Ontmusic26. Critique of Nelson Goodman's Perfection Requirement for Song Identity
Nelson Goodman has proposed that the score is the absolute determinant of musical identity. Goodman writes:
“If we allow the least deviation [from the score], all assurance of work-preservation and score-preservation is lost; for by a series of one-note errors of omission, addition, and modification, we can go all the way from Beethoven’s Fifth Symphony to Three Blind Mice. Thus while a score may leave unspecified many features of a performance, and allow for considerable variation in others within prescribed limits, full compliance with the specifications given is categorically required.” (bold not in original)
- 1 Goodman's Perfection Requirement
- 2 The Sorites, or Problem of the Heap
- 3 The Ship of Theseus
- 4 Goodman and Sorites Reductio Ad Absurdums
- 5 Other Objections to Goodman's Perfection Requirement
- 6 NOTES
Goodman's Perfection Requirement
- Let's call Goodman's necessary and sufficient condition for song identification and song performance the perfection requirement.
- Goodman's NECESSARY CONDITION for work identity: full compliance with the specifications given in a musical score so one wrong note and the work has not been performed or played.
- Goodman's SUFFICIENT CONDITION for work identity: Any musical performance in full compliance (no wrong notes played) with the specifications given by a musical score are performances of that specific work.
- Most ordinary people would not agree with Goodman's strict determination of a song's identity as requiring perfection of playing to the score. The evidence for this would be the result of a survey where the question is asked, "If a musician plays a song perfectly, according to the musical score, but plays one wrong note, has the musician played the song?" Most people would reply in the affirmative, contradicting Goodman's perfection requirement. Assuming this is correct, however, doesn't yet make Goodman's proposal false or mistaken. It does show that the majority of ordinary Western culture exposed individuals have intuitions at least contrary to Goodman's theory because it is too rigid for determining song performance identity.
- Goodman gives an argument supporting his absolutely strict criteria for song identification and performance. He argues that "work-preservation and score-preservation is lost [whenever there is ANY variation from the score] for by a series of one-note errors of omission, addition, and modification, we can go all the way from Beethoven’s Fifth Symphony to Three Blind Mice."
What exactly is this argument and how is it supposed to be so decisive in supporting Goodman's perfection requirement?
- How can one get from Beethoven's Fifth to Three Blind Mice by one note errors? Why is this relevant for song performance identity? Presumably what Goodman is claiming is that if Beethoven's Fifth remains as a performance of Beethoven's Fifth even with one wrong note, then through a long series of identities each with one wrong note by commission or omission it would be possible to arrive at a performance that everyone would agree is that of Three Blind Mice. If this were accepted then "The Fifth Symphony" would be judged to be the very same song as "Three Blind Mice," and this everyone agrees must be wrong since it is thought that these are two different songs.
- Picture it this way. F1 is a perfect performance of the score for the Fifth Symphony. If F2 has one wrong note differing from F1 but is still judged to be the same song then it is being claimed F1 = F2 with respect to song identification. If now F3 is only one note different from F2 (but two notes different from F1) and F2 is judged identical to F3 (F2 = F3), and F1 = F2 then by transitivity of identity F1 must also be identical to F3 (F1 = F2 = F3). Because this series of one note differences by themselves doesn't affect the identity of song performance it is possible to have two different songs end up being identical to each other.
- The relevance of Goodman's argument is now clear. If one does not keep to strict identity of a performance to a musical score then it is theoretically possible that all songs are identical to each other and this is an unwanted consequence for most theories and intuitions regarding song identity.
- What exactly is going on here? Goodman's argument relates to both the sorties paradoxes as well as to problems of diachronic identity in the ship of Theseus puzzle.
The Sorites, or Problem of the Heap
- The Sorites puzzle, or problem of the heap, goes like this. Start with a big pile or heap of sand. Remove only one grain of sand from the heap. Now ask if it is still a heap of sand? The answer is that it would still be a heap of sand. These considerations seems to provide a reason to believe that the following principle is true. Removing one grain of sand can never make a heap of sand go from having been a heap to now becoming a non-heap. Following this logic out to its final conclusion while picturing the continual removal of only one grain of sand at a time implies that one could never get to a non-heap of sand if starting with a heap. We know this to be false, however, since eventually through grain removal one ends up with no sand. By removal of the final single grain of sand one certainly produces a non-heap. Even before the very final grain of sand is removed the heap of sand has already become a non-heap. Therefore, non-heap production CAN occur via one grain at a time removal. Somewhere along the lines one apparently must have violated the alleged rule because we started with a heap and went to a non-heap.
