[hist-analytic] A 'Series' of Anscombianisms!

Jlsperanza at aol.com Jlsperanza at aol.com
Fri Feb 6 08:32:05 EST 2009


I'm pleased with S. Bayne's careful reading of "Philosophical  
Investigations". He writes down a 'series' of Wittgenstein quotes:

143,  145, 151:

To wit:

143: 

>Do not balk at the expression 
>"series of  numbers"; it 
>is not being used wrongly here."

'balk' is not part of my repertoire, and it's  not a germane German  word, so 
I'll blame that one on Anscombe!
 
145:
>Suppose the pupil now writes 
>the series 0 to 9 to 
>our satisfaction"
 
Oddly, while my mother (a teacher of the old school) does use 'pupil' in  
ways that irritate me, I _always_ used 'student' and 'instructee' if I must! I  
associate 'pupils' with boarding schools in cold climates!
 
It's amusing how Wittgenstein seems to be more concerned with 'emotional'  
factors than anything else: "don't balk!" "not used _wrong_!", "our  
satisfaction".
 
Finally, 
 
151:
>[he] writes series of numbers down...
>tries to find a law for the sequence"
 
Indeed, there seems to be two 'actions' here: writing down a series, and  
finding the 'law' for the sequence. This relates to some wrong uses of 'period'  
(my mother pointed out to me that one!) as used by journalists! as in the  
otiose:
 
          long periods of  time
 
It is true that a 'period', mathematically, is like a series.
But it also means 'lapse'. And local journalists have been heard to use  
'short lapse of time', as if it could be a short lapse of something other than  
time.
 
Anyway, back to series.
Is it true that a series _entails_ a 'law' or 'rule'? 
It's one of those  trick of Latin names, like 'species' (cfr. speciesism) 
that one wonders what  gender they are, and the presence of final 's' is 
confusing, and in that the  plural identifies the singular. Enough reasons, I find, to 
contradict  Grice!
 
                GRICE (to Austin), I don't care what the dictionary says
                AUSTIN: And _that_'s where you make your big mistake.
 
The Short/Lewis is not strictly enlightening, but it notes:
 
   -- it can be synonymous with 'ordo' which brings me to another  petpeeve, 
"in no particular order". I thought this was _logically  contradictory_. 
Surely there _is_ a particular order, even if it is a _random_  one!
 
    One cite in Latin refers, Short/Lewis think, to 
 
    "the connection of words"
 
which is a good one, "Colourless ideas furiously sleep green" 
 
"tantum series juncturaque pollet"
and comes from Horatius, A. P. 242 .
 
It relates the etymology to 'serere'. This in turn they make cognate with  
(via root sa-) with Greek saô, sêthô, to sift) and it's related to 'to beget': a 
 series being, say what is _beget_ (sp?) by a rule, or ruler, rather, since 
it  can mean line of descendants.
 
The OED brings the Romantic side to us: Italian!
 
English 'series' is from Latin L. series row, chain, series, f. serere to  
join, connect. Cf. F. série, It., Sp., Pg. serie.] Are there any quotes worth  
spreading ('diseminare')? Yes:
 
1812 MISS MITFORD in L'Estrange Life (1870) I. 191 In Oxfordshire, where I  
saw a landscape, or rather a series of landscapes, of singular beauty. 
 
1709 FELTON Diss. Classics (1718) 188 The worst Province an Historian can  
fall upon, is a Series of barren Times, in which nothing remarkable happeneth. 
 
1886 Act 49 & 50 Vict. c. 44 §13 That the repayment of the money to be  
borrowed should be spread over a series of years.
(ordered sequence,  succession. JLS)
 
1656 EARL OF MONMOUTH tr. Boccalini's Advts. fr. Parnass. I. lxxx. (1674)  
108 [They] made a long and exact Series of many abuses which reigned in that  
State. 
(In no particular order, I hope! JLS)
 
1748 Anson's Voy. I. x. 98 We had a series of as favourable weather, as  
could well be expected. 
 
1779 JOHNSON L.P., Watts (1868) 450 The series of his works I am not able  to 
deduce.

I am, typically, in a rush, so I'll end this with (luckily) what I think is  
the relevant 'use', which the OED has as "Math." and defines (I don't usually 
do  OED for definitions, but here you are) as
 
        a set of terms in  succession 
        (finite or infinite in number) 
 
[*not* _pace_ Dummett!]
 
 
           the value of  each of which is determined 
          by its ordinal  position according to a 
          definite rule known  as the 
         
                           law 
 
          of the series;  [Latin 'lex', don't think so. I was
          examining that  English 'law' has not really
          Latin cognates. JLS] 
          esp. a set of such  terms continuously 
          added  together.

See ARITHMETICAL,  GEOMETRICAL, RECURRING, etc. 
 
1671 J. GREGORY in Rigaud Corr. Sci. Men (1841) II. 224 
Reducing all of them [sc. equations] to infinite serieses. 
 
1736 Gentl. Mag. VI. 739/1 
Any one who is conversant in Series. 
 
1750 Phil. Trans. XLVII. 20 
The operation, by having two or more series's to multiply into one another,  
becomes very troublesome. 
 
1791 Ibid. LXXXI. 148 
The serieses deduced should converge. 
 
1839 R. MURPHY Algebr. Equat. 92 
Recurring Series have been much used..in the solution of algebraical  
equations. 
 
1874 GROSS Algebra II. 153 
Summation of Series.

Also, the OED has it, used allusively (in that use, one  expects): 
 
1836 J. GILBERT Chr. Atonem. ii. 59 
To examine in detail the series, of which the computed sum betrays at once  
somewhere in the calculation so gross an error. 
 
1853 [WHEWELL] Plural. Worlds v. 76 
We have here to build a theory without materials;to sum a series of which  
every term, so far as we know, is nothing.

This Whewell last should be interesting. 

Cheers,

JL









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