language and the self-reference paradox - ime-uspjstern/papers/papersjs/jmschk2.pdf · cybernetics...

Cybernetics And Human Knowing. Vol. 14, no. 4, pp.71-92

Language

Heinz Von Forester charathat is, as discrete, separenvironment. Previous amathematical formalism and have shown that theeigen-solutions in the pralanguage in the emergenconnections with the sem

“If the str

“The most beautiful true art and all sci

pause to wonder a

1 Introduction

In Stern (2007a) it is sare naturally representare routinely stated as

and most often take th

discusses why the eigstability, and composaof science is natural anfor testing hypotheses,factors), have well knsharp hypotheses. Tmethodological, system

The same article unorthodox Bayesianmathematical and staparticular, it is shown hsolutions in the practiessential characteristic

1. Institute of Mathematics an

and the Self-Reference Paradox

Julio Michael Stern1

cterizes the objects “known” by an autopoietic system as eigen-solutions,able, stable and composable states of the interaction of the system with itsrticles have presented the FBST, Full Bayesian Significance Test, as aspecifically designed to access the support for sharp statistical hypotheses,se hypotheses correspond, from a constructivist perspective, to systemicctice of science. In this article several issues related to the role played by

ce of eigen-solutions are analyzed. The last sections also explore possibleiotic theory of Charles Sanders Peirce.

ing is too tight it will snap, but if it is too loose it will not play.”Siddhartha Gautama

thing we can experience is the mysterious. It is the source of allence. He to whom this emotion is a stranger, who can no longernd stand rapt in awe, is as good as dead: His eyes are closed.”

Albert Einstein

hown how the eigen-solutions found in the practice of scienceed by statistical sharp hypotheses. Statistical sharp hypotheses natural laws, conservation principles or invariant transforms,e form of functional equations, like h(x)= c. The article alsoen-solutions’ essential properties of discreteness (sharpness),bility, indicate that considering such hypotheses in the practiced reasonable. Surprisingly, the two standard statistical theories classical (frequentist p-values) and orthodox Bayesian (Bayesown and documented problems for handling or interpreting

hese problems are thoroughly reviewed, from statistical,ic and epistemological perspectives.presents the FBST, or Full Bayesian Significance Test, an

significance test specifically designed for this task. Thetistical properties of the FBST are carefully analyzed. Inow the FBST fully supports the test and identification of eigen-ce of science, using procedures that take into account all thes pointed by Von Forester. In contrast to some alternative belief

d Statistics, University of São Paulo, Brazil. Email: [email protected]

72

Julio Michael Stern

calculi or logical formaon continuous statistichypotheses, asymptotithe representation oconstructivism as a coFBST formalism, andConstructivism plus FB

The discussion in we will try to answer inimportance of languasection 2. In answerinwar” metaphor of cognin section 4, this is skepticism or solipsismsummarized in sectionBohr concerning quangive concrete examplemystery) related to theconcerns of Bohr’s phhis famous “dirty dishe

Washing dishes and latowels and neverthelesunclear terms and a logsucceed in using it to b

The second queCogCon+FBST frameSemiotics and Peirceamy final remarks.

Before ending thissolution are reviewedrecurrent state is theautopoietic system.

Living systems as unienter into interactionorganization continuoucyclic process). Eachenvironment) be satisfithe prediction that an ithe system maintains prediction. In a continenvironment does no corganization of the livactions. Every interact

lisms based on discrete algebraic structures, the FBST is basedal models. This makes it easy to support concepts like sharp

c convergence and stability, and these are essential concepts inf eigen-solutions. The same article presents cognitiveherent epistemological framework that is compatible with the vice-versa. We will refer to this setting as the CognitiveST formalism, or CogCon+FBST framework for short.

Stern (2007a) raised some interesting questions, some of which the present article. The first question relates to the role and the

ge in the emergence of eigen-solutions and is discussed ing it, we make extensive use of the William Rasch “two-frontitive constructivism, as exposed in Rasch (2000). As explained

the war against dogmatic realism at one front, and against, at the second. The results of the first part of the paper are

5. To illustrate his arguments, Rasch uses some ideas of Nielstum mechanics. In section 3, we use some of the same ideas tos of the topics under discussion. The importance (and also the role of language in the practice of science was one of the majorilosophical writings, see Bohr (1987, I-IV), as exemplified bys” metaphor:

nguage can in some respects be compared. We have dirty dishwater and dirtys finally succeed in getting the plates and glasses clean. Likewise, we haveic limited in an unknown way in its field of application – but nevertheless wering clearness to our understanding of nature. Bohr (2007)

stion, posed by Søren Brier, which asks whether thework is compatible with and can benefit from the concepts ofn philosophy, is addressed in section 6. In section 7, I present

section a few key definitions related to the concept of eigen-. As stated in Maturana and Varela (1980), the concept of key to understand the concept of cognitive domain in an

ts of interaction specified by their conditions of being living systems cannots that are not specified by their organization. The circularity of theirsly brings them back to the same internal state (same with respect to the internal state requires that certain conditions (interactions with theed in order to proceed to the next state. Thus the circular organization impliesnteraction that took place once will take place again. If this does not happenits integrity (identity with respect to the observer) and enters into a newuously changing environment these predictions can only be successful if thehange in that which is predicted. Accordingly, the predictions implied in theing system are not predictions of particular events, but of classes of inter-ion is a particular interaction, but every prediction is a prediction of a class of

Language and the Self-Reference Paradox

73

interactions that is defiits circular organizatioinferential systems, anp.10)

The epistemological iprocesses and their eigrecursive) states, bothinvestigated in Von For

The meaning of recurcertain conditions theragain the same solutiodepending on which dbehaviors, etc. (Von Fo

Objects are tokens fortoken itself for gold heused to gain admittancare the token names wabout the experience asomething you call a bthat behavior which yointo what takes place wpp. 127-128)

Von Forester alsosolutions, as quoted incharacteristics can be tprime importance wframework.

Eigenvalues have beenontogenetically to arOntologically, Eigenvmanifestation of a subp. 266)

2 Eigen-solutions and

Goudsmit (1998, Objebetween the form in wMaturana:

Generally, Von Foreste(iterative) applicationperformance, which isof the existence of

ned by those features of its elements that will allow the living system to retainn after the interaction, and thus, to interact again. This makes living systemsd their domain of interactions a cognitive domain. (Maturana & Varela, 1980,

mportance of this circular (cyclic or recursive) regenerativeen (auto, equilibrium, fixed, homeostatic, invariant, recurrent, in concrete and abstract autopoietic systems, are furtherester and Segal:

sion is to run through one’s own path again. One of its results is that undere exist indeed solutions which, when reentered into the formalism, producen. These are called “eigen-values,” “eigen-functions,” “eigen-behaviors,” etc.,omain this formation is applied -in the domain of numbers, in functions, inrester & Segal, 2001, p. 145)

eigen-behaviors. Tokens stand for something else. In exchange for money (ald by one’s government, but unfortunately no longer redeemable), tokens aree to the subway or to play pinball machines. In the cognitive realm, objectse give to our eigen-behavior. When you speak about a ball, you are talkingrising from your recursive sensorimotor behavior when interacting with thatall. The “ball” as object becomes a token in our experience and language foru know how to do when you handle a ball. This is the constructivist’s insighthen we talk about our experience with objects. (Von Forester & Segal, 2001,

establishes several essential characteristics of these eigen- the following paragraph from Von Forester. These essential

ranslated into very specific mathematical properties, that are ofhen investigating several aspects of the CogCon+FBST

found ontologically to be discrete, stable, separable and composable, whileise as equilibria that determine themselves through circular processes.alues and objects, and likewise, ontogenetically, stable behavior and theject’s “grasp” of an object cannot be distinguished. (Von Forester, 2003c,

Language

cts as warrants for eigenvalues), finds an apparent disagreementhich eigen-solutions emerge, according to Von Forester and

r’s concept of eigenvalue concerns the value of a function after a repeated of a particular operation. ... This may eventually result in a stable an eigenvalue of the observer’s behavior. The emerging objects are warrantsthese eigenvalues. ... contrary to Von Forester, Maturana considers the

74

Julio Michael Stern

consensuality of distiattainment of consen(Goudsmit, 1998, sec.

