Karl Pearson and the Logic of Science: Renouncing Causal Understanding (the Bride) and Inverted Spinozism
KKarl Pearson and the Logic of Science:Renouncing Causal Understanding(the Bride) and Inverted Spinozism
Julio Michael SternSouth American Journal of Logic, v.4, n.1, pp.219-252, 2018.
Abstract
Karl Pearson is the leading figure of XX century statistics. He andhis co-workers crafted the core of the theory, methods and language of frequentist or classical statistics – the prevalent inductive logic of con-temporary science. However, before working in statistics, K.Pearson hadother interests in life, namely, in this order, philosophy, physics, and bi-ological heredity. Key concepts of his philosophical and epistemologicalsystem of anti-Spinozism (a form of transcendental idealism) are carriedover to his subsequent works on the logic of scientific discovery.This article’s main goal is to analyze K.Pearson early philosophicaland theological ideas and to investigate how the same ideas came to in-fluence contemporary science, either directly or indirectly – by the useof variant theories, methods and dialects of statistics, corresponding tovariant statistical inference procedures and their specific belief calculi.
Keywords:
Causality and natural laws, Inductive logic and probabilistic in-ference, Phenomenology, Logical Positivism, Karl Pearson, Baruch Spinoza.
Mathematics Subject Classification (2010):
Scientific research can reduce superstition by encouraging people tothink and view things in terms of cause and effect. Certain it is that aconviction, akin to religious feeling, of the rationality and intelligibilityof the world lies behind all scientific work of a higher order. This firmbelief, a belief bound up with a deep feeling, in a superior mind thatreveals itself in world of experience, represents my conception of God.In common parlance this may be described as “pantheistic” (Spinoza).
Albert Eistein, Ideas And Opinions, (1988, p.46, 262). a r X i v : . [ s t a t . O T ] A ug Julio Michael Stern !הָלַכּ תאflרְקִל י£דוֹד ה¨ְל!הָלַכּ לַע Nָתָח שׂוּשְׂמִכּ (cid:155)¢יָה•לֱא (cid:155)¢יַלָע שׂי⁄שׂ‡י!הָלִחְתּ הָב(cid:181)שֲׁחַמְבּ ה‹שֲׂעַמ Pוֹס ה¨וּס(cid:158)נ M«דֶקִמ שׁא‚רֵמ
Let’s go, beloved, let’s meet the bride:Your God will rejoice over you, As the groom rejoices over his bride;Before the beginning she was offered, Planned from start, Created at end.XVI century verses by Rabbi Shlomo Halevi Alkabetz
Karl Pearson (1857-1936) is the leading figure of XX century statistics. Un-der his direct tutelage or influence, George Udny Yule (1871-1951), Ronald A.Fisher (1890-1962), Jerzy Neyman (1894-1981), Egon S. Pearson (1895-1980),and many others defined the methods, language and epistemology of the fre-quentist school of mathematical statistics, that is, of XX century mainstreamstatistics – the prevalent belief calculus used for inductive reasoning in thepractice of contemporary science. This formalism translates K.Pearson’s epis-temological and philosophical position on the logic of scientific discovery, aposition he calls: “Inverted-Spinozism – a Spinozism modified by Fichte”.Today, K.Pearson is known for his work in Statistics. However, his in-tellectual journey has many roots. Before working in Statistics, he studiedand worked in philosophy, theology, physics, heredity and eugenics. More-over, his work in these fields had a compelling influence in his later workin statistics. Nowadays, many didactic text-books present K.Pearson’s philo-sophical positions very unfaithfully, in watered-down pseudo-positivist or insterilized decision-theoretic versions. Like the roots of a tall tree, the origins ofK.Pearson’s philosophy are now deeply buried and often concealed, Neverthe-less, like the branches of the same three, its epistemological and methodologicalconsequences are clearly seen and its influence strongly felt all over the realm ofcontemporary statistical science. Moreover, since statistical test of hypothesesbecame the de facto standard for validating scientific research, this influenceis exerted much further. In this and following articles we analyze the histori-cal and conceptual development of K.Pearson philosophy, and consider how ithas influenced statistical inference procedures and the logic of correspondingbelief-calculi.The main goal of this paper is to present Pearson’s epistemological views,as he presented them in academic articles and books, and also as presentedallegorically in his novel
The New Werther . Section 2 presents my interpreta-tion of K.Pearson’s mystical journey of “Renouncing the bride”, as narrated in
The New Werther . Section 3 details more technical aspects of his philosophical arl Pearson, Spinoza & Causal Understanding
K.Pearson arrives at his philosophical concept of Inverted-Spinozism after areligious and spiritual crisis, and presents his positions in several forms, includ-ing: His influential book
The Grammar of Science (1892); some review articlesabout the philosophy of Spinoza (1880, 1883) and, most importantly in ourcontext; his novel
The New Werther – by Locki (1880). This novel presentshis philosophy in a romantic and mystical context, that we explore in Section2.2 via Spinoza’s philosophical roots in Jewish philosophical and mystical writ-ings by Moshe ben Maimon (1135-1204), Abraham Abulafia (1240-1291) andJoseph Gikatilla (1248-1310). Section 2.3 presents some of the motivations andsome epistemological consequences of K.Pearson’s Inverted-Spinozism.
The New Werther
K.Pearson describes the style of
The New Werther as schw¨armerisch roman-ticism, using the term Schw¨armerei in the sense of enthusiastic fervor. InGerman, this term usually means rapture or infatuation, and it is also usedin religious literature to denote zealotry, in the sense of utmost commitmentto ethical values and self-renunciation, see Levine (2010). In the next subsec-tions, I present a philosophical and mystical interpretation of this outstandingand unusual work, that I see as an act of true philosophical and spiritual re-nunciation, namely,
Renouncing the Bride , as explained in the sequel. I alsoexplain why I see
The New Werther as the point of departure and the fulcrumfor all of K.Pearson latter works in science and statistics. Nevertheless, thereader should be aware that my interpretation differs from existing ones, spe-cially from that of K.Pearson’s main biographer, Theodore Porter (2004, Ch.3,p.43-68).
The New Werther describes the journey of Arthur, a young Englishmenin Germany, his adventures visiting Heidelberg university, and his wanderingabout the scenic routes of the Black Forest. The novel’s full title,
The New Julio Michael Stern
Werther – by Locki , reveals its fictional author, Locki – named after the shapeshifter, trickster and subversive Germanic god – that plays the role of a FaustianMephistopheles, the scatterer and forgerer of lies, !רֶק(cid:181)שׁ לֶפֹתּ Zִפֵמ , as in Job 13:4.This epistolary novel involves three main characters: Arthur; Ethel, Arthur’sfiance; and Raphael, Arthur’s friend at the university.Arthur unequivocally represents K.Pearson himself. According to Porter(2004, p.54-55) well documented interpretation, Raphael is a fictional charac-ter partially based on Raphael Wertheimer, K.Pearson’s friend and Law stu-dent at Heidelberg. Furthermore, Porter (2004, p.55-56) concludes that “therole of Ethel was an elaboration of Pearson’s friendship with Robert Parker”,K.Pearson’s study partner and colleague at Cambridge. Furthermore Porterconsiders their relationship suggestive of the “upper-class male relationshipsat school in the Victorian era, and the efflorescence of homosexual activity atKing’s College”, pondering however that “there is no evidence to support, andmuch reason to doubt, that this friendship was ever explicitly sexual”.In the next subsections I offer an alternative reading of
The New Werther ,including an alternative interpretation of the characters Ethel and Raphael. Ido not deny the validity of Porter’s interpretation, not least because I do nothave access to K.Pearson correspondence and other sources used by Porter inhis biographical studies. Moreover, I do not consider these interpretations tobe mutually exclusive. Perhaps, all sexual tensions so accurately alluded byPorter could be considered as earthly affairs contrasting, and in this way com-plementing and highlighting, the spiritual and philosophical concerns discussedin the next subsections. After all, in the human soul ( ψυχη , Psyche), severalaspects of sex, love and thought and their representations appear to be deeplyintertwined, as suggested by the ancient Greek myths of (cid:15)ρ o ς , Eros, in his twoforms: either the playful young god of love, or his older form, φανης – Phanes,the shiny god of revelation. Hence, it should not be surprising to see all theseaspects emerge together in the turmoil of K.Pearson’s religious and spiritualcrisis. The New Werther presents K.Pearson’s doctrine of Inverted-Spinozism in theaforementioned schw¨armerisch-romantic style, and is permeated by mysticalelements. As an example, let us quote from the first encounter of Arthur andRaphael:
I was in the library, looking for a copy of Maimonides, to whom my studyof Spinoza had led me, when I found a queer-looking person busily readingin a corner the very book I wanted. He had a distinctly Jewish face, and yetbeneath his raven-black and straggling locks there was an apostolic nobility arl Pearson, Spinoza & Causal Understanding and depth. He seemed to know by inspiration what I had come for, andwith a salutation offered me the book.
