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 JON NEIVENS: Hi Gary,
Many thanks for your replies, I’ve tried to respond to them in one mail. I’ve snipped most of the original Monk/Russell stuff just to save space, but hopefully the context is still clear enough. Me Previously:
Russell's paradox is the most famous of the
logical or set-theoretical paradoxes.
The
paradox arises within naive set theory
by
considering the set of all sets that
are
not members of themselves.
Much of this would apply to what we have been saying about open and closed systems, that closed systems are artificial constructs necessarily taken out of their existential [living]/ historical/, etc, contexts. I would say the problem of the set that does not include itself reflects the problem that no set, in the first place, is ever complete, in existential reality is never ever self-enclosed except for artificial containment for the purposes of working upon and within it, that all 'sets' refer to the necessary living reality of me, myself and I, Gary Moore [regrettably lacking a better referent point, but the job was given to me, I did not volunteer, and only get around that by the illusion I work within a 'real' public world, that is, THE WORLD AS WILL AND REPRESENTATION, the world as the final case of the facts of the matter, A.K.A. Wittgenstein's TRACTATUS], and, of course, as thgis pitiful final referent and cause, I am woefully powerless, incomplete, ignorant, willful, whimsical, foolish, and emotional altogether. So the set of all sets is included in its own set not out of logical conclusion but out of living reality.
I’d come at it from a different direction,
and say that closed sets are actually
the
norm. If one considers the kinds of
things
we actually use sets for, something
like
“All the sheep that are marked with
a ‘J’
belong to Farmer Jones” then that kind
of
set is closed enough to have got someone
hanged for sheep thieving until not
too long
ago. It’s only when we place no limit
on
the “all” and speak of “the set of
all sheep”
that we have something that, whilst
theoretically
closed, is beyond the scope of our
practical
imagination, and may as well be open
to the
extent that for as long as there are
sheep
it will be added to.
Your point is very well taken and I
completely
agree with it. It CLEARLY denotes the
practical
use of classes whereas the Idealistic
approach
is shown to be totally bogus. Did you
read
the Ray Monk quote about Poincare's
dispute
with Russell I think I put in a letter
to
Richard? I agree with Poincare completely
while Russell will still suffer from
an Hegelian
Idealistic eczema – until his meeting
with
Wittgenstein, the most unidealistic
of all
thinkers [very much like Doctor Hannibal
Lecter the most materialist of the
materialists],
and the most nominalistic of the nominalists?
– a long time even after Poincare's
point
was so indelibly made. Reading about Russell's life is usually disgusting,
even perverted, in his stringent, extremely
strange way of trying to be perfectly
moral
and causing so much harm by doing so.
He
is literally carrying his intellectual
Idealism
into his life and destroying other
people's
lives – and then making the pain linger
on
and on in the name of perfect morality.
And
yet he is so nice and polite and truly
kind
and generous to his professional colleagues,
so unlike Ludwig Wittgentein, the professional
killer and professional survivor who
would
shred his opponents as if they were
dead
meat, the coldest, bleakest man in
the world
unless he was angry until, possibly,
he went
to New York before he coldly, bleakly
died,
never gave kind consideration to anyone
[except
in WWII he served as an orderly in
the English
hospitals which must have been an absolutely
horrendous job during the bombing but
nothing
like surviving the Russian Front from
1914
to 1917 under incompetent commanders
and
being overrun again and again by bloodthirsty
Russians – especially if you were Jewish
which Wittgenstein thought he was to
his
utter shame – the major portion of
what remained
of the Jewish population in Galicia
fled
to the environs of Vienna – a truly
Lithuanian
Lecter tale. I once asked a Ranger
who served
two tours in Vietnam if anyone ever
had to
resort to cannibalism, and he replied,
his
eyes glazed over as if looking into
a great
distance, 'You do what you have to
do', in
the most chilling way I ever heard
in my
life including the movies.] Idealist
morality
in practical life Russell thoroughly
demonstrates
is a horrible and sterile disaster.
