Changing one plank of a 1000-plank ship does not alter the identity of the ship (the difference is too small to make a difference) so, since the ship in Dock A at minute 1t only differs by one plank, at minute 1t the ship in Dock A is The Spirit of Athens. Yet, the ship in Dock A at minute 2t only differs from that in Dock A at 1t by one plank — a difference which we just claimed did not alter the identity of the ship — so the ship in Dock A at minute 2t is the same ship as that in Dock A at minute 1t, namely The Spirit of Athens. In general, since changes to the original Spirit of Athens are only made one plank at a time, and such changes are too small to make a difference to the ship's identity, the ship in Dock A at minute 1000t — Ship A — is still Theseus's ship, The Spirit of Athens.

ARGUMENT IN SUPPORT OF SHIP B: Consider Ship B, on the other hand. There would appear to be an equally compelling reason for thinking it is The Spirit of Athens. Surely a complex whole object such as a ship is nothing but the sum of its parts in a determinate arrangement. Now, the ship in Dock B at minute 1000t is composed of exactly the same planks as the ship in Dock A at minute 0t (The Spirit of Athens) in exactly the same determinate arrangement. So this ship, namely that in Dock B at minute 1000t — Ship B — is Theseus's ship The Spirit of Athens.

Walker, James S. Physics. New Jersey: Pearson Education 2004.

Noonan, Harold. Identity. The Stanford Encyclopedia of Philosophy. First published: Dec 15 2004. http://library.usyd.edu.au/stanford/entries/identity/ accessed 8th April 2007.

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