![\"Saints](\"https:\/\/wp-media.patheos.com\/blogs\/sites\/186\/2020\/06\/Sacrament-Meeting-cropped.jpg\")
<\/a>This column in the Deseret News<\/em> is worth a look: \u201cPerspective: Online influencers aren\u2019t accurately representing Latter-day Saint reality:\u00a0Disaffected influencers might be leaving a religious movement, but they\u2019re not leading one\u201d<\/a><\/p>\n So is this piece, from the Deseret News Editorial Board: \u201cOpinion: Regaining trust in vaccinations\u201d<\/a><\/p>\n And this, too: \u00a0\u201cReady to join the new counterculture? Braver Angels\u2019 leader says it will take courage:\u00a0In a culture of widening contempt, we have the power to choose something better, says Maury Giles\u201d<\/a>\u00a0 (Scarcely relevant footnote: Years ago, I participated \u2014 at his invitation \u2014 in three small meetings organized by David Blankenhorn: one Malaga, in southern Spain; one at the Carter Center in Atlanta; and one on the Mediterranean island of Malta. \u00a0They were attempts to foster dialogue between the West and the Islamic Middle East. \u00a0I haven\u2019t been involved in Braver Angels, but I applaud its intent. \u00a0David Blankenhorn is always trying to improve conversation across yawning divides.)<\/p>\n Responding to a comment following my blog entry \u201cCalling All Experts!\u201d<\/a>\u00a0I remarked that, on medical subjects, \u201cas I do in many areas of my life, I tend to accept the consensus of experts.\u201d<\/p>\n Unsurprisingly, that remark draw mockery from my groupies at the Peterson Obsession Board. \u00a0After all, they follow me with absolutely rapt attention pretty much twenty-four hours a day, seven days a week, and many of them are either incapable of accurately understanding what I say or too intoxicated with hatred to care about attempting such an understanding.<\/p>\n \u201cFolks,\u201d says one of them, \u201cyou can\u2019t make this stuff up\u201d \u2014 a formulaic comment that is commonly used on the Obsession Board, as in this case, to signal that something made-up has just been presented or is about<\/em> to be presented. \u00a0After all, he says, Peterson is a guy \u201cwho employs [sic<\/em>] LDS academics for the express purpose of going against the consensus of experts.\u201d \u00a0Which, I guess, is supposed to be a contradiction. \u00a0Which, comments another groupie, proves me a \u201chypocrite.\u201d<\/p>\n Except, of course, that it doesn\u2019t<\/em>.<\/p>\n Why? \u00a0I\u2019ll try to explain this so clearly that any reasonably intelligent and minimally honest reader should be able to follow me. \u00a0How my groupies at the Obsession Board<\/em> will react, of course, is a different matter.<\/p>\n The four corners of the chart shown above represent the four basic forms of propositions recognized in classical (Aristotelian) logic:<\/p>\n A<\/strong> propositions, or universal affirmatives<\/em>, take the form: All S are P <\/em>or Every S is a P.<\/em> On the assumption made within classical (Aristotelian) categorical logic, that every category contains at least one member, the following relationships hold within the square:<\/p>\n Firstly, A<\/strong> and O<\/strong> propositions are contradictory<\/strong><\/em>, as are E<\/strong> and I<\/strong> propositions. Propositions are contradictory when the truth of one implies the falsity of the other, and conversely. Thus, the truth of a proposition of the form All S are P<\/em> implies the falsity of the corresponding proposition of the form Some S are not P<\/em>. \u00a0For example, if the proposition \u201cAll expert consensus opinions are trustworthy\u201d (A)<\/strong> is true<\/em>, then the proposition \u201cSome expert consensus opinions are not trustworthy\u201d (O)<\/strong> must be false<\/em>. Similarly, if \u201cNo expert consensus views are trustworthy\u201d (E)<\/strong> is false<\/em>, then the proposition \u201cSome expert consensus views are trustworthy\u201d must be true<\/em>.<\/p>\n Secondly, A<\/strong> and E<\/strong> propositions are contrary<\/strong><\/em>. Propositions are contrary when they cannot both<\/em> be true. An A<\/strong> proposition \u2014 e.g., \u201cAll experts are right\u201d \u2014 cannot be true at the same time as the corresponding E<\/strong> proposition: \u201cNo experts are right.\u201d Please note, however, that A<\/strong> and E<\/strong> propositions, while they are contrary, are not contradictory. While they cannot both be true<\/em>, they can <\/em>both be false<\/em>; \u201cAll experts are right\u201d and \u201cNo experts are right\u201d don\u2019t exhaust the logical possibilities: \u00a0\u201cSome experts are right\u201d (a proposition of form I<\/strong>), if it is the case, obviously falsifies the corresponding A<\/strong> and E<\/strong> propositions.