Ontdef3. What is the definition of jazz?
🎷 SECTION UNDER CONSTRUCTION: Especially Needs Editing 🎷
- 1 Discussion
- 2 Controversy over Defining Jazz
- 3 The Importance of Defining Jazz
- 4 What is Meant by Definition
- 5 How Jazz Can Be Defined
- 5.1 Jazz Could be Defined If It Had Essential Properties
- 5.2 Does Jazz Have Essential Properties?
- 5.2.1 The Importance of Improvisation
- 5.2.2 Reasons to Believe A) Improvisation is "the most defining feature of" and "central" to jazz and (B) Armstrong, Ayler, Coleman, and Coltrane each played jazz improvisations are False
- 5.2.3 Reasons to Believe A) Improvisation is "the most defining feature of" and "central" to jazz and (B) Armstrong, Ayler, Coleman, and Coltrane each played jazz improvisations are True
- 188.8.131.52 Louis Armstrong (August 4, 1901 - July 6, 1971)
- 184.108.40.206 Ornette Coleman (March 9, 1930 - June 11, 2015)
- 220.127.116.11 John Coltrane (September 23, 1926 - July 17, 1967)
- 18.104.22.168 Albert Ayler (July 13, 1936 - November 25, 1970)
- 5.3 What Is Meant By Essential?
- 5.4 Are There Any Necessary Conditions For Playing Jazz?
- 5.4.1 Are There Any Necessary Conditions For Playing Music?
- 5.4.2 Necessary Conditions For A Musical Performance
- 5.4.3 True Necessary Conditions For A Musical Performance
- 5.4.4 False Necessary Conditions For A Musical Performance
- 5.5 Are There Any Sufficient Conditions For Playing Jazz?
- 6 Paul Rinzler's Definition of Jazz
- 7 The Galactic Model for Defining Jazz
- 8 Overview and Summary of Defining Jazz
- 9 NOTES
Controversy over Defining Jazz
Numerous scholars, theorists, critics, music reviewers, and many famous jazz musicians have all disdained or pooh-pooed, or even outright rejected the possibility of producing a successful, satisfying, and correct definition of jazz.
Here's what they said and when:
- Wikipedia on Defining Jazz makes these claims regarding problems of defining jazz:
"Jazz has proved to be very difficult to define, since it encompasses such a wide range of music spanning a period of over 100 years, from ragtime to the 2010-era rock-infused fusion. Attempts have been made to define jazz from the perspective of other musical traditions, such as European music history or African music. But critic Joachim-Ernst Berendt argues that its terms of reference and its definition should be broader,  defining jazz as a "form of art music which originated in the United States through the confrontation of the Negro with European music"  and arguing that it differs from European music in that jazz has a "special relationship to time defined as 'swing'", involves "a spontaneity and vitality of musical production in which improvisation plays a role" and contains a "sonority and manner of phrasing which mirror the individuality of the performing jazz musician." In the opinion of Robert Christgau, "most of us would say that inventing meaning while letting loose is the essence and promise of jazz."
A broader definition that encompasses all of the radically different eras of jazz has been proposed by Travis Jackson: "it is music that includes qualities such as swing, improvising, group interaction, developing an 'individual voice', and being open to different musical possibilities."
Krin Gibbard has provided an overview of the discussion on definitions, arguing that "jazz is a construct" that, while artificial, still is useful to designate "a number of musics with enough in common to be understood as part of a coherent tradition".
In contrast to the efforts of commentators and enthusiasts of certain types of jazz, who have argued for narrower definitions that exclude other types, the musicians themselves are often reluctant to define the music they play. As Duke Ellington, one of jazz's most famous figures, said: "It's all music".
- At It's All Music Johannes Luebbers explains why he can find it problematic for himself to have the label of jazz placed upon the music he composes and performs. Luebbers explains that:
In my experience as a composer, the defining of genres can also be limiting to the creation of work. In the same way that I find the label 'jazz composer' inadequate as a description of myself to others, I find it can actually limit me when I sit down to write. The parameters imposed by the genre, perceived or otherwise, can become a prison from which it is hard to escape. Within the jazz genre there are, as in any genre, certain stylistic conventions and traditions, and as soon as you think of yourself as a 'jazz composer' the ability to escape these conventions becomes increasingly difficult."
