{"id":2289,"date":"2016-03-01T00:00:22","date_gmt":"2016-02-29T22:00:22","guid":{"rendered":"http:\/\/le-bars.net\/yoann\/?p=2289"},"modified":"2017-05-08T00:14:43","modified_gmt":"2017-05-07T22:14:43","slug":"william-had-a-good-razor","status":"publish","type":"post","link":"https:\/\/le-bars.net\/yoann\/en\/2016\/03\/01\/william-had-a-good-razor\/","title":{"rendered":"William had a good razor!"},"content":{"rendered":"<figure style=\"width: 400px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:William_of_Ockham_-_Logica_1341.jpg\" title=\"The picture on Wikimedia\u00a0Commons\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/a\/ab\/William_of_Ockham_-_Logica_1341.jpg\" width=\"400\" height=\"373\" alt=\"Guillaume d\u2019Ockham\" class \/><\/a><figcaption class=\"wp-caption-text\">William of Ockham, sketch from manuscript <em>Summa Logicae<\/em> (William\u00a0of\u00a0Ockham, 1323) \u2013 public domain image <em>via<\/em> <a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:William_of_Ockham_-_Logica_1341.jpg\" title=\"The picture on Wikimedia\u00a0Commons\" target=\"_blank\">Wikimedia\u00a0Commons<\/a>.<\/figcaption><\/figure>\n<p>The law of parsimony \u2013 sometimes called Ockham\u2019s razor after the English Franciscan monk <a href=\"https:\/\/en.wikipedia.org\/wiki\/William_of_Ockham\" title=\"William\u00a0of\u00a0Ockham\" target=\"_blank\">William\u00a0of\u00a0Ockham<\/a> (circa 1285 \u2013 1347), a pioneer in logic \u2013 is a principle common to philosophy and science. In fact, it has been stated before, the oldest occurrence that I have found is due to <a href=\"https:\/\/en.wikipedia.org\/wiki\/Aristotle\" title=\"Aristotle\" target=\"_blank\">Aristotle<\/a><span class=\"footnote_referrer\"><a role=\"button\" tabindex=\"0\" onclick=\"footnote_moveToReference_2289_1('footnote_plugin_reference_2289_1_1');\" onkeypress=\"footnote_moveToReference_2289_1('footnote_plugin_reference_2289_1_1');\" ><sup id=\"footnote_plugin_tooltip_2289_1_1\" class=\"footnote_plugin_tooltip_text\">1<\/sup><\/a><span id=\"footnote_plugin_tooltip_text_2289_1_1\" class=\"footnote_tooltip\">\u1f08\u03c1\u03b9\u03c3\u03c4\u03bf\u03c4\u03ad\u03bb\u03b7\u03c2, \u03a6\u03c5\u03c3\u03b9\u03ba\u1f74 \u1f00\u03ba\u03c1\u03cc\u03b1\u03c3\u03b9\u03c2. <a href=\"http:\/\/www.isnature.org\/Files\/Aristotle\/Bekker_Physics.pdf\" title=\"Physics\" target=\"_blank\">Available on-line<\/a>. An English translation by Robin\u00a0Waterfield: David\u00a0Bostock (editor), 1999. <em>Physics<\/em>, Oxford University Press. <a href=\"http:\/\/classics.mit.edu\/\/Aristotle\/physics.html\" title=\"Physics\" target=\"_blank\">Available on-line<\/a>.<\/span><\/span><script type=\"text\/javascript\"> jQuery('#footnote_plugin_tooltip_2289_1_1').tooltip({ tip: '#footnote_plugin_tooltip_text_2289_1_1', tipClass: 'footnote_tooltip', effect: 'fade', predelay: 0, fadeInSpeed: 200, delay: 400, fadeOutSpeed: 200, position: 'top right', relative: true, offset: [10, 10], });<\/script> (384 \u2013 322 BC), who attributes it to <a href=\"https:\/\/en.wikipedia.org\/wiki\/Empedocles\" title=\"Empedocles\" target=\"_blank\">Empedocles<\/a> (circa 490 \u2013 about 435 BC). However, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Proclus\" title=\"Proclus\" target=\"_blank\">Proclus<\/a> (412\u00a0AD \u2013 485) traces it back to <a href=\"https:\/\/en.wikipedia.org\/wiki\/Pythagoras\" title=\"Pythagoras\" target=\"_blank\">Pythagoras<\/a> (about 580 \u2013 about 495 BC)<span class=\"footnote_referrer\"><a role=\"button\" tabindex=\"0\" onclick=\"footnote_moveToReference_2289_1('footnote_plugin_reference_2289_1_2');\" onkeypress=\"footnote_moveToReference_2289_1('footnote_plugin_reference_2289_1_2');\" ><sup id=\"footnote_plugin_tooltip_2289_1_2\" class=\"footnote_plugin_tooltip_text\">2<\/sup><\/a><span id=\"footnote_plugin_tooltip_text_2289_1_2\" class=\"footnote_tooltip\">The only version I know of the work in question is this German edition, which appears to be considered the reference: Manitius, C. (\u00e9ditor et translator), 1909. Procli Diadochi hypotyposis astronomicarum positionum (Bibliotheca scriptorum Graecorum et Romanorum Teubneriana), Teubner, Leipzig. Reprinted in 1974: Teubner, Stuttgart.