Pearson (NW, p.22).K.Pearson structures his philosophical doctrine of inverted-Sponizism around(and against) three major principles of Spinozian philosophy and epistemology,namely:(1)
Deus sive natura ;(2)
Cognitione causae and
Leges naturae universales ;(3)
Amor Dei intellectualis .These epistemological principles are presented in axiomatic form at BaruchSpinoza’s magnum opus, namely, his
Ethica – Ordine Geometrico Demonstrata of 1677. K.Pearson had great familiarity, and also strong opinions aboutSpinoza’s works and his commentators, even publishing in 1880 a review of
Pollock’s Spinoza at the
Cambridge Review . K.Pearson was also well aware ofprecursors of these epistemological principles rooted in medieval Jewish philos-ophy, as clearly attested by his article
Maimonides and Spinoza published at
Mind in 1883. As examined in this section, these medieval philosophical pre-cursors are expressed in a language and permeated by forms of argumentationthat are perceived by contemporary readers as essentially mystical in nature,for further comments see Stern (2017) and also Fraenkel (2006), Harvey (2007)and Idel (2000).In our context, the mystical route to Spinoza’s epistemological principles of-fers some advantages over the axiomatic (ordine geometrico) exposition, amongothers: (a) It is in the best spirit of
The New Werther , a main object of studyin this article; (b) It offers efficient short-cuts, allowing for close and effectiveconnections with and between topics concerning causal analysis in natural sci-ence to be studied in the next sections. Having the aforementioned objectivesand justifications in mind, let us explore Spinoza’s epistemological principlesvia the Maimon-to-Spinoza mystic route.
Deus sive natura
Spinoza’s principle of
Deus sive natura – God, or equivalently, nature – finds aprecursor in Moshe ben Maimon (1135-1204) classical formula: ha-pe ( ulot ha- ) elohiyoth , ha-pe ( ulot ha-teb ( ayoth , !תוֹיעַבֶטַה תוֹלuעְפַה תוֹיִה•לְֶאַה תוֹלuעְפַה ; meaning:In the world we live in – Actions of God (are just) actions of nature.Abraham Gikatilla (1248-1310) explains Maimonides’ formula using formsof sylleptic argumentation that are typical of Jewish medieval philosophy andmysticism, see Stern (2017). His argument is based on the careful examinationof the !שׁ«רֹשׁ , shoresh , root or stem !עבט . On one hand, this stem generatesthe word !עַבֶט , teba , a substantive meaning nature or substance; On the otherhand, this stem generates the word !עַבַט , tab ( a , a verb meaning sank, stamped,24 Julio Michael Stern coined or formulated; including the derived form !ַעֵבְּטַמ , matbe ( a , coin, type,formula. Also of interest is the expression !N¢יַע˚תוּעיִבְט , tebiyoth– ( ayn , meaningintuition or insight, literally, eye-impression; see Klein (1987, p.239-240, 337.Gikatilla conclusion from this philological analysis is that “things”, as theypresent themselves in nature, are coined, patterned, and also behave accordingto ideal types or abstract formulas, types and formulas that convey the will ofGod.Interestingly, the Latin words causare, causa , (to) cause; are etymologicallyrelated to cudere, cusum , (to) strike, hammer, forge, stamp, coin; suggestingan analogy that parallels Maimonides formulation and its later interpretationby Gikatilla. The same analogy is repeated in the Portuguese (the languageof Spinoza’s country of origin) words causa/ cousa , the cause (of something)/(some)thing (caused). Cognitione causae and Leges naturae universales
The preceding analysis of Spinoza’s first epistemological principle, Deus sivenatura, brings us directly to his second principle – The understanding of causesand universal natural laws. In the next paragraphs we reproduce this principlein abridged form, for the full version see Ethics (1677, Part I, Axiom 4; Pref.for Part III & IV).So, the cause or reason why God, or nature, acts, and the cause or reasonwhy He exists, are therefore one and the same. ... The eternal and infiniteBeing, which we call God or Nature, acts by the same necessity as thatwhereby it exists. ... The knowledge of an effect involves and depends onthe knowledge of its cause. ... and therefore, one and the same should bethe method of understanding the nature of all things whatsoever, namely,through nature’s universal laws and rules. Amor Dei intellectualis
Once the first and second principles are stated and accepted, one questionpresents itself: Can mankind, even if in approximate form, have knowledgeof the ideal types or abstract formulas that regulate nature? Spinoza’s thirdprinciple is to state the answer in the affirmative, this statement being also Ratio igitur seu causa, cur Deus seu natura agit et cur existit, una eademque est. ...Aeternum namque illud et infinitum ens, quod Deum seu naturam appellamus, eadem, qua ex-istit necessitate agit. ... Effectus cognitio a cognitione causae dependet et eandem involvit. ...atque adeo una eademque etiam debet esse ratio rerum qualiumcumque naturam intelligendi,nempe per leges et regulas naturae universales. arl Pearson, Spinoza & Causal Understanding !;וְֹבּ Mי£ד(cid:159)רֹי(cid:158)ו Mִלֹע Mיִה•לֱא יֵכֲאְלַמ הƒנִה(cid:158)ו הָמ(cid:158)יָמ(cid:181)שַׁה ַעי¢גַּמ וֹשׁא‚ר(cid:158)ו הָצ(cid:159)רַא בָצuמ Mָלuס הƒנִה(cid:158)ו M•לֲחfiיfiו
He [Jacob] had a dream, a ladder was set on the earth with its top reachingto heaven; and behold, the angels of God were ascending and descendingon it.
Abraham Abulafia, in his book Light of the Intellect (1285), !לֶכ‹שַׂה רוֹא , Orha-Sekhel , analyzes Maimonides philosophy in general and this third epistemo-logical principle in particular, and reiterates the nature of the ascending anddescending movements at Jacob’s ladder, namely, this (e)motion is love! Loveof Divine insight, ahabah elohut sikhlut , !תוּל˙⁄שׂ תוּה•לֱא הַבַהַא , meeting the love ofhuman understanding, ahabah enoshut sikhlut , !תוּל˙⁄שׂ תוּשׁוֹנֱא הַבַהַא .Furthermore, in his book Life of the Soul (1275), !שֶׁפ“נַה יƒיַח רֶפֵס , sepher chayeihanephesh , Abulafia compares the joy of this Divine and human intellectualencounter at Jacob’s ladder to the delight, tha ( anug , !גוּנֲעַתּ , of the groom andthe bride, ha-chathan ve-ha-kalah , !הָלַכּהו Nַתַּחה .Abulafia’s romantic analogy conceals sylleptic arguments typical of Jewishmedieval philosophy and mysticism, see Stern (2017). On one hand, the verb !Nֵתוֹח , chothen , (to) marry, also carries the meanings of (to) circumcise and (to)join, connect. On the other hand, the word for bride, !הָלַכּ , also means – tobe completed, that is related to the roots !לֹכ , all, whole; !לַלָכּ , (to) complete,perfect, generalize; and !לָלְכּ general rule, principle or law. More detailed discussion of the topics presented in this subsection can befound in Fraenkel (2006), Harvey (2007) and Idel (2000). These articles givevery erudite views of these topics, commenting several aspects beyond the scopeof the present paper. For example, some of these articles show how to rephrasephilological and sylleptic arguments into gematrical calculations, a recoursetypical of medieval kabalah.
