🚀 go-pugleaf

In article <71kqssj@lynx.unm.edu> lgorbet@carina.unm.edu (Larry P Gorbet ANTHROPOLOGY) writes:
>In article <1992Nov17.162358.22391@guinness.idbsu.edu> holmes@garnet.idbsu.edu (Randall Holmes) writes:
>>I agree with Mikhail that logic is a moral obligation, but I don't
>>think that sentences have "meanings" (the sentences themselves do fine
>>as propositions, and refer to their truth-values).  It is possible to
>>analyze the reference of sentences formally, and no "meanings" prove
>>to be needed (and this is on the level of semantics, not syntax).
>
>So sentences which differ in that the words _radius_, _hypotenuse_,
>_chord_ (etc.) are interchanged are all synonymous, since these terms have
>identical reference in all cases (since each line segment in the
>Euclidean plane is a radius, is a hypotenuse,....).  My point is that
>reduction of meaning to reference gives up most of the reason we have
>a word _meaning_ in the first place.
>

This is nonsense.  Words like "radius", "hypotenuse", and "chord" are
implicit relation terms (radius of what circle?) -- they do not simply
refer to a line, but indicate its relation to some other geometrical
figure as well, so they are not interchangeable.

"The square on the hypotenuse is the sum of the squares on the legs"
is not intertranslatable with "the square on the radius is the sum of
the squares on the legs" (the latter being nonsense) because the first
sentence abbreviates a sentence of the form "For any right triangle T,
the square on the hypotenuse of T is the sum of the squares on the
legs of T".  In the latter form of the sentence, it is clear why
substituting "radius" for "hypotenuse" would be silly (T does not have
a radius).

-- 
The opinions expressed		|     --Sincerely,
above are not the "official"	|     M. Randall Holmes
opinions of any person		|     Math. Dept., Boise State Univ.
or institution.			|     holmes@opal.idbsu.edu