Confirmation for the pseveral of his articles.

I propose to continue tthis term becomes mepossesses available einteraction, such that ithe self-organizing sysof pre-given objective

Confirmation for the pseveral of his articles.

Objectivity. Objects aconsensual distinctionWithout language and coordinations of actionFor living systems thatnot part of their cogni(1988, sec. 9, p. iv)

The standpoint of from Brier:

The process of humadifference between theextent, create the worldin some way before wand we do it on some kdoes not make sense tohand it does not makimagination.” “...it isexperiencing or conve2005, p. 374)

In order to understanviewpoints, or at leasponderate and precisepositions assumed in Mhave had in mind thearticle.

Einstein said, and macreations of the human

nctions as necessary for the bringing forth of objects. It is through thesual distinctions that individuals are able to create objects in language.2.3.3)

osition attributed by Goudsmit to Von Forester can be found inIn Von Forester, for example, one finds:

he use of the term ‘self-organizing system,’ whilst being aware of the fact thataningless, unless the system is in close contact with an environment, whichnergy and order, and with which our system is in a state of perpetualt somehow manages to ‘live’ on the expenses of this environment. ... So bothtem plus the energy and order of the environment have to be given some kindreality for this view points to function.(Von Foerster, 2003a, p. 3)

osition attributed by Goudsmit to Maturana can also be found inIn Maturana, for example, one finds:

rise in language as consensual coordinations of actions that in a domain ofs are tokens for more basic coordinations of actions, which they obscure.outside language there are no objects because objects only arise as consensuals in the recursion of consensual coordinations of actions that languaging is.

do not operate in language there are no objects; or in other words, objects aretive domains. ... Objects are operational relations in languaging. (Maturana

Maturana is further characterized in the following paragraphs

n knowing, is the process in which we, through languaging, create the world and ourselves; between the self and the non-self, and thereby, to some by creating ourselves. But we do it by relating to a common reality which ise made the difference between ‘the world’ and ‘ourselves’ make difference,ind of implicit belief in a basic kind of order ‘beneath it all’. I do agree that it claim that the world exists completely independently of us. But on the other

e sense to claim that it is a pure product of our explanations or conscious clear that we do not create the trees and the mountains through ourrsation alone. But Maturana is close to claim that this is what we do.(Brier,

d the above comments, one must realize that Maturana’st his rhetoric, changed greatly over time, ranging from the statements in Maturana and Varela (1980), to some extreme

aturana (1991, p. 30-52, see next paragraph). Maturana must celebrated quote by Albert Einstein at the beginning of this

ny other scientists have agreed with him, that scientific theories are free mind, and he marveled that through them one could understand the universe.


75

The criterion of validobserver, however, perthat there is nothing m

Scientific explanationsthrough operations thain fact there is no confcan have one. (Matura

Quantification (or meexplanation but do noverificability, or Confira cognitive domain transcendental reality i

Nature is an explanatohuman beings constitunature as the domain i1991, p. 44)

Brier further contrasts

Von Forester is more position one has to deEigenfunctions do not of nature and its ‘thingto talk about. Von Foreleads into further accep

While the positioobjective, the one adoCan these two differenwe have to choose betboth? This is one of th

In Stern (2007a) invariant) to illustrate Historically, this examdebacle of classical pimportant historical Historically, this exammechanics. This is one

3 The Languages of S

At the end of the 19thIts glory was consensucentury, a few experiphysics. The problem

ation of scientific explanation as operations in the praxis of living of themit us to see how it is that the first reflection of Einstein is valid, and how it isarvelous in that it is so. (Maturana, 1991, p. 36)

arise operationally as generative mechanisms accepted by us as scientistst do not entail or imply any supposition about an independent reality, so thatrontation with one, nor is it necessary to have one even if we believe that wena, 1991, p. 38)

asurements) and predictions can be used in the generation of a scientifict constitute the source of its validity. The notions of falsifiability (Popper),mation would apply to the validation of scientific knowledge only if this werethat revealed, directly or indirectly, by denotation or connotation, andependent of what the observer does. (Maturana, 1991, p. 38)

ry proposition of our experience with elements of our experience. Indeed, wete nature with our explaining, and with our scientific explaining we constituten which we exist as human beings (or languaging living systems). (Maturana,

the standpoint of Maturana with that of Von Forester:

aware of the philosophical demand that to put up a new epistemologicalal with the problem of solipsism and of pure social constructivism.” “Thejust come out of the blue. In some, yet only dimly viewed, way the existences’ and our existence are intertwined in such a way that makes it very difficultster realizes that to accept the reality of the biological systems of the observertance about the structure of the environment. (Brier, 2005, p. 375)

n adopted by Von Forester appears to be more realistic orpted by Maturana seems more idealistic or (inter) subjective.t positions, which may seem so discrepant, be reconciled? Doween an idealistic or a realistic position, or can we rather havee questions we address in the next sections. we used an example of physical eigen-solution (physical

the ideas in discussion, namely, the speed of light constant, c.ple is tied to the birth of Special Relativity theory, and thehysics. In this article we will illustrate them with anotherexample, namely, the Einstein-Podolsky-Rosen paradox.

ple is tied to questions concerning the interpretation of quantum of the main topics of the next section.

cience

century, classical physics was the serene sovereign of science.al and uncontroversial. However, at the beginning of the 20th

mental results challenged the explanatory power of classicals appeared in two major fronts that, from a historical

76

Julio Michael Stern

perspective, can be linrelativity and quantum

At that time, the geopen problems could,classical physics. Crastructure of ether (the for atomic structure, wartfully maneuvering insisted, building up a

The difficulties wpersisted, but also greclassical physics had were acclaimed as the the development of qu

One of the first ste1924 by Louis de Brostates that every movin

where

h

is Planck’s con

its mass and velocity. Iexplaining all known qlatter confirmed by nesee Tomonaga (1962) uses a mathematical foof the descriptive langu

There is, howeverQM. When describingentity, as if each side emathematical formalis

Notice how our languareally means that we csend. These signals wmoving (back and forththat we are not claiminup those particle detec

From Schrödingerwhich states that we cdown every single detreality. One instance osimultaneously measurOne way of interpretinfollows: In classical Nmeasurement devices

ked to the theories (at that time still non existent) of special mechanics. neral perception of the scientific community was that these few should and would be accommodated in the framework offting sophisticated structural models such as those for themedium in which light was supposed to propagate), and thoseas typical of the effort to circumvent these open problems byclassical physics. But physics and engineering laboratoriesbarrage of new and challenging experimental results. ith the explanations offered by classical physics not onlyw in number and strength. In 1940 the consensus was that

been brutally defeated, and relativity and quantum mechanicsnew sovereigns. Let us closely examine some facts concerningantum mechanics (QM). ps in the direction of a comprehensive QM theory was given inglie, who postulated the particle-wave duality principle, whichg particle has an associated pilot wave of wavelength λ = h/mv,stant and mv is the particle’s momentum, that is, the product of

n 1926 Erwin Schrödinger stated his wave equation, capable ofuantic phenomena, and predicting several new ones that where

w experiments. Schrödinger theory is known as orthodox QM,and Pais (1988) for detailed historical accounts. Orthodox QMrmalism based on a complex wave equation, and shares muchage of de Broglie’s particle-wave duality principle.

, something odd in the wave-particle descriptions of orthodox a model we speak of each side of a double faced wave-particlexisted by itself, and then inextricably fuse them together in them. Quoting Cohen:

ge shapes our imagination. To say that a particle is moving in a straight linean set up particle detectors along the straight line and observe the signals theyould be consistent with a model of the particle as a single chunk of mass) in accordance with Newtonian particle physics. It is important to emphasizeg that we know what the particle is, but only what we would observe if we settors.(Cohen, 1989, p. 87)

’s equation we can derive Heisenberg’s uncertainty principle,an not go around measuring everything we want until we pinail about (the classical entities in our wave-particle model of)f the Heisenberg uncertainty principle states that we can note a particle position and momentum beyond a certain accuracy.g this instance of the Heisenberg uncertainty principle goes asewtonian physics our particles are “big enough” so that our

can obtain the information we need about the particle without


77

disturbing it. In QM, ooperation will always order to illuminate therelative to the particle consequence is that simultaneously measumomentum. Hence, wlanguage.