<\/span><\/span><script type=\"text\/javascript\"> jQuery('#footnote_plugin_tooltip_2289_1_2').tooltip({ tip: '#footnote_plugin_tooltip_text_2289_1_2', tipClass: 'footnote_tooltip', effect: 'fade', predelay: 0, fadeInSpeed: 200, delay: 400, fadeOutSpeed: 200, position: 'top right', relative: true, offset: [10, 10], });<\/script>.<\/p>\n<p>This principle is not always well understood, as it is sometimes used in a manner denoting a misunderstanding about what it actually means. I propose you to see a brief history of this law before commenting on what it means. This article is therefore one of <a href=\"http:\/\/le-bars.net\/yoann\/en\/2015\/08\/20\/how-i-extended-galileos-work\/\" title=\"How I extended Galileo\u2019s work\">the series on history of science and popularisation<\/a> I started <a href=\"http:\/\/le-bars.net\/yoann\/en\/2015\/09\/15\/everything-is-relative-my-dear-bruno\/\" title=\"Everything is relative, my dear Bruno!\">with a view from here<\/a>.<\/p>\n<p>No, I have not yet specified what states this law. This is a barely honest process that aims to create an almost unbearable suspense to make you captive of my prose, so that you will read this whole article. However, do not worry: the explanation comes in a few lines!<\/p>\n<p><!--more--><\/p>\n<h2>Ockham\u2019s razor has been sharpened before William of Ockham<\/h2>\n<p>As noted above, the first mention of this law that I found is due to Aristotle. Here is how he expressed it in the first volume of his Physics, 4, 188a17:<\/p>\n<blockquote><p>\u2018You should used fewer principles and in a limited number, as does Empedocles.\u2019<\/p><\/blockquote>\n<p>The law of parsimony is sometimes summed up as indicating that between two equivalent explanations you should select the simplest one. Note that as early as Aristotle\u2019s times, this is not how it is presented. Aristotle does not invite us to look for the simplest explanation, but not to multiply the \u201cprinciples.\u201d Still, it is necessary to clarify what he means when using the word \u201cprinciple.\u201d<\/p>\n<p>To explain a phenomenon, whatever it is, one uses a variety of mechanisms. Take for example the falling bodies \u2013 I take this example as it is in <a href=\"http:\/\/le-bars.net\/yoann\/en\/2017\/04\/04\/falling-bodies-galileo-sets-up-aristotle-to-the-fall\/\" title=\"Falling bodies: Galileo sets up Aristotle to the fall\">the next article on history of science on this website<\/a>. For Aristotle, whose model of the World <a href=\"http:\/\/le-bars.net\/yoann\/en\/2015\/09\/15\/everything-is-relative-my-dear-bruno\/\" title=\"Everything is relative, my dear Bruno!\">I have already presented<\/a>, the natural motion of bodies made of element earth or water is orientated downward, while the speed depends on the ability of the body to cleave the element air, which capacity depends on the weight and body shape. To explain the phenomenon of falling bodies, Aristotle therefore uses several mechanisms, which he calls \u201cprinciple\u201d: the mechanism of natural movement of elements, the ability to cleave the element air, the weight and the body shape. The law of parsimony, as expressed here, invites us not to multiply mechanisms when explaining a given phenomenon.<\/p>\n<p>This principle will be integrated in <a href=\"https:\/\/en.wikipedia.org\/wiki\/Scholasticism\" title=\"Scholaticism\" target=\"_blank\">scholasticism<\/a> and therefore in Christian thinking. It is found for example in <a href=\"https:\/\/en.wikipedia.org\/wiki\/Thomas_Aquinas\" title=\"Thomas\u00a0Aquinas\" target=\"_blank\">Thomas\u00a0Aquinas<\/a> (1225 \u2013 1274)<span class=\"footnote_referrer\"><a role=\"button\" tabindex=\"0\" onclick=\"footnote_moveToReference_2289_1('footnote_plugin_reference_2289_1_3');\" onkeypress=\"footnote_moveToReference_2289_1('footnote_plugin_reference_2289_1_3');\" ><sup id=\"footnote_plugin_tooltip_2289_1_3\" class=\"footnote_plugin_tooltip_text\">3<\/sup><\/a><span id=\"footnote_plugin_tooltip_text_2289_1_3\" class=\"footnote_tooltip\">Thomas de Aquino, 1265 \u2013 1274. Summa theologi\u00e6. <a href=\"http:\/\/www.corpusthomisticum.org\/sth0000.html\" title=\"Summa theologi\u00e6\" target=\"_blank\">Available on-line<\/a>. An English translation: Thomas Aquinas, 1981. Summa Theologica, Christian Classics. <a href=\"http:\/\/www.intratext.com\/IXT\/ENG0023\/\" title=\"Summa Theologica\" target=\"_blank\">Available on-line<\/a>.