[Fis] _ response to Pedro, response to Salthe

2016-02-24 Thread Maxine Sheets-Johnstone

Because I am unclear about just what was received by FIS members
and what was not, I am copying my response to Salthe and my response
to Pedro below. Kindly excuse the repeat performance if it is one--
it won't happen again!

Cheers,
Maxine

Response to Pedro:

With respect to nonhuman animal dances, in The Descent of Man and 
Selection
in Relation to Sex, Darwin describes the "Love-Antics and Dances" of 
male
birds, and later, more generally, describes male "love-dances"—-all in 
the

context of male-male competition, or what Darwin describes in upward of
460 pages,starting with mollusks and crustaceans and beetles and working 
his

way through fish, amphibians, reptiles, birds (four chapters), mammals
(two chapters), then finally and specifically human mammals (two 
chapters),

as “the law of battle.”
Jane Goodall describes a movement sequence that is part of a male
chimpanzee's kinetic repertoire, a sequence that a male performs in 
conjunction
with his "sexual signalling behavior" or "courtship display." “The 
bipedal swagger,”
as she identifies the behavior or display, is typically an upright male 
sequence

of movements and occurs only rarely in females.
Primatologist C. R. Rogers amplifies Goodall’s description of a male’s 
bipedal
swagger in describing what he identifies as a male chimpanzee’s “short 
dance.”
Female choice in relation to male-male competition is described by 
Darwin, particularly
in relation to birds, but also in suggestive ways with respect to 
mammals. More
recently, the topic of female choice was taken up by William Eberhard. 
His hypothesis:
“sexual selection by female choice, proposes that male genitalia 
function as ‘internal

courtship’ devices” (Eberhard 1985).
Simply as an event of possible evolutionary interest and one that is 
both innovative and

provocative, I attach a write up of “A Human Enclosure at Edinburgh Zoo”

Cultural differences exist not only in dance but in everyday life—-for 
example,
in everyday interpersonal spatial relationships. Cultural distinctions 
in these
relationships are commonly made in terms of whether one is in front of 
or behind
another, whether one is above or below another; whether one is small or 
large in
relation to another, and so on. Anthropologist Raymond Firth, who 
studied Tikopia
culture, wrote of the postural and gestural practices of Tikopians and 
then compared

their practices to those of his own experience in British culture.
In the process of doing so, Firth made interesting observations with 
respect to the
different practices. In The Roots of Power: Animate Form and Gendered 
Bodies, I
discussed Firth’s research and the research of others and gave an 
evolutionary genealogy

of diverse intercorporeal relationships.

As for Tango: I do not know what the “informational implications” of 
Tango might be,
but I might well ask Adriana Pegorer who teaches Tango-Argentino-style, 
a style that
she says is different from ballroom Tango that requires swift head 
turning.  She has
taught Tango to visually impaired people for years and has also combined 
Tango with
Contact Improvisation, an internationally practiced form of dance that 
commonly involves
non-dancers as well as dancers. (Her work is mentioned in an extended 
endnote on cultural
differences in an article titled “On Movement and Mirror Neurons: A 
Challenging and
Choice Conversation” that was published in Phenomenology and the 
Cognitive Sciences.)


And thanks for your reminder regarding food, where it goes, and what it 
does, all of
which recalled Richard Wrangham and Rachel Carmody’s thesis in Catching 
Fire.


Cheers,
Maxine

Response to Salthe:

Theories are based on first-person observations. Observations are 
first-person real-life, real-time experiences and are duly recorded in 
support of theory. Descent with modification was a theory that Darwin 
put forth on the basis of his observations that had to do with 
morphology, but not only with morphology. See, for example, his last 
book on worms and the intelligence of worms; see also his third book 
devoted to emotions.
I am unaware of Darwin’s denying a concern with origins and would 
appreciate knowing more about his denial by way of a reference. I know 
that what he did not deny was “[t]hat many and grave objections may be 
advanced against the theory of descent with modification through natural 
selection” (Origin of Species, p. 435). Clearly, “descent with 
modification” has to do not just with morphology but with history. 
History has to do with timelines, and in this instance with origins and 
extinctions.  I would add that because “descent with modification” 
involves a history and not just a  morphological comparison as in your 
human hand and chicken foot example, the phrase is actually pertinent to 
the current discussion in evolutionary biology as to how single-celled 
organisms gave rise to multi-celled organisms. If, as is currently 
suggested, the way a protein wiggles can result in a mutation so 

[Fis] Follow-up to my response to Pedro

2016-02-24 Thread Maxine Sheets-Johnstone

In my response to Pedro, I wrote,

“Simply as an event of possible evolutionary interest and one
that is both innovative and provocative, I attach a write up of
'A Human Enclosure at Edinburgh Zoo'.