After studying in depth the philosophy of Spinoza and its precursors, K.Pearsonbegins to depart from its core principles, finally arriving at his “Inverted- Gesenius (1906, p.368, 477-483) and Klein (1987, p.237, 276-278) offer etymologicalanalyses based on classical methods of comparative linguistics. Clark (1999, p.118-119 p.293-301), Gesenius (1910, p.99-102), Frajzyngier (1979) and Horowitz (1993) suggest possiblederivations based on formation pathways from biliteral bases to triliteral roots, or from ageminate root to its gradational variants. Julio Michael Stern
Spinozism – a Spinozism modified by Fichte”. As he so honestly acknowl-edges, these modifications take him so far away from Spinoza that their philoso-phies become, in many aspects, antithetic; hence the name Inverted-Spinozism.More technical aspects of this philosophical position are analyzed in Section 3,see also Jacobi (1994, p.502), Limnatis (2008, p.119-120) and Schelling (1994,p.107-108). In this section we pay close attention to
The New Werther narra-tive.My reading of
The New Werther tells a tale of a groom, Arthur – repre-senting K.Pearson, that rejects his bride. In this reading, Raphael becomes aspokesman for the philosopher Baruch Spinoza, while Ethel, Arthur’s belovedbride, becomes a representation of Greek Sophia ( σ o φια , wisdom) or HebrewShekinah (from the root !Nכשׁ shochen, to dwell within – meaning Divine under-standing as it can and does dwell within a human being), that is often sym-bolically represented in the kabalistic literature as the ‘cosmic bride’. That is,Ethel becomes a representation of human profound understanding or intuitiveinsight that can be achieved by God’s grace. In his scientific and philosoph-ical papers, K.Pearson rejects the possibility of this kind of understanding,whereas, in The New Werther , Arthur rejects the love of Ethel, doing so in themost dramatic way and with the most tragic consequences.The extent to which K.Pearson accepts “Inverted Spinozism” and, there-fore, breaks away from the love of Ethel-Sophia, with all its philosophical andspiritual consequences, becomes clearer as we read
The New Werther accordingto my proposed interpretation. The following key passages, that I for conve-nience have labeled (i) to (vii), provide stepping stones for reading
The NewWerther according to this interpretation.In the first quotation, (i), Arthur presents his reasons for staying away fromhis (formerly) beloved Ethel. His motives still have an exploratory or tentativecharacter, but his arguments will mature as the novel progresses, strengtheningthe determination of his decisions, and also the gravity of its consequences.(i)
Let us show that the two great schools of materialism and idealism,which have divided the world against itself, are really at one; that theinexorable laws under which science asserts that the universe must forever roll on, are not empiric, but deducible from the pure reason; and that,though the sway of the intellect shall thus be extended from the logical tothe empirical, yet that the intellectual, the manly, shall itself be so boundup with feeling, the womanly, that the two shall be united in one being andin one life, as we have been. Let us prove that the Ideal is not a worldinvented by the painter and the poet, but that it exists in every Actual; thatthe Deity is not a cause outside and separate from material man; that thecause must not be sought outside, but rather in the effect – nay, perhaps, arl Pearson, Spinoza & Causal Understanding is that effect itself. With this end, best of friends [Ethel, Sophia] , havewe renounced each other. (NW, p.11).The next set of quotations, labeled (ii) to (v), give key snapshots of thisnovel climax, turning points and anti-climax. In the next scene of interest,he Germans are celebrating Walpurgisnacht, also known as Hexennacht – thenight of the witches. At this ancient Germanic pagan festival, celebratedaround bonfires at the hilltops, Arthur has a cathartic moment. At (ii), Arthur(K.Pearson) tries to convince Raphael (Spinoza) to turn his philosophy upside-down, to replace the absolute God by an absolute Ego – an Ego that is capableof ripping the veil from the face of nature. Raphael’s answers (iii) with sar-castic questions: How could a mere mortal take command of the universe?How could a finite human being acquire infinite knowledge? How could such aclaim be something more than arrogant hubris? Arthur is incapable of answer-ing the unanswerable, but promises to seek justification for his position withinthe theoretical framework of German Idealism. As an indication of Pearson’scommitment to German culture it is interesting to mention that, during histrip to Germany, he replaced his English given name by its German version– from Carl to Karl. Finally, at (v), Arthur expresses a feeling of guilt, as ifhe had done something terribly wrong: His heart senses he betrayed the loveof Ethel (Sophia), and anticipates the dangers that lay ahead; Nevertheless,his mind is already committed to follow the way of departure, renouncing hispromised bride.(ii)
Do you not feel, said I [Arthur, to Raphael] , on a night like this, atitanic fire burning in your soul; that Nature is for the moment, your slave;that the Spirit of the Universe is at hand, and that you can compel it toraise its veil? (iii)
Raphael: But how can you, who believe in the pantheism of Spinoza,allow that the part can possibly compel the whole; that man, an infinites-imal portion of the Godhead, can command the Spirit of the Universe? (NW, p.25-26).(iv)
I [Arthur] have determined to read those German reasoners, and thenagain to discuss the matter with Raphael [Spinoza]. (NW, p.28).(v)
The morning was cool, yet my head felt on fire. It seemed to me asif someone had told me I had wronged you, Ethel [Sophia]; and I knew itwas not true. (NW, p.29).A few pages later, Arthur presents the core of his philosophy in a conciseand well articulated form. The similarities with Fichte’s philosophical position28
Julio Michael Stern and the influence of the Inverted-Spinozism metaphor, as defined by Jacobiand expanded by Schelling, are fully acknowledged.(vi)
The spirit, to be an “I”, must have a nature of its own; a naturedenotes constancy; constancy we term a law. The I, in order to exist,must follow this law; the permanency of forms which this law gives toour perceptions we term space and time. The thought-law which dictatespermanency to the perceptions, compels us to look upon space and time asinfinite and eternal. Thus we see how Eternity and Infinity, which stoodbefore as twin giants, laughing at and ready at once to crush and obliteratethe feeble actions of a finite humanity, are but the necessary creations ofour own inner nature.
Pearson (NW, p.39).Nothing good will come from following the advice of Locki, the trickster,no light will be found at the end of a path set by the father of Hell. Arthur isno longer interested in Rafael’s friendship, and suggests that Raphael makesa visit to Ethel, who lives in Paris, the city of light (and love). For the nextmonths, Arthur wanders trough the black forest in an individuation journey ofsorts, that he makes having as sole companion his loyal dog, Gaspar, see Franz(1990, p.137; 2000, p.59).Emerging from the forest, he goes to Paris, only to find Ethel (Sophia)and Raphael (Spinoza) deeply in love with each other. Arthur has an enragedtantrum, and after an outburst of jealousy and a melodramatic speech of falseforgiveness, commits suicide. At the last pages of
The New Werther , its fic-tional author, Locki, assumes the narrative, for poor Arthur is no longer incondition to fulfill this role. The very last words of
The New Werther bringLocki’s concluding message (vii), that he delivers pronouncing the words of thecharacter Mephistopheles in Goethe’s Faust:(vii)
Ich bin der Geist, der stets verneint!Und das mit Recht; denn alles, was entsteht,Ist werth, daß es zu Grunde geht;Drum besser w¨ar’s, daß nichts entst¨unde. [I am the spirit that all negates!And rightly so, for all that originates,Should rightly to its destruction run;’Twere better then that nothing were begun.]
In order to fully understand the consequences of the alternative interpretationof
The New Werther presented in the last section, we have to examine the ori- arl Pearson, Spinoza & Causal Understanding “I am” and “There are things outside me”. Speculative philosophy hadto try to subordinate one of these propositions to the other; to derive theformer from the latter or the latter from the former – exhaustively, in theend – so that there would be but one being and one truth before its eye, theall-seeing one! ... Thus the two main avenues, materialism and idealism,or the attempt to explain everything from a self-determining matter aloneor from a self-determining intelligence, have the same aim. Their opposingcourses do not take them apart at all, but rather bring them graduallynearer to each other until they finally touch.Strange, that the thought never occurred to Spinoza of inverting his philo-sophical cube; of making the upper side, the side of thought which he calledthe objective, into the lower, which he called the subjective or formal; andthen of investigating whether his cube still remained the same thing; stillfor him the one and only true philosophical shape of reality. Everythingwould have transformed itself without fail under his hands at the exper-iment. The cube that had hitherto been “substance” for him – the onematter of two entirely different beings – would have disappeared before hiseyes, and in exchange a pure flame would have flared up, burning all byitself, with no need of place or material to nourish it: Transcendental Ide-alism! ... I chose this image because I first found entry into the Doctrineof Science [Wissenschaftslere (1813)] through the representation of an in-verted Spinozism.