<\/span><\/span><script type=\"text\/javascript\"> jQuery('#footnote_plugin_tooltip_2289_1_3').tooltip({ tip: '#footnote_plugin_tooltip_text_2289_1_3', tipClass: 'footnote_tooltip', effect: 'fade', predelay: 0, fadeInSpeed: 200, delay: 400, fadeOutSpeed: 200, position: 'top right', relative: true, offset: [10, 10], });<\/script>. In the Summa Theologica, part I, Q. 2, art. 3, obj. 2, the law of parsimony is stated as follows:<\/p>\n<blockquote><p>\u2018[\u2026] quod potest compleri per pauciora principia, non fit per plura.\u2019<\/p><\/blockquote>\n<p>It can be translated into \u2018what can be accomplished by principles in small numbers is not done by many more principles.\u2019 Again, the idea is not to multiply mechanisms to explain a phenomenon.<\/p>\n<p>However, the most famous formulation of this law is due to William\u00a0of\u00a0Ockham. He stated it several times, the first that I could identify is in Book II of Quaestiones et decisiones in quatuor libros Sententiarum cum centilogio theologico<span class=\"footnote_referrer\"><a role=\"button\" tabindex=\"0\" onclick=\"footnote_moveToReference_2289_1('footnote_plugin_reference_2289_1_4');\" onkeypress=\"footnote_moveToReference_2289_1('footnote_plugin_reference_2289_1_4');\" ><sup id=\"footnote_plugin_tooltip_2289_1_4\" class=\"footnote_plugin_tooltip_text\">4<\/sup><\/a><span id=\"footnote_plugin_tooltip_text_2289_1_4\" class=\"footnote_tooltip\">Gulielmus Occamus, 1319. Quaestiones et decisiones in quatuor libros Sententiarum cum centilogio theologico<\/span><\/span><script type=\"text\/javascript\"> jQuery('#footnote_plugin_tooltip_2289_1_4').tooltip({ tip: '#footnote_plugin_tooltip_text_2289_1_4', tipClass: 'footnote_tooltip', effect: 'fade', predelay: 0, fadeInSpeed: 200, delay: 400, fadeOutSpeed: 200, position: 'top right', relative: true, offset: [10, 10], });<\/script>:<\/p>\n<blockquote><p>\u2018Pluralitas non est ponenda sine necessitate.\u2019<\/p><\/blockquote>\n<p>Which can be translated as \u2018a plurality should not be put with no necessity.\u2019 Again, the idea is not to multiply hypotheses if it is possible to avoid such a multiplication.<\/p>\n<p>Note that the expression \u201cOckham\u2019s razor\u201d is not due to William\u00a0of\u00a0Ockham. The earliest mention of this law under this name that I could find comes from <a href=\"https:\/\/en.wikipedia.org\/wiki\/Sir_William_Hamilton,_9th_Baronet\" title=\"William\u00a0Hamilton\" target=\"_blank\">William\u00a0Hamilton<\/a> (1788 \u2013 1856)<span class=\"footnote_referrer\"><a role=\"button\" tabindex=\"0\" onclick=\"footnote_moveToReference_2289_1('footnote_plugin_reference_2289_1_5');\" onkeypress=\"footnote_moveToReference_2289_1('footnote_plugin_reference_2289_1_5');\" ><sup id=\"footnote_plugin_tooltip_2289_1_5\" class=\"footnote_plugin_tooltip_text\">5<\/sup><\/a><span id=\"footnote_plugin_tooltip_text_2289_1_5\" class=\"footnote_tooltip\">William\u00a0Hamilton, 1852. Discussion in Philosophy, Literature and Education, Longman, Brown, Green and Longmans, Londres.<\/span><\/span><script type=\"text\/javascript\"> jQuery('#footnote_plugin_tooltip_2289_1_5').tooltip({ tip: '#footnote_plugin_tooltip_text_2289_1_5', tipClass: 'footnote_tooltip', effect: 'fade', predelay: 0, fadeInSpeed: 200, delay: 400, fadeOutSpeed: 200, position: 'top right', relative: true, offset: [10, 10], });<\/script>.