It was not possible to attach the file. If anyone would like a
copy, kindly email me directly at
m...@uoregon.edu
and I will send it on to you.
Cheers,
Maxine
___
Fis mailing list
Fis@listas.unizar.es
http://listas.unizar.es/cgi-bin/mailman/listinfo/fis


[Fis] Response to Salthe's response

2016-02-24 Thread Maxine Sheets-Johnstone

Response to Salthe's response:

So, as I understand the discussion, we are using the term origin in
at least two different senses: origin as in Darwin's "origin of 
species,"

which passes muster, and origin as a big bang of some order or other,
which does not pass muster, muster in the sense of being objectively
attainable by science.

I agree that “there can be no First Person observation of an 
evolutionary

origin.” I would say that there can be only deductive observations of
evolutionary origins on the basis of fossil evidence. The same holds for
extinctions. But I wonder, as in the case of passenger pigeons, for 
instance.
You state that no one “would actually SEE its death,” but wasn’t the 
death

of the last passenger pigeon seen? I take the following from Wikepedia:

The last captive birds were divided in three groups around the turn of 
the
20th century, some of which were photographed alive. Martha, thought to 
be
the last passenger pigeon, died on September 1, 1914, at the Cincinnati 
Zoo.
The eradication of this species has been described as one of the 
greatest and

most senseless extinctions induced by humans.

Regarding movement and phenomenology: Husserl spelled out an exacting 
methodology
with respect to phenomenology. That methodology is not always recognized 
and
respected in the so-called practice of phenomenology or in discussions 
of phenomenology.

In my original article in the special issue of FIS, I pointed out common
definitions/understandings of movement that are, well, off the wall in 
terms of
grasping the foundational dynamic nature of movement. Alas! I quote from 
that article:


Movement is indeed the essential measure of being alive.
Like other forms of animate life, we humans come into the
world moving: we are precisely not stillborn (for more on this
particular kinetic reality see Sheets-Johnstone 1999/exp. 2nd
ed. 2011). To understand movement from this living, essentially
experienced perspective, one must necessarily cast aside such
common definitions and understandings of movement as
“movement is a change of position” and movement takes place
in time and space. In doing phenomenology, that is, in the
practice of the phenomenological method, one indeed separates
oneself from standard texts and assumptions, long-held beliefs,
and so on, and thereby makes the familiar strange. In doing so
with respect to movement, one plunges into a bona fide
phenomenological investigation of dynamics, the dynamics that
undergird both kinesthetic experiences of movement and
kinetic-visual experiences of movement. Let us think for a
moment along the lines of such a plunge and of what such an
investigation reveals.

Many thanks for your comments!--and
Cheers,
Maxine
___
Fis mailing list
Fis@listas.unizar.es
http://listas.unizar.es/cgi-bin/mailman/listinfo/fis


[Fis] Response to Steven Ericcson-Zenith

2016-02-24 Thread Maxine Sheets-Johnstone

Response to Steven Ericcson-Zenith:

Thank you for the reference. One might possibly relate King's notion of
"catastrophic evolutionary pressure" to Stephen J. Gould's 21st century
thesis of "punctuated equilibrium," though Gould hardly dismisses
"natural selection by incremental mutation" in the process of 
documenting

his thesis.
Maxine
___
Fis mailing list
Fis@listas.unizar.es
http://listas.unizar.es/cgi-bin/mailman/listinfo/fis


[Fis] Response to Alex Hankey

2016-02-18 Thread Maxine Sheets-Johnstone

As I wrote in the extended abstract: “These qualitative aspects
of movement are separable only reflectively, that is, analytically,
after the fact; experientially, they are all of a piece in the global
qualitatively felt dynamic phenomenon of self-movement.”

There are further comments I would make.

First, when learning a new skill of any kind, one not infrequently
pays attention to the qualitative dynamics of one’s movement,
specifically, for example, to the tensional or areal quality-—the degree
of effort or the range of the movement. In such instances, one is not
attending to the globally-felt dynamic but to particular aspects of the
dynamic. Precisely by such attention, one perfects the skill one is 
learning.