The Importance of Defining Jazz
As pointed out by Matthew W. Butterfield in Oxford Bibliographies in 2011:
Defining jazz has been central to delineating the disciplinary purview of jazz scholarship, but this has never been easy. As a body of more or less “popular” music disseminated in recorded form, the music has undergone rapid development over the course of its history, and each transformation in style has prompted debate among jazz musicians, critics, and fans as to whether or not the new style was in fact jazz. Such debates have often revolved around the role of improvisation and its relative emphasis in any given style, the degree to which each new form of the music could be understood to “swing”—i.e., to exhibit a valued rhythmic quality thought to be essential to good jazz—and the extent to which each new style manifested certain core African or African American musical concepts and principles. The latter consideration has prompted many scholars to eschew parochial considerations of style altogether and situate jazz not as a distinctive form of music in its own right but as one expression among many within the very broad category of “black music.”
To follow this latter path and not try to determine how "jazz is a distinctive form of music" is to give up trying to define it musically. It is amazing how many theorists adopt this attitude just because jazz is hard to define. Think about how defeatist this is. Would a cancer researcher ever say, "Well, you know, cancer is so hard to figure out exactly what it is, so instead of trying to define it biologically we are just going to treat it as merely "one expression among many within the very broad category of" how someone can die?! This would never happen. Similarly, then, just because cancer and jazz are hard to define does not actually supply a reason why such an investigation should not continue.
What is Meant by Definition
How Jazz Can Be Defined
Jazz Could be Defined If It Had Essential Properties
Anything with essential properties can be defined. Essential properties are those that determine the essence of something, meaning what it is.
The Stanford Encyclopedia of Philosophy explains the nature of, as well as differences and relationships between, essential and non-essential, or accidental, properties:
"The distinction between essential versus accidental properties . . . is currently most commonly understood in modal terms: an essential property of an object is a property that it must have while an accidental property of an object is one that it happens to have but that it could lack. . . . the use of the word “must” reflects the fact that necessity is invoked, while the use of the word “could” reflects possibility. The notions of necessity and possibility are interdefinable: to say that something is necessary is to say that its negation is not possible; to say that something is possible is to say that its negation is not necessary; to say that an object must have a certain property is to say that it could not lack it; and to say that an object could have a certain property is to say that it is not the case that it must lack it."
Does Jazz Have Essential Properties?
The Importance of Improvisation
At the Scolastic Magazine website titled "Culture and Change: Black History in America" as they review the history of jazz in America often admiring Wynton Marsalis's insights into jazz and using his audio clips to explain improvisation under the section titled Improvisation: The Expression of Freedom it says:
"Improvisation is the most defining feature of jazz. Improvisation is creating, or making up, music as you go along. Jazz musicians play from printed music and they improvise solos. From the collective improvisation of early jazz to the solo improvisation of Louis Armstrong to the free jazz of Albert Ayler, Ornette Coleman, and John Coltrane, improvisation is central to jazz."
From these observations at least two main points can be discerned, and the second one is surprising from Wynton Marsalis's neo-classicist conservative point of view. The two points are:
(A) Improvisation is "the most defining feature of" and "central" to jazz.
(B) Armstrong, Ayler, Coleman, and Coltrane each played jazz improvisations.
Examining these two claims (A) and (B), it can be seen that both are problematic until further clarifications and justifications are given for believing them to be true.
Reasons to Believe A) Improvisation is "the most defining feature of" and "central" to jazz and (B) Armstrong, Ayler, Coleman, and Coltrane each played jazz improvisations are False
Why (A) is false: If the "most defining feature" of improvisation were to mean either or both a necessary and/or sufficient condition for being jazz is that it contain improvisation, then each of these claims is false. Improvisation is neither a sufficient nor a necessary condition for music to qualify as jazz.