<\/p>\n<p>The purpose of this article is not to produce an exhaustive list of all the times this law has been formulated: it would be particularly daunting, I am not sure this is possible and it would not be very useful. Simply note that it has been reiterated both in philosophy and science. One of the latest formulations of the parsimony law comes from statistical algorithmic. This formulation is due to <a href=\"https:\/\/en.wikipedia.org\/wiki\/Ray_Solomonoff\" title=\"Ray\u00a0Solomonoff\" target=\"_blank\">Ray\u00a0Solomonoff<\/a> (1926 \u2013 2009) in the form of inductive inference theory<span class=\"footnote_referrer\"><a role=\"button\" tabindex=\"0\" onclick=\"footnote_moveToReference_2289_1('footnote_plugin_reference_2289_1_6');\" onkeypress=\"footnote_moveToReference_2289_1('footnote_plugin_reference_2289_1_6');\" ><sup id=\"footnote_plugin_tooltip_2289_1_6\" class=\"footnote_plugin_tooltip_text\">6<\/sup><\/a><span id=\"footnote_plugin_tooltip_text_2289_1_6\" class=\"footnote_tooltip\">Ray\u00a0Solomonoff, 1964. A Formal Theory of Inductive Inference Part I, Information and Control 7 (1), pp. 1 \u2013 22. <span style=\"font-variant: small-caps;\">Doi<\/span>: <a href=\"https:\/\/dx.doi.org\/10.1016%2FS0019-9958%2864%2990223-2\" title=\"A Formal Theory of Inductive Inference Part I\" target=\"_blank\">10.1016\/S0019-9958(64)90223-2<\/a>.<\/span><\/span><script type=\"text\/javascript\"> jQuery('#footnote_plugin_tooltip_2289_1_6').tooltip({ tip: '#footnote_plugin_tooltip_text_2289_1_6', tipClass: 'footnote_tooltip', effect: 'fade', predelay: 0, fadeInSpeed: 200, delay: 400, fadeOutSpeed: 200, position: 'top right', relative: true, offset: [10, 10], });<\/script>\u202f<span class=\"footnote_referrer\"><a role=\"button\" tabindex=\"0\" onclick=\"footnote_moveToReference_2289_1('footnote_plugin_reference_2289_1_7');\" onkeypress=\"footnote_moveToReference_2289_1('footnote_plugin_reference_2289_1_7');\" ><sup id=\"footnote_plugin_tooltip_2289_1_7\" class=\"footnote_plugin_tooltip_text\">7<\/sup><\/a><span id=\"footnote_plugin_tooltip_text_2289_1_7\" class=\"footnote_tooltip\">Ray\u00a0Solomonoff, 1964. A Formal Theory of Inductive Inference Part II, Information and Control 7 (2), pp. 224 \u2013 254. <span style=\"font-variant: small-caps;\">Doi<\/span>: <a href=\"https:\/\/dx.doi.org\/10.1016%2FS0019-9958%2864%2990131-7\" title=\"A Formal Theory of Inductive Inference Part II\" target=\"_blank\">10.1016\/S0019-9958(64)90131-7<\/a>.<\/span><\/span><script type=\"text\/javascript\"> jQuery('#footnote_plugin_tooltip_2289_1_7').tooltip({ tip: '#footnote_plugin_tooltip_text_2289_1_7', tipClass: 'footnote_tooltip', effect: 'fade', predelay: 0, fadeInSpeed: 200, delay: 400, fadeOutSpeed: 200, position: 'top right', relative: true, offset: [10, 10], });<\/script>. In this context, among all the explanations describing the observations perfectly, those requiring fewer computations are provided with a stronger weight. The inductive inference is used in artificial intelligence, specifically in machine learning.<\/p>\n<h2>Let us use our razor without cutting ourselves!<\/h2>\n<p>As we have just seen, the law of parsimony has been stated and successfully used several times in history. It invites us, you guessed it, to use parsimony in (not to multiply) assumptions and mechanisms we invoke to explain a phenomenon. Thus, among many explanations of a given phenomenon, provided they are all as satisfactory \u2013 therefore, an explanation not describing accurately the phenomenon should be eliminated \u2013, the one requiring the fewest assumptions should be favoured. For example, <a href=\"http:\/\/le-bars.net\/yoann\/en\/2015\/09\/15\/everything-is-relative-my-dear-bruno\/\" title=\"Everything is relative, my dear Bruno!\">in my article on the principle of relativity<\/a>, we saw <a href=\"https:\/\/en.wikipedia.org\/wiki\/Nicolaus_Copernicus\" title=\"Nicolaus\u00a0Copernicus\" target=\"_blank\">Nicolaus\u00a0Copernicus<\/a> has noted that the heliocentric system matched better the law of parsimony that the geocentric one.<\/p>\n<p>Using it should therefore limit the use of undocumented assumptions, which is a way to strengthen the coherence of an explanation to the phenomena it intends to enlighten. Indeed, adding assumptions that have not been validated by observations increases the risk that one or more of the assumptions underlying the explanation is not consistent with the facts to which it relates. Conversely, with a minimum of undocumented assumptions, the explanation is less likely to be invalidated.