Category Archives: Formal Fallacies

Some beaches are illicit conversions

OK, so I’ve been watching football.  And there are occasions to think about logic.  During the beer commercials.  First, though, a quick tutorial on deductive semantic fallacies.  An argument is fallacious on deductive semantic grounds when the truth of the argument’s premise does not guarantee the truth of the argument’s conclusion (provided the proper analysis of the terms of the logic). A classic fallacious move to make inferences between two forms of statements in categorical A-Form.

All S are P, so All P are S

The pattern is conversion – you switch the subject and predicate term in the proposition form.  It’s valid for E- and I-Forms, so it’s fine for these:

No S are P, so No P are S

No cats are lizards, so No lizards are cats

Some S are P, so Some P are S

Some Texans are Republicans, so Some Republicans are Texans

The trouble is that with A-form propositions, conversion is fallacious.  So we can intuitively see the fallacy with the following conversion forms:

All triangles are polygons, so All polygons are triangles

All cats are mammals, so All mammals are cats

That’s fallacious, and since it’s a bad way to convert, we call it illicit conversion.  Now, to the commercials.  See the following Corona commercial, effectively playing during every timeout for every NFL game this weekend.  HERE.  Here’s the free association that stands in for reasoning:

Some beaches have sand; Some beaches are backyards; Some beaches inspire ideas; Some beaches have beats; Some beaches are better after sunset; Every beach is different, but All beaches have Corona

The commercial has scenes of beaches, bars, mixing rooms, back yards, concerts, campgrounds and so on. Each is some poignant scene, but not all have beers in them.  The inductive evidence presented is that, given their special definition of beach (effectively meaning ‘special place’), it’s not the presence of Corona that makes them that.  Rather, it, at best, is that the presence of Corona can contribute to a place being a beach.  Consequently, it isn’t that All beaches have Corona that they’ve shown.  It only takes the first scene (the sandy beach with no beers) to be a counter-example.  Instead, the best that the evidence could show is that All places where there are Coronas are beaches in the relevant sense.  Trouble is, they conclude with All beaches have Corona.  Illicit conversion off weak evidence for enumerative induction.

Bad company

People do a lot of things–eat, sleep, exercise, believe in proposition p or q, and so on.  Sometimes those things overlap with the activities of serial killers, Nazis, and terrorists.  This overlap may or may not be significant.  If the activity is morally abhorrent, like, say, genocide, then comparisons are made.  If the activity is innocuous, then well, nothing.  Everyone eats, the Nazis eat, ergo ipso fatso. 

Eating doesn't make people Nazis.  Nor does speaking German.  Or being German.  Or believing in the capacity of government to do some things, like provide highways, ports, police, or health care.  These things don't make anyone a Nazi because those beliefs do not just belong to Nazis. 

So, for instance, the Nazis embraced euthanasia.  They advanced all sorts of eugenic arguments for it.  They also embraced a healthy lifestyle, and traditional marriage (sometimes)–and they advanced all sorts of eugenic arguments for these things as well.  This does not mean traditional marriage is inherently Nazi.

This is something like the argument of a recent op-ed in the Vatican Observer (L'osservatore romano) on the occasion of the publishing of Nazi tract on euthanasia.  Here's a taste:

Binding and Hoche, in fact, maintain that life cannot be considered life in the full sense of those who, because of diseases, are exposed to a painful and hopeless agony, or the life of incurable idiots whose existence drags with no purpose or usefulness, imposing on the community a heavy and pointless burden. With regard to these people, the two scholars invented a new definition which was to enjoy great success even after the defeat of Nazism: “lives unworthy of being lived”. A definition which paved the way to the elimination of the sick and the unfit, permitting these homicides to be justified with a morally appreciable motivation: they in fact spoke of “charitable death” (Gnadentod). These are the same words that recur today recur in the writings of many contemporary bioethicists, and of many politicians who support legislative proposals of a euthanasic type. As the editors write in the introduction, “the notion of life as a good that deserves protection is henceforth cast off from the anchor of any metaphysical postulation, any doctrine of natural law, and is led towards a semantics of concreteness and immanence: life has value as long as it procures pleasure and is free from pain”. We therefore see that this book, precisely because of its grimly up to date characters, must strongly embarrass those who champion euthanasia in the belief that it has nothing to do with Nazism.