The need to exercilesson learned by 20thearlier. A classical exathe Russell’s catalog (call catalogues not men... Both decisions lead

Robert (1988) indiof them imply imposstatements. Under anyposed statement and, a1 & 2) and Dugundji (was a fundamental ac(notions such as mass,

of

R

n

are included, and(non-measurable) sets(1960/1999) for a stanFBST formalism. The of extending the languin section 6.6 and also

All the precedingcommon: When craftinstatements are accepteto valid statements. Scoherence.

The issue of whatinteresting and still subSolvay conference of Einstein. Ruhla (1992

variables

) give very inexpertise. Without thedebate as: While BohrEinstein advocated fosuggested a

gedanken

argument supporting Econtributed to the deb

n the other hand, the particles are so small that the measurementdisturb the particle. For example, the light we have to use in scene, so we can see where the particle is, has to be so strong,size, that it “blows” the particle away changing its velocity. The

we cannot (neither in practice, nor even in principle)re with arbitrary precision, both the particle’s position ande have to learn how to tame our imagination and constrain our

se a strict discipline over what kinds of statements to use was a century physics – a lesson that mathematics had to learn a bitmple from set theory of a statement that cannot be allowed islass, set), defined in Robert (1988, p. x) as: “The ‘catalogue of

tioning themselves.’ Should one include this catalogue in itself?to a contradiction!”cates several ways to avoiding this paradox (or antinomy). Alling a (very reasonable) set of rules on how to form valid of these rules, Russell’s definition becomes an invalid or ill-s such, should be disregarded, see also Halmos (1998, chapters1966, chapter 1). Measure theory (Borel, Lebesgue, Haar, etc.)hievement of 20th century mathematics. It defines measures volume and probability) for parts of Rn. However not all parts we must refrain of speaking about the measure of inadmissible, see Ulam (1943) for a short article, Kolmogorov and Fomindard text, and Nachbin (1965) for extensions pertinent to themain subject in Robert (1988) is Non Standard Analysis, a formages of both Set Theory and Real Analysis, see the observations Davis (1977, sec. 3.4 ), Goldblatt (1998) and Nelson (1987). examples of mathematical languages have one thing ing a specific language, one has to carefully define what kinds of

d as valid ones. Proper use of the language must be constraineduch constraints are necessary in order to preserve language

kinds of statements should be accepted as valid in QM is ansisting issue, epitomized by the famous debate at the Brussels

1930 between Niels Bohr and his friend and opponent Albert, chapters 7 & 8) and Baggott (1992, under the topic hiddentuitive reviews of the subject, requiring minimal mathematical details concerning the physics involved, one can describe the suggested very strict rules for admissible statements in QM,r more amiable ones. In 1935 Einstein, Podolsky and Rosenexperiment, known as the EPR paradox, as a compellinginstein’s point of view. D. Bohm, in 1952 and J. Bell, in 1964,ate by showing that the EPR paradox could lead to concrete

78

Julio Michael Stern

experiments providing1972 that the first EPRevidence from these ex

One of today’s stafor a very readable texalternative formalism (1987, I-IV) and Costasee for example KolmaQM, which is very cleaall basic calculations aspaces. In a second probabilities of obtaRijsbergen (2004). Onthat it naturally avoidlanguage. Cohen provi

Historically, ... quantuassumptions and thenequations and their mathematics of Hilber(Cohen, 1989, p. vii)

From the above histori

3.1. Each of the Qwave-particle abstract QM, olanguage. He s

3.2. It seems also tus the objects Von Forester.

3.3. Exercising a stin a given lang

3.4. It is far from tthat it works, p

3.5. Even when evempirical evid

As indicated by anexist in a vacuum, bulanguages. This bring language structures an

analyses between obje(1975) for an early refe

a way to settle the debate on empirical grounds. It was only in experiment could be performed in practice. The observationalperiments seems to favor Bohr’s point of view! ndard formalisms for QM is Abstract QM, see Hughes (1992)t and Cohen (1989) for a concise and formal treatment. For anbased on Niels Bohr’s concept of complementarity, see Bohr and Krause (2004). Other formalisms may also become useful,novskii and Nosov (1986, sec.2.3) and Zubov (1983). Abstractn and efficient, can be stratified in two layers. In the first layer,

re carried out using an algebra of operators in (Rigged) Hilbertlayer, the results of these calculations are interpreted as

ining specific results in physical measurements, see alsoe advantage of using the stratified structure of abstract QM iss (most of) the danger of forming invalid statements in QMdes the following historical summary:

m mechanics developed in three stages. First came a collection of ad hoc a cookbook of equations known as (orthodox) quantum mechanics. Thephilosophical underpinning were then collected into a model based ont space. From the Hilbert space model came the abstraction of quantum logics.

cal comments we draw the following conclusions:

M formalisms discussed in this section, namely, de Broglie duality principle, Schrödinger orthodox QM and Hilbert space perates like a language. Maturana stated that objects arise in eems to be right. hat new languages must be created (or discovered) to provide corresponding to the structure of the environment, as stated by

rict discipline concerning what kinds of statements can be used uage and context, seems to be vital in many areas. rivial to create, craft, discover, find and/or use a language so roviding us the “right” objects (eigen-solutions).

erything looks (for the entire community) fine and well, new ence can bring our theories down as a castle of cards.

anonymous referee, abstract formalisms or languages do nott sit on top of (or are embedded in) natural (or less abstract)us to the interesting and highly relevant issues of hierarchicald constructive ladders of objects, including interdependencects at different levels of such complex structures, see Piagetrence. For a recent concrete example of the scientific relevance


79

of such interdependencmodel, see Shedler antopics addressed in Ste

4 The Self-Reference

The conclusions estabhowever, what exactlyobjects we more or leslanguage we currently

There! I have jusparadox. Don’t worryunavoidable, especialllanguage.

Rasch (2000, p. 73paradox and some of it

having it both ways seway, nor skeptically denying reality nor derealism, but (cognitive

What do we call this oand marriage, horse an

Cognitive constructivireality, and that of anyfront war” metaphor tfurther, the enemies ofsaying that Dogmatismstatements and reasoninfallible truth; Solipsiin the world. Solipsisestablishing any stableCaygill (1995, entry: some of the above term

Any military strateRasch, which alternatesubjugated, but the enethis conundrum, even r

There is a third choicebe a distinction mind /on that perfect center, mind (system) side, b

es in the field of Psychology, using a factor analysis statisticald Westen (2004, 2005); These issues are among of the mainrn (2006b, 2007b) and other forthcoming articles.

Paradox

lished in the previous section may look reasonable. In 3.4, are the “right” objects? Clearly, the “right” objects are thoses clearly see and can point at, using as reference language theuse.t fallen, head-on, into the quicksands of the self-reference (or do worry), but note this: The self-reference paradox isy as long as we use English or any other natural human

, 85) has produced a very good description of the self-references consequences:

ems a necessary consequence. ... One cannot just have it dogmatically onethe other. ... One oscillates, therefore, between the two positions, neithernying reality’s essentially constructed nature. One calls this not idealism or) constructivism. (Rasch, 2000, p. 73)

scillation? We call it paradox. Self-reference and paradox -- sort of like loved carriage. (Rasch, 2000, p. 85)

sm implies a double rejection: that of a solipsist denial of dogmatic knowledge of the same reality. Rasch uses the “twoo describe this double rejection. Carrying the metaphor a bit cognitive constructivism could be portrayed, or caricatured, by

despotically requires us to believe in its (latest) theory. Itss should be passively accepted with fanatic resignation assm’s anarchic distrust wishes to preclude any established orderm wishes to transform us into autistic skeptics, incapable of knowledge about the environment in which we live. We refer todogmatism) for a historical perspective on the Kantian use ofs. gist will be aware of the danger in the oscillation described byly exposes a weak front. The enemy at our strong front will bemy at our weak front will hit us hard. Rasch sees a solution toecognizing that this solution may be difficult to achieve:

: to locate oneself directly on the invisible line that must be drawn for there to body (system / environment) in the first place. Yet when one attempts to landone finds oneself oscillating wildly from side to side, perhaps preferring theut over compensating to the body (environment) side --or vice versa. The

80

Julio Michael Stern

history of post-Kantianorigin or neutral grouperfect transparent mifollows and rejects thoscillation. (Rasch, 20

5 Objective Idealism

We are now ready fdefinitions should helpaccording to the CogC

5.1. Known (knowsystem’s interasomewhat mor

5.2. Objective (howessential prope

5.3. Reality: A (mainteracting wit

5.4. Idealism: Belion the systems

5.5. Realism: Belieon the environ

5.6. Solipsism, Ske5.7. Dogmatic or M5.8. Realistic or O5.9. “Something in

is a marker or

Cog-Con+FBST assumlabels some ill posed dto access something in

• Something that an • Something that an• Something that an

with it (or disturbivariations.