- Improvisation cannot be a necessary condition for being jazz because jazz exists with no improvisation at all. Everyone believes Duke Ellington wrote and performed jazz with his orchestra without improvisation, although some of it could sound like it was being improvised. Non-improvisational jazz would be impossible if improvisation were a necessary condition for music to qualify as jazz.
- Improvisation cannot be a sufficient condition for being jazz because much improvised music exists that everyone believes NOT to be jazz. Rock musicians, Indian musicians on tablas and sitars, even Mozart, each has improvised music without having played any jazz.
- Improvisation cannot be BOTH a necessary condition and a sufficient condition for being jazz if improvisation is neither necessary nor sufficient for being jazz.
Why (B) is false: Wynton Marsalis has been critical of free(er) jazz and free improvisations and might well deny that the free improvisations of John Coltrane, Albert Ayler, and Ornette Coleman were actually jazz improvisations, even while being artistically valuable. The primary reason Marsalis could give for denying these impressive improvisations as qualifying as jazz is that by its very nature free jazz being free conforms to no rules of jazz. Marsalis and others could argue that It is of the essence of completely free improvisation that it could not be jazz because if it was jazz then it wouldn't be free. This is the reason why entirely 'free' jazz could never qualify as jazz. This free music follows no rules or principles so disqualifies itself from being jazz.
Reasons to Believe A) Improvisation is "the most defining feature of" and "central" to jazz and (B) Armstrong, Ayler, Coleman, and Coltrane each played jazz improvisations are True
Why (A) is true: (A) is true because improvisation IS central to mainstream and standard form jazz.
Why (B) is true: (B) would be true if Louis Armstrong, as well as Ornette Coleman, John Coltrane and Albert Ayler in their freer moments were still playing jazz.
Why could this be true?
Consider each musician in turn. They are not all the same, to say the least, so need to be judged and evaluated individually.
Louis Armstrong (August 4, 1901 - July 6, 1971)
Louis Armstrong Discography
Ornette Coleman (March 9, 1930 - June 11, 2015)
Ornette Coleman Discography
- JazzDisco's Ornette Coleman album index
- All Music's Ornette Coleman Discography with album covers
- Discogs's Ornette Coleman Discography with album covers
- Columbia University Short List
- Ornette Coleman albums Rated
- Ornette Coleman Big Album Covers
- Wikipedia's Ornette Coleman Discography
John Coltrane (September 23, 1926 - July 17, 1967)
Which of John Coltrane's recordings are the most free jazz?
John Coltrane Discography
- Wikimedia on John Coltrane's Discography
- John Coltrane Discography: The Official Website with album covers
- John Coltrane Discography by JazzDisco.org with complete song titles and personnel listings
- John Coltrane album index by JazzDisco.org
Albert Ayler (July 13, 1936 - November 25, 1970)
“As a teenager, Ayler attended John Adams High School on Cleveland's East Side, and graduated in 1954 at the age of 18. He later studied at the Academy of Music in Cleveland with jazz saxophonist Benny Miller. Ayler also played the oboe in high school. As a teenager, Ayler’s understanding of bebop style and mastery of standard repertoire earned him the nickname of “Little Bird", after Charlie “Bird” Parker, in the small Cleveland jazz scene.”
“In 1952, at the age of 16, Ayler began playing bar-walking, honking, R&B-style tenor with blues singer and harmonica player Little Walter, spending two summer vacations with Walter's band. In 1958, after graduating from high school, Ayler joined the United States Army, where he switched from alto to tenor sax and jammed with other enlisted musicians, including tenor saxophonist Stanley Turrentine. Ayler also played in the regiment band. In 1959 he was stationed in France, where he was further exposed to the martial music that would be a core influence on his later work. After his discharge from the army, Ayler tried to find work in Los Angeles and Cleveland, but his increasingly iconoclastic playing, which had moved away from traditional harmony, was not welcomed by traditionalists.”(bold not in original)
- When he joined the army and began playing with Stanley Turrentine, among others, he switched to tenor saxophone, although occasionally playing alto and soprano as well.