The expression Inverted-Spinozism was further disseminated by FriedrichWilhelm Joseph von Schelling (1775-1854), and by several commentators eversince; In Schelling (1827, 1994, p.108) we find the following extended expla-nation of why Fichte’s philosophy can be well characterized as an InvertedSpinozism:
There was no alternative there, if one did not wish to move once againinto the absolute object, witch destroys everything free in the subject, thanto move to the opposite – to the all-destroying subject, which was now no Julio Michael Stern longer the empirical subject of Descartes, but only the absolute subject, thetranscendental I. ...
Since this I was not the empirical I, then for Fichte the
I am , which hemade into the highest principle of philosophy, could also not be an em-pirical fact – Fichte declared it to be an action (Thathandlung, literally‘deed-action’) and showed how the I could in no way exist independently ofthis action as a dead, immobile thing , but only in this act of self-positing[Selbstsetzung] in which he recognized not just a temporal, and also not justa transitory beginning which had begun the movement at some time, butthe beginning which was always equally eternal – thus that, wherever andwhenever one wanted to begin, this act of self-positing always had to be thebeginning. Fichte’s idealism thus is the complete opposite of Spinozismor is an inverted
Spinozism, because it opposes to Spinoza’s absolute ob-ject, which destroys everything subjective, the subject in its absoluteness,opposes the deed [Thathandlung, deed-action] to the merely immobile be-ing (seyn) of Spinoza; the I is for Fichte, not as it is for Descartes, justsomething assumed for the purposes of philosophising, but the real, thetrue being, the absolute
Prius of everything.
The next sub-sections examine how K.Pearson faithfully and fully acceptsthe implications of being a philosopher of Inverse-Spinozism. Sections 4, 5,and following articles will examine how he carried these positions to his wayof doing science in general and statistics in particular. The next subsectionsfocus on two specific aspects of great importance, namely, the epistemologicalor ontological status of the external world, and the role (or lack thereof) ofcausal or metaphysical explanations in the practice of science.
Pearson restates the same views expressed at the last quotations of
The NewWerther using a strictly academic voice, see next quotation.
We require in fact a kind of inverted Spinozism, a Spinozism modified byFichte. ... There is no need of the pre-established Harmony ... The outerworld, as we conceive it, is the production of the conceiving ‘Ego’, notan objective reality enforcing its laws upon the subjective sensitive centre.When we talk about a law of physical nature, we only mean a necessary lawof thought, any such law is only an intellectual law, the necessary methodin which we are compelled to view our sensations. When we talk of wavetheories, molecular theories, laws of attraction, etc., they are nothing in-dependent of ourselves but intellectual constructions, necessary to simplify arl Pearson, Spinoza & Causal Understanding the complices of sensation which we call light, heat, planetary motion, etc.
Pearson (1880), Pollock’s Spinoza, p.95.Jacobi’s metaphor of Inverted Spinozism presents Transcendental Idealismas – the flaring up of a pure flame, burning all by itself, with no need of placeor material to nourish it. An external cosmos would provide such a place forthe Transcendental Ego’s flame to exist, and natural laws governing materialentities in this cosmos would provide this flame with a base or nourishment.Nowadays, many didactic texts in statistics present K.Pearson philosophicalpositions as a form of mild subjectivism, a subjectivism that, on one hand,opposes naive or dogmatic forms of realism but, on the other hand, still allowsthe scientist to (in some form) relate to the external reality or to connectto existing objects in the world-out-there. In other words, a subjectivismthat allows the scientist to establish some form of harmony between the lawsgoverning the way objects “are” in the field of study of his science, a realmthat stands by itself, and the rules of thought used to think about the sameobjects. This is absolutely not the position taken by K.Pearson, as it couldbe deduced from either Fichte’s definition or Schelling’s explanation of theexpression Inverse Spinozism.Further explanations concerning the error of seeking some harmony be-tween rules of though and laws of nature, or between internal representationsand external order, can be found in Pearson (1897), Philosophy of NaturalScience, see following quotations, where K.Pearson criticizes the ideas of PaulVolkmann concerning this topic. For further details on the physical and epis-temological ideas of Paul Volkmann, see Corry (2004, p.61-63) and Volkmann(1896, 1900). Volkmann is not only a scientist, but also a physics’ profes-sor greatly concerned with good didactic practices. As such, he comes to theconclusion that teaching physics as an axiomatic system is a bad idea, for itis neither a faithful depiction of how science is actually built, nor a way ofpresentation that favors its understanding. Instead, Volkmann suggests an it-erative approach as the best option for both understanding and explaining therole played by the several elements that constitute a scientific theory.Volkmann presents his epistemological ideas using the metaphor of –
Thescientific system as a vaulted arch : As the stones in a vaulted dome, theelements of a scientific system mutually support each other; as the constructivepieces of an arched bridge, the elements of a scientific work of architecture arekept in place by their mutual interaction. This beautiful metaphor is furtherexplained in Volkmann’s own words in the following quotation:
You can immediately ask for the deeper underlying reason concerning whythere is a need, in the physical sciences, for an iterated cycle of knowledge. Julio Michael Stern
The reason can easily be seen in the form of emergence and internal opera-tion of the physical sciences: The conceptual system of physics should notbe understood as a system that is constructed in the manner of a building,from the bottom-up. Rather, it should be understood as a system of cross-references that is constructed like a vaulted dome or the arch of a bridge.In this way, it is a system that demands various mutual and reciprocalreferences, in which future results should be known from the start and,on the other way around, several previously stipulated conditions must besustained retrospectively. Physics, in short, is a conceptual system that isretroactively consolidated. Paul Volkmann’s epistemological position is far from any form of na¨ıve ordogmatic realism. Instead, perhaps way ahead of his time, I would charac-terize him as a protoconstructivist. Nevertheless, Vokmann is also far awayof K.Pearson’s science of the Absolute Ego. Accordingly, K.Pearson dissectsVolkann’s work, pin-pointing what he considers to be his fundamental mis-take. This fine critical exercise forces him to express his points of view ina very clear and candid fashion; this adversarial exercise forces K.Pearson tomake it abundantly clear how far he is willing to walk his path of Inverted-Spinozism or Transcendental Idealism. Specifically, K.Pearson emphasizes theepistemological error of conferring an ontological status or simply acknowledg-ing any thing-in-itself standing alone outside the conceiving Ego, an Ego thatultimately conceives everything into existence. According to K.Pearson, anyattempt to represent, to connect to, or even to learn from an external order ofthings in themselves, leads to a dead end.
We might pass to Dr. Volkmann and show the vagueness of his definitions,the unphilosophical character of his epistemology, and indicate the dangerwhich arises when loose analogies drawn from natural science are appliedto other fields of thought. ... For him [Volkmann] natural laws like thelaw of gravitation lie outside us while the conclusions of mathematics are Sie k¨onnen gleich hier nach dem tiefer liegenden Grunde fragen, warum f¨ur diephysikalische Wissenschaft ein wiederholter Kreislauf der Erkenntniss nothwendig ist. DieserGrund ist nach Entstehung und Betrieb der physikalischen Wissenschaft einfach darin zu se-hen, dass das physikalische Begriffssystem nicht etwa aufzufassen ist als ein System, welchesnach Art eines Geb¨audes von unten aufgef¨uhrt wird, sondern als ein durch und durch gegen-seitiges Bezugssystem, welches nach Art eines Gew¨olbes oder eines Br¨uckenbogens aufgef¨uhrtwird und fordert, dass ebenso die mannigfaltigsten Bezugnahmen auf k¨unftige Resultate biszu einem gewissen Grade von vorneherein vorweg genommen werden m¨ussen, wie umgekehrtbei sp¨ateren Ausf¨uhrungen die mannigfaltigsten Zur¨uckverweisungen auf fr¨uhere Verf¨ugungenund Festsetzungen statthaben m¨ussen. Die Physik ist kurz ein Begriffssystem mit r¨uckwirk-ender Verfestigung.