And we have the full Godwin here: the only person who should be strongly embarassed is the author of this very sad excuse of an objection to euthanasia.  To the extent that I am aware, no one is currently advocating that any state embrace Nazi eugenic policies regarding euthanasia; and no one is using those arguments to make the case for euthanasia.

You know what the Nazis also believed?  Probably global warming.  On that, see here.

How the Rich Saved Democracy

Did Ross Douthat just jump the shark? Yes:

With the Republican primary season winding down, it’s time to celebrate two heroes of participatory democracy, two champions of the ordinary voter, two men who did everything in their power to make the ballot box matter as much as the fundraising circuit.

I speak, of course, of Sheldon Adelson and Foster Friess.

Adelson is the casino billionaire whose super PAC donations enabled Newt Gingrich to upset Mitt Romney in South Carolina and give him a scare in Florida. Friess is the investment manager whose super PAC donations enabled Rick Santorum to prolong the race through February and March. Both men are controversial; both have been cited as prime examples of the corrupting influence of great wealth on our politics. But both did more than anyone else to prevent the Republican primary from turning into a straightforward “money talks” affair.

Adelson and Friess, in a paradoxical judo move, have somehow preserved popular democracy and prevented the Republican primary from turning into a "money talks" affair by giving sh*tloads of money to two candidates who, unlike Romney and his "sturdy donor base," can't raise money via popular methods. 

Anomalous regularity

There are a couple of people I now consider it completely safe to ignore: George Will, Charles Krauthammer, Michael Gerson, and of course, David Brooks.  These are the guys who inspired this whole project.  Every now and then, however, it's fun to go back and see what's up with them.  Via Alex Parene at Salon, here's a gem from David Brooks:

Jeremy Lin is anomalous in all sorts of ways. He’s a Harvard grad in the N.B.A., an Asian-American man in professional sports. But we shouldn’t neglect the biggest anomaly. He’s a religious person in professional sports.

We’ve become accustomed to the faith-driven athlete and coach, from Billy Sunday to Tim Tebow. But we shouldn’t forget how problematic this is. The moral ethos of sport is in tension with the moral ethos of faith, whether Jewish, Christian or Muslim.

We have grown accustomed to this anamoly.  You'd think an editor would have gotten that. 

Made me think of this headline from the Onion: NFL Star Thanks Jesus after Successful Double Homicide.

Things that don’t go together, part CXL

Francis Cardinal George, Archbishop of Chicago, caused ire and some headscratching when he expressed concern about the gay rights movement:

You know, you don’t want the gay liberation movement to morph into something like the Ku Klux Klan, demonstrating in the streets against Catholicism. So I think if that’s what’s happening, and I don't know that it is, but I would respect the local pastor’s, you know, position on that.

The Cardinal's remarks were occasioned by the not unreasonable desire of the pastor of a church on the route of the Chicago Pride Parade.  The pastor worried that the parade of gay people would interfere with his church's staunch anti-gay stance, or that parishoners leaving Sunday mass would be tempted away to gayness.  Ok, in all seriousness, he said it would cause a traffic problem for the churchgoers.  Fair enough, and the two groups (the Pride Parade and Our Lady of Caramel) worked it out.

What has remained are the the Cardina's puzzling remarks about the gay-hating KKK, however.  In fact, the fallacy of the undistributed-middle endorsing Cardinal has reiterated his concerns that two groups that have nothing in common could make common cause of their hatred for the Catholic Church.  He remarked:

Organizers (of the pride parade) invited an obvious comparison to other groups who have historically attempted to stifle the religious freedom of the Catholic Church,” the cardinal said in a statement issued Tuesday. “One such organization is the Ku Klux Klan which, well into the 1940s, paraded through American cities not only to interfere with Catholic worship but also to demonstrate that Catholics stand outside of the American consensus. It is not a precedent anyone should want to emulate.