- Musicians that Ayler played with include Don Cherry (pocket trumpet), Sunny Murray (drums), Gary Peacock (bass), Alan Silva (double bass), Roswell Rudd (trombone) and Cecil Taylor (piano). These musicians helped to found the free(er) and free jazz movement(s).
- Musicologists find in Ayler's music sounds that remind them of both church and military music. The church like influences can be heard and read into Ayler's album, "Spiritual Unity," which was recorded in Ayler's most prolific recording year of 1964.
“In 1963, Ayler returned to the US and settled in New York City, where he continued to develop his personal style and occasionally played alongside free jazz pianist Cecil Taylor. 1964 was the most well-documented year of Ayler’s career, during which he recorded many albums, the first of which was "Witches and Devils" in March of that year. Ayler also began his rich relationship with ESP-Disk Records in 1964, recording his breakthrough album (and ESP’s very first jazz album) "Spiritual Unity" for the then-fledgling record label. ESP-Disk came to play an integral role in recording and disseminating free jazz.
There is certainly music on record with Ayler playing that qualifies as jazz. Where the controversy arises is in Ayler's more unstructured moments. We know from his biography above that he was certainly trained originally in standard jazz practices. You don't get the nickname "Little Bird" if you cannot play Bebop in a conventional manner and Bebop is agreed on by all counts to qualify as jazz so it is certain that early on Ayler played jazz. The question remains about his (later) recordings.
Albert Ayler Discography
- Albert Ayler album index by JazzDisco.org
- Albert Ayler Discography by JazzDisco.org
- Albert Ayler catalog index by JazzDisco.org with listing of which personnel played on individual songs
- Albert Ayler session index by JazzDisco.org
|1962||The First Recordings Vols. 1 & 2||Bird Notes|
|1963||My Name Is Albert Ayler||Debut Records|
|1964||Swing Low Sweet Spiritual||Osmosis|
|1964||Albert Smiles With Sunny [Live]||Inrespect|
|1964||New York Eye And Ear Control||ESP|
|1964||Albert Ayler [Live]||Philology|
|1964||The Copenhagen Tapes||Ayler|
|1964||The Hilversum Session||Osmosis|
|1965||Sonny's Time Now||Jihad|
|1966||At Slug's Saloon, Vol. 1 & 2 [Live]||ESP|
|1966||Lörrach / Paris 1966 [Live]||Hathut Records|
|1966||Albert Ayler in Greenwich Village [Live]||Impulse! Records|
|1967||Love Cry||Impulse! Records|
|1968||New Grass||Impulse! Records|
|1969||Music Is the Healing Force of the Universe||Impulse! Records|
|1969||The Last Album||Impulse! Records|
|1970||Nuits de la Fondation Maeght Vol. 1||Shandar|
|1970||Live on the Riviera [Live]||ESP|
|2004||Holy Ghost: Rare & Unissued Recordings (1962–70)||Revenant Records|
|2006||The Complete ESP-Disk Recordings||ESP|
Reasons: high form skill, difficult, admired and admirable, challenging, why musicians like and value jazz, requires skill, allows for spontaneous group interaction and the emergent properties that spontaneous composition can achieve, KIND OF BLUE level solos with virtually no rehearsal.
What Is Meant By Essential?
Are There Any Necessary Conditions For Playing Jazz?
On the surface it is likely going to be difficult to find any necessary conditions that are uniquely distinctive of jazz. The reason for this being that if there were such necessary conditions that were unique to jazz they would already have been discovered and be known. These features, were they to exist, would be obvious. In a minute numerous candidates for possible necessary conditions possibly unique to jazz (but they aren't) will be considered, examined, and rejected as necessary candidates. Before this is done, let us consider a preliminary matter first.
What necessary conditions are required for something even to qualify as music?