Such a set appears to be a member of itself
if and only if it is not a member of
itself,
hence the paradox. Some sets, such
as the
set of all teacups, are not members
of themselves.
[i.e., as set of teacups is not itself
a
teacup—Jon] Other sets, such as the
set of
all non-teacups, are members of themselves
[i.e., the set of things which are
not teacups
is itself not a teacup—Jon] Call the
set
of all sets that are not members of
themselves
"R." If R is a member of
itself,
then by definition it must not be a
member
of itself. Similarly, if R is not a
member
of itself, then by definition it must
be
a member of itself. [In other words,
if we
now move on to gather all those sets,
like
the set of all teacups, that are not
members
of themselves into a new set, we can
then
ask whether _this_ set is a member of itself. If it is not
a member of itself, then it is a set
which
is not a member of itself, and hence
it is
a member of itself. But if it is a
member
of itself, then it does not belong
in the
set of sets which are not members of
themselves—Jon
again]
Since an unlimited set theory was crucial
to Frege’s attempt to discover the
logical
basis of arithmetic, this paradox had
a devastating
effect on his work.
I think Monk's analysis of G. E. Moore's
that a proposition is not linguistic analysis
but ontological [or existential/living?]
complex of concepts or facts or particulars
support what I said above and bypasses
Frege's
problem, and that Russell is on the
right
track, though I think wrong in trying
to
get rid of his 'shadowy concepts',
that is
false propositions are constructed
from true
facts, therefore 'Mont Blanc is made
of cheese'
is a false proposition made up of the
true
concepts 'Mont Blanc' and 'cheese'.
Or as
Wittgenstein might say, If this is
the facts
of the matter, then this is the facts
of
the matter – learn to live with it.
Also,
what he says about logic being solely
composed
of tautologies maybe relevant here. I don’t know enough about Moore to comment
on that, but it does sound similar
to what
Wittgenstein asserts in the Tractatus—that
a proposition ‘mirrors’ reality, i.e.,
the
arrangement of concepts laid out in
a proposition
mirrors the arrangement of facts in
the world
(and Wittgenstein says at 1.1 that
“The world
is the totality of facts, not things.)
Now this is something I profoundly disagree
with, but see below for more on this.
What that damn 'Moore' said that I keep getting
letters from is that Ray Monk said
'Thus,
for Moore, and, even more crucially,
for
Russell, analysis is not as it is commonly
understood now – a linguistic activity,
but
an ontological one. To analyse a proposition
is not to investigate a portion of
language,
it is not to attend to words, it is,
so to
speak, to carveup the world so that
it begins
to make some sort of sense. 'A thing
intelligible
first', writes Moore, 'when it is analysed
into its constituent concepts' [pg
117].
Now Ray Monk's sense of analogy may have
got away from his control. What I seem
to
get from Moore is that the only 'reality',
itself just a word, is words NOT TO
BE CONSTRASTED
TO AN UNINTELLIGIBLE 'OTHER' REALITY
WE CANNOT
SPEAK ABOUT. Words are the only 'reality'
we have, therefore, ontologically,
you do
not 'attend' to words as distinguished
from
. . . whatever . . . but, ontologically
there
are only words. When we pretentiously
try
to analyse sensation, we are investigating
one portion of language about another
portion
of language. When we seriously try
to describe
'sensation itself' outside of words,
we may
start with a vague agreement that soon
starts
to break down in specific application,
'This
iron ball is heavy' versus 'I do not
think
it is so heavy especially when compared
to
this rock' – to vast disagreement about
pleasure
–'I think sex is fun!' versus 'Sex
cannot
possibly be fun when one thinks of
all the
responsibilities that go with it!'
Words
stretch. Always. Wittgenstein's language
games show how, when language stretches
into
another game's territory, it becomes
absurd.
There is no way to get away from 'stretching'.
Therefore, ontologically, language
is a very
loose bag containing an unsystematizable
hodge podge of 'things' only 'unified'
or
'systematized' by being in the loose
bag
of language. BUT I have NOT read this damn Moore's actual
paper.