Second, whether in dance, in sports, or in washing the dishes, movement 
is

movement. It may be attended to in various ways and indeed awareness may
alternate among the spatio-temporal-energic aspects of movement-—what 
you

name “digitized procedures”--and the global phenomenon. With respect to
professionals, whether they be in dance, sports, or yoga, the 
professionals

have spent time learning to do what they do and hence the dynamics of
movement run off fluidly, in seeming effortless ways.

Third, other forms of movement analysis exist.  Labananalysis and
Eshkol-Wachmann analysis are graphic forms. I have been told by 
researchers
in both areas that the phenomenological analysis of movement is 
complementary

in many respects to those graphic forms—-Labananalysis in dance and
Eshkol-Wachmann in studies of wolves, mice, and other mammals (see the 
studies

of ethologists John Fentress and Ilan Golani on the latter.)

Finally, one of the obstacles to veridical accounts of movement is the 
confusion
of movement with objects in motion, which commonly carries with it an 
inability
to separate movement from objects in motion together with a tendency to 
give
preferential attention to objects in motion over movement. An analogy 
might be
made to particles and waves in physics with respect to the latter 
tendency and
possibly even to neurons over dynamic networks in brain studies. The 
tendency
appears to stem from a predilection for what is solid and spatially 
pointillist
over what is fluid and does not stay in place. Indeed, as pointed out in 
the
extended abstract, common notions of movement—-that movement is a force 
in time
and in space, and that movement is a change of position—-overlooks a 
primary
kinetic fact: any and all movement creates its own distinctive dynamic, 
whether

a tennis serve, an ocean wave, the hammering of a nail, or a sneeze.

Maxine Sheets-Johnstone
___
Fis mailing list
Fis@listas.unizar.es
http://listas.unizar.es/cgi-bin/mailman/listinfo/fis


[Fis] _ Discussion

2016-04-11 Thread Maxine Sheets-Johnstone

To all colleagues,

I hope I may voice a number of concerns that have arisen in the course
of the ongoing discussions that are ostensibly about phenomenology and
the life sciences.

The concerns begin with a non-recognition of what is surely the ground
floor of real-life, real-time realities, namely, animation, not in the
sense of being alive or in opposition to the inanimate, but in the sense
of motion, movement, kinetics. As Aristotle cogently remarked,
“Nature is a principle of motion and change. . . . We must therefore see
that we understand what motion is; for if it were unknown, nature too
would be unknown” (Physics 200b12-14).

Through and through--from animate organisms to an ever-changing world--
movement is foundational to understandings of subject and world, and of
subject/world relationships, and this whether subject and world are
examined phenomenologically or scientifically. In short, movement is at
the core of information and meaning, at the core of mind and 
consciousness,

at the core of both gestural and verbal language, at the core of nervous
system and organic functionings, at the core of molecular 
transformations,
at the core of ellipses, electrons, gravity, waves, particles, and so 
on,
and further, at the core of time, the concept, measurement, and meaning 
of

time.

I enumerate below specifics with respect to what is essentially the
foundational dynamic reality. The summary concerns are followed by
references that document each concern. If further specifics are wanted 
or

if specific articles are wanted, kindly contact m...@uoregon.edu

(1). Instincts and/or feelings motivate animate organisms to move.
Without such instincts or feelings there would be no disposition
to move. An ‘animate organism’ would in truth be akin to a statue,
a statue Condillac described two and a half centuries ago as having
first this sense given to it, then that sense given to it, but that,
lacking movement, is powerless to gain knowledge of the world. Such
a movement deficient creature would furthermore lack the biological
capacity of responsivity, a near universal characteristic of life.
The startle reflex is a premier example. Can what is evolutionarily
given be “illogical”? Clearly, feelings are not “illogical,” but move
through animate bodies, moving them to move. Without feelings of
curiosity, for example, or awe, or wonder, there would be no exploration
of the natural world, no investigations, hence no “information.”
Furthermore, without feelings of movement—initially, from an 
evolutionary
perspective, no proprioception, and later, no kinesthesia--there would 
be

no near and far, no weak and strong, no straight and curved, and so on,
hence, no determinations of Nature. In short, there would be no 
information

and no meaning. (See Note #1: The Primacy of Movement)