What features necessarily apply to jazz by virtue of jazz being music?
Are There Any Necessary Conditions For Playing Music?
What are necessary properties of music?
This is a large and difficult topic. Rather than try to give a definitive answer first consider candidates for necessary conditions. It will help to delimit the problem if we start with necessary conditions for the performance of music.
Necessary Conditions For A Musical Performance
What happens necessarily during a musical performance?
True Necessary Conditions For A Musical Performance
- Musicians are required to cause the music to exist.
- The musicians are persons.
- The persons are intentional agents.
- The musician is intentionally producing the music.
False Necessary Conditions For A Musical Performance
- False Necessary Condition The music consists of sounds that can be heard. If neither sounds exist or if the sounds cannot be heard then no music has been performed.
As intuitive as it might seem that music requires hearable sounds, this Is a false claim. Several philosophers, including Andrew Kania in his article, “Silent Music,” have argued for the existence of music that even when performed both makes no sounds and is not hearable.
What does it mean to be hearable? Just as important, hearable by whom?
Hearable is tricky because there are ambiguities as well as degrees.
One of the ambiguities concerns whether one means potentially or actually hearable/heard.
- Something is potentially hearable if someone could possibly hear it.
- Potentially Hearable Items, but not heard:
- - The proverbial falling tree with no one nearby to hear it.
- - A far enough away hummingbird's wings flapping sound.
- - A meteor hitting the Moon's surface.
- - Very quiet sounds that no one hears but could be amplified to be heard with equipment.
- - Very low sounds below 20 cycles per second that is below the threshold of typical human hearing ranges.
being meant or actually hearable.
Because people can easily suffer frequency damages to their hearing what one person can hear another with frequency damage to their hearing might not be able to hear the same sounds. It is clear that the person who can hear the music would agree it is music, so the person who cannot hear it cannot correctly claim that no music has been performed. It was performed, but not heard by you is not a contradiction.
Martian High Frequency Music Objection to Hearability Requirement
Wikipedia states that non-humans have a hearing range that can surpass humans in both hearing extra low frequencies or extra high frequencies, with typical humans having a hearing range of 20-20,000 Hz (cycles per second).
“Several animal species are able to hear frequencies well beyond the human hearing range. Some dolphins and bats, for example, can hear frequencies up to 100 kHz. Elephants can hear sounds [as low as] 14–16 Hz, while some whales can [even] hear subsonic sounds as low as 7 Hz (in water).”
Below is a table of animal hearing ranges and as can easily be observed there are many species with superior hearing ranges than humans, at both ends of the spectrum, but especially the higher frequencies.
If this is correct, then imagine Martians who have the hearing range of dogs from 60 Hz to 44Hz. Dogs and hypothetical Martians who are adult persons of an advanced civilization can hear sounds above double the best human hearing to over 40,000 cycles per second. Such high frequencies can be heard by dogs and Martians, but not by humans. Suppose Martian music is in this high frequency range not hearable by standard humans. The fact no humans can actually hear the Martian high frequency music does not entail no music exists. It just is the case that some music cannot be heard by humans. There is no reason to limit what ontologically is music to what can be heard sonically by humans. This would be a form of a priori auditory speciesism.
Objection to Requiring Conscious Intention for Music Production
Can a sleeping musician while sleepwalking play the piano and be playing music? If the answer is "Yes" then this intention to play music can be unconscious and need not be consciously intended. DEVELOP THIS ARGUMENT
A second reason for not requiring a direct conscious intent to produce all music is because musicians when playing and improvising can get into an egoless flow state. In such a flip state, musicians have muscle memory and the production of the music can be by effortless mastery. No direct conscious intentions are required during these flow states. The music plays you, and your intentions do not dictate the flow if musical performance. As soon as deliberate and reflective conscious intention occurs then this self-awareness drops one out of a flow state.
Everyone agrees that jazz is music? Why?
