Disjunctive syllogism

Today’s Zippy:

“It’s outta here … or my name isn’t Saxby Chambliss.” A disjunction, with the logical form P ∨ Q. (P in this case is something like “I’ll hit it out of the park”, expressed colloquially as “It’s outta here”.)

One use for such sentences is to use them in contexts where ¬Q is given, from which, by Disjunctive Syllogism, in the form:

P ∨ Q, ¬Q ∴ P

we conclude P. So, P ∨ Q (“I’ll hit it out of the park, or I’m a monkey’s uncle”) in a context where it’s clear that the speaker is not in fact a monkey’s uncle (Q is transparently false) leads to the conclusion P, “I’ll hit it out of the park”.

In the Zippy case, Q is itself a negation, ¬R (“My name isn’t Saxby Chambliss”), so the relevant variant of Disjunctive Syllogism is

P ∨ ¬R, R ∴ P

In a context where R (“My name is Saxby Chambliss”) is transparently true, P ∨ ¬R (“I’ll hit it out of the park, or my name isn’t Saxby Chambliss”) leads to the conclusion P, “I’ll hit it out of the park”.

Ah, but then R is the problem: Is Mr. Toad’s name Saxby Chambliss (the name of the senior U.S. Senator from Georgia)? Is that Mr. Toad’s secret life, serving as a U.S. Senator? If so, then Mr. Toad is predicting that he will hit the pitch out of the park. If not, then we’re faced with:

P ∨ ¬R, ¬R

from which, if ∨ is inclusive disjunction, we can conclude nothing beyond the premise P ∨ ¬R. If ∨ is exclusive disjunction, though, then only one of the disjuncts (P and ¬R) can be true, so that if ¬R is true, P is false: Mr. Toad is predicting that he won’t hit it out of the park.

So everything hangs on the identity, or identities, of Mr. Toad. He doesn’t look much like Saxby Chambliss to me, but he just might be cleverer at adopting identities than I’m giving him credit for.

(Why Saxby Chambliss?, you ask. Probably because Bill Griffith is a fan of unusual and interesting names, and Saxby Chambliss is certainly one of those. And it’s phonologically attractive: an alliterative double trochee, with the same vowel in the accented syllables of the two feet and with phonologically very similar vowels in the unaccented syllables, plus the consonant patterning /s … b … b … s/.

Sen. Chambliss did play baseball for the University of Georgia in his college years. I haven’t found any evidence on his prowess at batting.

No, I don’t know where the wet boxer shorts came from.)

3 Responses to “Disjunctive syllogism”

  1. h.s. gudnason Says:

    I’ve recently been watching episodes of the 1960s TV series Thriller, hosted by the doubly-trochaic Boris Karloff. He introduces each episode promising the viewer excitement “or my name isn’t Boris Karloff.” I’ve been puzzling over that statement (just as I puzzled over Mr. The Toad’s when I first saw it this morning), because the man’s name was in fact William Henry Pratt, though at that point he’d been “Boris Karloff” for ±30 years. It seems like a dangerous disjunctive syllogism for a pseudonymous person to use.

  2. Transitivity fail « Arnold Zwicky's Blog Says:

    […] Arnold Zwicky's Blog A blog mostly about language « Disjunctive syllogism […]

  3. Chris Waigl Says:

    I was wondering if this is a reference to something and also had the vague feeling at the back of my mind that this trope is not uncommon in German. Not sure about the latter, but as for the former, a lot point to Winnie the Pooh (“If anyone knows anything about anything, it’s Owl who knows something about something or my name’s not Winnie-the-Pooh”, and there’s also an “… or my name isn’t Eeyore”

    A German site claims all American children know the Orville Redenbacher popcorn commercials: “You’ll taste the difference, or my name isn’t Orville Redenbacher.”

    And the site tvtropes.com has a collection of TV instances (in the US): http://tvtropes.org/pmwiki/pmwiki.php/Main/ptitlewqw2hwqk .

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