Some readers maypreferring to use, inparenthesis” (approximas something in itselfexample, this elaboratdifferences between co

German idealism is a history of the failed search for this perfect middle, thisnd outside both mind and body that would nevertheless actualize itself as and/body within history. Thus, much of contemporary philosophy that bothat tradition has become fascinated by, even if trapped in, the mind/body00, p. 85)

and Pragmatism

or a few definitions of basic epistemological terms. These us build epistemic statements in a clear and coherent form

on+FBST perspective.

able) Object: An actual (potential) eigen-solution of a given ction with its environment. In the sequel, we may use a e friendly terminology by simply using the term Object. , less, more): Degree of conformance of an object to the rties of an eigen-solution. ximal) set of objects, as recognized by a given system, when h single objects or with compositions of objects in that set. ef that a system’s knowledge of an object is always dependent ’ autopoietic relations. f that a system’s knowledge of an object is always dependent

ment’s constraints. pticism: Idealism without Realism. etaphysical Realism: Realism without Idealism.

bjective Idealism: Idealism and Realism. itself”: This expression, used in reference to a specific object, label for ill posed statements.

es an objective and idealistic epistemology. definition 5.9ogmatic statements. Often, the description of the method used itself looks like:

observer would observe if the (same) observer did not exist, or observer could observe if he made no observations, or observer should observe in the environment without interacting ng it in any way), and many other equally nonsensical

not like this form of labeling this kind of invalid statement,stead, a more elaborate terminology, such as “object inately) as object, “object without parenthesis” (approximately)

, and so forth. There may be good reasons for doing so; fore language has the advantage of automatically stressing thenstructivist and dogmatic epistemologies (see Maturana, 1988;


81

Maturana & Poerksendefinitions in agreemen

Objectivity as definedepistemology; but, paacceptance of its termiof an epistemological to co-opt terminology so difficult. The term o

Among the definitionshow well an eigen-sconsequently, how gooobjectivity can not be methods of a given emis presented. Hence, dmetaphysical argumenby some philosophica

Pragmatism

,” CP 5.46

“Suffice it to say oncedetermine any truth ofof abstract concepts. meanings of words asuccessful sciences (ireached the degrees ofbeing itself nothing buthem’. (CP 5.464-465)

Definition 5.2 also restatistical significance,of an eigen-solution. Ineigen-solution naturallthe mathematical propean eigen-solution as perfectly adequate to scientific language. AmStern (2007a), we find

Continuity: Give

differentiable

, on theappropriate regularity Consistency: Provide

measure for a given shTherefore, the FBS

and consistently, the significance measure,

, 2004); Steier, 1991). Nevertheless, we have chosen ourt with some very pragmatic advice given in Bopry:

by a (dogmatic) realist epistemology may not exist within a constructivistrt of making that alternative epistemology acceptable is gaining generalnology. As long as the common use of the terms is at odds with the conceptsposition, that position is at a disadvantage. Alternative forms of inquiry needin a way that is consistent with its own epistemology. I suggest that this is notbjective can be taken back. (Bopry, 2002, p. 13)

5.1 to 5.9, definition 5.2 plays a key role. It allows us to sayolution manifests Von Forester’s essential attributes, andd (objective) is our knowledge of it. However, the degree of

assessed in the abstract, it must be assessed by the means andpirical science, namely the one within which the eigen solutionefinition 5.2 relies on an “operational approach,” and not onts. Such an operational approach may be viewed with disdainl schools. Nevertheless, for C.S.Peirce it is “The Kernel of4-465:

more that pragmatism is, in itself, no doctrine of metaphysics, no attempt to things. It is merely a method of ascertaining the meanings of hard words and... All pragmatists will further agree that their method of ascertaining thend concepts is no other than that experimental method by which all then which number nobody in his senses would include metaphysics) have certainty that are severally proper to them today; this experimental methodt a particular application of an older logical rule, ‘By their fruits ye shall know

quires a belief calculus specifically designed to measure the that is, the degree of support of empirical data to the existence Stern (2007a) we showed why confirming the existence of an

y corresponds to testing a sharp statistical hypothesis, and whyrties of FBST e-values correspond to the essential properties of

stated by Von Forester. In this sense, the FBST calculus issupport the use of the term Objective and correlated terms inong the most important properties of the e-value mentioned in

: a measure of significance that is smooth, i.e. continuous and hypothesis parameters and the sample statistics, under

conditions of the statistical model. a consistent, that is, asymptotically convergent significancearp hypothesis. T calculus is a formalism that allow us to assess, continuouslyobjectivity of an eigen-solution, by means of a convergentsee Stern (2007a). We should stress, once more, that achieving

82

Julio Michael Stern

comparable goals usinmay be, in general, raton Rasch’s perfect cen

Any dispute abouknowledge), should bprogram. This programempirical science in wcalculus, used to evalexperimental data.

Even if over optimflag of Calculemus, as

Quo facto, quando oriquam inter duos Compmutuo (accito si placet

A contemporary transl

Actually, if controverphilosophers, rather tcomputers and, in frien

6 The Philosophy of C

In the previous sectiopragmatic objective idcharacteristics of the pby Søren Brier, that wcompatible with, and philosophy?

In Stern (2007a) wentities, can be namedForester in Segal:

There is an additionalpossibilities, recursivegenerates discrete, ideimportant consequenceout of an infinite numbof your-self with yours

We believe that thidentifying them by siand structure our livessuch as signification a

g alternative formalisms based on discrete algebraic structuresher difficult. Hence, our answer to the question of how to landter is: Replace unstable oscillation by stable convergence! t objectivity (epistemic quality or value of an object ofe critically examined and evaluated within this pragmatic (in Luhmann’s sense) includes the means and methods of the

hich the object of knowledge is presented, and the FBST beliefuate the empirical support of an object, given the available

istic (actually hopelessly utopian), it is worth restating Leibniz’found in Gerhardt:

entur controversiae, non magis disputatione opus erit inter duos philosophos,utistas. Suffciet enim calamos in manus sumere sedereque ad abacos, et sibi amico) dicere: Calculemus. (Gerhardt, 1890, v. 7, pp. 64-65)

ation could read:

sies were to arise, there would be no more need for dispute between twohan between two statisticians. For them it would suffice to reach theirdly understanding, say to each other: Let us calculate!

. S. Peirce

ns we presented an epistemological perspective based on aealism. Objective idealism and pragmatism are also distinctivehilosophy of C. S. Peirce. Hence the following question, posede examine in this section: Is the CogCon+FBST frameworkcan it benefit from, the concepts of semiotics and Peircean

e had already explored the idea that eigen-solutions, as discrete, that is become signs in a language system, as pointed by Von

point I want to make, an important point. Out of an infinite continuum of operations carve out a precise set of discrete solutions. Eigen-behaviorntifiable entities. Producing discreteness out of infinite variety has incrediblys. It permits us to begin naming things. Language is the possibility of carvinger of possible experiences those experiences which allow stable interactionself. (Segal, 2001, p. 128)

e process of recursively “discovering” objects of knowledge,gns in language systems, and using these languages to “think” as self-conscious beings, is the key for understanding conceptsnd meaning. These ideas are explored, in a great variety of


83

contexts, in Bakken anand Lukens (1990), EiBrown, and Heath (199the key underlying com

The key to the understanimals and we humaaround us but also proThe organization of sigmuch the principles ofand meaning and theresign processes for thethrough social self-conthrough texts. But of c

When studying the orsemantic concepts sucfinality, intent and pincreasing complexitydomains of phenomenoleave the domains of nBrent and Bruck (2006