- Wikipedia on Necessity and Sufficiency
- Stanford Encyclopedia of Philosophy on Necessary and Sufficient Conditions
- Internet Encyclopedia of Philosophy on Necessary and Sufficient Conditions
Are There Any Sufficient Conditions For Playing Jazz?
A sufficient condition is one where if it is met then whatever this is a sufficient condition for must exist, or the condition would fail to be such a condition.
If one could find a set of musical properties such that everyone agrees that were all of these properties to exist concurrently within and during a musical performance that that performance would be jazz, then this might count as a sufficient set of conditions. An immediate problem with this proposal is its dependence on unanimity of all individuals doing the judging. It is well known that unamity about musical performances being or not being jazz can be hard to come by.
To avoid the need for unanimous judgment, consider a different tact. Suppose a set of musical conditions could be found that on the face of it most people would agree this conglomeration of conditions, when found in a musical performance, sounds like jazz to them, then challenge any nay-sayers to find a musical performance that most people agree fails to be jazz, but that meets all of the musical factors specified in the sufficient set of conditions under consideration? The idea simplified is this. Can anyone find a counter-example to claim that these particular musical factors are always sufficient to guarantee jazz is being played? If the answer is that no counter-examples can be found, or at least, have yet to be found, lends support and justification that this set of conditions is sufficient for jazz performance.
The three elements central to the jazz tradition are improvisation, syncopation, and the synthesizing and hybridizing of the diatonic and pentatonic musical scales. If one considers a form of music that has all three of these plus the performers are using what are called standard (jazz) harmonies, then this is a sufficient condition for being jazz music.
Because a blues player when playing blues, but not playing jazz, could be improvising, syncopating, and hybridizing the diatonic and pentatonic musical scales, these three conditions when satisfied are not always sufficient fir playing jazz. If the fourth condition is added of using standard (jazz) harmonies, then it is claimed there are no non-jazz counter-examples to the claim of sufficiency.
Isn't it cheating because of circularity she nvolved in the sufficiency conditions? One cannot have a satisfactory set of sufficient conditions for playing jazz if it were claimed that it sufficient for playing jazz whenever one us playing jazz. Isn't this basically all that is happening when the fourth condition is added of using standard jazz harmonies when defining jazz?
The answer to the question of circularity can be answered if a non-question begging way of characterizing standard (jazz) harmonies can be found.
So, what are standard (jazz) harmonies?
Paul Rinzler's Definition of Jazz
Rinzler's Fuzzy Logic Approach in The Contradictions of Jazz
“Quote a bunch of Rinzler.”
Timothy Williamson's Objection to Fuzzy Logic
Timothy Williamson defends traditional logic even for vague concept applications. He has argued that the law of excluded middle for truth-values of true or false holds for all meaningful statements, including vague language, even if we cannot tell which is correct. His primary arguments supporting the law of excluded middle are his objections to the alternative views such as those that use fuzzy logic.
Fuzzy logic denies that every meaningful statement must always be merely true or false. Instead there can be degrees of truth and falsity and there can be a continuum of degrees of truth and falsity between perfectly true and perfectly false with all sorts of intermediate degrees of truth in between.
What is Williamson's objection to fuzzy logic?
His main objection is that fuzzy logic commits itself to making implausible and incorrect claims.
“The kind of alternatives that fuzzy logic proposes does a much worse job of handling these paradoxes. One of the best known alternatives to standard logic is fuzzy logic. When you follow out the consequences of fuzzy logic for these problematic cases, it says some very implausible things.”
Imagine, says Williamson that there are two qualitatively identical twins named Fred and Ted who each are going bald at exactly the same rate and in exactly the same way. When Fred loses a hair so simultaneously does Ted. Suppose they are now borderline cases where, according to Williamson's understanding of fuzzy logic, it claims that when Fred and Ted start to reach the point of hairlessness where it is unclear whether they are or are not yet bald, fuzzy logic can say of Fred that it is precisely half true that Fred is bald. On the other hand/head, it would also be half true to say that Fred is bald, but Ted isn't.
