ONT Re: Differential Logic
DLOG. Note D53
Digression: A Reflection on Use and Mention
| Reflection is turning a topic over in various aspects and in various lights
| so that nothing significant about it shall be overlooked -- almost as one
| might turn a stone over to see what its hidden side is like or what is
| covered by it.
| John Dewey, 'How We Think', [Dew, 57]
The contrast drawn in logic between the "use" and the "mention" of a proposition
corresponds to the difference that we observe in functional terms between using
"J" to indicate the region J^(-1)(1) and using "J" to indicate the function J.
You may think that one of these uses ought to be proscribed, and logicians
are quick to prescribe against their confusion. But there seems to be
no likelihood in practice that their interactions can be avoided.
If the name "J" is used as a sign of the function J, and if the
function J has its use in signifying something else, as would
constantly be the case when some future theory of signs has
given a functional meaning to every sign whatsoever, then
is not "J" by transitivity a sign of the thing itself?
There are, of course, two answers to this question.
Not every act of signifying or referring need be
transitive. Not every warrant or guarantee or
certificate is automatically transferable,
indeed, not many. Not every feature of
a feature is a feature of the featuree.
Otherwise we'd have an inference like:
If a buffalo is white, and white is
a color, then a buffalo is a color.
But a buffalo is not, only buff is.
The logical or pragmatic distinction between use and mention
is cogent and necessary, and so is the analogous functional
distinction between determining a value and determining what
determines that value, but so are the normal techniques that
we use to make these distinctions apply flexibly in practice.
The way that the hue and cry about use and mention is raised
in logical discussions, you might be led to think that this
single dimension of choices embraces the only kinds of use
worth mentioning and the only kinds of mention worth using.
It will constitute the expeditionary and taxonomic tasks of
that future theory of signs to explore and to classify the
many other constellations and dimensions of use and mention
that are yet to be opened up by the generative potential of
fully fledged sign relations.
| The well-known capacity that thoughts have -- as doctors have discovered --
| for dissolving and dispersing those hard lumps of deep, ingrowing, morbidly
| entangled conflict that arise out of gloomy regions of the self probably rests
| on nothing other than their social and worldly nature, which links the individual
| being with other people and things; but unfortunately what gives them their power
| of healing seems to be the same as what diminishes the quality of personal experience
| in them.
| Robert Musil, 'The Man Without Qualities', [Mus, 130]