<\/p>\n<p><P>However, the use of this law also has some pitfalls that one needs to avoid.<\/p>\n<p>First, be wary of assumptions that actually hide some other complex assumptions. For example, once it has been established that the light behave like a wave, since all waves hitherto observed were propagated in a medium, it has been postulated that light was spreading in what was then called the luminiferous aether<span class=\"footnote_referrer\"><a role=\"button\" tabindex=\"0\" onclick=\"footnote_moveToReference_2289_1('footnote_plugin_reference_2289_1_8');\" onkeypress=\"footnote_moveToReference_2289_1('footnote_plugin_reference_2289_1_8');\" ><sup id=\"footnote_plugin_tooltip_2289_1_8\" class=\"footnote_plugin_tooltip_text\">8<\/sup><\/a><span id=\"footnote_plugin_tooltip_text_2289_1_8\" class=\"footnote_tooltip\">The earliest foreshadowing of what will become the luminiferous aether that I could find comes from: Isaac\u00a0Newton, 1704. Opticks: or, a treatise of the reflexions, refractions, inflexions and colours of light, Royal Society, Londres. It has been republished several times, for instance: Isaac\u00a0Newton, 1998. Opticks: or, a treatise of the reflexions, refractions, inflexions and colours of light. Also two treatises of the species and magnitude of curvilinear figures, Octavo, Palo Alto, California.<\/span><\/span><script type=\"text\/javascript\"> jQuery('#footnote_plugin_tooltip_2289_1_8').tooltip({ tip: '#footnote_plugin_tooltip_text_2289_1_8', tipClass: 'footnote_tooltip', effect: 'fade', predelay: 0, fadeInSpeed: 200, delay: 400, fadeOutSpeed: 200, position: 'top right', relative: true, offset: [10, 10], });<\/script>.<\/p>\n<p>However, it turned out that the luminiferous aether should have had very special properties. In particular, in order to transmit light from distant stars, it would have to be almost infinitely stiff, but it also had to show no resistance to objects motions. Ultimately, this aether was a complex hypothesis. Thus, when proposing the theory of special relativity, Albert\u00a0Einstein notices, among other things, that luminiferous aether poses more problems than it solves and draws the conclusion that light travels in emptiness<span class=\"footnote_referrer\"><a role=\"button\" tabindex=\"0\" onclick=\"footnote_moveToReference_2289_1('footnote_plugin_reference_2289_1_9');\" onkeypress=\"footnote_moveToReference_2289_1('footnote_plugin_reference_2289_1_9');\" ><sup id=\"footnote_plugin_tooltip_2289_1_9\" class=\"footnote_plugin_tooltip_text\">9<\/sup><\/a><span id=\"footnote_plugin_tooltip_text_2289_1_9\" class=\"footnote_tooltip\">Albert\u00a0Einstein, 1905. Zur Elektrodynamik bewegter K\u00f6rper, Annalen der Physik, n\u00b0\u00a017, pp. 891 \u2013 921. <a href=\"http:\/\/users.physik.fu-berlin.de\/~kleinert\/files\/1905_17_891-921.pdf\" title=\"Zur Elektrodynamik bewegter K\u00f6rper\" target=\"_blank\">It can be read on-line.<\/a> An English version translated by George\u00a0Barker\u00a0Jeffery <a href=\"http:\/\/www.fourmilab.ch\/etexts\/einstein\/specrel\/www\/\" title=\"On The Electrodynamics of Moving Bodies\" target=\"_blank\">is available on-line<\/a>.<\/span><\/span><script type=\"text\/javascript\"> jQuery('#footnote_plugin_tooltip_2289_1_9').tooltip({ tip: '#footnote_plugin_tooltip_text_2289_1_9', tipClass: 'footnote_tooltip', effect: 'fade', predelay: 0, fadeInSpeed: 200, delay: 400, fadeOutSpeed: 200, position: 'top right', relative: true, offset: [10, 10], });<\/script>. Rather, the middle of light propagation is emptiness, as recent advances in physics, especially in quantum physics, invite us to reconsider the notion of emptiness \u2013 I will not develop this any further here, but tell me in comments if you are interested in me to write an article on this subject. Finally, not to use luminiferous aether induced fewer assumptions, even if no other wave propagating in emptiness had been observed at the time.