Given that Fred and Ted's baldness situations are identical, Williamson finds these conclusions of fuzzy logic odious and problematic. Why? Presumably, Williamson believes that it is either contradictory, or at the very least unhelpful for decision makers, to claim of two identical scenarios that one is half true and the other is half false.
Williamson puts it this way:
“That's a completely false description of the situation because it is absolute clear that if one of them is bald, then so is the other [one] and there is no truth at all to the claim that one of them is bald and the other isn't. 
Possible Replies to Williamson's Objections to Fuzzy Logic
Intuitions can differ for different people, different philosophical views, and even within oneself one may have opposing intuitions in different scenarios that end up conflicting. Williamson seems strongly committed to the intuitions lying behind the law of excluded middle for trite cakes if true or false for meaningful statements. It may be that these powerful intuitions are driving some if Williamson's beliefs and it certain seems to be so as represented in the following argument given by Williamson from his book, Vagueness.
“Conjunction may be taken first. Suppose that p is true to the same degree as q. Thus the first and second conjuncts of p & q match the first and second conjuncts of p & p respectively in degree of truth. By generalized truth-functionality, it follows that p & q is true to the same degree as p & p. Since p & p is true to the same degree as p, p & q is true to the same degree as p. Now imagine someone drifting off to sleep. The sentences 'He is awake' and 'He is asleep' are vague. According to the degree theorist, as the former falls in degree of truth, the latter rises. At some point they have the same degree of truth, an intermediate one. By what has just been argued, the conjunction 'He is awake and he is asleep' also has that intermediate degree of truth. But how can that be? Waking and sleep by definition exclude each other. 'He is awake and he is asleep' has no chance at all of being true. Our man is not in an unclear area between the cases in which the conjunction is true and those in which it is false, for there are no cases of the former kind. If intermediate degrees of truth are a matter of vagueness, they characterize cases in which a sentence is neither clearly correct nor clearly incorrect. Since the conjunction in question is clearly incorrect, it should not have an intermediate degree of truth. It is clearly incorrect, although neither conjunct is; one must be careful to distinguish what can be said of the conjunction from what can be said of each conjunct. Thus degree-functionality fails for conjunction.” 
Notice Williamson's fundamental assumption made during presentation of his counter-example when he baldfacedly claims that “waking and sleeping by definition exclude each other.” It is this kind of thinking that appears to miss the entire point of fuzzy logic, which is that it may well be that the state of waking and the state of being asleep are not mutually exclusive domains and that it is possible to end up in a gray area where the same person is kind of awake and not awake at the same time. It may well be that these phenomena come in degrees, as fuzzy logic presumes is possible.
When a person falls asleep they typically go through several stages of different types of both consciousness and neurology.
Notice some of the oddish claims being made by the author(s) of an internet wellness website discussing the four stages of sleep.
“The Beginnings of Sleep: During the earliest phases of sleep, you are still relatively awake and alert. The brain produces what are known as beta waves, which are small and fast. As the brain begins to relax and slow down, slower waves known as alpha waves are produced. During this time when you are not quite asleep, you may experience strange and extremely vivid sensations known as hypnagogic hallucinations. Common examples of this phenomenon include feeling like you are falling or hearing someone call your name.
NREM Stage 1: Stage 1 is the beginning of the sleep cycle, and is a relatively light stage of sleep. Stage 1 can be considered a transition period between wakefulness and sleep. In Stage 1, the brain produces high amplitude theta waves, which are very slow brain waves. This period of sleep lasts only a brief time (around 5-10 minutes). If you awaken someone during this stage, they might report that they were not really asleep.” (bold not in original)
Williamson would freak out from much of what was said above given his view that waking and sleep are diametrically opposed and one must be in only one of these two states at all times when alive. Instead, the article asserts that "during the earliest phases of sleep you are still awake". Williamson finds this to be a contradiction. On Williamson's mutually exclusive views, it is impossible to have any transition state between waking and sleeping since on his view one can only be in one or the other of the two conditions. There cannot be any transition stage on his understanding of the relevant conditions. Furthermore, Williamson has either to claim that what a person reports upon awaking from Stage 1 sleep that "he or she was not really asleep " that this is either false because they were asleep or true because they were never in Stage 1 sleep. But these reactions belay the facts. The person was in Stage 1 and they believe of themselves that they were not yet in a sleep condition.
