![\"\"](\"http:\/\/aristotle2digital.blogwyrm.com\/wp-content\/uploads\/2017\/10\/Spock-and-Android.png\")
<\/a><\/p>\nBut a curious aspect of Vulcans, in general, and Mr. Spock, in particular, is their illogical devotion to logic.\u00a0 Although the original show frequently emphasized that logic wasn\u2019t enough (often through the intuition or hunches of Kirk, McCoy, or Scott) and that the human experience transcends logic, there is no portrayal that the Vulcans ever examine the basis of logic.\u00a0 As a race, they never seem to engage in meta-logic, the logical look at the underpinnings of logic and an exploration of what it can do well and where it fails.<\/p>\n
Clearly this point is not the central concern for the show nor should it be.\u00a0 Nonetheless, it is fun to speculate what Spock might have done should the writers had known about the limits of logic.\u00a0 I\u2019m not speaking of something as sophisticated as the implications of G\u00f6del\u2019s theorem.\u00a0 Rather, I am talking about the simple and obvious issues associated with logic.\u00a0 The need for reasoning to be based on the finite knowledge of beings, the need for first principles or axioms, and the boot-strapping needed to go from a guess to a hypothesis to a theory with strong evidentiary support.\u00a0 In short, inductive reasoning.<\/p>\n
Induction is the key pillar of scientific advances; it is the method by which all knowledge of the physical world is explored and gathered.\u00a0 Induction is inherently probabilistic in the way it tries to link cause and effect (think of the number of times Kirk asked Spock for the odds that such-and-such a thing would happen) and has been remarkable successful in helping mankind grope its way to a better understanding of the physical world.\u00a0 But despite its success, its logical foundations are weak.<\/p>\n
A nice discussion about the issues associated with inductive reasoning is found in Chapter 5 of Introduction to Logic<\/em>, by Harry J. Gensler and I\u2019ve cited Gensler and his discussions in several posts in the past.<\/p>\n What struck me about the arguments found towards the end of Chapter 5 is the remarkably fragile way that the whole logical structure holds together when examined closely.\u00a0 In other words, logic examining logic finds itself disappointing in two areas \u2013 the proper formulation of induction principles and the justification for believing an inductive argument.<\/p>\n The element of probability inherent in induction can lead to some absurd and laughable conclusions.\u00a0 Gensler offers this statistical syllogism by way of illustration.<\/p>\n Of course, this is a nonsense argument; but before being quick to dismiss it consider these three areas where arguments like this are not easy to spot and can do damage.\u00a0 First is the student (at any age) who is learning a subject for the first time.\u00a0 Unless the entire curriculum is memorization, somewhere along the line the student will need to infer something based on the knowledge in hand.\u00a0 This step is usually where beginners make their mistakes \u2013 jumping to an unwarranted conclusion precisely because their induction skills (their intuition) haven\u2019t been honed within the broader context.\u00a0 This leads to frustration and, far to often, abandonment of the subject.\u00a0 Extending this idea to machine-based inference engines, ones whose intuition can\u2019t be improved through learning (at least not in the way humans learn), brings to the forefront the fact that the need for rigorous laws of inductive inference is far more acute.\u00a0 Even though it makes for engaging science fiction, we don\u2019t want a machine in our lives coming up with an absurd conclusion just because of sloppy rules.\u00a0 And finally, large components of society are constantly being grifted by arguments of the Cleveland-voter sort.\u00a0 We see it in politics, advertising, and all the other sophistical interactions surrounding us.\u00a0 To quote P.T. Barnum, \u201cThere\u2019s a sucker born every minute.\u201d\u00a0 Unfortunately, as Gensler goes to great pains to point out, there doesn\u2019t seem to be a way to make the rules of inductive inference tighter.\u00a0 Even principles, like Occam\u2019s Razor, are merely guidelines that must be applied with judgement.\u00a0 Or, as I like to phrase it, there doesn\u2019t seem to be a way to make inductive logic \u2018sucker-proof\u2019.<\/p>\n Even more interesting is the fact that justification of inductive arguments seems to be self-referential and circular.\u00a0 Gensler discusses the criticism leveled by David Hume against induction and the five responses that have arrived over the intervening years.\u00a0 I won\u2019t go over all five in detail but will confine the discussion to the three most interesting ones.<\/p>\n But here we have a problem, we are using modus ponens to justify modus ponens.\u00a0 The justification, even in the firm ground of deductive logic, leaves something to be desired.<\/li>\n<\/ol>\n In the end, it seems that we have to simply accept that logic has its limits and that, as a race, we\u2019ve bootstrapped our way to our present level of knowledge.\u00a0 This holds for inductive and deductive logic, with the former providing the basis for the latter (i.e., experience has taught us that deductive logic axioms are the ones we need to assume to get the whole thing to work).\u00a0 Gensler concludes with:<\/p>\n Inductive reasoning has been very useful.\u00a0 Instructively, we assume that it will continue to be useful.\u00a0 In our lives, we can\u2019t do without it.\u00a0 But the intellectual basis for inductive reasoning is shaky.<\/p>\n It would have been interesting to hear Mr. Spock discuss these points, to argue these a bit with the more intuitive Kirk.\u00a0 But perhaps a serious examination would have undermined the entire purpose that he served on the show.\u00a0 Perhaps it would have undermined the very reason for Vulcan to be, and maybe that would have been an episode worth seeing.<\/p>\n","protected":false},"excerpt":{"rendered":"
\nThis non-Democrat is a Cleveland voter
\nThis is all we know about the matter
\nTherefore, it\u2019s 60 percent probable that this non-Democrat is a Democrat<\/div>\n\n
\nThe truth table for modus ponens never gives true premises and a false conclusions.
\nTherefore, modus ponens is valid.<\/div>\n