<\/p>\n Next, I<\/strong> and O<\/strong> propositions are what classical Aristotelian logic terms subcontrary<\/strong><\/em>. Propositions are subcontrary when it is impossible for both to be false<\/em>. Because \u201cSome experts are infallible\u201d is false, \u201cSome experts are not infallible\u201d must be true. Please notice, however, that it is possible for corresponding I<\/strong> and O<\/strong> propositions both to be true<\/em>, as with \u201cSome authorities are reliable,\u201d and \u201cSome authorities are not reliable.\u201d Again, I<\/strong> and O<\/strong> propositions are subcontrary, but they are neither contrary nor contradictory.<\/p>\n Finally, two propositions are deemed to stand in the relation of subalternation<\/strong><\/em> when the truth of the first (the \u201csuperaltern\u201d) implies the truth of the second (the \u201csubaltern\u201d), but not<\/em> conversely. A<\/strong> propositions stand in the relation of subalternation with the corresponding I<\/strong> propositions. The truth of the A<\/strong> proposition \u201cAll experts are fallible\u201d implies the truth of the proposition \u201cSome experts are fallible.\u201d However, the truth of the O<\/strong> proposition \u201cSome experts are not correct\u201d does not imply the truth of the E<\/strong> proposition \u201cNo experts are correct.\u201d In traditional logic, the truth of an A<\/strong> or an E<\/strong> proposition implies the truth of the corresponding I<\/strong> or O<\/strong> proposition, respectively. Consequently, the falsity of an I<\/strong> or O<\/strong> proposition implies the falsity of the corresponding A<\/strong> or E<\/strong> proposition, respectively. However, the truth<\/em> of a particular proposition does not imply the truth of the corresponding universal proposition, nor does the falsity of a universal proposition carry downwards to the respective particular propositions.<\/p>\n To return to my own specific case: \u00a0I wrote that, in many areas of my life, I tend to accept the consensus of experts. \u00a0I did not<\/em> say that I always<\/em> accept the consensus of experts in all<\/em> areas of my life. \u00a0What I actually did<\/em> say can be translated into an I<\/strong> proposition, as follows: \u00a0[Peterson believes that] Some consensus views of experts are worthy of trust<\/em>, i.e., that Some S are P<\/em>. \u00a0Is it possible, though, for an I<\/strong> proposition to be true at the same time that an O<\/strong> proposition \u2014 Some S are not P \u2014<\/em> is true? \u00a0Yes, it is. \u00a0See above. \u00a0They are subcontraries. \u00a0They are not contrary statements, nor are they contradictory statements. \u00a0It is possible \u2014 and it doesn\u2019t make one a \u201chypocrite\u201d \u2014 to believe, at the same time, that Some consensus views of experts are worthy of trust\u00a0<\/em>and that Some consensus views of experts are <\/em>not worthy of trust.<\/em><\/p>\n Thus, I can be inclined to accept consensus medical and pharmacological views while, at the same time \u2014 and with neither hypocrisy nor self-contradiction \u2014 I dissent from consensus views about some aspects of pre-Classical Mesoamerica and related matters.<\/p>\n I doubt, of course, that this little excursus into the first week of Logic 101 \u2014 drawn quite unoriginally from https:\/\/iep.utm.edu\/sqr-opp\/<\/a> \u2014 will help my groupies over at the Obsession Board. \u00a0I doubt that they want<\/em> help. \u00a0Still, although I\u2019m retired from the university, I remain by disposition a teacher. As the late Geoffrey Chaucer put it:<\/p>\n A Clerk ther was of Oxenford also, A Clerk there was also, from Oxford,<\/a><\/a>
\nE<\/strong> propositions, or universal negations<\/em>, take the form: No S are P <\/em> or No S is a P<\/em>.
\nI<\/strong> propositions, or particular affirmatives<\/em>, take the form: Some S are P <\/em>or Some S is a P.<\/em>
\nO<\/strong> propositions, or particular negations<\/em>, take the form: Some S are not P<\/em> or Some S is not P.<\/em><\/p><\/blockquote>\n
\nThat unto logyk hadde longe ygo. . . .
\nSownynge in moral vertu was his speche,
\nAnd gladly wolde he lerne and gladly teche.<\/p>\n
\nThat had gone into the study of logic long ago. . . .
\nHis speech was always consistent with moral virtue,
\nAnd gladly would he learn, and gladly teach.<\/p>\n<\/div>\n<\/blockquote>\n<\/a>
(LDS.org)<\/figcaption><\/figure>\n<\/div>\n