There is a commonly used device in literature that big, important events start small.\u00a0 I don\u2019t know if that\u2019s true.\u00a0 I don\u2019t know if small things are heralds of momentous things but I do know that I received a fairly big shock from a small, almost ignorable footnote in a book.<\/p>\n
I was reading through Theory and Problems in Logic<\/em>, by John Nolt and Dennis Rohatyn, when I discovered the deadly aside.\u00a0 But before I explain what surprised me so, let me say a few words about the work itself.\u00a0 This book, for those who don\u2019t know, is a Schaum\u2019s Outline.\u00a0 Despite that, it is actually a well-constructed outline on Logic.\u00a0 The explanations and examples are quite useful and the material is quite comprehensive.\u00a0 I think that the study of logic lends itself quite nicely to the whole approach of Schaum\u2019s since examples seem to be heart of learning logic and the central place where logicians tangle is over some controversial argument or curious sentence like \u2018this sentence is false\u2019.<\/p>\n As I was skimming Nolt and Rohatyn\u2019s discussion about how to evaluate arguments I came across this simple exercise<\/p>\n Tommy T. reads The Wall Street Journal<\/em> Their answer (which is the correct one) is that the argument above is not deductive.\u00a0 At the heart of their explanation for why it isn\u2019t deductive is the fact that while it is highly unlikely that anyone 3 months old or younger could read The Wall Street Journal<\/em>, nothing completely rules it out.\u00a0 Since the concept of probability enters into the argument, it cannot be deductive.<\/p>\n So far so good. \u00a0Of course, this is an elementary argument so I didn\u2019t expect any surprises.<\/p>\n Nolt and Rohaytn go on to say that this example can be made to be deductive by the inclusion of an additional premise.\u00a0 This is the standard fig-leaf of logicians, mathematicians, and, to a lesser extent, scientists the world over.\u00a0 If at first your argument doesn\u2019t succeed, redefine success by axiomatically ruling out all the stuff you don\u2019t like.\u00a0 Not that that approach is necessarily bad; it is a standard way of making problems more manageable but usually causes confusion in those not schooled in the art.<\/p>\n For their particular logical legerdemain, they amend the argument to read<\/p>\n This argument is now deductive because they refuse to allow the possibility (no matter how low in probability) that those amongst us who are 3 months old are younger cannot read The Wall Street Journal<\/em>. They elevate to metaphysical certitude the idea that youngsters such as they can\u2019t by simple pronouncement.<\/p>\n Again there are really no surprises here and this technique is a time honored one.\u00a0 It works pretty well when groping one\u2019s way through a physical theory where one may make a pronouncement that nature forbids or allows such and such, and then one looks for the logical consequences of such a pronouncement.\u00a0 But a caveat is in order.\u00a0 This approach is most applicable when a few variables have been identified and\/or isolated as being the major cause of the phenomenon that is being studied.\u00a0 Thus it works better the simpler the system under examination is.\u00a0 It is more applicable to the study of the electron than it is to the study of a molecule.\u00a0 It is more applicable to the study of the molecule than to an ensemble of molecules and so on.\u00a0 By the time we are attempting to apply it to really complex systems (like a 3-month old) its applicability is seriously in doubt.<\/p>\n Imagine then, my surprise by the innocent, little footnote associated with this exercise that reads<\/p>\n Note the language used by the pair of logicians.\u00a0 Not that the deductivism school of thought wants to minimize the use of inductive arguments or maximize the use of deductive ones.\u00a0 Not that its adherents want to limit the abuses that occur in inductive arguments.\u00a0 Nothing so cautious as that.\u00a0 Rather the blanket statement that \u201cthere are no genuine inductive arguments.\u201d<\/p>\n A few minutes of exploring on the internet led me to slightly deeper understanding of the school of deductivism but only marginally so.\u00a0 What could be meant by no genuine arguments?\u00a0 A bit more searching led me to some arguments due to Karl Popper (see the earlier column on Black Swan Science<\/a>).<\/p>\n These arguments, as excerpted from Popper\u2019s The Logic of Scientific Discovery<\/em><\/a>, roughly summarized, center on his uneasiness with inductive methods as applied to the empirical sciences.\u00a0 In his view, an inference is called inductive if it proceeds from singular statements to universal statements.\u00a0 As his example, we again see the black-swan\/white-swan discussion gliding to the front.\u00a0 His concern is for the \u2018problem of induction\u2019 defined as<\/p>\n Under his analysis, Popper finds that any \u2018principle of induction\u2019 that would solve the problem of induction is doomed to failure since it would necessarily be a synthetic statement, not an analytic one.\u00a0 From this observation, one would then need a \u2018meta principle of induction\u2019 to justify the principle of induction and a \u2018meta-meta principle of induction\u2019 to justify that one and so on, to an infinite regress.<\/p>\n Having established this initial work, Popper jumps into his argument for deductivism with the very definite statement<\/p>\n And off he goes. By the end, he has constructed an argument that banishes inductive logic from the scientific landscape, using what, in my opinion, amounts to a massive redefinition of terms.<\/p>\n I\u2019ll not try to present anymore of his argument.\u00a0 The interested reader can follow the link above and read the excerpt in its entirety.\u00a0 I would like to try to ask a related but, in my view, more human question.\u00a0 To what end is all this work leading?\u00a0 I recognize that it is important to understand how well a scientific theory is supported.\u00a0 It is also important to understand the limits of knowledge and logic.\u00a0 But surely, human understanding and knowledge are not limited by our scientific theories nor are they adequate described by formal logic.\u00a0 Somehow, human understanding is a balance between intuition and logic, between deduction and induction.<\/p>\n Popper\u2019s critiques sound too much like the sounds of someone obsessing over getting the thinking just so without stopping to ask if such a task is worth it.\u00a0 Scientific discovery happens without the practitioners knowing exactly how it happens and what to call each step.\u00a0 Should that be enough?<\/p>\n Of course, objectors to my point-of-view will be quick to point out all the missteps that logicians can see in the workings of science \u2013 all the black swans that fly in the face of a white-swan belief.\u00a0 My retort is simply \u201cso what?\u201d<\/p>\n Human existence is not governed solely by logic nor should it be.\u00a0 If it were, a part of the population would be frozen in indecision because terms were not defined properly, another part would be stuck in an infinite loop, and the last part would be angrily arguing with itself over the proper structure.\u00a0 There is a duality between induction and deduction that works for the human race \u2013 a time to generalize from the specific to the universal and a time to deduce from the universal to the specific.<\/p>\n Perhaps someday, someone will perfect deductivism in such a way so that scientific discovery can happen efficiently without all the drama and controversy and uncertainty.\u00a0 Maybe\u2026 but I doubt it.\u00a0 After all, we know that we humans aren\u2019t perfect \u2013 why should we expect one of our enterprises to be perfectible?<\/p>\n","protected":false},"excerpt":{"rendered":" There is a commonly used device in literature that big, important events start small.\u00a0 I don\u2019t know if that\u2019s true.\u00a0 I don\u2019t know if small things are heralds of momentous… Read more ><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-272","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=\/wp\/v2\/posts\/272","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=272"}],"version-history":[{"count":0,"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=\/wp\/v2\/posts\/272\/revisions"}],"wp:attachment":[{"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=272"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=272"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/aristotle2digital.blogwyrm.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=272"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n$\\therefore$ Tommy T. is over 3 months old.<\/p>\n
\nTommy T. reads The Wall Street Journal<\/em>
\n$\\therefore$ Tommy T. is over 3 months old.<\/p>\n