My translation of Volkmann (1896, 1910, p.113-114), as restated inVolkmann (1900, p.3-4), see also Volkmann (1896, 1910, p.245) and Corry (2004, p.61-63). arl Pearson, Spinoza & Causal Understanding thought-laws which lie inside us: “Diese Naturnothwendigkeiten ausser unsnirgends in Widerspruch treten mit den Denknothwendigkeiten in uns.” [These necessities of nature outside us, nowhere contradict the necessitiesof thought in us.] This arises apparently from a pre-established harmony the source of whichis accounted for in a manner which the writer tells us is the “Kernpunktmeiner erkenntnistheoretischen Studien auf naturwissenschaftlichem Bo-den.” [The core of my epistemological studies concerning the foundationsof natural sciences.] It [the harmony] lies namely in this: “dass die Logik in uns ihren Ur-sprung in dem gesetzm¨assigen Geschehen der Dinge ausser uns hat, dassdie ¨aussere Nothwendigkeit des Naturgeschehens unsere erste und rechteigentliche Lehrmeisterin ist.” [That the logic in us has its origin in theregular happenings of things outside us, that the external necessity of thenatural events actually is our genuine and true instructor.] We are onlygiven this sentence, without one word more description of the process bywhich such harmony has been established!
In conclusion, taking Jacobi’s metaphor of
Inverted Spinozism in its fullextent, we can understand how K.Pearson reached the conclusion, see
TheGrammar of Science (1911, p.109-110), that the science of TranscendentalIdealism can neither be an internal version or representation of external laws,nor the product of a harmony between internal rules of reasoning and externallaws governing the cosmos. Instead, so-called laws of nature must be theproduct of internal harmonizations of distinct aspects or faculties within theconceiving Ego. That is, according to K.Pearson, a scientist should recognizethat the laws of science result from... ...the harmony between his perceptive and reasoning faculties... Thus boththe material and the laws of science are inherent in ourselves rather thanin an outside world. Our groups of perceptions form for us reality, and theresults of our reasoning on these perceptions and the conceptions deducedfrom them form our only genuine knowledge.
If it is an error to seek for “laws of nature”, even if such laws are derivedfrom a pre-existent or constructed harmony between rules of thought and rulesgoverning objects of an external order, then it must be an even greater mistaketo ask for causal explanations, that is, to seek valid answers to questions asking Pearson (1896) gives only the German text; my translations are added in square brackets. Julio Michael Stern why “things” behave the way they do (according to a given law of nature).The next quotation, from Pearson (1901, The Prostitution of Science, p.50),further analyzes the absurdity of any metaphysical quest, that is, the nonsenseof searching for such causal explanations.
To argue from the harmony existing among my sensations to a like har-mony and order in the
Dinge an sich [things-in-themselves] is to multiplyneedlessly the causes of natural phenomena... If the human perceptive fac-ulty is capable of so co-ordinating sensations that all the groups maintaintheir own sequence, and are in perfect harmony with each other, shortlythat ‘order’ and ‘design’ appear in natural phenomena, what advantage dowe gain by needlessly multiplying causes and throwing back the ‘order’ andharmony of our sensations upon the
Dinge an sich , and an unknowableintellectuial faculty behind them?
In a very condescending manner, K.Pearson speaks to the addicted to meta-physics, the seekers of causal explanations, trying to save them from wanderingtheir erroneous path:
In all these cases we are dealing with the sequences of various types of mo-tion, into which we analyze or reduce a variety of sense-impressions. Justas in the special case of gravitation, we can also describe these sequencesand can frequently give a measure to the motions which we conceive totake place, but we are still wholly unable to state why these motions occur.We may talk, if we please, about the forces [and causes, and parameters]... but in using such phrases we do not introduce an iota of new knowl-edge, but too often a whole alphabet of obscurity. We hide the fact thatall knowledge is concise description, all cause is routine.
Pearson (1911,Ch.IV Cause and Effect - Probability, p.133).Of course, many sensible scientists and philosophers were not so easily con-vinced to abandon the mission of explaining and understanding laws of nature,for they knew full well how important causal reasoning can be in the process ofapplying these laws to real problems in their fields of expertise, in conceivingnew scientific hypotheses or theories, in implementing new experiments or re-search projects, etc. Lord Arthur James Balfour (1894, 1902) was among thosetotally unconvinced by K.Pearson’s anti-metaphysical arguments. K.Pearson(1897) answers to lord Balfour are very illuminating. Once more, the adver-sarial style used in this disputation makes it clear how committed he is infollowing his path of Inverted-Spinozism.
Mr. Balfour speaks contemptuously of those who regard the Universe asa “mere collection of hypostatised sense-perceptions packed side by side in arl Pearson, Spinoza & Causal Understanding space and following each other with blind uniformity in time.” He wants“ideas of wider sweep and richer content”, and considers that the workof Science would be beneath contempt if it only provided a machinery bywhich the re-occurrence of feelings and ideas might be adequately accountedfor.
Pearson (ChD, p.195).
It does not matter whether it be Spinoza with his Infinite Substance, orKant with his Dinge-an-sich, or the naturalist with his molecule, or thetheologian with his personal God – one and all can tell us nothing of thereal mode of action of his idolum specus . Pearson (ChD, p.193).
The physicist, who projects his concepts into the unknowable beyondsense-impression, is as unphilosophical and as dogmatic as the metaphysi-cian or theologian.
Pearson (ChD, p.202).If the product of scientific research shall never be projected outside theconceiving Ego, if science can not go beyond accommodations between distinctproperties of the perceiving, reasoning and conceiving Ego, what shall be thepurpose of science? According to K.Pearson, the purpose of science is purelydescriptive. This descriptive function encompasses past and future observa-tions, that is, this role of description includes prediction, and this must be thesole motivation of scientific research. This point is made unequivocally clearin K.Pearson essay answering Balfour objections: ...how is Science related to the phenomenal world? Simply as provid-ing comprehensive descriptive formula – so-called laws – summed up in aconceptual model which more or less completely figures past and rehearsesfuture experience. The symbols of Science are not “things in themselves,”nor are they perceptions – nay, as a rule, they do not even stand as equiv-alents for concrete and actual phenomena.
Pearson (ChD, p.203). [T]he mission of Science is not to explain but to describe; to discover adescriptive formula which will enable men to predict the nature of futureperceptions; such descriptive formulae are, in the only consistent sense ofthe word, knowledge, they form that “economy of thought”, which is thename happily devised by a philosophical physicist to describe and defineScience.
Pearson (ChD, p.200).This last conclusion can be taken as the net result of K.Pearson’s approachto philosophy of science. The role played by descriptive/ predictive formulasin science offers, on one hand, a touchstone for validation criteria and, on theother hand, avoids any metaphysical involvements and complications. This isK.Pearson’s key to open the realm of epistemology. K.Pearson’s motivations36
Julio Michael Stern in the philosophy of Spinoza and Fichte are today almost forgotten. Never-theless, the descriptive/ predictive approach to scientific hypotheses gainedwide acceptance, being developed over the first four decades of the XX centuryinto the philosophical basis for the Frequentist school of statistics. In latteryears, K.Pearson himself gave little emphasis to his early undertakings in Tran-scendental Idealism. Instead, he concentrated his efforts to advance the morepragmatical thesis of description/ prediction as the ultimate goal of scientifichypotheses, and to construct (Frequentist) Statistics as a language designedas a tool commissioned to best achieve this goal. The last quotation of thissection, stated and restated by K.Pearson in his last years, is typical of thispragmatic approach:
The Laws of Nature are only constructs of our minds; none of them canbe asserted to be true or to be false, they are good in so far as they givegood fits to our observations of Nature, and are liable to be replaced by abetter ‘fit’...
Pearson (1935) as quoted in Inman (1994, p.6).For K.Pearson, Goodness-of-fit, and nothing else, becomes the ultimate cri-terion of good science, a criterion that motivates and directs the developmentof Frequentist statistics. In contrast, according to K.Pearson, causal reasoning,laws of nature and their explanation, and similar efforts for metaphysical un-derstanding have no legitimate role to play in the development of contemporaryscience, see Section 4 for further comments.