2006, when this articleAs observed in Br

from more objective oto higher hierarchical objects of knowledge out by Von Forester, rCogCon+FBST framew

S-1. Some perceivorganization o

S-2. Some perceivstructure of the

S-3. Some object (on the particulthe autopoietic

This triadic characC. S. Peirce, offering mFor example, we are csemiotic project for thesee Ferreira, 2006). Wforthcoming articles.

d Hernes (2002), Brier (1995), Ceruti (1989), Efran, Lukens,bel-Eibesfeldt (1970), Ibri (1992), Piaget (1975), Wenger, Pea,9), Winograd and Flores (1987) and many others. Conceivably,mon principle is stated by Brier :

anding of understanding, consciousness, and communication is that both thens live in a self-organized signification sphere which we not only projectject deep inside our systems. Von Uexküll calls it “Innenwelt” (Brier 2001).ns and the meaning they get through the habits of mind and body follow very second order cybernetics in that they produce their own Eigenvalues of signby create their own internal mental organization. I call this realm of possible signification sphere. In humans these signs are organized into languagescious communication, and accordingly our universe is organized also as andourse that is not an explanation of meaning. (Brier, 2005, p. 395)

ganization of self-conscious beings and trying to understandh as signification and meaning, or teleological concepts such asurpose, we move towards domains concerning systems of that are organized as higher hierarchical structures, like thelogical, psychological or sociological sciences. In so doing, we

atural and technical sciences behind, at least for a moment, see) and Muggleton (2006), in last month’s issue of Nature (March was written), for two perspectives on future developments. ier (2001), the perception of the objects of knowledge, changesr realistic to more idealistic or (inter) subjective as we progresslevels. Nevertheless, we believe that the fundamental nature ofas eigen-solutions, with all the essential characteristics pointedemains just the same. Therefore, a sign, as understood in theork, always stands for the following triad:

ed aspects, characteristics, and so forth, concerning the f the autopoietic system.ed aspects, characteristics, and so forth, concerning the system’s environment.

discrete, separable, stable and composable eigen-solution based ar aspects stated in S-1 and S-2) concerning the interaction of system with its environment.

ter of signs bring us, once again, close to the semiotic theory ofany opportunities for further theoretical and applied research.

urrently using statistical psychometric analyses in an applied development of software user interfaces (for related examplese defer, however, the exploration of these opportunities to

84

Julio Michael Stern

In the remainder obelieve, is a necessaryclear conceptual horizresearch. The purpose framework can find aphilosophy. We proceconcepts used to deanalogous concepts incaution: The work ofinterpretations. Our gopossible interpretation

The FBST is a conconceptual mapping adto a Peircean perspectthe use of such a forma

6.1 Probability andformalism. Casupport in cona concept in Pconceptual maabsolute chanc

6.2 Continuity: Aspursues the staformalism. Thmathematics iswe have to askan analogous ccan be establiselement in ourof philosophicimportance in involving true

6.3 Eigen-Solutionperspective is concept of EigPeirce’s philosor “Insistency”“The existence“Reality is insirrational insisexperience, tha

f this section we focus on a more basic investigation that, we preliminary step that must be undertaken in order to acquire aon that will assist a sound and steady progress in our futureof this investigation is to find out whether the CogCon+FBST truly compatible ground in the basic concepts of Peirceaned establishing a conceptual mapping of the fundamentalfine the Cog-Con+FBST epistemological framework into Peircean philosophy. Before we start, however, a word of

C.S.Peirce is extremely rich, and open to many alternativeal is to establish the compatibility of CogCon+FBST with one

, and not to ascertain reductionist deductions, in any direction. tinuous statistical formalism. Our first step in constructing thisdresses the following questions: Is such a formalism amenable

ive? If so, which concepts in Peircean philosophy can supportlism?

Statistics: The FBST is a probability theory based statistical n the probabilistic concepts of the FBST find the necessary cepts of Peircean philosophy? We believe that Tychism is such eircean philosophy, providing the first element in our pping. In CP 6.201 Tychism is defined as: “... the doctrine that e is a factor of the universe.” stated in the previous section, the CogCon+FBST program ble convergence of the epistemic e-values given by the FBST e fact that FBST is a belief calculus based on continuous essential for its consistency and convergence properties. Again : Does the continuity concept used in the FBST formalism have oncept in Peircean philosophy? We believe that the analogy hed with the concept of Synechism, thus providing the second conceptual mapping. Synechism is defined as: “that tendency al thought which insists upon the idea of continuity as of prime philosophy and, in particular, upon the necessity of hypotheses continuity” (CP 6.169).s: A key epistemological concept in the CogCon +FBST the notion of eigen-solution. Although the system theoretic en-solution cannot possibly have an exact correspondent in ophy, we believe that Peirce’s fundamental concept of “Habit” offers an adequate analog. Habit, and reality, are defined as: of things consists in their regular behavior” (CP 1.411).

istency. That is what we mean by ‘reality’. It is the brute tency that forces us to acknowledge the reality of what we t gives us our conviction of any singular. (CP 6.340).


85

However, the CogForester by several esmapping under construaccordingly. In the fosharpness (discretenes

represented.

6.3a—Sharpness: TForester is discimportant to reForester to quaon the specificsingular, etc. Aformulated as

Can Peircean philbelieve that the answethat clear (see also Eis

an object (a thing) ISselected. (Ibri, 1992, p

Existence involves chconcreteness of one of

.as a plane is a bi-dimtopic discontinuity, bup. 85)

Whatever is real is thpossibility of sensation

In fact, habits, from trelation, and therefore,the permanence of mas(CP 1. 415)

6.3b—Stability: ThForester is staboperator, definor computed) aoperator. Undefor instance) thdepend on the

A similar notion o

Con+FBST concept of eigen-solution is characterized by Vonsential properties. Consequently, in order for the conceptualction to be coherent, these characteristics have to be mapped

llowing paragraphs we show that the essential properties ofs), stability and compositionality can indeed be adequately

he first essential property of eigen-solutions stated by Von reteness or sharpness. As stated in Stern (2007a), it is alize that, in the sequel, the term ‘discrete’, used by Von lify eigen-solutions in general, should be replaced, depending context, by terms such as lower-dimensional, precise, sharp, s physical laws or physical invariants, sharp hypotheses are

mathematical equations.

osophy offer a good support for sharp hypotheses? Again wer is in the affirmative. The following quotations should makeele, 1976, p.136-137 & CP 6.203).

only in comparison with a continuum of possibilities from which it was. 84)

oice; the dice of infinite faces, from potential to actual, will have the them. (Ibri, 1992, p. 85)

ensional singularity, relative to a tri-dimensional space, a line in a plane is at each of this elements is continuous in its proper dimension. (Ibri, 1992,

e law of something less real. Stuart Mill defined matter as a permanent. What is a permanent possibility but a law? (CP 1.487)

he mode of their formation, necessarily consist in the permanence of some on this theory, each law of nature would consist in some permanence, such ass, momentum, and energy. In this respect, the theory suits the facts admirably.

e second essential property of eigen-solutions stated by Von ility. As stated in Stern (2005), a stable eigen-solution of an ed by a fixed-point or invariance equation, can be found (built s the limit of a sequence of recursive applications of the r appropriate conditions (such as within a domain of attraction, e process convergence and its limiting eigen-solution will not starting point.

f stability for an object-sign complex is given by Peirce:

86

Julio Michael Stern

That for which it (a sigto which it gives rirepresentation of whirepresentations, each rits limit. (CP 1.339)

6.3c—CompositioVon Forester iStern (2006), cthe credibility,elementary coany theory of lsee Peirce quois, how the com

If two forces are combThus, intelligibility, or

A physical law is absointo a motion a compo6.23)

In order to estabCogCon+FBST to whi

6.4 Extra variabilitof noise and flto the problemfollowing exceused to exprespractice inevitais “the doctrin

There is no difficulty itheir persistent forcingmere dream. Reality, persistent, they (are) lfor facts bearing on tha