<\/p>\n<p>One should also be wary of explanations that explain nothing. Indicating that bodies fall because of God\u2019s will \u2013 the purpose of this article is not to discuss whether there is a god, it is here considered as an explanation of phenomena \u2013, besides that the divine hypothesis is a complex one, so complex that, in the introduction to the Summa Theologica, Thomas Aquinas made the observation that there is no positive definition of God, it actually gives no explanation: it is equivalent to say that things are what they are because that is the way the world works. Whether God exists or not, the fact remains that it does not clarify the phenomenon and gives nothing to make some previsions.<\/p>\n<p>The great virtue of the law of parsimony is to help avoid ad\u00a0hoc hypotheses. An ad\u00a0hoc hypothesis is an assumption that is added to a theory to be able to use it in spite it has been refuted. For example, it is clear that there is no evidence showing the existence of <a href=\"https:\/\/en.wikipedia.org\/wiki\/Leprechaun\" title=\"Leprechaun\" target=\"_blank\">leprechauns<\/a>, some fairy from the Irish folklore. To continue to defend the existence of leprechauns, simply add the ad\u00a0hoc assumption that, particularly shy, they are very careful not to be noticed and that, moreover, they are invisible. By dint of ad hoc assumptions, we obtain leprechauns who have neither form nor smell, who are invisible and inaudible, who interact with nothing, leave no trace, are undetectable, but who nevertheless exist\u00a0\u2026<\/p>\n<p>Of course, few people are likely to defend at all costs the existence of leprechauns. In fact, it is one of the reasons I have chosen this example, as it is very unlikely anyone will blame me having indicated leprechauns does not exist. However, the use of ad\u00a0hoc hypotheses is common when someone sees an explanation she\/he cares about to be rebutted, and it can sometimes be difficult to identify these hypotheses. In this context, I think it is useful to remember that being wrong is never something serious if one is ready to acknowledge and correct errors. It does not question someone existence and, as, among other things, this series on history of science try to illustrate, the brightest minds had been wrong at one time or another. The law of parsimony is not always easy to use, but it can help.<\/p>\n<div class=\"speaker-mute footnotes_reference_container\"> <div class=\"footnote_container_prepare\"><p><span role=\"button\" tabindex=\"0\" class=\"footnote_reference_container_label pointer\" onclick=\"footnote_expand_collapse_reference_container_2289_1();\">Notes<\/span><span role=\"button\" tabindex=\"0\" class=\"footnote_reference_container_collapse_button\" style=\"display: none;\" onclick=\"footnote_expand_collapse_reference_container_2289_1();\">[<a id=\"footnote_reference_container_collapse_button_2289_1\">+<\/a>]<\/span><\/p><\/div> <div id=\"footnote_references_container_2289_1\" style=\"\"><table class=\"footnotes_table footnote-reference-container\"><caption class=\"accessibility\">Notes<\/caption> <tbody> \r\n\r\n<tr class=\"footnotes_plugin_reference_row\"> <th scope=\"row\" class=\"footnote_plugin_index_combi pointer\"  onclick=\"footnote_moveToAnchor_2289_1('footnote_plugin_tooltip_2289_1_1');\"><a id=\"footnote_plugin_reference_2289_1_1\" class=\"footnote_backlink\"><span class=\"footnote_index_arrow\">&#8593;<\/span>1<\/a><\/th> <td class=\"footnote_plugin_text\">\u1f08\u03c1\u03b9\u03c3\u03c4\u03bf\u03c4\u03ad\u03bb\u03b7\u03c2, \u03a6\u03c5\u03c3\u03b9\u03ba\u1f74 \u1f00\u03ba\u03c1\u03cc\u03b1\u03c3\u03b9\u03c2. <a href=\"http:\/\/www.isnature.org\/Files\/Aristotle\/Bekker_Physics.pdf\" title=\"Physics\" target=\"_blank\">Available on-line<\/a>. An English translation by Robin\u00a0Waterfield: David\u00a0Bostock (editor), 1999. <em>Physics<\/em>, Oxford University Press. <a href=\"http:\/\/classics.mit.edu\/\/Aristotle\/physics.html\" title=\"Physics\" target=\"_blank\">Available on-line<\/a>.