Auguste Comte (1798-1857) had a multifaceted life and personality, and sois his philosophical work and legacy, see Lacerda (2009), Manuel (1962) andScharff (1995). As mentioned in the introduction, nowadays many text-booksin statistics present K.Pearson’s philosophy as akin to Positivism. K.Pearson’sown opinion was quite different: On one hand, he gave Comte the merit ofindicating the vanity of causal reasoning but, on the other hand, he contendedComte was never able to completely break away from metaphysical forms ofthinking. In K.Pearson’s candid evaluation of the historical influence and im-portance of Comte’s philosophical ideas: ...the writings of Comte have at the very least acted as a stimulus – if onlyof the irritant kind –
Pearson (1911; The Grammar of Science, p.570).As in previous sections, I use K.Pearson’s adversarial arguments to high-light and clarify his full commitment to his Inverted-Spinozism. For K.Pearson,Comte relapses into metaphysics in (at least) two crucial occasions, namely, arl Pearson, Spinoza & Causal Understanding
Religion of Humanity ; and (b) the
Scala Intellectus schema for classi-fication of scientific disciplines.(a) The Religion of Humanity is an enterprise of Comte’s late life, onlymarginally successful in Comte’s native France and some other countries. To-day the Religion of Humanity has in Rio de Janeiro and Porto Alegre, Brasil,its last working temples, see Lins (1967) and Valentin (2010). Comte’s reli-gious enterprise got him in trouble with many of his own followers, and wasdisregarded without further consideration by later versions of Positivism, in-cluding the prestigious Logical Positivism movement of the Wiener Kreis. ForK.Pearson, the Religion of Humanity was not only incompatible with his anti-metaphysical principles, but also did not sit well with his moral and politicalideals. – we act morally, that is, socially. Positivism has recognised in a vagueimpracticable fashion this, the only possible basis of a rational morality;it places the progress of mankind in the centre of its creed, and veneratesa personified Humanity.
Pearson (1901; The Moral Basis of Socialism,p.303).(b) K.Pearson’s objections to Comte’s
Scala Intellectus or staircase of theintellect schema for classification of scientific disciplines is far more importantfor the purposes of this paper. In this schema, reminiscent of the Jacob’sLadder studied in Stern (2017), scientific disciplines are ranked according toa progressive order of complexity of their fields of interest, each being indis-pensable for the study of the next one in ascending order. Specific disciplinesare ranked at a seven-step-ladder, starting from mathematics and progressingto astronomy, physics, chemistry, biology, sociology, and ethics. According toPearson (1892, 1911; The Grammar of Science, The Classification of Sciences,p.592):
From Comte [we learn] that there is in reality an interdependence in thesciences, so that a clear understanding of one may necessitate a previousstudy of several others.
For K.Pearson, this “interdependence in the sciences” must be unaccept-able, for it implicitly opens the door for causality relations, even if in concealedforms or in indirect ways, between the objects of study of the distinct disci-plines, following the very same links according to which these disciplines arehierarchically chained into a great chain of being. Furthermore, only gettingrid of Comte’s artificial hierarchy, can K.Pearson allow and justify crafting ofgood-fitting descriptive formulae for phenomena of interest of a given disci-pline to be a task that can and should be accomplished without recourse to38
Julio Michael Stern concepts of lower ranking disciplines in the same hierarchy. Therefore, it is easyto understand his conclusion stated in Pearson (1892, 1911; The Grammar ofScience, The Classification of Sciences, p.570):
It is clear that we have in Comte’s staircase of the intellect [scala intellec-tus] a purely fanciful scheme, which, like the rest of his System of PositivePolity, is worthless from the standpoint of modern science.
Finally, it is worth mentioning that, as it should be expected, also in thetopic at hand (concerning causal chains of being) we find K.Pearson’s Inverted-Spinozism standing diametrically opposed to the philosophy of Spinoza. Thiscontrast is made clear in Pearson (1901, Ethics of Renunciation, p.84):
In his [Spinoza] system, God, we have seen, is identified with the realityof things, not things regarded as phenomena, but as links in an infinitechain of intellectual causality. He is the λ o γ o ς which dwells in and is allexistence; ‘laws of nature’ are only the sensuous expression of the laws ofthe divine intellect; the story of the world is only the phenomenalising ofthe successive steps in the logic of pure thought. This and previous sections’ main goal was to understand key aspects ofK.Pearson’s philosophical studies, starting from Spinoza and his medieval pre-cursors, and ending at a Fichtean type of Inverted-Spinozism. Furthermore,some consequences of K.Pearson’s particular version of Inverted-Spinozismhave been highlighted by comparison and contrast with views and ideas ofother thinkers, like Friedrich Jacobi, Friedrich von Schelling, Paul Volkmannand Auguste Comte.
This section gives a brief overview of K.Pearson work in science, from thetime of his spiritual crisis and its subsequent philosophical solution to the endof his life. K.Pearson’s work in science and philosophy proper lost nowadaysmost of its prestige and influence. Nevertheless, this section is intended as abridge, providing historical and logical links for the next section, dedicated toK.Pearson subsequent work in developing the methods and language of classical or frequentist statistics . Nowadays, statistical science provides the standardaccepted tools for hypothesis testing and validation, providing in this sense apragmatic logic for scientific inference. Therefore, it is important to analyzeand understand how the language of classical statistics continues to propagateK.Pearson’s epistemological ideas, even if some of its underlying philosophicalprinciples are now discredited, outdated or just forgotten. arl Pearson, Spinoza & Causal Understanding In a series of papers from 1884 to 1891, K.Pearson develops some researchtopics in the area of Ether Physics. Today this area of research is all butforgotten, being only of historical interest, see Schaffner (1972) and Whittaker(1953). However, during the XIX century, Ether or Aether physics was animportant field of study, and a main battle ground between the proponents ofatomic or molecular theories and their antagonists. One of the main goals ofEther physics was to replace physical theories explained by effects caused byhypothetical atomic or molecular entities by purely phenomenological modelsbased on the hydrodynamic or elastic properties of an imponderable mediumcalled Ether.K.Pearson sees the Atom as an archetypical agent of causality. For exam-ple, at physics intra-murus, atoms are agents of causality linking the realmof classical mechanics to that of thermodynamics, the causal link itself beingexplained and understood via the tools of statistical physics. Extra-murus,atoms and molecules are agents of causality linking the discipline of physicsto that of chemistry, justifying a link in the great chain of being of AugusteComte’s hierarchical schema of
Scala Intellectus . Therefore, K.Pearson’s mo-tivations and commitment to the development of Ether Physics are easy tounderstand. Notice that although modern statistical physics was developed inthe XX century, atomic models explaining thermodynamic effects are as old asRobert Boyle’s (1627-1691) volume-temperature law of gases, see Brush (1983),Needham (2004), Newman (1996, 2006) and Rosenfeld (1953).Unfortunately for K.Pearson, the whole subject of Ether Physics was atthat time already loosing prestige, until it came to an abrupt end in the
Annusmirabilis of 1905, the year of Albert Einstein’s papers in
Annalen der Physik concerning Special Relativity, the photoelectric effect and Brownian motion.The autopsy of Ether physics reveals two causes for its sudden death: On onehand, Einstein’s papers on Special Relativity replace Galileo’s transformationsby Lorentz transformations as the fundamental invariance group of physicaltheory, see Stern (2011) and references therein. This elegant substitution solvesand explains with astonishing simplicity a host of problems that the Etherphysics program was for many decades unsuccessfully trying to circumventusing always more complex and cumbersome phenomenological models. On theother hand, Einstein’s papers concerning the photoelectric effect and Brownianmotion, with the support of subsequent experimental work by Jean Perrin(1908, 1911) and Robert Millikan (1914, 1916), gave sufficient reasons for theoverwhelming majority of the scientific community to abandon Ether modelsin favor of atomic or molecular theories, for further details and references seeStern (2014, 2017).40
Julio Michael Stern
In the early twentieth century, the Grammar was understood by many,including by Pearson himself, as a philosophical rationale for statistics,though in fact he took up statistics only after completing its first edition[1892]. Thereafter, right to the end of his life, Pearson would make it hismission to reshape science using the tools of statistical mathematics. From1893 to about 1905 he published a series of papers that gave a new directionto the field of statistics. In 1901 he founded, in collaboration with FrancisGalton and W.F.R. Weldon, the journal Biometrika, which was dedicatedto this project.