… the biography discussed a very difficult
analysis of a conversation between
Russell
and Frege over Meinong's problem of
'the
snows of Mount Blanc'. Does that really
contain
a 'knowledge' of Mount Blanc itself
or not?
Frege says no, Russell says yes. It
involves
an analysis of Hume's - but Hume is
unmentioned
- scepticism about the 'belief' in
the 'truth'
of a statement. To Hume, belief is
belief
whether in 2+2=4 or God and equally
unreliable
and I agree. Russell brings in a distinction
of 'objective correlative' from the
'subjective
correlative' and I started getting
a head
ache.
I’m not sure I understand Hume’s view. My
initial reaction is that if someone
says
“Jon believes that England won the 2002 World
Cup”
This can be tested by asking me who won the
tournament, and to test whether my
belief
is itself true one can look up who
won in
2002 and, finding that it was in fact
Brazil,
conclude that my belief is false. If
Hume
is simply pointing out that our beliefs
_can_ be false, and are hence unreliable in the
sense of not being absolutely certain,
I
can agree with that but I’d question
whether
that kind of absolute certainty is
an appropriate
standpoint from which to judge belief.
Is there a clear-cut line between what one
believes and what one does? I’d say
not always—I’d
assume that one would have to bleed
into
the other, though perhaps this is a
two way
process. My point above was that some
beliefs
are more easily verified than others,
so
I’d hesitate to treat them all as equal.
(And I’d want Moore to provide some
justification
for his use of ‘merely’ in ‘merely
mental.’)
As it happens, one of the most interesting
books I’ve read on belief is Wittgenstein’s
_On Certainty_. It contains one of my favourite quotes:
“I am sitting with a philosopher in
the garden; he says again and again
‘I know
that’s a tree’,
pointing to a tree that is near us. Someone
else arrives and hears us and I tell
him:
‘This
fellow isn’t insane. We are only doing philosophy.’“ [#467]
Wittgenstein’s main point is that there are
specific contexts where we use the
word ‘believe’
or ‘know’ and we get into tangles when
we
try to use these terms outside such
contexts.
Generally only philosophers and madmen
say
things like ‘I know that’s a tree’
when pointing
to a nearby tree.
GARY. C. MOORE: You are perfectly correct except that I think 'belief' has always an Idealist tinge, an assertion that something out there, the confirmation of 'reality', supports my proposition whereas – I think – what Moore is getting at is that knowledge and truth are merely the logical agreements of words within their contexts and say nothing about any outside reality. There can be INTRUSION as with pain, something uncontrollable, something from an unknown source until you put it within a linguistic context and world, something profoundly unwelcome and truly irresistible. But as soon as it is immediately noticed it is put into a linguistic context. And, of course, this happens with all other sensation but even more so.
This notion of a ‘complex’ seems to be a good example of the kind of metaphysical mistake I was discussing previously with Jud. Since the sentence ‘Mont Blanc is more than 4,000 metres high’ can be divided into subject and predicate (as would corresponding ‘proposition it expresses’) then these sentence parts each correlate with ‘objective parts’ which go together to make up the ‘complex’ that is Mont Blanc.
I agree. Is your thinking here agreeable to what I said about the infinite fragmentalisation of each composing fact of either a true or false proposition, each becoming in turn a 'whole' or 'unity' that Russell at this point adores, and then which again breaks down into its component facts?
JON NEIVENS: I guess that depends on whether you’d accept
that this is primarily a fact of language
and not of the world. In other words,
it
depends whether the kind of infinite
fragmentation
you’re talking about would depend on
some
notion of a ‘substance/property’ division,
in the sense of a particular ‘substance’
having different types of ‘properties.’
For
me the substance/property division
is simply
an attempt to project the subject/predicate
distinction onto the world, from already
having made the assumption that the
structure
of language reveals the structure of
the
universe.