(2). An excellent lead-in to scientific understandings of movement and
its inherent dynamics lies in the extensive research and writings of
J. A. Scott Kelso, Pierre de Fermat Laureate in 2007. Kelso was founder
of the Center for Brain and Behavioral Studies and its Director for 
twenty
years. His rigorous multi-dimensional experimental studies are anchored 
in

coordination dynamics, an anchorage that is unconstrained by dogma. The
breadth of his knowledge and his sense of open inquiry is apparent in 
the
literature he cites in conjunction with his articles and books. His 
recent

article in Biological Cybernetics that focuses on “Agency” is strikingly
relevant to the present FIS discussion. It takes experience into 
account,
specifically in the form of “positive feedback,” which obviously 
involves
kinesthesia in a central way. Moreover his upcoming Opinion piece in 
Trends
in Cognitive Science should be essential reading. (See Note #2: “The 
Coordination
Dynamics of Mobile Conjugate Reinforcement” and The Complementary 
Nature)


(3). As pointed out elsewhere, “Certainly words carry no patented 
meanings,
but the term ‘phenomenology’ does seem stretched beyond its limits when 
it
is used to denote either mere reportorial renderings of perceptible 
behaviors
or actions, or any descriptive rendering at all of perceptible behaviors 
or
actions. At the least, ‘phenomenology’ should be recognized as a very 
specific
mode of epistemological inquiry invariably associated with the name 
Edmund Husserl. . . . ”
Phenomenological inquiries are tethered to a very specific methodology, 
one as
rigorous as that of science. Phenomenological findings are furthermore 
open to

verification by others, precisely as in science. Moreover two forms of
phenomenological analysis warrant recognition: static and genetic, the 
former
being a determination of the essential character of the object of 
inquiry, the
second being a determination of how the meaning of that object of 
inquiry came

to be constituted, hence an inquiry into sedimentations of meaning, into
protentions and retentions, into horizons of meaning, and so on. Thus 
too,
what warrants 

[Fis] _ FIS discusion

2016-04-30 Thread Maxine Sheets-Johnstone

To FIS colleagues,

First, an open-to-all response to Lou Kaufmann:

Thank you for your lengthy tutorial—some time back--but I wonder and am
genuinely puzzled given the “phenomenology-life sciences theme” why none
of the articles that I referenced were read and a response generated at 
least

in part on the basis of that reading in conjunction with your own work.

Is there some reason why they were not taken up, especially perhaps the 
article

identified as being a critique of Godels’s incompleteness theorem from a
phenomenological perspective? I would think that you and perhaps FIS 
persons
generally would feel particularly inquisitive about that article. I 
would think
too that people in FIS would be particularly inquisitive about the 
reference to
Biological Cybernetics. Viewpoints that differ from one’s own are by 
some thought
a waste of time, but for my part, I think they rightly broaden a 
discussion, which
is not to say that entrenched or deeply held views are not solidly 
based, much less
wrong, but that they have the possibility of being amplified through a 
consideration

of the same topic from a different perspective.

For example: Language did not arise deus ex machina, and it certainly 
did not arise
in the form of graphs or writing, but in the form of sounding.  
Awareness of oneself
as a sound-maker is basic to what we identify as a ‘verbal language’. 
Moreover this
awareness and the verbal language itself are both foundationally a 
matter of both
movment and hearing. A recognition of this fact of life would seem to me 
to be of
interest, even primordial interest, to anyone concerned with 
‘SELF-REFERENCE', its

essential nature and substantive origins.

With respect to ‘substantive origins’, does it not behoove us to inquire 
as to the genesis
of a particular capacity rather than take for granted that ‘this is the 
way things are and
have always been’?. For example, and as pointed out elsewhere, the 
traditional conception
of language being composed of arbitrary elements—-hence 
“symbols”--cannot be assumed with
either epistemological or scientific impunity. Until the origin of 
verbal language is accounted
for by reconstructing a particular lifeworld, there is no way of 
understanding how arbitrary
sounds could come to be made  . . . let alone serve as carriers of 
assigned meaning.
What is essential is first that arbitrary sounds be distinguished from 
non-arbitrary sounds,
and second, that a paradigm of signification exist. Further, no creature 
can speak a language
for which its body is unprepared. In other words, a certain 
sensory-kinetic body is essential
to the advent of verbal language. In short, in the beginning, thinking 
moved along analogical
lines rather than symbolic ones, hence along the lines of iconicity 
rather than along arbitrary
lines. See the extensive writings of linguistic anthropologist Mary 
LeCron Foster and
Sheets-Johnstone’s The Roots of Thinking, Chapter 6, "On the Origin of 
Language." Foster's
finely documented analyses show that the meaning of the original sound 
elements of language
was the analogue of their articulatory gestures. Similarly, in my own 
analysis, I start not with
symbols or symbolic thought but at the beginning, namely, with a 
sensory-kinetic analysis of the

arbitrary and the non-arbitrary.