Let's put this syllogistically:

  1. The Klan are Catholics-protestors
  2. Teh Gays are Catholics-protestors
  3. Therefore, the Klan are the Gays.

Well, obviously three doesn't follow on account of the fact there is no middle term between the KKK and the Pride Parade organizers in Chicago.  The simple fact of objecting to some aspect of Catholicism is obviously inadequate to draw a line between the two groups.  The KKK objected to Catholicism on ethnic grounds; gay activists (some of whom are actually catholic) object to the Church's using its influence to deny people rights. 

Besides, I should remark that it's a shame that the Cardinal endeavors to influence the state to hold back the recognition of obvious human rights to oppressed minorities, much in same the way the KKK sought to prohibit the lawful practice of Catholicism.  It's alarming that the Cardinal would invite comparisons to virulently anti-Catholic sentiments.


It's Easter Monday (or Pasquetta), so let's have a contest.  In traditional term logic, a syllogism whose conclusion distributes the minor term but whose minor premise does not is guilty of the fallacy of the illicit minor, or the Father O'Malley Fallacy.  A student of mine today suggested another name, the Father McPheeley Fallacy. 

Anyone have any other suggestions?

And in the tradition of making up gestures descriptive of the fallacies, the one for this one is moon walking.


Another squirmish* in the culture wars

In the category of self-refuting worries (by now noticed by all of the web), here is disgraced former Speaker of the House, Newt Gingrich:

"I have two grandchildren: Maggie is 11; Robert is 9," Gingrich said at Cornerstone Church here. "I am convinced that if we do not decisively win the struggle over the nature of America, by the time they're my age they will be in a secular atheist country, potentially one dominated by radical Islamists and with no understanding of what it once meant to be an American."

A secular atheist country dominated by religious fundamentalists.  


Berkeley’s Master Fallacy?

I'm currently teaching Modern Philosophy, and we are reading Berkeley's Three Dialogues.  Philonous's presentation of what Gallois (1974 Phil Review) calls Berkeley's "Master Argument"  (MA) was always particularly striking to me.   The majority of my concern about the argument was along Bertrand Russell's line of resistance: there is a confusion between imagining, say, a tree independent of mind and holding that the tree, in imagination, is dependent on the mind.  So I'm not sure the argument is sound.  I still have that concern, but yesterday morning I found myself having another problem with the argument.  Maybe NonSequitur readers can help me out here, because I, now, don't even think the argument is valid.  But it can be revised.  Here goes.

Here's Philonous's presentation of the MA (edited for space):

I am content to put the whole upon this issue.  If you can conceive it possible for … any sensible object whatsover to exist without the mind, then I will grant it actually to be so….

Is it not as great a contradiction to talk of conceiveing  a thing which is unconceived?

Now, I've always understood the MA to be one that establishes the falsity of materialism (or non-mentalism) and the truth of idealism (as the two being mutually exclusive and exhastive options).  That is, if you show the falsity of one, you've established the other.  The MA is a demonstration that materialism is false.  But as stated, it doesn't do so validly.  Here's a formalized version:

P1) If it is possible to conceive of a sensible object w/o a mind, then it is possible that those things exist without minds. 

P2) It is not possible to concieve of a sensible object w/o a mind.

C) It is not possible that there are sensible objects without minds.

