Pears gives many interesting exegesis of Russell's most obscure points. One
I found of especial interest is that Russell keeps swinging between an
absolute sense of atomicity and a relative one, when perhaps there is just
one. By 'relative atomicity', as Pears notes, Russell means "relative to me",
i.e. "Russell" -- even if Russell found "Russell" NOT a logically proper
name.
In a message dated 9/13/2015 4:06:47 P.M. Eastern Daylight Time,
donalmcevoyuk@xxxxxxxxxxx quotes from Pears.
Pears writes: "The two views -- [Empiricism and Rationalism] may be
combined without any incoherence. They share the same conclusion, logical
atomism, and they both incorporate the assumption of a general correspondence
between language and reality. They differ only in their methods of
establishing
the conclusion. According to one view [Empiricism], it is established
empirically [inductively? Speranza], like [Goldbach's] conjecture that every
even number is the sum of two prime numbers, while the other view
[Rationalism] takes it to be [merely] provable, as it is hoped [as an IDEAL OF
REASON?] that the arithmetical conjecture will be proved one day. So Russell
was
not wrong when he allowed both views to be represented in his treatment of
logical atomism."
McEvoy's problem with this: "There is a lead up and follow-on to this and
both may be read to put it in context. There remains the following puzzle:
Pears speaks of a conjecture "like the conjecture that every even number is
the sum of two prime numbers", and says this example illustrates one of the
two delineated "methods of establishing the conclusion", and further says
"According to one view, it is established empirically." But such a
conjecture cannot be established empirically i.e. by 'observation'. We cannot
ever
observe [in an empiricist SENSE], for example, whether "every even number
is the sum of two prime numbers [We cannot "observe" an even number or a
prime number either, in an empiricist sense of "observe"]. Even the empiricist
view of such conjectures is not that they are established "empirically"
(by way of observation) but analytically"
I think that as one of my previous posts pointed out, there are quite a few
takes on how to even INTERPRET Goldbach's conjecture, never mind 'prove'
it!
"hence the view we may find in Hume and expounded in, say, Ayer's
Hume-based version of "Logical Positivism" Language, Truth and Logic - that the
only true propositions with sense are those true by virtue of the meaning of
their terms (analytically true) and those verifiable by sense experience
(empirically true). Is this just a slip by Pears? A slip where he does not mean
such claims or conjectures are "established empirically" (as this is not
even the view of the empiricist)?"
While I should bring Lakatos's misuse of Popper's use of 'conjecture', I am
reminded that Goldbach never used 'conjecture' for the simple reason that
he didn't speak English. He said:
"Vermutung"
from "vermuten".
***** INTERLUDE ON WHAT GOLDBACH THOUGHT and why Euler never answered his
letter *********
Back a few centuries, there used to be a verb in Germany, "muten".
And that basically meant "to want something".
People wanted all kinds of things back then, but ironically not this verb.
So it disappeared.
But there was one prefix-version of it too… of course. And that survived.
And Goldbach exploited it.
Vermuten.
It means to suppose or to guess.
As when Goldbach wrote to Euler about what he was SUPPOSING or GUESSING.
Oh dear ver-prefix… thank you for another “how on earth”-moment.
Ich vermute, dass morgen gutes Wetter wird.
I suspect/suppose that tomorrow the weather will be good.
Or to use Pears's example:
I suppose that every even number is the sum of two prime numbers.
Vermutlich kommt Thomas wieder zu spät.
Presumably, Thomas will be late again.
Conjecturally, every even number is the sum of two prime numbers.
“Weißt du, wieso der Kaffee immer so schnell alle ist?”
“Ich weiß es nicht aber ich habe eine Vermutung… der neue nimmt immer was
mit nach hause.”
“Do you know why the coffee runs out so fast.”
“I don’t know it for fact but I have a surmise/theory.. the new guy
always takes some home.”
Do you know, Euler, if every even number is the sum of two prime numbers?
No, my dear Goldbach, but, like you, I conjecture that it is!
So… the ver-prefix sometimes, I repeat, sometimes expresses the idea of
for.
For example to forgive means vergeben.
And if we now say that whatever we “suppose” is one of 2 alternatives and
we “want” that alternative… like… that would be our choice if we had to
bet money on which alternative will become reality… we kind of "muten"
(want) for that alternative … like, that’s what we would put our money on
because we consider it likely and that doesn’t mean this is also the outcome
we
personally would wa… what?
That explanation is confusing and hard to follow?
Well… I’m sorry… it’s not my fault that German prefixes are so overly
demanding, or that Goldbach did not use "conjecture" even if brilliant Pears
does!
************************ END OF INTERLUDE
McEvoy goes on:
"Does Pears instead mean by "established empirically" that they are
established, on one view [EMPIRICISM], 'according to an empiricist theory of
knowledge' (even though this empiricist theory of knowledge holds that such
claims are _not_ "established empirically")? But this would make Pears'
expression the very opposite of what he terms "tolerably clear". JLS has spoken
of Pears' "genius" and perhaps will find it no trouble to clear this one up."
Well, apparently, Pears uses 'tolerably clear' twice, and perhaps he was
reading H. D. Lewis, "Clarity is not enough" (reprinting Price, "Clarity is
not enough).
Tolerable clarity is perhaps enough?
Pears says that while Russell's theses "are questionable, their meaning and
interconnections are tolerably clear."
He also notes that the concept of acquaintance is "tolerably clear": "it is
the way", Pears writes, "in which the mind apprehends things which in the
case of perception and memory of perception."
But Pears writes that not in the essay we are discussing but in "The
function of acquaintance in Russell's philosophy" (1981).
I must say that I find the phrase 'tolerably clear' charming and worth a
repeat or two!
In the Intro we are discussing the actual phrase is
"Though many of Russell's doctrines are questionable, their meaning and
interconnections are tolerably clear."
Pears is obviously having in mind Russell's doctrine of acquaintance which
Pears had found "tolerably clear", as far as its function is concerned.
Pears is being tolerably clear here:
He is opposing EMPIRICISM and RATIONALISM and using, as a simile,
Goldbach's Vermutung. According to EMPIRICISM, the conclusion is reached
INDUCTIVELY. According to RATIONALISM, it isn't, and it is posed as an IDEA [to
be
reached DEDUCTIVELY, not INDUCTIVELY] OF THEORETICAL reason, and assessed,
qua conclusion, as merely _provable_ (to be hopefully "proved one day", Pears
charmingly adds -- without specifying any exact date, cautious as he ever
was in his use of English -- in this he is what I call the English
Goldbach).
For surely, if it is proved one day, it is RATIONALLY provable.
Pears must be making a pun, too, on Lakatos's pun ("Proofs and refutations:
the logic of mathematical discovery") on Popper ("Conjectures and
refutations: the growth of scientific knowledge") -- since Pears liked a pun.
Cheers,
Speranza
REFERENCES
Deshouillers, J.-M.; Effinger, G.; te Riele, H. & Zinoviev, D. "A
complete Vinogradov 3-primes theorem under the Riemann hypothesis" (PDF).
Electronic Research Announcements of the American Mathematical Society 3
Doxiadis, Apostolos. Uncle Petros and Goldbach's Conjecture. New York:
Bloomsbury. ISBN 1-58234-128-1
Lakatos, Proofs and refutations: the logic of mathematical discovery
Montgomery, H. L. & Vaughan, R. C. "The exceptional set in Goldbach's
problem. Collection of articles in memory of Jurii Vladimirovich Linnik". Acta
arithmetica 27
Pears, Intro to Russell, Logical Atomism.
Popper, Conjectures and refutations: the growth of scientific knowledge.
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