The Ship of Theseus
- The ship of Theseus is a related puzzle to that of the Sorities because it too concerns issues/questions of identity relative to small changes in single parts over time. Where the heap of sand is made up of individual sand grains, the ship of Theseus is made up of individual planks of wood.
- The story goes like this. Change out just one plank from the original ship and the ship REMAINS (identical to) the same ship of Theseus as before the changed out plank. Save that removed plank. Repeat this procedure one plank at a time until every plank from the old ship has been replaced. On the original argument this totally differently planked ship has remained the ship of Theseus. Now take all of the old saved planking and rebuild a ship with them. This reconfigured ship has identical planking to that of the original ship of Theseus. But now we have apparently two ships of Theseus that in principle are identical to each other. This doesn't on the surface seem possible because the new ship has entirely different planks from the old rearranged ship, but according to the theory they must be identical to each other even though they are not identical in materials to each other. This is a contradiction so one could argue by reductio ad absurdism that the one plank changed out ship must not be identical to the original ship of Theseus. This would mean, however, that as soon as one repairs one's ship it is now no longer the same ship that you used to own.
Goodman and Sorites Reductio Ad Absurdums
- Notice how this in effect is Goodman's argument. If there is any significant change over time from some standard model, then the two items in question can never be identical. In Goodman's case two songs or musical works cannot be identical if they have different notes, just like two ships cannot be identical if they have different planks (i.e., their parts).
- Just like Goodman's perfection requirement requires no deviation whatsoever from a standard, the use of the ship of Theseus as a reductio ad absurdum argument implies the impossibility of diachronic identity. Diachronic identity is identity of things at different times. Since the time items are different one of the items must be either younger or older than the other item. It also can occur that the two items under consideration have different parts. For example, consider the original ship of Theseus and later a plank is removed, but not replaced. The two 'ships' do not have all of the same parts. Because these can count as differences between the two ships or items, it is claimed to follow that this suffices to guarantee the non-identity of the two items.
Is diachronic identity then impossible? 
If it were then any particular human being at different times could never be identical to themselves. This would cause havoc for many issues, such as for ownership. I buy a boat today. Tomorrow I am older than yesterday. If diachronic identity is impossible, then the older me is not and cannot be identical to the younger me. So, older me did NOT buy a boat and hence cannot own that boat. To own that boat older me and younger me must be the same me.
- Consider the boat with one missing plank. It is true the original ship had that plank and the later ship is missing it. Is this enough to prove non-identity between the two ships? We certainly hope it does not sinvpce if it followed nothing could ever be identical to,itself at different times because there will always be changes and missing parts. Yesterday you had a particular hair on your head, but the next day that one hair is missing. Does that make older you non-identical to younger you? It doesn't on some theories of diachronic identity such as that four-dimensionalism.
- The four-dimensionalist considers the three standard spatial dimensions together with time making up the fourth dimension or parameter. A human being while admittedly having different spatio-temporal parts, where these parts are not identical to each other, nevertheless maintains that elder Fred can be the same person as baby Fred, who has many different properties than elder Fred because each is a spatio-temporal chunk of the same space-time worm extending over time making diachronic identity possible for the two time slices of Fred.
- The moral of the story is that just as we should worry about the correctness of the reductio ad absurdum argument against diachronic identity we should also worry about Goodman's perfection argument as a reductio proving no changes or alterations in songs are possible for identity to occur.
Other Objections to Goodman's Perfection Requirement
Existence of Notated Score Not Necessary for Song Identity
- These are not the only problems for Goodman's perfection requirement. This requirement is entirely dependent on the existence of written musical notation. According to Goodman's perfection requirement for song identity to be possible there must exist a written musical score. Without such a written score there is no standard of comparison for determining whether a piece of music has been played correctly or not. Yet, many songs in the history of music have no notated score. On Goodman's theory then such musical works have no identity even to themselves with a complete performance since identity determination demands conformity of the performance to a previously existent score. No score, no identity and this seems wrong. Surely any musical performance can be identical to itself. This suggests that a score is irrelevant for identity determination and Goodman's theory must be wrong.
- A further consideration against the need for a written musical score for determining song identity is this thought experiment. Many composers of music are themselves performers. As performers each musician often must have tremendously accurate memories. Many pianists have memorized pieces that take an hour to play and they can perform these pieces note for note flawlessly. Assuming we have such a musician with an excellent auditory memory. Call this person Ludwig.
