Wednesday, March 11, 2009

Sophistry

Let's have good clean sophistical fun. Consider the sentences:

  1. He can not come to the phone right now.
  2. He cannot come to the phone right now.
They obviously mean something else. If he is both free to come and to not come, then (1) is true, and (2) is false. (Oftentimes, of course, (1) is a misspelled version of (2). That's annoying. I once came across this misspelling in Kant. I couldn't make sense of the "can not" claim. I had to go back to the German—even though I didn't know German—and then it became obvious there was just a typo in the translation.) Therefore:
  1. Claims (1) and (2) are different.
But:
  1. Two things that differ by nothing are the same.
  2. Claims (1) and (2) differ by a space.
  3. A space is nothing.
  4. Therefore, claims (1) and (2) are the same and different.
  5. Therefore, the sky is green. (By Explosion)

(The lesson, of course, is that one shouldn't identify symbols with physical objects, though some symbols are implemented by a kind of physical object.)

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5 comments:

  1. Tim LacyMarch 11, 2009 at 2:47 PM

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  2. Tim LacyMarch 11, 2009 at 2:48 PM

    Alex,

    Thanks for this. In my haste, I have often overlooked the logical implications of the difference between "can not" and "cannot" in favor of just stylistic or usage considerations.

    Then again, the differences in meaning here, and hence logical implications, are often more apparent in the emphasis and inflection of the speaker. For instance, it is quite rare these days for one to say: "He can not come to the phone right now" (with even the slightest emphasis on "can"). But one frequently hears: "He cannot come to the phone right now."

    In other words, your distinguishing between (1) and (2) is ~almost~ a false one. Most all usage leans toward (2).

    But this is just me spoiling the true fun which is your sophistry with symbols.

    - TL

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  3. UnknownMarch 12, 2009 at 2:04 AM

    That was a great post! I see you applied Plato's notion that, "things differ by relative non-being," in your latter premises.

    This is off-subject, but given your own interest in modal cosmological arguments, I was wondering what you thought of Robert Maydole's so-called "Modal Third Way." http://www.bu.edu/wcp/Papers/Reli/ReliMayd.htm

    I confess that I'm a novice when it comes to modal logic, but would you endorse this argument?

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  4. MandMMarch 15, 2009 at 4:15 PM

    Very funny, though somewhat frustrating for those of us who make typos and for whom correct grammar does not come easy.

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  5. Alexander R PrussMarch 16, 2009 at 1:44 PM

    MandM:

    I think there is a difference between people for whom the primary form of English is the written form and people for whom the primary form of English is the spoken form.

    Linguists tend to think of the spoken form as primary. For me, the primary form is the written. That's why for years I didn't realize that "there", "their" and "they're" are often (always?) pronounced the same way--until I started seeing student papers and online stuff with these confused. When I say a word like that, I sometimes see the written form flashing before my mind, disambiguating the spoken word (not that it helps my interlocutor!)

    Also, having English be one's second language--as it is for me--helps with spelling and grammar. My posts are still full of typos, though (most often, extra or omitted words, I think). :-)

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