[FOM] 23 syllables

[Hartley Slater]

Bill Greenberg says:

>Take (1,2,) as premises,
>
>1) Des('Het', Het) <-> Het=Het                                   Premise
>2) -(G)(Des('Het',G) <-> Het=G)                                 Premise
>
>We then have the following:
>
>3) Des('Het', Het)        
>1
>4) (EG)-(Des('Het',G) <-> Het=G))     			                    2
>5) -(Des('Het',G) <-> Het=G)                                        
>		4,EI
>6) (Des('Het',G) & -Het=G) v (Het = G & -(Des('Het',G))       5
>7) -(Het = G & -(Des('Het',G))
>          3, Leibniz's Law
>8)  Des('Het',G) & -Het=G
>           6,7
>9)  Des('Het', Het) & Des('Het',G) & -Het=G                           2,8
>
>Do you accept (9)?  If not, which of (1,2) is false?


I am not sure what Bill is asking.  (1) and (2) say that 'Het' 
designates Het, but not uniquely, i.e. that not everything that 'Het' 
designates is Het.  But (9) just says this in another way (as it 
must, since it is deduced from them).  So where is the problem?  My 
point was that the standard definition of heterologicality simply 
entailes (2) - which means that the designation relation cannot be 
1-1.

The context was a discussion of Berry's paradox, and I was showing 
that a similar attention to basic logic as resolved that also 
resolved Grelling's.  I referred readers to the very end of my recent 
paper 'Epsilon Calculi' 
(http://jigpal.oxfordjournals.org/cgi/content/full/14/4/535), where I 
make the general point, amongst other things:

>In an earlier treatment of this same paradox Priest, like Copi, 
>Thomason, and Asher and Kamp, derived a contradiction assuming that 
>the denotation relation was 1-1 [94, p.162]. But again the 
>conclusion must be that all that Priest has proved is that if the 
>denotation relation is univocal then there is a contradiction. 
>Hence, we may deduce, the denotation relation is not univocal - 
>although we must also realise that that does not mean a more liberal 
>semantic denotation relation could be defined.

The specific point in connection with '23 syllables' I demonstrate 
immediately before this, where I say, amongst other things, that 
there is no problem with lon(DN19) not being in DN19 (i.e. the least 
ordinal not in the set of ordinals denotable in less than 19 words 
not being in the set of ordinals denotable in less than 19 words), 
since there is no requirement to also affirm the reverse.  If 'the 
least ordinal not denotable in less than 19 words' uniquely denoted 
an ordinal then that ordinal would both be and not be denotable in 
less than 19 words.  Hence it does not uniquely denote an ordinal - 
indeed it then need not denote an ordinal at all, being 
non-attributive, like (informally) Donnellan's 'the man drinking 
martini' and (formally) many epsilon terms.

The general problem with the period when the so-called 'paradoxes' 
were such a concern to people was its Formalism, since that involves 
the resultant, more specific belief that the structure and semantic 
content of a term ought to tell one what it denotes (Russell's Theory 
of Descriptions, of course, reinforced this idea).  The appeal of 
this is that, if it was the case then attending just to the words 
found in books, and on computer screens, would be justifiably enough 
(so we could, for instance, work just meta-mathematically with 
axiomatic arithmetics without any thought of there being other models 
than the standard model).   It was this monastic calling that was 
fundamentally under threat, in this period, since it banishes all 
questions of ambiguity and wider context, and also, in the resolution 
of such features, the normal, everyday, pragmatic actions and choices 
we make in the world beyond books and screens.   It is no accident, 
of course, that Hilbert's Epsilon Calculus is often called 'The 
Choice Calculus'.
-- 
Barry Hartley Slater
Honorary Senior Research Fellow
Philosophy, M207 School of Humanities
University of Western Australia
35 Stirling Highway
Crawley WA 6009, Australia
Ph: (08) 6488 1246 (W), 9386 4812 (H)
Fax: (08) 6488 1057
Url: http://www.philosophy.uwa.edu.au/staff/slater