<\/td><\/tr>\r\n\r\n<tr class=\"footnotes_plugin_reference_row\"> <th scope=\"row\" class=\"footnote_plugin_index_combi pointer\"  onclick=\"footnote_moveToAnchor_2289_1('footnote_plugin_tooltip_2289_1_2');\"><a id=\"footnote_plugin_reference_2289_1_2\" class=\"footnote_backlink\"><span class=\"footnote_index_arrow\">&#8593;<\/span>2<\/a><\/th> <td class=\"footnote_plugin_text\">The only version I know of the work in question is this German edition, which appears to be considered the reference: Manitius, C. (\u00e9ditor et translator), 1909. Procli Diadochi hypotyposis astronomicarum positionum (Bibliotheca scriptorum Graecorum et Romanorum Teubneriana), Teubner, Leipzig. Reprinted in 1974: Teubner, Stuttgart.<\/td><\/tr>\r\n\r\n<tr class=\"footnotes_plugin_reference_row\"> <th scope=\"row\" class=\"footnote_plugin_index_combi pointer\"  onclick=\"footnote_moveToAnchor_2289_1('footnote_plugin_tooltip_2289_1_3');\"><a id=\"footnote_plugin_reference_2289_1_3\" class=\"footnote_backlink\"><span class=\"footnote_index_arrow\">&#8593;<\/span>3<\/a><\/th> <td class=\"footnote_plugin_text\">Thomas de Aquino, 1265 \u2013 1274. Summa theologi\u00e6. <a href=\"http:\/\/www.corpusthomisticum.org\/sth0000.html\" title=\"Summa theologi\u00e6\" target=\"_blank\">Available on-line<\/a>. An English translation: Thomas Aquinas, 1981. Summa Theologica, Christian Classics. <a href=\"http:\/\/www.intratext.com\/IXT\/ENG0023\/\" title=\"Summa Theologica\" target=\"_blank\">Available on-line<\/a>.<\/td><\/tr>\r\n\r\n<tr class=\"footnotes_plugin_reference_row\"> <th scope=\"row\" class=\"footnote_plugin_index_combi pointer\"  onclick=\"footnote_moveToAnchor_2289_1('footnote_plugin_tooltip_2289_1_4');\"><a id=\"footnote_plugin_reference_2289_1_4\" class=\"footnote_backlink\"><span class=\"footnote_index_arrow\">&#8593;<\/span>4<\/a><\/th> <td class=\"footnote_plugin_text\">Gulielmus Occamus, 1319. Quaestiones et decisiones in quatuor libros Sententiarum cum centilogio theologico<\/td><\/tr>\r\n\r\n<tr class=\"footnotes_plugin_reference_row\"> <th scope=\"row\" class=\"footnote_plugin_index_combi pointer\"  onclick=\"footnote_moveToAnchor_2289_1('footnote_plugin_tooltip_2289_1_5');\"><a id=\"footnote_plugin_reference_2289_1_5\" class=\"footnote_backlink\"><span class=\"footnote_index_arrow\">&#8593;<\/span>5<\/a><\/th> <td class=\"footnote_plugin_text\">William\u00a0Hamilton, 1852. Discussion in Philosophy, Literature and Education, Longman, Brown, Green and Longmans, Londres.<\/td><\/tr>\r\n\r\n<tr class=\"footnotes_plugin_reference_row\"> <th scope=\"row\" class=\"footnote_plugin_index_combi pointer\"  onclick=\"footnote_moveToAnchor_2289_1('footnote_plugin_tooltip_2289_1_6');\"><a id=\"footnote_plugin_reference_2289_1_6\" class=\"footnote_backlink\"><span class=\"footnote_index_arrow\">&#8593;<\/span>6<\/a><\/th> <td class=\"footnote_plugin_text\">Ray\u00a0Solomonoff, 1964. A Formal Theory of Inductive Inference Part I, Information and Control 7 (1), pp. 1 \u2013 22. <span style=\"font-variant: small-caps;\">Doi<\/span>: <a href=\"https:\/\/dx.doi.org\/10.1016%2FS0019-9958%2864%2990223-2\" title=\"A Formal Theory of Inductive Inference Part I\" target=\"_blank\">10.1016\/S0019-9958(64)90223-2<\/a>.<\/td><\/tr>\r\n\r\n<tr class=\"footnotes_plugin_reference_row\"> <th scope=\"row\" class=\"footnote_plugin_index_combi pointer\"  onclick=\"footnote_moveToAnchor_2289_1('footnote_plugin_tooltip_2289_1_7');\"><a id=\"footnote_plugin_reference_2289_1_7\" class=\"footnote_backlink\"><span class=\"footnote_index_arrow\">&#8593;<\/span>7<\/a><\/th> <td class=\"footnote_plugin_text\">Ray\u00a0Solomonoff, 1964. A Formal Theory of Inductive Inference Part II, Information and Control 7 (2), pp. 224 \u2013 254. <span style=\"font-variant: small-caps;\">Doi<\/span>: <a href=\"https:\/\/dx.doi.org\/10.1016%2FS0019-9958%2864%2990131-7\" title=\"A Formal Theory of Inductive Inference Part II\" target=\"_blank\">10.1016\/S0019-9958(64)90131-7<\/a>.<\/td><\/tr>\r\n\r\n<tr class=\"footnotes_plugin_reference_row\"> <th scope=\"row\" class=\"footnote_plugin_index_combi pointer\"  onclick=\"footnote_moveToAnchor_2289_1('footnote_plugin_tooltip_2289_1_8');\"><a id=\"footnote_plugin_reference_2289_1_8\" class=\"footnote_backlink\"><span class=\"footnote_index_arrow\">&#8593;<\/span>8<\/a><\/th> <td class=\"footnote_plugin_text\">The earliest foreshadowing of what will become the luminiferous aether that I could find comes from: Isaac\u00a0Newton, 1704. Opticks: or, a treatise of the reflexions, refractions, inflexions and colours of light, Royal Society, Londres. It has been republished several times, for instance: Isaac\u00a0Newton, 1998. Opticks: or, a treatise of the reflexions, refractions, inflexions and colours of light. Also two treatises of the species and magnitude of curvilinear figures, Octavo, Palo Alto, California.