Socratic principle

**''...Thus the density of the nebular distribution increases outwards, symmetrically in all directions, leaving the observer in a unique position. '''Such a favoured position, of course, is intolerable'''; moreover, it represents '''a discrepancy with the theory''', because the theory postulates homogeneity. Therefore, in order to restore homogeneity, and to escape '''the horror of a unique position'''{{#tag:ref|Similar embarrassment known from history of science, or philosophy, respectively, and related to [[vacuum]], was articulated by the famous expression ''"[[horror vacui]]."''|group=note}}, the departures from uniformity, which are introduced by the recession factors, must be compensated by the second term representing effects of spatial curvature.''**''...Thus the density of the nebular distribution increases outwards, symmetrically in all directions, leaving the observer in a unique position. '''Such a favoured position, of course, is intolerable'''; moreover, it represents '''a discrepancy with the theory''', because the theory postulates homogeneity. Therefore, in order to restore homogeneity, and to escape '''the horror of a unique position'''{{#tag:ref|Similar embarrassment known from history of science, or philosophy, respectively, and related to [[vacuum]], was articulated by the famous expression ''"[[horror vacui]]."''|group=note}}, the departures from uniformity, which are introduced by the recession factors, must be compensated by the second term representing effects of spatial curvature.''- Although not explicitly mentioning the Socratic principle, [[Richard Feynman]] effectually comments that the reluctance to adopt it and an effort to replace it with [[prejudice]] in case of a so called unique position of [[Earth]] in the [[universe]] stems barely from [[embarrassment]] and not [[exact sciences|scientific rigor]] (emphasis added): ''"I suspect that '''the assumption of uniformity''' of the universe reflects a [[prejudice]] born of a sequence of overthrows of [[geocentric]] ideas...It would be embarrassing to find, after stating that we live in an ordinary [[planet]] about an ordinary [[star]] in an ordinary [[galaxy]], that our place in the universe is extraordinary...to avoid embarrassment we cling to the hypothesis of uniformity"''{{cite book |title=Feynman Lectures on Gravitation |author=Richard Phillips Feynman et al. |publisher=Westview Press |year=2002 |page=166 |isbn=978-0813-340388 |url=http://books.google.com/books?id=jL9reHGIcMgC&dq=Feynman+lectures+on+gravitation&source=bl&ots=_nuGcNOn2_&sig=VyTgUmNcfeCOiwisdwoTEgKK9og&hl=en&sa=X&ei=gaYyUMHwIcfP4QTm5YD4Ag&redir_esc=y}}. Slovak mathematician Adam Roman maintains that scientists should base their research on starting point where except verifiable [[fact]]s no biased ''[[a priori]]'' assumptions are made. Furthermore, scientists should bear the [[burden of proof]] in any case of [[reductionism|reducing]] the set of [[explanation in science|explanatory]] possibilities. Narrowing down options requires [[Scientific evidence|proof]] from one who argues that this narrowing (such as ''"the theory postulates homogeneity"''; ''a favoured position...is intolerable''; ''"we cling to the hypothesis of uniformity"'') should take place.{{cite web |title=Kto má pravdu dokazovat? (Who should bear the burden of proof)|author=Adam Roman|date=November 1, 2001|accessdate=June 7, 2013|url=http://adam.humanisti.sk/?p=31|language=Slovak|quote=Ludia pravdu iba zistujú a dokazujú (ak sa im to darí). Isteže, pri objavení neocakávanej pravdy je bremeno dôkazu na nich: ked donedávna ani len nevedeli, co je pravda, a teraz to zistili, s radostou to oznámia celému svetu. Vedci k objavenej pravde radi pripoja aj dôkaz, aby im druhí rozumeli (a uverili, lenže to je už druhoradé: ak rozumieme, môžeme verit). Ten, kto novú, doteraz nepoznanú pravdu objavil, ju rád a bez mucenia aj dokáže. ...Z toho všetkého už zacína citatel tušit, kto je povinný pravdu dokazovat: každý, kto ju odhalil, vychádzajúc z predpokladov, ktoré okrem každým overitelných faktov nic a priori nepredpokladali.  ...A máme tu druhé kritérium pre to, kto má znášat bremeno dôkazu: ten, kto tvrdí, že sa deje jedna z mnohých (apriórne rovnako pravdepodobných!) možností. Ak by niekto tvrdil, že mu pri hode kockou vypadne stále císlo šest, tvrdil by, že sa uskutocní iba jedna zo šiestich možností a mal by preto dokázat, preco akurát vypadne jedno císlo a nikdy nie ostatných pät. Pochopili ste? Zúženie možností si vyžaduje dôkaz od toho, kto tvrdí, že k tomu zúženiu dôjde. Ten, kto tvrdí, že môže vypadnút hocaké císlo, nic dokazovat nemusí, lebo jeho tvrdenie nezavrhuje žiadne možnosti. Napríklad Pytagorova veta sa dokazuje preto, lebo tvrdí, že súcet plôch štvorcov nad odvesnami nie je hocaká plocha, ale akurát plocha štvorca nad preponou. Pytagorova veta, ako každé slušné matematické tvrdenie, zužuje apriórne možnosti, a preto sa musí dokázat. Každé pravdivé tvrdenie je zaujímavé práve preto, že zužuje možnosti. Poznávanie sveta stojí na tom, že vieme co nie je možné. Pre malé dieta je možné všetko, svet (rozumného) dospelého je už chudobnejší na možnosti.