6.5 Bayesian statisPeirce has a stprobabilities.

The majority of mathunclear conception of head of ‘inverse proba

n) stands is called its object; that which it conveys, its meaning; and the idease, its interpretant. The object of representation can be nothing but ach the first representation is the interpretant. But an endless series ofepresenting the one behind it, may be conceived to have an absolute object at

nality: The third essential property of eigen-solutions stated by s compositionality. As stated in Stern (2007a) and Borges and ompositionality properties concern the relationship between or truth value, of a complex hypothesis, H, and those of its nstituents, Hj, j =1 ...k. Compositionality is at the very heart of anguage, see Noeth (1995). As an example of compositionality, tations below. Peirce discusses the composition of forces, that

ponents are combined using the parallelogram law.

ined according to the parallelogram of forces, their resultant is a real third... reason objectified, is what makes Thirdness genuine. (CP 1.366)

lute. What it requires is an exact relation. Thus, a physical force introducesnent motion to be combined with the rest by the parallelogram of forces.(CP

lish a minimal mapping, there are two more concepts inch we must assign adequate analogs in Peircean philosophy.

y: In Stern (2007a) the importance of incorporating all sources uctuation, that is, all the extra variability statistically significant under study, into the statistical model is analyzed. The rpt from Peirce indicates that his notion of falibilism may be s the need for allowing and embracing all relevant (and in ble) sources of extra variability. According to Peirce, falibilism

e that there is no absolute certainty in knowledge”

n conceiving existence as a matter of degree. The reality of things consists in themselves upon our recognition. If a thing has no such persistence, it is athen, is persistence, is regularity. ... as things (are) more regular, more

ess dreamy and more real. Fallibilism will at least provide a big pigeon-holet theory. (CP 1.175)

tics: FBST is an Unorthodox Bayesian statistical formalism. rong and unfavorable opinion about Laplace’s theory of inverse

ematical treatises on probability follow Laplace in results to which a veryprobability led him. ... This is an error often appearing in the books under thebilities.’ (CP 2.785)


87

Due to his theory oprecursors of modern and Peirce’s philosophonly dissipates potentiStern (2007a).

Two main argumprobabilities. In the fpresent an up-to-date a

6.5a—Dogmatic p

Laplace maintains thaparticular determinationothing. ... Laplace hoof each continuum of

possibles”

in a quantit

The dogmatic rhedistributions can easiarguments for the chosymmetry relations (seContemporary argumeanalysis, for finite sasamples (see DeGrootthat Peirce would be ptheories have renderedinto oblivion.

6.5b—Assignmentsupport structu

Laplace was of the otheory; and that doctrimost ridiculous resultwhat probability is. Prwhen certain predetermlong run in which thattotal number of times5.169)

In the second partunderstanding of havispace, that is, he admitprobability statementsand epistemic probabiwe examine the reason

f inverse probabilities, Laplace is considered one of the earliestBayesian statistics. Is there a conflict between CogCon+FBSTy? We believe that a careful analysis of Peirce’s arguments notal conflicts, but also reinforces some of the arguments used in

ents are presented by Peirce against Laplace’s inverseollowing paragraphs we will identify these arguments andnalysis based on the FBST (unorthodox) Bayesian view:

riors vs. Symmetry and Maximum Entropy arguments:

t it is possible to draw a necessary conclusion regarding the probability of an of an event based on not knowing anything at all about [it]; that is, based onlds that for every man there is one law (and necessarily but one) of dissection alternatives so that all the parts shall seem to that man to be “egalementative sense, antecedently to all information. (CP 2.764)

toric used at the time of Laplace to justify ad hoc priorly backfire, as it apparently did for Peirce. Contemporaryice of prior distributions are based on MaxEnt formalism ore Dugdale, 1996; Eaton, 1989; Kapur, 1989; Nachbin, 1965).nts also examine the initial choice of priors by sensitivitymples, and give asymptotic dissipation theorems for large, 1970; Gelman et al., (2003); Stern, 2004). We can only hopeleased with the contemporary state of the art. These powerful ad hoc priors unnecessary, and shed early dogmatic arguments

of probabilities to (sharp) hypotheses vs. FBST possibilistic res:

pinion that the affirmative experiments impart a definite probability to thene is taught in most books on probability to this day, although it leads to thes, and is inherently self-contradictory. It rests on a very confused notion ofobability applies to the question whether a specified kind of event will occurined conditions are fulfilled; and it is the ratio of the number of times in the

specified result would follow upon the fulfillment of those conditions to the in which those conditions were fulfilled in the course of experience. (CP

of the above excerpt Peirce expresses a classical (frequentist)ng probability in the sample space, and not in the parameters predictive probability statements but does not admit epistemic. The FBST is a Bayesian formalism that uses both predictivelity statements, as explained in Stern (2007a). However, when presented by Peirce for adopting this position, in the first part

88

Julio Michael Stern

of the excerpt, we finStern (2003, 2004, 20testing sharp hypothes

(sharp hypothesis) bei

possibility

. In Stern (2probability to a given namely, those procedu

6.6 Measure Theordiscuss a technand the FBST some form of founding fatheuncomfortableusing measureare called evenand Savage (19gambling metaBayesian statismeasurable seproperties of a

Events are restricted to

the class of all subsets

reason that could justif1975, v. 2, p. 259)

In order to proceFinetti’s argument, roohinge on the perceived

the generally acceptedentities, being synthesnature. This punctate real numbers --the ‘ari

Among the alternathere are more geomeuse an arithmetical set“ultimate parts” ofnonpunctiform, that iperspectives for the cPeirce, H. Poincaré, L.E. Nelson, and many

d a remarkable coincidence with the arguments presented in06, 2007a) against the orthodox Bayesian methodology fores: The FBST does not attribute a probability to the theory

ng tested, as do orthodox Bayesian tests, but rather a degree of003, 2004, 2006, 2007a) we analyze procedures that attribute atheory, and came to the exact same conclusion as Pierce did,res are absurd.

y: Let us now return to the Peircean concept of Synechism, to ical point of contention between orthodox Bayesian statistics unorthodox Bayesian approach. The FBST formalism relies on Measure theory, see comments in section 3. De Finetti, the r of the orthodox school of Bayesian statistics, feels very having to admit the existence of non-measurable sets when theory in dealing with probabilities, in which valid statements ts, see de Finetti (1975, 3.11, 4.18, 6.3, & appendix). Dubins 76, p. 8) present similar objections, using the colorful phors that are so characteristic of orthodox (decision theoretic) tics. In order to escape the constraint of having non-

ts, de Finetti readily proposes a deal: to trade off other standard measure, like countable (σ) additivity:

be merely a subclass (technically a σ-ring with some further conditions) ofof the base space. In order to make σ-additivity possible, but without any realy saying to one set ‘you are an event,’ and to another you are not.’ (di Finetti,

ed with our analysis, we have to search for the roots of dets that, we believe, lay outside de Finetti’s own theory, for they structure of the continuum. Bell states:

set-theoretical formulation of mathematics (is one) in which all mathematicalized from collections of individuals, are ultimately of a discrete or punctatecharacter is possessed in particular by the set supporting the ‘continuum’ ofthmetical continuum’. (Bell, 1998, p. 2)

tives to arithmetical punctiform perspectives of the continuum,trical perspectives. Such geometrical perspectives allow us to as a coordinate (localization) system in the continuum, but the the continuum, called infinitesimals, are essentiallys, non point like. Among the proponents of infinitesimalontinuum one should mention G. W. Leibniz, I. Kant, C. S. E. J. Brouwer, H. Weyl, R. Thom, F. W. Lawvere, A. Robinson, others. I refer you to Bell (2005) for an excellent general


89

historical review, andinfinitesimal perspectiv

any of its (the continuon the other hand, is bcontinuum. (Bell, 1998

According to Bell,of the infinitesimal consaw as the efficiency oas constituting the “gluidentity (Bell, 2005, following quotations: the points of a line areconsist of indivisibles,its continuity is rupture

De Finetti’s argumsubsets of

R

n

have equthe arithmetical punctiperfect sense, and we as does orthodox Bayeus to overcome a maphilosophy, namely, th

At this point it semphatically affirmaticlear how well he kneteacher however, he letthe invitation that brousemiotics and Peircean