Husserl wrote that "each free act [i.e., an act involving reason] has 
its comet’s tail of Nature.”
In effect, living meanings are, from a phenomenological perspective, 
historically complex phenomena.
They have a natural history that, in its fullest sense, is bound not 
both ontogenetically
and phylogenetically. Like living forms, living meanings hold—-and have 
held—-possibilities
of further development, which is to say that they have evolved over time 
and that investigations
of their origin and historical development tell us something fundamental 
about life in general and
human life, including individual human lives, in particular. WITH 
RESPECT TO ORIGINS AND HISTORICALLY

COMPLEX PHENOMENA, consider the following examples:

Information is commonly language-dependent whereas meaning is not.
We come into the world moving; we are precisely not stillborn.
We humans all learn our bodies and learn to move ourselves.
Movement forms the I that moves before the I that moves forms movement.
Infants are not pre-linguistic; language is post-kinetic.
Nonlinguistic corporeal concepts ground fundamental verbal concepts.


To all FIS colleagues re Alex Hankey's presentation:

I thought at first that we might be talking past each other because it 
was my understanding
that this 4-part discussion was about phenomenology and the life 
sciences. What this means to
me is that we conjoin real-life, real-time first-person experience, thus 
methodologically
anchored phenomenological analyses, with real-life-real-time 
third-person experience, thus
methodologically anchored empirical analyses. With this last 
conversation between Rafael and
Alex, the terrain seems 

[Fis] re Gödel discussion

2016-05-02 Thread Maxine Sheets-Johnstone

Many thanks for your comments, Lou and Bruno. I read and pondered,
and finally concluded that the paths taken by each of you exceed
my competencies. I subsequently sent your comments to Professor
Johnstone—-I trust this is acceptable—asking him if he would care to
respond with a brief sketch of the reasoning undergirding his critique,
which remains anchored in Gödel’s theorem, not in the writings of others
about Gödel’s theorem. Herewith his reply:


Since no one commented on the reasoning supporting the conclusions 
reached
in the two cited articles, let me attempt to sketch the crux of the case 
presented.


The Liar Paradox contains an important lesson about meaning. A statement 
that says of itself that it is false, gives rise to a paradox: if true, 
it must be false, and if false, it must be true. Something has to be 
amiss here. In fact, what is wrong is the statement in question is not a 
statement at all; it is a pseudo-statement, something that looks like a 
statement but is incomplete or vacuous. Like the pseudo-statement that 
merely says of itself that it is true, it says nothing. Since such 
self-referential truth-evaluations say nothing, they are neither true 
nor false. Indeed, the predicates ‘true’ and ‘false’ can only be 
meaningfully applied to what is already a meaningful whole, one that 
already says something.


The so-called Strengthened Liar Paradox features a pseudo-statement that 
says of itself that it is neither true nor false. It is paradoxical in 
that it apparently says something that is true while saying that what it 
says it is not true. However, the paradox dissolves when one realizes 
that it says something that is apparently true only because it is 
neither true nor false. However, if it is neither true nor false, it is 
consequently not a statement, and hence it says nothing. Since it says 
nothing, it cannot say something that is true. The reason why it appears 
to say something true is that one and the same string of words may be 
used to make either of two declarations, one a pseudo-statement, the 
other a true statement, depending on how the words refer.


Consider the following example. Suppose we give the name ‘Joe’ to what I 
am saying, and what I am saying is that Joe is neither true nor false. 
When I say it, it is a pseudo-statement that is neither true nor false; 
when you say it, it is a statement that is true. The sentence leads a 
double life, as it were, in that it may be used to make two different 
statements depending on who says it. A similar situation can also arise 
with a Liar sentence: if the liar says that what he says is false, then 
he is saying nothing; if I say that what he says is false, then I am 
making a false statement about his pseudo-statement.


This may look like a silly peculiarity of spoken language, one best 
ignored in formal logic, but it is ultimately what is wrong with the 
Gödel sentence that plays a key role in Gödel’s Incompleteness Theorem. 
That sentence is a string of symbols deemed well-formed according to the 
formation rules of the system used by Gödel, but which, on the intended 
interpretation of the system, is ambiguous: the sentence has two 
different interpretations, a self-referential truth-evaluation that is 
neither true nor false or a true statement about that self-referential 
statement. In such a system, Gödel’s conclusion holds. However, it is a 
mistake to conclude that no possible formalization of Arithmetic can be 
complete. In a formal system that distinguishes between the two possible 
readings of the Gödel sentence (an operation that would considerably 
complicate the system), such would no longer be the case.



