[FOM] Simmons' denotation paradoxes

Hartley Slater slaterbh at cyllene.uwa.edu.au
Tue Feb 25 22:56:19 EST 2003

Sandy Hodges (FOM Digest Vol 2 issue 25) is more concerned than me 
about differences, in the context previously presented (FOM Digest 
Vol 2 issue 20), between Heloise's, Alberic's and my own (possible) 
utterance of  "The sum of the numbers referred to attributively by 
Peter Abelard, in his utterances about which there is no choice as to 
whether they are attributive or not."  In assigning these utterances 
references, I believe one can assign the same to all three.  Hodges 
seems to be misled, at least in one part of his thinking, by the 
modal fallacy which mixes 'L(p -> q)' with 'p -> Lq'.  he says

Hartley Slater says:
  (6)   "There is a choice as to whether Peter Abelard's second utterance
refers attributively or not."

Suppose Hartley were to say:
(7)    "The sum of the numbers referred to attributively by Peter
                in his utterances about which there is no choice
                  as to whether they are attributive or not."

... I hope sentence (6) correctly states Slater's position.   If it does,
then I think (7) must refer to 17.    But the most important question
is, does (7) refer to 17 attributively without any choice?

Certainly if the two sum expressions uttered by Abelard and Heloise 
(Hodges now numbers them (2) and (4)) refer attributively, though 
through choice, then my (7) (= Heloise's (4), = Alberic's (5)) must 
refer to 17.  But that 'must' refers to the force of the conditional, 
not the force of the consequent, and so there is no conflict with the 
content of (7).  Also, given the constraint is that (2) and (4) 
cannot both refer attributively when this is not a matter of choice, 
the remaining alternatives include not only that they refer 
attributively by choice, but also that they refer non-attributively. 
So the antecedent of the conditional I have just stated is not 
necessarily true.

Hodges goes on 'Harvey (sic) Slater says: "But what is the novelty?"', and ends

...we have two choices: we can say the observer
expression has different status that the loop expression, in spite of
being the same formula.   This is the token-relative option.   Or we can
say that the observer expression has the same status as the loop
expression, but we don't mind asserting an expression having this
status, when we state our position.   Graham Priest's dialetheism is an
example of this.   We can call this the "Liar-asserting" option, since
proponents are willing to assert "The Liar sentence is true."

Into which of these categories, token-relative or Liar-asserting,
Hartley Slater's system falls, or if it manages to escape them both, is
what I am attempting to discover.

First, Hodges has moved over to a different problematic: asserting 
sentences rather than just uttering referring phrases.  I have said 
quite a deal on this other matter elsewhere, and I take a third line 
which Hodges does not mention  - see, for instance, in the list of 
selected publications on my website, those referenced 1986(d), 
1991(b), 1995(a), 1999, 2001(a), 2002(a)(b)(c), and 2002(e).  But, 
secondly, Hodges has had for some while a new paper I emailed him, 
'Choice and Logic', which sums up my views on most of the paradoxes 
(including The Liar, and Strengthened Liar), and the relevance of 
choice to them all.
Barry Hartley Slater
Honorary Senior Research Fellow
Philosophy, School of Humanities
University of Western Australia
35 Stirling Highway
Crawley WA 6009, Australia
Ph: (08) 9380 1246 (W), 9386 4812 (H)
Fax: (08) 9380 1057
Url: http://www.arts.uwa.edu.au/PhilosWWW/Staff/slater.html

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