}} An [[argument]] where ''a priori'' assumptions (cf. "a... must be avoided at all costs... Therefore, we accept ..., and assume that ...") are masquerading as [[proof|evidence]] for making [[conclusion]]s (''"the universe must be pretty much alike everywhere and in all directions"'') is in effect a form of [[circular reasoning]].{{cite book+ Although not explicitly mentioning the Socratic principle, [[Richard Feynman]] effectually comments that the reluctance to adopt it and an effort to replace it with [[prejudice]] in case of a so called unique position of [[Earth]] in the [[universe]] stems barely from [[embarrassment]] and not [[exact sciences|scientific rigor]] (emphasis added): ''"I suspect that '''the assumption of uniformity''' of the universe reflects a [[prejudice]] born of a sequence of overthrows of [[geocentric]] ideas...It would be embarrassing to find, after stating that we live in an ordinary [[planet]] about an ordinary [[star]] in an ordinary [[galaxy]], that our place in the universe is extraordinary{{#tag:ref|cf. ''"Most advocates do not defend their theses out of conviction that they are true, but rather because they once declared them to be true."'' (Georg Christoph Lichtenberg){{cite book |title=Lexikon der populären Irrtümer: 500 kapitale Mißverständnisse, Vorurteile und Denkfehler von Abendrot bis Zeppelin Piper|author=Walter Krämer, Götz Trenkler|publisher=Piper Verlag GmbH |year=1998|page=258|isbn= 9783492224468 |url=http://www.amazon.de/Lexikon-popul%C3%A4ren-Irrt%C3%BCmer-Walter-Kr%C3%A4mer/dp/3492224466/ref=sr_1_1?ie=UTF8&qid=1370885779&sr=8-1&keywords=Walter+Kr%C3%A4mer+Lexikon+der+popul%C3%A4ren+Irrt%C3%BCmer|language=German}}|group=note}}...to avoid embarrassment we cling to the hypothesis of uniformity"''{{cite book |title=Feynman Lectures on Gravitation |author=Richard Phillips Feynman et al. |publisher=Westview Press |year=2002 |page=166 |isbn=978-0813-340388 |url=http://books.google.com/books?id=jL9reHGIcMgC&dq=Feynman+lectures+on+gravitation&source=bl&ots=_nuGcNOn2_&sig=VyTgUmNcfeCOiwisdwoTEgKK9og&hl=en&sa=X&ei=gaYyUMHwIcfP4QTm5YD4Ag&redir_esc=y}}. Slovak mathematician Adam Roman maintains that scientists should base their research on starting point where except verifiable [[fact]]s no biased ''[[a priori]]'' assumptions are made. Furthermore, scientists should bear the [[burden of proof]] in any case of [[reductionism|reducing]] the set of [[explanation in science|explanatory]] possibilities. Narrowing down options requires [[Scientific evidence|proof]] from one who argues that this narrowing (such as ''"the theory postulates homogeneity"''; ''a favoured position...is intolerable''; ''"we cling to the hypothesis of uniformity"'') should take place.{{cite web |title=Kto má pravdu dokazovat? (Who should bear the burden of proof)|author=Adam Roman|date=November 1, 2001|accessdate=June 7, 2013|url=http://adam.humanisti.sk/?p=31|language=Slovak|quote=Ludia pravdu iba zistujú a dokazujú (ak sa im to darí). Isteže, pri objavení neocakávanej pravdy je bremeno dôkazu na nich: ked donedávna ani len nevedeli, co je pravda, a teraz to zistili, s radostou to oznámia celému svetu. Vedci k objavenej pravde radi pripoja aj dôkaz, aby im druhí rozumeli (a uverili, lenže to je už druhoradé: ak rozumieme, môžeme verit). Ten, kto novú, doteraz nepoznanú pravdu objavil, ju rád a bez mucenia aj dokáže. ...Z toho všetkého už zacína citatel tušit, kto je povinný pravdu dokazovat: každý, kto ju odhalil, vychádzajúc z predpokladov, ktoré okrem každým overitelných faktov nic a priori nepredpokladali.  ...A máme tu druhé kritérium pre to, kto má znášat bremeno dôkazu: ten, kto tvrdí, že sa deje jedna z mnohých (apriórne rovnako pravdepodobných!) možností. Ak by niekto tvrdil, že mu pri hode kockou vypadne stále císlo šest, tvrdil by, že sa uskutocní iba jedna zo šiestich možností a mal by preto dokázat, preco akurát vypadne jedno císlo a nikdy nie ostatných pät. Pochopili ste? Zúženie možností si vyžaduje dôkaz od toho, kto tvrdí, že k tomu zúženiu dôjde. Ten, kto tvrdí, že môže vypadnút hocaké císlo, nic dokazovat nemusí, lebo jeho tvrdenie nezavrhuje žiadne možnosti. Napríklad Pytagorova veta sa dokazuje preto, lebo tvrdí, že súcet plôch štvorcov nad odvesnami nie je hocaká plocha, ale akurát plocha štvorca nad preponou. Pytagorova veta, ako každé slušné matematické tvrdenie, zužuje apriórne možnosti, a preto sa musí dokázat. Každé pravdivé tvrdenie je zaujímavé práve preto, že zužuje možnosti. Poznávanie sveta stojí na tom, že vieme co nie je možné. Pre malé dieta je možné všetko, svet (rozumného) dospelého je už chudobnejší na možnosti.}} An [[argument]] where ''a priori'' assumptions (cf. "a... must be avoided at all costs... Therefore, we accept ..., and assume that ...") are masquerading as [[proof|evidence]] for making [[conclusion]]s (''"the universe must be pretty much alike everywhere and in all directions"'') is in effect a form of [[circular reasoning]].{{cite book

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