- Ludwig is a composer and often composes musical compositions in his mind. He works out a short piece of a song that has only five hundred notes in total. Ludwig is a musician who has played pieces perfectly from memory that has thousands of notes in the piece. So, we can fairly well trust this person's memory and recognition of notes and their sequencing and properties as being consistently accurate. If you want add to this story that scientists have tested Ludwig from three up to two thousand notes and he has never made a mistake in twenty-five trial experiments in memorizing and then recalling from memory the correct sequencing and musical properties. The scientists play on the piano a series of notes and then Ludwig plays these notes back to the scientists both immediately and also ten days later showing he has retained the note sequences in long term memory. With this scenario in mind imagine Ludwig has the following experiences. He comprises an original song with five hundred notes. He thinks to himself, "I think this section might be better if I change it at this point and use these notes instead. After thinking about this and maybe even playing it on the piano he rejects the changes as being inferior to the original series of notes. He then goes through the original sequence of notes in memory and thinks to himself, "Yes, this original series of notes without the changes is the SAME SONG as I composed before." On Goodman's perfection requirement this is logically impossible since there has never been a written musical score against which to compare and determine if these two events are representations of the same song or not."
- What can we learn from the Ludwig has a good memory counter-example? One answer is that there is nothing special about needing to have a song be written down. The existence of paper and writing is not a requirement for song identity to be possible. If written scores are required, then no songs can exist with diachronic identity (playing the same song at two different times) in all societies lacking written musical notation. This cannot be correct in most people's views since it implies songs cannot exist with identity until writing comes into existence. Since we know that speech precedes writing in human civilizations and songs often start from vocalizations, then songs certainly did exist prior to writing. One caveman says to another, "sing me that same song you sang me the other night." On Goodman's theory this request is impossible. Since the request intuitively at least seems not to be impossible, Goodman's perfection requirement is wrong as a theory of song identity.
Problems with Multiple Scores
- It is a fact that Beethoven had his musical works collected and published. During this process he sometimes added or changed some parts from an earlier score of this very work about to be published. Both scores exist as musically notated of the same Symphony. Both are signed and approved by Beethoven. Given Goodman's perfection requirement it would be logically impossible for these two scores to both be of the Fifth Symphony.
- Suppose then there are two different scores both with the title "Fifth Symphony" and both written by Beethoven and both intended by Beethoven to be his Fifth Symphony. What should be said about the identity relationships between B1 and B2. On Goodman's theory it is impossible for either of these works to be identical to each other since they have different musical scores. Is this a good conclusion to draw?
- Are there good reasons to believe something other than non-identity for B1 and B2? Suppose Beethoven believes he has improved on the previous publication of the Fifth and claims that this is the best version of the Fifth. Is the earlier version no longer the Fifth symphony if played by an orchestra? If we say, as we are inclined to do, that it was a performance of Beethoven's Fifth, but it was the earlier version, then we appear to be committing ourselves to a theory of two different versions OF THE SAME THING. Each is a version of the ONE Beethoven's Fifth Symphony. On Goodman's perfection theory this talk is meaningless and logically impossible.
Two Versions of Same Song
- Here are some considerations for believing Goodman's rejection of the possibility of there existing two different versions of the same song is not a good conclusion. Beethoven was a composer. Composer's often change their minds. When his scores were going to published in the definitive edition of his music he modified a few notes from an earlier score. What was Beethoven thinking when he modified his old score. He could have thought to himself along these lines. These new notes are a change in the earlier symphony. The earlier symphony is still an effective piece of music. The changes made were done so as to improve the earlier symphony. Call the changed work the later symphony. How are the earlier and later symphonies related to each other in terms of song identity? Could it be that the earlier and the later symphonies are not two different musical works, but merely variations or versions of the same work? How could different scores with some different notes be of the same musical work when the two scores are not identical?
What kind of theory would permit two variations of the same musical work to be possible?
- Music as structure perhaps. See: Holding On to Reality: The Nature of Information at the Turn of the Millennium by Albert Borgmann, Chapter Nine, p. 94, University of Chicago Press, 2008.
A Musical Score Underdetermines A Song's Content
- There is also the problem of the undetermination of any written musical notation. It is not possible to notate every aspect of a musical performance. There are variations in tone, volume, and rhythm in every performance of a piece. If these are in any way part of a song then the song cannot be identical to its written musical score alone.
- What if the musical score leaves out some information that should be included? On Goodman's theory, this is impossible because the score is the only thing that determines song identity. Therefore, his theory must be wrong because every score always leave out crucial information for how to actually play a piece of music since every score underdetermines what is to be played.
- Nelson Goodman, Languages of Art: An Approach to a Theory of Symbols, 2nd ed., Indianapolis: Hackett Publishing, 1976, pp. 186-87.