Porter (2004, p7,8)The short quotation opening this subsection describes the chronology ofa transition period of K.Person’s career. On one hand, his
The Grammar ofScience became a resounding success. Far from the romantic and mysticalstyle of
The New Werther , and avoiding the most peculiar eccentricities ofTranscendental Idealism, this book was written to present his epistemologicalideas to the working scientist. On the other hand, the scientific research projecthe had chosen to show-case his philosophy, Ether physics, was a completefailure. Therefore, at this point in time, K.Pearson desperately needed a newresearch project that could be used to demonstrate the usefulness of his ideas,and could also provide a refuge for himself as a working scientist.K.Pearson was able to find a safe harbor in the fields of biometry, heredityand evolution biology. In 1891 he starts to collaborate with the zoologist WalterFrank Raphael Weldon (1860-1906), who soon introduces him to Francis Galton(1822-1911) – from then on K.Pearson’s great protector, benefactor and rolemodel in life. A common interest of these scientists was to study the inheritanceof measurable characteristics in biological populations. How to best approachthis problem was at that time a matter of great controversy, concerning theexistence (or not) and the role played by “genes” – (hypothetical) corpusculacarrying elementary units of genetic information and/or causing the inheritanceof specific characteristics.On one hand, the role played by genes in biology is, from an epistemologicalpoint of view, quite similar to the role played by atoms in physics or moleculesin chemistry. On the other hand, the chronologies of acceptance of the “molec-ular hypothesis” in physics and chemistry, and the “genetic hypothesis” inbiology are quite different. Indirect evidence for the inheritance of discretegenes controlling specific characteristics of biological organisms was availablesince the work of Gregor Johann Mendel (1822-1884). However, Mendel (1865)work, done in seclusion at a Moravian monastery, was completely forgotten un-til his hypotheses postulating discrete genetic coding units were rediscoveredby Hugo de Vries (1901, 1903). Even so, the nature of these (at that time arl Pearson, Spinoza & Causal Understanding correlationcoefficients and linear regression models. For historical accounts, see Cowan(1972), Fancher (1989), Gorroochurn (2016a,b) and Kevles (1985). Galtondeveloped these techniques in order to study the simplest non-deterministicconnections between cause and effect, namely, connections that are normallydistributed, linear and unidirectional. For his satisfaction, Galton ascertainsthat such linear models produce a very good fit to his populational data banks.Nevertheless, for his great surprise, Galton finds the same linear models to beapplicable either forwards or backwards in time, contradicting his concepts oftemporal unidirectionality for cause and effect. Galton also realizes that, bothconceptually and mathematically, such a system could be conceived as drivenentirely by a Gaussian stochastic process, with no need to an additional forceor agency causing the system to drift into a preset direction. Consequently,Galton felt the need for a paradigm shift – abandoning genetic causal theoriesin favor of non-causal and phenomenological statistical models for biologicalheredity.It is at this juncture that Galton and K.Pearson start their work together.Each man had gone trough a crisis of his own, from which they emerged readyto make the same sacrifice: Renouncing the bride. After a conceptual crisis,both men were committed to build up a science that is purely descriptive-predictive in nature and strictly non-metaphysical, with no place for causalentities or explanations.K.Pearson was a talented mathematician and, when the time came, he wasready to help Galton and make progress in the development of mathematicalstatistics. K.Pearson was also a skilful (and sometimes ruthless) administratorof human resources. In time, he would regiment many bright minds to workfor the cause (no pun intended), always running a tight ship and keeping asteady course in pursuit of his and Galton’s basic programmatic goals. Thenext quotation, from 1896, presents K.Pearson’s pledge of allegiance to joinforces with Galton. The main objective of following articles will be to showhow the Frequentist school of mathematical statistics developed its means andmethods so that they were tailor made to perfectly suit the aforementionedprogrammatic goals.42
Julio Michael Stern
A considerable portion of the present memoir will be devoted to the ex-pansion and fuller development of Mr. Galton’s ideas, particularly theirapplication to the problem of bi-parental inheritance. ... The causes inany individual case of inheritance are far too complex to admit of exacttreatment; and up to the present the classification of the circumstancesunder which greater or less degrees of correlation between special groups ofparents and offspring may be expected has made but little progress. This islargely owing to a certain prevalence of almost metaphysical speculation asto the causes of heredity, which has usurped the place of that careful col-lection and elaborate experiment by which alone sufficient data might havebeen accumulated, with a view to ultimately narrowing and specializing thecircumstances under which correlation was measured. We must proceedfrom inheritance in the mass to inheritance in narrower and narrowerclasses, rather than attempt to build up general rules on the observation ofindividual instances. Shortly, we must proceed by the method of statistics,rather than by the consideration of typical cases.
Person (1896, p.255).MCTE
One of the traditional goals and most exalted accomplishments of science is togive mankind understanding about the world, to provide deep insights on howit works, or some intuition on why it is the way it is. Not for K.Pearson: Hisconception of science is strictly phenomenological, its only goal being accuratedescription and prediction of sense-impressions. But if not for wisdom andunderstanding, what is science worth?
I am afraid I am a scientific heretic – an outcast from the true orthodoxfaith – I do not believe in science for its own sake. I believe only inscience for man’s sake. ... The first condition for State support is that we[anthropologists] show our science to be utile by turning to the problemsof racial efficiency, of race-psychology, and to all those tasks that Galtondescribed as the first duty of a nation – ‘in short, to make every individualefficient both through Nature and by Nurture.’
K.Pearson (1920, pp.136,148)Pearson’s conception of science is utilitarian to the core. In the case of hisscientific programs in biometry and heredity, the intended use was eugenics:
The term National Eugenics is here defined as the study of the agenciesunder social control that may improve or impair the racial qualities offuture generations either physically or mentally.
K.Pearson (1930, p.222). arl Pearson, Spinoza & Causal Understanding
Heredity: Given any organ in a parent and the same or any other organin its offspring, the mathematical measure of heredity is the correlationof these organs for pairs of parent and offspring. The word organ heremust be taken to include any characteristic which can be quantitativelymeasured. If tile organs are not those of parent and offspring, but of anytwo individuals with a given degree of blood relationship, the correlation ofthe two organs will still be the proper measure of the strength of heredityfor the given degree of relationship.
Pearson (1896b p.259).K.Pearson’s strictly phenomenological and uninhibitedly utilitarian viewof science may have been one of the contributing factors that lead him topledge his support to most unscrupulous political projects, like in the followingquotation from a speech from 1934 delivered at University College, London.Pearson died two years later, in 1936. Had he lived a few years longer, hemay have recognized in this political project the hand of Mephistopheles – thescatterer and forgerer of lies – the fictional author of The New Werther, thebook of romantic dreams of his youth.
The Royal Society Council having passed a resolution that mathematicsand biology should not be mixed, Biometrika was founded with Galton asconsultant and Weldon and myself as joint editors. Buccaneer expeditionsin too many fields followed; fights took place on many seas, but whether wehad right or wrong, whether we lost or won, we did produce some effect.The climax culminated in Galton’s preaching of Eugenics and his founda-tion of the Eugenics Professorship. Did I say ‘culmination’ ? No, that liesrather in the future, perhaps with
Reichskanzler
Hitler and his proposals toregenerate the German people. In Germany a vast experiment is in hand,and some of you may live to see its results. If it fails it will not be for wantof enthusiasm, but rather because the Germans are only just starting the Julio Michael Stern study of mathematical statistics in the modern sense!
K.Pearson (1934,p.23), also quoted in Senn (2003, p.144, 238).
