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Don't trust the grammar

OdradekOdradek
edited 2012-03-09 15:37:49 in General

The way to see this is to think a bit about the nature of defeasible warrant, or non-monotonic reasoning (inferences for which ‘if P the Q’ holds good by default, but which can be invalidated by the addition of sets of additional premises). There is a useful distinction to be had here between global non-monotonicity and local non-monotonicity. The former is what we have in mathematics. It isprecisely deductive, in such a way that absolutely no addition of further premises can undermine a good inference. The latter is more complicated, and very important, insofar as it is what is made explicit by the panoply of possible modal operatorsThus, for any sentence containing a definite description, grammatical form is misleading as to logical form. For example, 'The inventor of silly putty got rich' is of subject-predicate form grammatically but not logically-it is not really about the inventor of silly putty. According to Russell's famous theory of descriptions, a simple subject-predicate sentence of the form 'The F is G' does not express a singular proposition, of the subject-predicate form 'a is G,' but a general, existential proposition, what might be called a "uniqueness proposition." The quantificational structure of such a proposition is revealed only after the definite description is "broken up," to yield (in modern notation) the form '(Ex)((y)(Fy_ y=x) & Gx),' in which the description, not being a semantic unit, does not even appear.5 Accordingly for Russell, if a proper name is a disguised description, e.g., if 'George Kistiakowski' is short for 'the inventor of silly putty,' the bearer of the name does not enter into the proposition expressed by a sentence in which the name occurs. This is not because the name has a sense (in Frege's sense of 'sense') but because it abbreviates a definite description. (e.g., historical necessity, physical necessity, political possibility, etc.). We might say that these latter kinds of reasoning are imprecisely deductive, insofar as they depend on a more or less implicit form of restriction very much like the more or less implicit forms of quantificational restriction we find outside of mathematical contexts. 

http://www.youtube.com/watch?v=-hu21NmpPfE

   Travelling in silent majesty along their orderd ways 
FZ2-33.23; E322|        In right lined paths outmeasurd by proportions of number weight  t602 
FZ2-33.24; E322|        And measure. mathematic motion wondrous. along the deep 
FZ2-33.25; E322|        In fiery pyramid. or Cube. or unornamented pillar   t603 
FZ2-33.26; E322|        Of fire far shining. travelling along even to its destind end 
FZ2-33.27; E322|        Then falling down. a terrible space recovring in winter dire 
FZ2-33.28; E322|        Its wasted strength. It back returns upon a nether course   t604 
FZ2-33.29; E322|        Till fired with ardour fresh recruited in its humble season   t605 
FZ2-33.30; E322|        It rises up on high all summer till its wearied course 
FZ2-33.31; E322|        Turns into autumn. such the period of many worlds 
FZ2-33.32; E322|        Others triangular right angled course maintain. others obtuse   t606 
FZ2-33.33; E322|        Acute Scalene, in simple paths. but others move   t607 
FZ2-33.34; E322|        In intricate ways biquadrate. Trapeziums Rhombs Rhomboids 
FZ2-33.35; E322|        Paralellograms. triple & quadruple. polygonic 
FZ2-33.36; E322|        In their amazing hard subdued course in the vast deep   t608

  
FZ2-34.1;   E322|        And Los & Enitharmon were drawn down by their desires 
FZ2-34.2;   E322|        Descending sweet upon the wind among soft harps & voices   t609 
FZ2-34.3;   E322|        To plant divisions in the Soul of Urizen & Ahania   t610 
FZ2-34.4;   E322|        To conduct the Voice of Enion to Ahanias midnight pillow

  
FZ2-34.5;   E322|        Urizen saw & envied & his imagination was filled 
FZ2-34.6;   E322|        Repining he contemplated the past in his bright sphere 
FZ2-34.7;   E322|        Terrified with his heart & spirit at the visions of futurity 
FZ2-34.8;   E322|        That his dread fancy formd before him in the unformd void

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