Fuzzy Logic approaches can easily deal with what appears to be contradictions (and so impossible to occur) from Williamson's point of view. It claims there can be degrees of wakefulness and degrees of being asleep. Indeed, that there are degrees of being asleep is reflected in the four stages a brain can find itself in during resting periods.
That there are degrees of both wakefulness and sleep seems a natural position to take. Different degrees of wakefulness do seem to occur. Here's a list:
- daydreaming: you are sort of awake and sort of not because it is harder to arouse a daydreamer using external stimulation. When aroused from a daydream, people do not typically say they were asleep. Instead they claim they were deep in thought and perhaps having strong visual imagery.
- falling asleep: as one falls asleep one can notice different consciousness transitions.
- being on drugs: like cocaine, ecstasy, or LSD can change one's energy levels and degrees of feeling wide awake.
- near death experiences: sometimes described as having your life flash before one's eyes would seem to be a different state of waking.
- Temporal slowdown: during an emergency situation some people report that it seems like time has slowed down for them and they can take advantage of this heightened state of consciousness to deal with a problem quickly in real time.
- lucid dreaming: some people claim to be aware of when they are in a dream state and can control their actions better when in this state than when not having a lucid dream.
- confused awake states: resulting from low blood sugar, or deprivations of sleep, food, or water can cause a lessening of one's normal conscious abilities compared to when not in such distressed states.
Rinzler's Onion Model Definition of Jazz
In his ground breaking book, The Contradictions of Jazz, Director of Jazz Studies and music theory at California Polytechnic State University in San Luis Obispo, Dr. Paul Rinzler explains his approaches and methodologies for mapping out which music qualifies as jazz.
“But not only that, jazz gives us clues as to how to make that happen. Improvisational jazz seems like it is primarily about the values of creativity, freedom, self-assertion, and individualism. Each player takes a turn, soloing without being confined to notes on a page. There are no absolutes.”
“But as scholar Paul Rinzler argues, jazz is ultimately about relating these characteristics to their opposites. Musical creativity is not random, but is ultimately built on the tradition and its rules. Freedom of expression is tempered by responsibility to the ensemble and to the audience. Self-assertion is balanced with openness to others and to the unknown. And individualism, found in the personal expression of the solo, is set in the context of the interconnectedness of the ensemble.”
The Galactic Model for Defining Jazz
It sure looks like it exists.
Overview and Summary of Defining Jazz
- Joachim E. Berendt, in The Jazz Book: From Ragtime to Fusion and Beyond, translated by H. and B. Bredigkeit with Dan Morgenstern, 1981, Lawrence Hill Books, p. 371.
- Joachim Ernst Berendt, in The New Jazz Book: a History and Guide, p. 278.
- Joachim E. Berendt, in The Jazz Book: From Ragtime to Fusion and Beyond, Translated by H. and B. Bredigkeit with Dan Morgenstern, 1981. Lawrence Hill Books, p. 371.
- Robert Christgau, "Christgau's Consumer Guide," in The Village Voice, New York, October 28, 1986. Retrieved September 10, 2015.
- In "Review of The Cambridge Companion to Jazz" by Peter Elsdon, FZMw (Frankfurt Journal of Musicology) No. 6, 2003.
- Mervyn Cooke and David G. Horn, The Cambridge Companion to Jazz, New York: Cambridge University Press, pp. 1, 6.
- Wikipedia on Albert Ayler.
- "Timothy Williamson on Vagueness," listen at Philosophy Bites.
- Timothy Williamson, Vagueness, New York: Routledge, 1996, p. 136. http://www.questia.com/read/108336551/vagueness.
- "The Four Stages of Sleep (NREM and REM Sleep Cycles)"