7 Final Remarks

The physician Rambamwrote

Shmona Perakim

human soul) based on

Ethics

(see Olitzky, 20human soul depends o

way

(shvil ha-zahav),excess (odef) and scar& “Temperaments,” §1

The straight path is thbe a clown or jokestepleasantness. And so w

to Robertson (2001) for the ideas of C. S. Peirce. In thee,

um) connected parts is also a continuum and, accordingly, divisible. A point,y its nature not divisible, and so (as stated by Leibniz) cannot be part of the, p.3)

in Peirce’s doctrine of synechism, he championed the retentioncept in the foundation of the calculus, both because of what hef infinitesimal methods, and because he regarded infinitesimalse” causing points on a continuous line to lose their individualp. 211). Bell further characterizes Perice’s views with the“The very word continuity implies that the instants of time or everywhere welded together,” and “[the continuum] does not

or points, or instants,and does not contain any except insofar asd” (Peirce quoted in Bell, 1998, p. 208).ent on non-measurable sets implicitly assumes that all pointal standing, that is, that the continuum has no structure. Under

form perspective of the continuum, de Finetti’s objection makesshould abstain from measure theory or alternative formalisms,sian statistics. This is how Peirce’s concept of synechism helpsjor obstacle (for the FBST) presented by orthodox Bayesiane objections against the use of measure theory.hould be clear that my answer to Søren Brier’s question isve. From Søren Brier’s comments and suggestions it is alsow the answer when he asked me the question. As a maieutic me look for the answers my own way. I can only thank him forght me for the first time into contact with the beautiful world of philosophy.

, Moshe ben Maimon (1135-1204), then caliphate of Cordoba,, a book on psychology (medical procedures for healing the

fundamental principles exposed by Aristotle in Nicomachean00; Rackham, 1926). Rambam explains how the health of then always finding the straight path (derech y’shara) or golden

at the perfect center between the two opposite extremes ofcity (choser), (see Maimonides, 2001, v.1: “Knowledge,” ch. 2, §2):

e middle one, that is equidistant from both extremes.... Neither should a manr, nor sad or mourning, but he should be happy all his days in serenity and

ith all the other qualities a man possesses. This is the way of the scholars.

90

Julio Michael Stern

Every man whose virtuv. 1, ch. 2, § 1 & 2)

Rambam explainssituation, may be morshould try to protect offset its position in orbias.

At the dawn of thescience handing out unstates. Dogmatism had

At the beginning oeconomy that seems environment, and our virtual reality of theirsolipsism.

Finally, Rambam wuseful precautionary taconsidered as a virtue pright of it, but at the pe

References

Baggott, J. (1992).

The meanin

Bakken, T., & Hernes, T. (20

perspective.

Copenhagen:Barbieri, D. (1992). Is genetic

Bell, J. L. (1998).

A primer of i

Bell, J. L. (2005).

The continuo

Bohr, N. (1987).

The philosoph

Bohr, N. (2007). Questions anFebruary 2006 from http:/

Bopry, J. (2002). Semiotics, ep

Borges, W., & Stern, J. M. (200uncertainty modelling (pp

Brent, R., & Bruck, J. (2006). C

Brier, S. (1995) Cyber-Semio

Human Knowing, 3

(1), 3-Brier, S. (2001). Cybersem

Umweltsbiologie),

134

(1Brier, S. (2005). The Constru

Forester’s metaphysical co

Caygill, H. (1995).

A Kant dict

Ceruti, M. (1989).

La Danza ch

Costa, N. C. A. da, & KrauseGabbay, & J. P. van Bend

Springer.Cohen, D. W. (1989). An introdDavis, M. (1977).

Applied nons

DeGroot, M. H. (1970).

Optim

Deitmar, A. (2005).

A first cour

Dugdale, J. S. (1996).

Entropy

Dugundji, J. (1966).

Topology

.

es reflect the middle, is called a chacham... a wise man. (Maimonides, 2001,

that a (always imperfect) human soul, at a given time ande prone to fall victim of one extreme than to its opposite, anditself accordingly. One way of achieving this protection is toder to (slightly over-) compensate for an existing or anticipated

20th century, humanity had in classical physics a paradigm ofquestionable truth, and faced the brutality of many totalitarian the upper hand, and we had to protect ourselves accordingly. f the 21st century we are enjoying the comforts of a hyperactiveto be blind to the constraints imposed by our ecological

children are being threatened by autistic alienation through the video games. It may be the turn of (an apathetic form of)

arns us about a common mistake: Protective offsets may be actic, or even a good therapeutic strategy, but should never beer se. The virtuous path is the straight path, neither left of it norrfect center.

g of quantum theory. Oxford: Oxford University Press.02). Autopoietic organization theory: Drawing on Niklas Luhmann’s social systems Copenhagen Business School Press. epistemology of any interest for semiotics? Scripta Semiotica, 1, 1-6.nfinitesimal analysis. Cambridge: Cambridge University Press. us and the infinitesimal in mathematics and philosophy. Milano: Polimetrica.ical writings of Niels Bohr (Vols. I-IV). Woodbridge, CT: Ox Bow Press.swered by Niels Bohr (1885-1962). Physikalisch-Technische Bundesanstalt. Retrieved/www.ptb.de/en/publikationen/blickpunkt/interviews/bohr.html. istemology, and inquiry. Teaching & Learning, 17, 1, 5-18.6). Evidence and compositionality. In J.Lawry et al. (Eds.)., Soft methods for integrated.307-315). New York: Springer.an computers help to explain biology? Nature, 440 (23), 416-417.

tics: On autopoiesis, code-duality and sign games in bio-semiotics. Cybernetics and14.iotics and Umweltlehre. Semiotica (Special issue on Jakob von Uexküll’s

/4), 779-814.ction of Information and Communication: A cyber-semiotic re-entry into Heinz Vonnstruction of second-order cybernetics. Semiotica, 154 (1/4), 355-399.

ionary. Oxford: Blackwell.e Crea. Milano: Feltrinelli.

, D. (2004). Complementarity and paraconsistency. In S. Rahman, J. Symons, D. M.egem (Eds.), Logic, epistemology, and the unity of science (pp.557-568). New York:

uction to Hilbert Space and quantum logic. New York: Springer.tandard analysis. New York: Dover.

al statistical decisions. New York: McGraw-Hill.se in harmonic analysis (2nd ed.). New York: Springer.and its physical meaning. London: Taylor & Francis.Boston: Allyn and Bacon.


91

Durbins, L. E., & Savage, L. J

Dover. Eaton, M. (1989). Group InvariEfran, J. S., Lukens, M. D., &

psychotherapy. New York:Eibel-Eibesfeldt, I. (1970).

Eth

Eisele, C. (Ed.) (1976)

.

The ne

Ferreira, J. (2006).

Semiotic ex

Wellington.Finetti, B. de (1975).

Theory of

Von Forester, H. (2003).

Unde

Verlag. (The following artEnvironments; p.1-19. (b)271. (d) For Niklas Luhm

Gelman, A., Carlin, J. B., Ster

Hall/CRC.Gerhardt, C. J. (1890).

Die

Buchhandlung. Goldblatt, R. (1998).

Lectures

Goudsmit, A. L. (1998).

Towa

University, Holland. RetriHalmos, P. R. (1998).

Naive se

Hughes, R. I. G. (1992).

The st

Press. Ibri, I. A. (1992).

Kosmos Noet

Kapur, J. N. (1989).

Maximum

Kolmanovskii, V. B., & Nosov,

Kolmogorov, A. N., & Fomin,

Dover. (originally publishLauretto, M., Pereira, C. A. B.,normal distributions using the i

17

, 147-168. Lauretto, M., & Stern, J. M. (2

on Bayesian Inference aPhysics Conference Proce

Madruga, M. R., Esteves, L. GMadruga, M. R., Pereira, C. A

Statistical Planning and InMaimonides, M. (2001). MishnMaturana, H. R., & Varela, F. JMaturana, H. R. (1988). Onto

domain of existence. In Cfor Cybernetics.

Maturana, H. R. (1991). ScienResearch and reflexivity (p

Maturana, H. R., & Poerksen, BMuggleton, S. H. (2006). ExceNachbin, L. (1965). The Haar Nelson, E. (1987). Radically elNoeth, W. (1995). Handbook oNosov, V. R., Kolmanovskii, V.Olitzky, K. (Ed.) (2000). ShemPais, A. (1988). Inward bound:Peirce, C. S. (1931–1935). The

[C. Hartshorne & P. WeissBurks (Ed.), same publisCP vol.paragraph).