Cheers,
Maxine
___
Fis mailing list
Fis@listas.unizar.es
http://listas.unizar.es/cgi-bin/mailman/listinfo/fis


[Fis] _ Concerns regarding a questioning of Goedel's theorem . . .

2016-05-01 Thread Maxine Sheets-Johnstone

To all concerned colleagues,

I appreciate the fact that discussions should be conversations about 
issues,
but this particular issue and in particular the critique cited in my 
posting
warrant extended exposition in order to show the reasoning upholding the 
critique.
I am thus quoting from specific articles, the first phenomenological, 
the second
analytic-logical--though they are obviously complementary as befits 
discussions

in phenomenology and the life sciences.

EXCERPT FROM:
SELF-REFERENCE AND GÖDEL'S THEOREM: A HUSSERLIAN ANALYSIS
Husserl Studies 19 (2003), pages 131-151.
Albert A. Johnstone

The aim of this article is to show that a Husserlian approach to the 
Liar paradoxes and to their closely related kin discloses the illusory 
nature of these difficulties. Phenomenological meaning analysis finds 
the ultimate source of mischief to be circular definition, implicit or 
explicit. Definitional circularity lies at the root both of the 
self-reference integral to the statements that generate Liar paradoxes, 
and of the particular instances of predicate criteria featured in the 
Grelling paradox as well as in the self-evaluating Gödel sentence 
crucial to Gödel's theorem. Since the statements thereby generated turn 
out on closer scrutiny to be vacuous and semantically nonsensical, their 
rejection from reasonable discourse is both warranted and imperative. 
Naturally enough, their exclusion dissolves the various problems created 
by their presence. . . .


VII: THE GOEDEL SENTENCE
Following a procedure invented by Gödel, one may assign numbers in some 
orderly way as names or class-numbers to each of the various classes of 
numbers (the prime numbers, the odd numbers, and so on). Some of these 
class-numbers will qualify for membership in the class they name; others 
will not. For instance, if the number 41 should happen to be the 
class-number that names the class of numbers that are divisible by 7, 
then since 41 does not have the property of being divisible by 7, the 
class-number 41 would not be a member of the class it names.
	Now, consider the class-number of the class of class-numbers that are 
members of the class they name. Does it have the defining property of 
the class it names? The question is unanswerable. Since the defining 
property of the class is that of being a class-number that is a member 
of the class it names, the necessary and sufficient condition for the 
class-number in question to be a member of the class it names turns out 
to be that it be a member of the class it names. In short, the number is 
a member if and only if it is a member. The criterion is 
circular--defined in terms of what was to be defined--and consequently 
not a criterion at all since it provides no way of determining whether 
or not the number is a member.
	The situation is obviously similar for the class-number of the 
complementary class of class-numbers--those that do not have the 
defining property of the class they name--since the criteria in the two 
cases are logically interdependent. The criterion of membership is 
likewise defined in circular fashion, and hence is vacuous. In addition, 
the criterion postulates an absurd analytic equivalence, that of the 
defining property with its negative. The question of whether the 
class-number is a member of the class it names is unanswerable, with the 
result that any proposed answer is neither true nor false. In addition, 
of course, any answer would generate paradox: the number has the 
requisite defining property if and only if it does not have it.
	As might be expected, the situation is not significantly different for 
the class-number of classes of which the definition involves semantic 
predicates. Consider, for instance, the class of class-numbers of which 
it is provable that they are members of the class they name. The 
question of whether the class-number of the class is a member of the 
class it numbers is undecidable. The possession by the class-number of 
the property requisite for membership is conditional upon the question 
of whether it provably possesses the property, with the result that the 
question can have no answer. Otherwise stated, the number has the 
defining property of the class it names if and only if it provably has 
that property. In these circumstances, the explanation of what it means 
for the class-number to have the property has to be circular in that it 
must define having the property in terms of having the property. The 
vacuity that results is hidden somewhat by the presence of the 
requirement of provability, but while provability might count as a 
necessary condition, in the present case it cannot be a sufficient one. 
In fact, its presence creates a semantically absurd situation: the 
analytic equivalence of having the property and provably having it. The 
statement of the possession of the property by the class-number in 
question is consequently both vacuous and semantically absurd, hence an 
undecidable