I am far from sure I understand what
you
are saying, but will give my rash and
untoward
thoughts anyway. This in part gets
back to
what I said about mirroring, that is,
if
you reflect something and know it is
a reflection,
for instance right/left switch, then
you
know the original. Though this is perfectly
true in one fashion, one has sensation,
sensation
and language are necessarily wholly
different
entities. One cannot 'know' sensation
the
same way one 'knows' language. Their
only
'real' relationship is that language
disturbs
sound waves in different patterns or
makes
figures on paper or screen. The 'meaningfulness'
of language, its 'revelation of the
structure
of the universe', only goes on in my
head.
Understanding of 'your' language only
goes
on in my head, elsewise it is only
marks
on a screen whose only unity is proximity
in a limited area. I would say the solipsistic dilemma, for
it cannot be systematic in anyway -
since now that my retarded mind thinks of it after
all this time - is sensation, perception, all purely dependent
on my standpoint VERSUS I KNOW I did
not
create your words myself, they come
out of
nowhere literally as intriguing strangers
tantalizing me away from my Georgian
and
Kazakh stamps, but become mine truly
as soon
as I read them hence THIS interpretation.
We do indeed know sensation but only
as sensation.
Its seriality gives the imagination
the ability
to invent time and all of the future
and
past, whereas in sensational reality
impressing
upon me it is ONLY now, now, now, now.
But
I do not know how much memory retention
and
comparison, the basic tools of imagination,
are really either imaginative or sensational.
They have been taken out of the sensational
context but I am reluctant to divorce
them
from pure sensation. Is this mere sentimentality,
mental insecurity, a clutching my teddy
bear?
I agree, although the way I’d put it is that
we can divide things up into assemblages
of parts or combine things into greater
assemblages,
but this is a fact of language, and
not of
the world we use language to describe.
Aristotle
describes a proposition as ‘a taking
apart
which puts together’ which is actually
quite
accurate, but again it would be a mistake
to assume that this tells us anything
about
the _structure_ of what we’re talking about. GCM: Synthesis and diaresis, right?
This is a good point to bring up. 'Structure' implies 'design'. There can be no design in nature, therefore no structure. In fact, swallowing up my own statement, like Ourannos eating Saturn [??], there can be no 'nature' in nature. In the beginning was sensation which literally being most firstest of all, all explanations both rely upon sensation to explain sensation but always using posthumous contexts to explain something that happened before, outside, and utterly without them. This is very obscure groping. We are using words to describe something wordless, yet know this and still really know what we are talking about, but after a lengthy process tend to blur the distinction between words and pure non-verbal experience. I found the discussion of teleology in Kant's CRITIQUE OF JUDGMENT fascinating in this regard. He explained the intense PASSION to discover design in nature, portrayed it excellently and convincingly, and then proceeded to show how entirely bogus it was right down to the bottom. I wish he had written more extensively and touch on the many different ways teleology fundamentally always influences our thinking, but what he did write was devastating – and illuminating. We always fall into the hidden shapes of teleology when we think abstractly. I hope this is not complete nonsense.
I don’t think it’s necessary to go that far.
The problem is the Rationalist notion
that
the Universe is rationally constituted,
and
that humans as rational animals are
uniquely
capable of uncovering that structure.
There
is a sense in which this very general
notion
applies to science, but the specific
point
concerns metaphysics. Here, the notion
is
that the ‘substance/property’ division
which
is inherent to language is a part of
the
structure of the Universe. It isn’t.
It’s
just part of the structure of language.
I
agree with Kant’s point about the passion
for structure, but the point here is
not
to use the notion of structure analogously.
Apologies that I’m labouring this point,
but it’s pretty important to my thinking
on these kinds of issues.
Thinking 'literally' is extremely difficult. It HAS to be 'belabored' because you are banging at the gates of sensation with language and they will never open.
Monk:
The other problem concerns false propositions.