Pereira, C. A. B., Stern, J. M. (Entropy Journal, 1, 69-80

Piaget, J. (1975). L’équilibratioRackham, H. (1926). Aristotle,Rahman, S., Symons, J., Gabb

science. New York: Spring

. (1976). How to gamble if you must: Inequalities for stochastic processes. New York:

ance Applications in Statistics. Inst. of Mathematical Statistics. Lukens, R. J. (1990). Language, structure and change: Frameworks of meaning in

W.W.Norton. ology: The biology of behaviour. New York: Holt, Rinehart and Winston. w elements of mathematics of Charles S. Peirce. The Hague: Mouton.plorations in computer interface design. Unpublished Ph.D. thesis, Victoria University,

probability: A critical introductory treatment (Vols.1 & 2). London: John Wiley. rstanding understanding: Essays on cybernetics and cognition. New York: Springer

icles in this anthology are of special interest: (a) On Self- Organizing Systems and their On Constructing a Reality; p.211-227. (c) Objects: Tokens for Eigen-Behaviors; p.261-ann: How Recursive is Communication? p.305-323.)n, H. S., & Rubin, D. B. (2003). Bayesian data analysis. Boca Raton, FL: Chapman-

philosophischen Schriften von Gottfried Wilhelm Leibniz. Berlin: Weidmannsche

on the hyperreals: An introduction to nonstandard analysis. New York: Springer. rds a negative understanding of psychotherapy. Unpublished Ph.D. Thesis, Groningeneved December 2007 from http://irs.ub.rug.nl/ppn/174290861t theory. New York: Springer. ructure and interpretation of quantum mechanics. Cambridge, MA: Harvard University

os. A Arquitetura Metafısica de Charles S. Peirce. São Paulo: Prespectiva. entropy models in science and engineering. New York: Wiley. V. R. (1986). Stability of functional differential equations. London: Academic Press. S. V. (1999). Elements of the theory of functions and functional analysis. Mineola, NY:ed in 1960 by MIR of Moscow, Portugese translation, 1982) Stern, J. M., & Zacks, S. (2003). Comparing parameters of two bivariate nvariant full Bayesian significance Test. Brazilian Journal of Probability and Statistics,

005). FBST for Mixture Model Selection. MaxEnt, 2005: 25th International Workshopnd Maximum Entropy Methods in Science and Engineering. American Institute ofedings, 803, 121-128. ., & Wechsler, S. (2001). On the Bayesianity of Pereira-Stern Tests. Test, 10, 291-299.. B., & Stern, J. M. (2003). Bayesian Evidence Test for precise hypotheses. Journal ofference, 117, 185-198.e Torah: Yad hachzakah. New York: Yeshivath Beth Moshe.. (1980). Autopoiesis and cognition: The realization of the living. Dordrecht: D. Reidel.logy of observing: The biological foundations of self consciousness and the physicalonference Workbook: Texts in Cybernetics (pp. 18-23). Felton, CA: American Society

ce and reality in daily life: The ontology of scientific explanations. In F. Steier (Ed.),p. 30-52). Thousand Oaks, CA: Sage Publications.. (2004). Varieties of objectivity. Cybernetics and Human Knowing, 11(4), 63-71.

eding human limits. Nature, 440 (23), 409-410.Integral. Princeton, NJ: Van Nostrand.ementary probability theory. Princeton, NJ: Princeton University Press.f semiotics. Bloomington, IN: Indiana University Press. B. (1986). Stability of functional differential equations. London: Academic Press.onah Perakim: A treatise on the soul by Moshe ben Maimon. New York: URJ Press. Of matter and forces in the physical world. Oxford: Oxford University Press. Collected Papers of Charles Sanders Peirce. Electronic edition reproducing Vols. I–VI (Eds.), Cambridge-MA: Harvard University Press, 1931–1935], Vols. VII–VIII [A. W.her, 1958]. Charlottesville: Intelex Corporation. (Citations use the common form:

1999). Evidence and credibility: Full Bayesian significance Test for precise hypotheses..n des structures cognitives: Problème central du développement. Paris: PUF.

Nicomachean ethics. Cambridge, MA: Harvard University Press.ay, D. M., & Bendegem, J. P. van (Eds.) (2004). Logic, epistemology, and the unity ofer.

92 Julio Michael Stern

Rasch, W. (2000). Niklas Luhm(especially chapter 3 andConstructivism as a two-Archipelago, or: How to L

Rijsbergen, C. J. van (2004). TRobert, A. M. (2003). NonstanRobertson, R. (2001). One, two

Knowing, 8 (1-2), 7-24.Ruhla, C. (1992). The physics oSantaella, L. (2002). SemióticaSegal, L. (2001). The dream ofShedler, J., & Westen, D. (20

American Journal of PsycShedler, J., & Westen, D. (2005

American Journal of PsycSteier, F. (Ed.) (1991) ResearchStern, J. M. (2003). significanc

Conference Proceedings: Stern, J. M. (2004). Paracon

Proceedings: Lecture NoteStern, J. M. (2006a). Decoupli

IME-USP-2006-07). Sao PStern, J. M. (2006b). Languag

IME-USP-2006-09). Sao PStern, J. M. (2007a). Cognitiv

Human Knowing, 14 (1), 9Stern, J. M. (2007b). Complex

2007-01). Sao Paulo: UnivStern, J. M., & Zacks, S. (2

Distribution: The power oTomonaga, S. (1962). QuantumUlam, S. M. (1943). What is a Wenger, E., Pea, R. Brown, J.

Cambridge: Cambridge UWinograd, T., & Flores, F. (198

Addison-Wesley.Zubov, V. I. (1983). Analytical

ann’s modernity. paradoxes of differentiation. Stanford, CA: Stanford University Press. 4. Also published as: Rasch, W. (1998). Luhmanns Widerlegung des Idealismus:

front war. Soziale Systeme, 4, 151-159; and Rasch, W. (1994). In Search of Lyotardive a Paradox and Learn to Like It. New German Critique, 61, 55-75.

he geometry of information retrieval. Cambridge: Cambridge University Press.dard analysis. Mineola, N Y: Dover., three, continuity: C. S.Peirce and the nature of the continuum. Cybernetics & Human

f chance: From Blaise Pascal to Niels Bohr. Oxford: Oxford University Press. Aplicada. São Paulo: Thomson Learning. reality: Heinz Von Forester’s constructivism. New York: Springer.04). Dimensions of personality pathology: An alternative to the five-factor model.

hiatry, 161, 1743-1754. ). Reply to T. A.Widiger, T. J.Trull: A simplistic understanding of the five-factor model.hiatry, 162(8), 1550-1551. and reflexivity. Thousand Oaks, CA: Sage Publications.

e tests, belief calculi, and burden of proof in legal and scientific discourse. Laptec-2003Frontiers in Artificial Intelligence and its Applications, 101, 139-147. sistent Sensitivity Analysis for Bayesian significance Tests. SBIA’04 Conferences Artificial Intelligence, 3171, 134-143.

ng, sparsity, randomization, and objective Bayesian inference (Technical Report MAC-aulo: University of Sao Paulo, Institute of Mathematics and Statistics.

e, metaphor and metaphysics: The subjective side of science (Technical Report MAC-aulo: University of Sao Paulo, Institute of Mathematics and Statistics.e constructivism, eigen-solutions, and sharp statistical hypotheses. Cybernetics and-36. Structures, Modularity and Stochastic Evolution. (Technical Report IME-USP-MAP-ersity of Sao Paulo, Institute of Mathematics and Statistics.002). Testing the independence of Poisson Variates under the Holgate Bivariate

f a new evidence test. Statistical and Probability Letters, 60, 313-320. mechanics (Vols. 1 & 2). New York: Wiley Interscience.

measure? The American Mathematical Monthly, 50 (10), 597-602. S., & Heath, C. (1999). Communities of practice: Learning, meaning, and identity.niversity Press.7). Understanding computers and cognition: A new foundation for design. New York:

dynamics of systems of bodies. Working paper. Leningrad University.

language and the self-reference paradox - ime-uspjstern/papers/papersjs/jmschk2.pdf · cybernetics...

Documents