<\/td><\/tr>\r\n\r\n<tr class=\"footnotes_plugin_reference_row\"> <th scope=\"row\" class=\"footnote_plugin_index_combi pointer\"  onclick=\"footnote_moveToAnchor_2289_1('footnote_plugin_tooltip_2289_1_9');\"><a id=\"footnote_plugin_reference_2289_1_9\" class=\"footnote_backlink\"><span class=\"footnote_index_arrow\">&#8593;<\/span>9<\/a><\/th> <td class=\"footnote_plugin_text\">Albert\u00a0Einstein, 1905. Zur Elektrodynamik bewegter K\u00f6rper, Annalen der Physik, n\u00b0\u00a017, pp. 891 \u2013 921. <a href=\"http:\/\/users.physik.fu-berlin.de\/~kleinert\/files\/1905_17_891-921.pdf\" title=\"Zur Elektrodynamik bewegter K\u00f6rper\" target=\"_blank\">It can be read on-line.<\/a> An English version translated by George\u00a0Barker\u00a0Jeffery <a href=\"http:\/\/www.fourmilab.ch\/etexts\/einstein\/specrel\/www\/\" title=\"On The Electrodynamics of Moving Bodies\" target=\"_blank\">is available on-line<\/a>.<\/td><\/tr>\r\n\r\n <\/tbody> <\/table> <\/div><\/div><script type=\"text\/javascript\"> function footnote_expand_reference_container_2289_1() { jQuery('#footnote_references_container_2289_1').show(); jQuery('#footnote_reference_container_collapse_button_2289_1').text('\u2212'); } function footnote_collapse_reference_container_2289_1() { jQuery('#footnote_references_container_2289_1').hide(); jQuery('#footnote_reference_container_collapse_button_2289_1').text('+'); } function footnote_expand_collapse_reference_container_2289_1() { if (jQuery('#footnote_references_container_2289_1').is(':hidden')) { footnote_expand_reference_container_2289_1(); } else { footnote_collapse_reference_container_2289_1(); } } function footnote_moveToReference_2289_1(p_str_TargetID) { footnote_expand_reference_container_2289_1(); var l_obj_Target = jQuery('#' + p_str_TargetID); if (l_obj_Target.length) { jQuery( 'html, body' ).delay( 0 ); jQuery('html, body').animate({ scrollTop: l_obj_Target.offset().top - window.innerHeight * 0.2 }, 380); } } function footnote_moveToAnchor_2289_1(p_str_TargetID) { footnote_expand_reference_container_2289_1(); var l_obj_Target = jQuery('#' + p_str_TargetID); if (l_obj_Target.length) { jQuery( 'html, body' ).delay( 0 ); jQuery('html, body').animate({ scrollTop: l_obj_Target.offset().top - window.innerHeight * 0.2 }, 380); } }<\/script>","protected":false},"excerpt":{"rendered":"<p>The law of parsimony \u2013 sometimes called Ockham\u2019s razor after the English Franciscan monk William\u00a0of\u00a0Ockham (circa 1285 \u2013 1347), a pioneer in logic \u2013 is a principle common to philosophy and science. In fact, it has been stated before, the oldest occurrence that I have found is due to Aristotle1\u1f08\u03c1\u03b9\u03c3\u03c4\u03bf\u03c4\u03ad\u03bb\u03b7\u03c2, \u03a6\u03c5\u03c3\u03b9\u03ba\u1f74 \u1f00\u03ba\u03c1\u03cc\u03b1\u03c3\u03b9\u03c2. Available on-line. An &hellip; <a href=\"https:\/\/le-bars.net\/yoann\/en\/2016\/03\/01\/william-had-a-good-razor\/\" class=\"more-link\">Continuer la lecture de <span class=\"screen-reader-text\">William had a good razor!<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":true,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[29,50],"tags":[110,98,138,107,69],"class_list":["post-2289","post","type-post","status-publish","format-standard","hentry","category-culture-en","category-science-en","tag-culture","tag-history-of-sciences","tag-philosophy","tag-science-en","tag-scientific-popularisation"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>William had a good razor! - A vue from here<\/title>\n<meta name=\"description\" content=\"The law of parsimony, sometimes called Ockham\u2019s razor, is often used indiscriminately. 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