Again, most folks object to P2.  That still seems right to me.  But even if you grant P2, the argument doesn't go through, because it's a fallacious form of inference: Denying the antecedent.  That is, the form of the argument is:

P1) If P, then M

P2) not-P

C) not-M

This is craziness.  Now, I think that there are two options for Berkeley-defenders to go here.  The first is to say that C, because it's not explicitly stated, isn't the conclusion.  But Philonous certainly seems to be convinced that he's shown not-M in the follow-up with Hylas.  And in the Principles, Berkeley takes it that MP on P1 with P2 establishes the falsity of idealism:

[I]f you can but conceive it possible for … any thing like an idea, to exist otherwise than in a mind perceiving it, I shall readily give up the cause. (PHK  22)

Now, this seems clear that he does think that P2 establishes certain truths, specifically, the truth of materialism and the falsity of idealism.  So I'm unsure that this first option is really a good interpretive one for Berkeley-defenders.  But it seems  plausible philosophically.

The second option is to read all those IF-clauses as ONLY IF-clauses. And so P1 should be, rather:

P1*)  I will agree that Materialism is true ONLY IF it is possible to concieve of a thing existing independently of a mind.

P2, then, works just fine to show that Materialism is false, by Modus Tollens, now.  So the other interpretive strategy is to read Berkeley's argument as needing a switch of antecedents and consequents.

This, by the way, seems even more philosophically plausible than the first option, as I think that P1* is much more plausible than P1.  Just because materialism is concievable, it doesn't mean that materialism is true (as P1 runs); but if materialism isn't even consistently conceivable, then that counts as very good evidence that it's false (as P1* runs). 

So this strategy saves the MA from the fallacy of denying the antecedent and has it with a more philosophically plausible first premise.  The only problem: you have to take it that Berkeley mixed up necessary and sufficient conditions.  When he's doing metaphysics.  That's uncharitable, to say the least.  Oh, and it also doesn't save it from the old Russell objection that P2 is just false. 

There’s no modern Socrates, so you must be…

Victor Davis Hanson is a classicist of some standing.  But he, unfortunately, isn't much for logic. Or, perhaps, simple consistency.  His recent article, "The New Sophists," over at National Review Online, exemplifies these two traits in spades.

Hanson's thesis is that there's just so much double-talk and empty rhetoric, especially from the left, and more especially regarding global warming.  Al Gore "convinced the governments of the Western world that they were facing a global-warming Armageddon, and then hired out his services to address the hysteria that he had helped create."  And the recent record snowfalls in the Northeast are clear evidence that global warming is a sham.  When climate scientists explained that events like this are not only consistent with global warming, but to be expected, Hanson retorts:

The New York Times just published an op-ed assuring the public that the current record cold and snow is proof of global warming. In theory, they could be, but one wonders: What, then, would record winter heat and drought prove?

It's not just climate science that has the double-talk, though.  Hanson sees it with discussions of the Constitution:

One, the Washington Post’s 26-year-old Ezra Klein, recently scoffed on MSNBC that a bothersome U.S. Constitution was “written more than 100 years ago” and has “no binding power on anything.”

To all of this, Hanson makes his analogy with classical Athens and the problem of the sophists:

One constant here is equating wisdom with a certificate of graduation from a prestigious school. If, in the fashion of the sophist Protagoras, someone writes that record cold proves record heat, . . . or that a 223-year-old Constitution is 100 years old and largely irrelevant, then credibility can be claimed only in the title or the credentials — but not the logic — of the writer.

OK. That's a nice point, at least if it were true about the cases he was discussing. (Did Hanson not read the reasons in the NYT article he never cites as to why we'd get crazy snowfalls because of global warming?  If he's going to talk about the article, talk about its argument, too.  Sheesh.  And Klein said it was over 100 years old, and that it's not binding, … but that doesn't matter to Hanson, I guess).  But it's on this point about sophists run amok that Hanson bemoans our fate:

We are living in a new age of sophism — but without a modern Socrates to remind the public just how silly our highly credentialed and privileged new rhetoricians can be.

So we don't have a modern Socrates.  So what's Hanson doing, then?  By that statement, he can't think he's Socrates or doing the job of criticizing the new rhetoricians, can he?  So what is he?  I think I know:  He's another sophist.