The main objective of this section is to indicate how K.Pearson’s philosophyultimately engenders the epistemological foundations of classical or frequentiststatistics (XX century mainstream school), strongly influences the evolution ofthe theoretical framework of statistical science in general (directly for the fre-quentist school, and indirectly for the Bayesian school), and imposes implicitguide-lines for the development of well-conforming operational methods andmodels. Moreover, the language and dialects developed by these statisticalschools were specifically designed to facilitate the acceptance of K.Pearson’sphilosophical principles in the practice of science, and to induce “epistemolog-ically correct” forms of expression and communication in scientific research.Although many of K.Pearson’s philosophical and scientific ideas are nowconsidered obsolete or discredited, the language of classical statistics, craftedby him and his co-workers, not only survives but thrives up to the present days.Since the second half of the XX century, statistical significance measures (fol-lowing the nomenclature of frequentist statistics) became the accepted standardby which scientific hypotheses must be judged. Therefore, we can understandhow K.Pearson’s philosophy ultimately spreads its influence far and wide, evenif rigorous philosophical principles got diluted along the way, hence exertingtheir influence in subtle, sometimes almost subliminal forms. Indeed, on onehand, mainstream contemporary statistics clearly upholds the descriptive/ pre-dictive and non-explanatory nature of statistical models in particular and ofscience in general while, on the other hand, downplays the historical origins andepistemological foundations of the same philosophy, rooted in K.Pearson’s ver-sion of Inverted-Spinozism. In the language of statistics, K.Pearson’s Inverted-Spinozism is translated as deprecation of inverse-probabilities, as explained inthe following paragraphs.Statistical models distinguish two classes of variables, namely: On onehand, there are variables in the sample-space. These variables are associatedwith observable phenomena, quantities of interest to which we assign directprobabilities. On the other hand, there are variables in the parameter-space.These variables are associated with latent or non-observable quantities thatoften correspond to hidden causes of the observed phenomena. The most basiclearning mechanism in statistical models, Bayes rule , is a formula used toupdate inverse probabilities according to newly available observations. arl Pearson, Spinoza & Causal Understanding
An Essay towards solving aproblem in the Doctrine of Chances , published at The Philosophical Transac-tions of the Royal Society in 1763. In this article, the ideas of the Presbyterianminister Rev. Thomas Bayes (1701-1761) were communicated posthumouslyby Rev. Richard Price (1723-1791), nominated by Bayes as his literary execu-tor. The motivations for Bayes work are clearly stated in his work, see nextquotation. At the time, the expression inverse-probability was not yet in use,instead, since parameters often stand for hidden causes for observed phenom-ena, the expression probabilities of causes was commonly used, see Fienberg(2006).
The purpose, is to shew [show] what reason we have for believing thatthere are in the constitution of things, fixed laws according to which eventshappen, and that, therefore, the frame of the world must be the effect ofthe wisdom and power of an intelligent cause; and thus to confirm theargument taken from final causes for the existence of the Deity [...and...]it will be easy to see that the problem solved in this essay is more directlyapplicable to this purpose; for it shews [shows] us, with distinctness andprecision, in every case of any particular order or recurrency of events,what reason there is to think that such recurrency or order is derived fromstable causes or regulations in nature, and not from any of the irregularitiesof chance.
Bayes (1763), as quoted in Barker (2001, p.84).Reading Bayes explanations, as presented by Price, is seems that theirresearch perfectly conforms to the Spinozian program of cognitione causae etleges naturae universales . In subsequent generations, probabilists like Pierre-Simon de Laplace (1749-1827) and George Boole (1815-1864) champion theefforts for modeling causal relations and computing probabilities of possiblecauses, developing the mathematical techniques needed to build and formallypresent the first workable statistical models. As explained in Sections 2, 3 and4, this course of development was turned around by the work of K.Pearson.Methodologically, the frequentist school can be characterized by allowingthe use of direct probability statements, that is, by considering observablesas random variables, while strictly forbidding inverse probability statements,that is, by never considering random variables in the parameter-space. The Fre-quentist school’s deprecation of inverse-probabilities is a 180 ◦ turn, a completereversal of a long-standing tradition in the history of probability and statis-tics, for inverse probability methods had been developed by leading figures ofpreceding generations, like Bayes, Laplace and Boole.The most powerful weapon K.Pearson developed for fighting his anti-metaphysicalwar was a new language, the language of the frequentist school (nowadays alsoknows as the classic school) of mathematical statistics. In this development46 Julio Michael Stern effort, K.Pearson had to fight in internal and external fronts. Externally, hehad to promote “classical” statistics as the language of choice for the analysisand validation of scientific research. Internally, he had to battle heresies insidethe statistical community, and assure the crafting of a language that is con-ducive of orthodox thinking, expressing arguments that are, by construction,free of metaphysical contamination. These battles are the primary focus offorthcoming articles, as further explained in the next section.
In this section present some final comments, propose some additional topicsfor further research, and give due acknowledgments.Spinoza, Bayes, Price, Comte, Boole and K.Pearson, all allowed their reli-gious believes to inspire their philosophical or epistemological principles that,in turn, directly motivated their scientific work and ideas. The study of his-torical interfaces and influences between science and religion seems to havegone out of fashion, with scientists and academic philosophers and theologiansoften in accordance about the necessity to separate their domains of study,an isolation effort intended to protect each specialty from possible harmfulinterference. The topics discussed in the present article and in Stern (2017)make me seriously doubt the viability and validity of artificially imposing suchhermetic seals. Further research in the following topics should help to claritythis position.
Following articles will show how K.Pearson an his coworkers cast the languageof mathematical statistics in order to enforce the tacit acceptance and practicaluse of his philosophical and epistemological ideas. Several key choices in theconstruction of modern statistics can not be explained solely by logical prop-erties and mathematical requirements. Instead, these key choices can onlybe understood as reflecting epistemological principles based on K.Pearson’sinverted-spinozism, even if at the expense of developing a formalism with feweror weaker functionalities and inconsistent logical properties, see Borges andStern (2007), Esteves et al. (2016), Madruga (2001), Pereira et al. (2008),Stern (2017, 2018), Stern and Pereira (2014), and Stern et al. (2017). More-over, following articles will show how K.Pearson managed to be very successfulin his campaign, using the language of frequentist statistics to promote andconsolidate the acceptance not only of his statistical methodologies, but alsoof his underlying (but far less advertized) philosophical principles. arl Pearson, Spinoza & Causal Understanding
Later versions of the Positivist movement, known as Logical Positivism, Em-pirical Positivism or Logical Empiricism, were developed under the influenceof the Wiener Kreis from 1907 to 1938, and subsequently around the world.These neopositivist programs abandon the goal of becoming all encompassingsystems of philosophy, taken instead a more pragmatic approach, concentrat-ing their efforts into specific epistemological questions and the development ofmathematical logic as a tool to support their research program.Rudolf Carnap (1932) stated as a main goal of the neopositivist programto be –
The Elimination of Metaphysics Through Logical Analysis of Language .Meanwhile, K.Pearson and his school were developing Frequentist statistics asa tool for building up a science free of metaphysics. This is a far more ambitiousand radical proposal since statistics, as conceived by K.Pearson, is not a tooldesigned to analyze science as it is and circumvent its metaphysical problems,but a tool designed for actually making scientific research in such a way thatscience becomes, by construction, free of metaphysics.I have the impression that the two approaches, based on their respectivesupporting languages, namely, mathematical logic and mathematical statistics,had the potential of greatly benefiting from each other. However, the interac-tion between researchers of the two groups and their mutual influence seems tohave been rather small. Nevertheless, in the second part of the XX century, sci-ence practitioners and writers of didactic textbooks have often confused ideascoming from neopositivism and Frequentist statistics, carelessly overlappingtopics that would require more careful treatment. I believe that confirmingthese first impressions and trying to understand these parallel courses of his-torical development are topics that deserve future research.
The author is grateful for the support of IME-USP – the Institute of Math-ematics and Statistics of the University of S˜ao Paulo; FAPESP – the Stateof S˜ao Paulo Research Foundation (grants CEPID 2013/07375-0 and CEPID2014/50279-4); and CNPq – the Brazilian National Counsel of Technologicaland Scientific Development (grants PQ 301206/2011-2 and PQ 301892/2015-6). Finally, the author is grateful for advice and comments concerning the firstversion of this paper received from Rafael Bassi Stern, Rabbi Ruben Stern-schein, Jean-Yves B´eziau, from anonymous referees, from participants of the2nd World Congress on Logic and Religion, held on June 18-22, 2017, at War-saw, Poland, and from participants of the X Principia International Sympo-sium, held on August 14-17, 2017, at Florian´opolis, Brazil.48
Julio Michael Stern
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Julio Michael SternInstitute of Mathematics and Statistics of the University of S˜ao Paulo.Rua do Mat˜ao 1010, CEP 05508-090, S˜ao Paulo, Brazil.