I was reminded of the recent query by James Propp involving the sentence *The people you know are the people who know all the people* *who know all the people you know* (noting that in the thread it was made clear that "know" was to be defined in such a way that for all A and B : [(A knows B) iff (B knows A)]) but at any rate this is only another example of a square root of tautology: it works out to F(I)=F(F(F(I))), or I=F(F(I)), where I is the self and F is the function of symmetric (reciprocated) familiarity. The next thing I thought of was color science, because color has been shown to be partly inseparable from language (see for example http://www.wired.com/wiredscience/2008/03/babies-see-pure/) and because color has three dimensions -- so you could imagine transforming a color by cycling the three axes on the color space {R->G->B->R}, or similarly by adding 120 degrees to the hue on the color wheel, and then it would take three steps to get back to the original color. But there are no words for "the hue that's 120 degrees further around on the color wheel" (in any natural language, I suspect). Then I hit on it: *Every Tuesday is the eve of the eve of the eve of the eve of the eve of the eve of the eve of a Tuesday.* where of course we define "eve" to mean "the day before". - Robert Munafo On Sun, Mar 6, 2011 at 11:18, Adam P. Goucher <apgoucher@gmx.com> wrote:
Dear all:
Negation and tautology are both square-roots of tautology, as:
"This statement is true." = "This statement is not not true."
Do there exist words (in any language) which act as cube-roots of tautology (excluding the trivial case of tautology itself)? Or, more generally, Nth roots of tautology, for arbitrary natural numbers N?
If we did have such words in the English language, what logical effect would they have on the meaning of a sentence?
Sincerely,
Adam P. Goucher
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