The idea that Mont Blanc itself is
a constituent
part of any truth concerning it, and
the
associated idea that the FACT
'Mont
Blanc is more than 4,000 meters high'
is
the object of the belief 'Mont Blanc
is more
than 4,000 meters high', seem initially
very
plausible. One might even think they
were
platitudes. But when Russell, following
Moore,
identifies the proposition 'Mount Blanc
is
more than 4,000 meters high', not with
the
belief but with the object, namely
the fact,
it becomes very difficult to say what
a FALSE
proposition is. What is the object
of the
belief that 'Mount Blanc is more than
4,000
meters high'? According to Meinong,
both
true and false beliefs alike had Objectives.
Where they differed was in whether
the Objective
subsisted or not. In Meinong's theory,
objects
had different kinds of being – particular
objects objects which occupied space
and
time EXISTED, abstract objects (like
numbers)
SUBSISTED, but some objects (unreal
particulars
like the characters of fiction and
mythology)
neither existed nor subsisted. Meinong
used
these distinctions to explain the difference
between true and false beliefs – true
beliefs
had Objectives which subsisted, false
beliefs
had Objectives which neither existed
nor
subsisted – they were, as Meinong put
it,
'beyond being'. Russell, however, was
unable
to accept Meinong's view that there
were
objects which lacked being of any kind.
For
him, false beliefs had false propositions
as their objects, and false propositions
had being just as much as true ones.
There are, then, such 'complex objects'
as false propositions. The view that
had
startled Frege thus becomes, in the
light
of this modification of Russell's theory
of propositions, more astounishing
still
– for now Mount Blanc itself, with
all its
snowfields, is a constituent part of
any
number of false propositions('Mount
Blanc
is made of cheese', 'Mount Blanc is
in England',
and so on). Eventually Russell despaired
of these 'shadowy objects' (as he later
called
them) that were false propositions,
and revised
his theory to get rid of them, but,
for the
moment, reluctant to abandon the 'liberating'
logic of propositions he had learnt
from
Moore, he was stuck with them.
This kind of problem arises from assuming the structure of language tells us about the structure of the world. In a false statement, the subject establishes a referent in the same way as does a true statement, with the difference that what is stated in the predicate is not appropriate to that referent. In neither case do we have a ‘complex’ of ‘Mont Blanc’ and ‘ more than 4,000 meters high’ or of ‘Mont Blanc’ and ‘made of cheese.’ We simply have words used to establish a referent and words which may or may not be appropriate in respect of that referent. Obviously if those words are appropriate, then our familiarity with the way those words are normally used can allow the statement to provide us with new information. I don’t know if any of this helps. I find Russell one of those characters in philosophy who’s ‘interestingly wrong.’
I would say language does tell you
something
about the structure of the world but
in a
way that does not at all disagree with
your
statement. I am assuming what you are
criticizing
in Russell is his early Idealist and
absolutist
stance to the effect you can know the
'realness'
of reality. Pioncare tales him to task
for
that and I need to print that portion
of
Ray Monk out. I have done so somewhere, God help me, and
related it to his dreadful application
of
Idealism to morality and real people.
His
biography daily life is not fun to
read but
is more like a very bad soap opera.
As Poincare [sp?] says, Euclid's axioms
say nothing about the world. They are
just
statements you can choose or not to
use and
see if they work. Russell violently
disagrees
with this, says they MUST tell us something
about reality, and I think he
is dead
wrong.
Knowledge is a piece meal affair. Sometime
I would like to go into set theory
but in
the opposite direction the early Russell
does because, in dealing with stamps,
specifically
with what are called 'definitives',
that
is, the standard stamps used for standard
usage, not like commemoratives or souvenir
sheets but just the stamps you use
to send
mail to people who do not care about
stamps
and find these plain, unattractive
stamps
not worth their attention and throw
them
away. History, inflation, changing
of rates
for other reasons, running out of a
printing
- changes over time what composes a
standard
set, eventually loosing all of the
initial
issues so that after a while what is
on hand
has little relation to the initial
issue.
Most of the changes are visually minor
but
important to time and place and what's
happening
around them.
