D oubleplusungood double privation and multiply modified artefact properties Tutorial in two parts Deparment of Computer Science Technical University of Ostrava 26 February & 1 March 2013. Bjørn Jespersen TU Ostrava Dept. Computer Science [email protected] relevant TIL literature.
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DOI 10.1007/s11225-012-9397-8, forthcoming
College Publications, London, forthcoming
G. Primiero), LNAI 6284 (2010), 252-71
If a property F has been multiplymodified in this or that manner, is an individual a that has the so modified property an F?
0M’ 0M 0F , ‘a happy bald child’
F/() (); M, M’/(() ()) ()
0M* 0M 0F, ‘a very happy child’
M* /((() ()) /(() ())) (() ())
0Ms 0Fwt0a 0Mp 0Fwt0a
A modal modifier, preliminarily speaking, is one that oscillates between being subsective and being privative.
Subsectionsays what something is; privation, what something isnot; and modal modification, what something may be.
DEFINITION 1 (first- and second-order modifier).
Apropositional modifier is of type (), forming a proposition from a proposition.
A property modifieris of type (), forming a property from a property, and is thus a first-order (in TIL: first-degree) modifier.
A modifier of property modifiersis of type
(() ()), i.e. a second-order (in TIL: second-degree) modifier.
DEFINITION 2 (subsective property modifier).
Let M/(); let gsrange over (()); let x range over ; let F/; let /((() (()))): it is true or else false that a particular modifier Mis an element of a particular set of modifiers. Then:
M is subsective w.r.t. F
iff Mg [0Req0F [gs0F]].
[0 [0[0Fwt 0a]]]
[[[0Mp* 0Mp] 0F]wt0a]
[[[0Fake* 0Fake] 0F]wt0a] ought obviously not to translate into 0 00Fwt0a
there’s negation, and there’s negation:
(La Palma Reyes et al. 1999, p. 255.)
[[0non [0non 0F]]wt0a]
DEFINITION 3 (privative property modifier).
Let M/(); let gprange over (()); let x range over ; let F/; let /((() (()))). Then:
M is privative w.r.t. F iff
Mgp[0Req [0non 0F] [gp0F]].
From Def. 3 we obtain the following elimination rule for privative modifiers Mp:
DEFINITION 4 (modal property modifier).
Let M/(); let gmrange over (()); let x range over ; let F/; let /((() (())));
let /(()) and /(()). Then:
M is modal w.r.t. F iff
M gm0Reqwtx0w´0t´0Mm 0Fwt x
0Fw’t’ x0w´´0t´´0Mm 0Fwt x0non 0Fw´´t´´ xgm 0F.
From Def. 4 we obtain the following conditional elimination rule for Mm:
w’ 0t’ 0Mmfwt0afw’t’0a
0w’’ 0t’’ 0Mmfwt0a0nonfw’’t’’0a
Gloss: “From a being an 0Mmf at w, t, infer that there is a w´, t´ such that if a is an 0Mmf at w, t then a is an f at w´, t´ and that there is an alternative w´´, t´´ such that if a is an 0Mmf at w, t then a is a 0nonfat w´´, t´´.”
[[0non [0Mp0F]]wt0a]/[[0Mp’ [0non 0F]]wt0a]
[[0non’ [0non 0F]]wt0a]
[[[0Ms* 0Ms] 0F]wt0a]
[[[0Mp* 0Mp] 0F]wt0a]
[[[0non* 0Mp] 0F]wt0a]/ [[[0Mp* 0non] 0F]wt0a]
[[[0non* 0non] 0F]wt0a]
[[[0Ms* 0Mp] 0F]wt0a]
[[[0Mp* 0Ms] 0F]wt0a]
[[[0non* 0Ms] 0F]wt0a]
Formally, non takes a (modified or basic) property to one of its contraries, leaving it open which particular contrary.
Imagine a residing in the capital of some country.
When a leaves the capital, a moves to a town in the province.
When a leaves that town, a has the choice between returning to the capital or going to some other town in the province.
From the point of view of the first town a goes to, its complement includes both the capital and all the other towns in the province. So each new privation introduces a shift in perspectiveas to what the complement is.
It is crucial not to confuse non, which operates on properties, with the complement function \, which operates on sets. The complement of a complement is the original set, thereby reinstalling the problem with Boolean negation.
‘is almost half a pound’
(1) What are the various ways of carving up the scopes of the adjective ‘doubleplusungood’? (Orwell, 1984, 1949)
(2) Is any one analysis superior?