The point of this is language does
tell you something about the structure
of
the world but only of one point at
a time
– you never are able to truthfully
systematize
all the points – then history changes
the
perception of the world – language
becomes
a very vague and loose guide at best,
at
worst completely distorts the truth
– and
you can NEVER say you have any handle
at
all on the whole matter of the 'world',
but,
if you are lucky, you have a handle
on a
tiny piece of it right now – whose
value
may already be sliding away.
Hopefully I’ve given a clearer picture of
what I mean on the language/structure
point.
So I’d make a strong distinction between
the idea that we can use language to
talk
about the structure of something, and
the
notion that the structure of language
tells
us about the structure of the universe.
In
one sense I agree that knowledge is
a piecemeal.
Or rather, what I’d say is that the
expansion
and acquisition of knowledge is often
a piecemeal
affair. But on the other hand, I like
the
notion of Quine’s holism:
As someone on the Analytic list recently
put it
“Our theories stand up to the tribunal of
experience as a corporate body. When
something
unexpected happens, it isn't necessarily
the specific theory under test that
you'll have to patch up or reject.”
One could probably say that the more unexpected
something is, the more patching we’ll
have
to do across the whole range of our
theories.
But another important point is that
our scientific
theories merge into our pre-theoretical
beliefs,
and the latter is to some extent built
upon
the former (although of course we can
and
do end up with scientific theories
that contradict
our original pre-theoretic beliefs.)
I guess
the point about theory in this sense
though
is its generality. It doesn’t really
touch
upon the kind of specific knowledge
you discuss
above.
Ah, but do not scientific revolutions start, in the beginning as irritating little 'unexpectantcies' ? For instance, the Ptolemaic Theory of the solar system DOES work, and is actually – they say – very nice for astrologers still, and remember astronomy was just a pastime for Kepler as it was for Newton, the important sciences were astrology and alchemy - but the Copernican Theory is, yuck, yuck, 'true' because it is vastly easier to work with, a mere matter of pragmatics – to some extent, and adjusted truth values. In fact one might still be able to get some interesting ideas out of the Ptolemaic system. Also, since false statements ARE composed
of true facts, there is always the
possibility,
however unlikely, of you feeling a
BIG bump
in the night and in the morning find
Mount
Blanc sitting outside your window.
If one
can establish a referent, it is –contingently,
my escape hatch – possible. The absurdity
of the possibility, which may be extreme,
is merely 'unreasonable' in the sense
that
such possibilities are unreasonable
for any
gentleman to seriously consider, and
that
is quite right and practical. BUT we
are
not talking about the practical here
but
the fact that facts place together
in a sentence
at this time and under these circumstances
are clearly impossible. But totally
change
the circumstances, or even, as I have
brought
up in other letters, the facts are
reconsidered
as whole, unifying abstractions themselves
that in turn can be analysed and their
necessary
incompleteness found, and a hole provided
by which yesterday's absurdity can
intrude
into today's world, and then Mont Blanc
might
be found in Sussex composed of limburger
cheese.
This may sound especially nit-picking but
I wouldn’t really want to say that
a false
statement is composed of true facts.
I’d
rather use the word ‘fact’ to refer
to what
a proposition as a whole says. As far
as
I know this is how Russell uses ‘fact’
which
is probably more important in this
instance.
The individual terms that make up a
false
proposition are of course meaningful,
as
is the proposition as a whole. Part
of the
problem for Russell is that he wants
to conflate
‘meaning’ and ‘reference’ so that a
false
yet meaningful proposition must nevertheless
have a referent. Although the sentence
‘Mont
Blanc is made of cheese’ is meaningful,
I
would say that’s simply because its
component
parts already have an established use.
GARY. C. MOORE: Though what you say is perfectly true,
I
would bring up the disturbing matter
that
all intellectuality, logic, mathematics,
science, cross word puzzles, is a product
and grounded thoroughly upon imagination
per se. Workable imagination, yes,
but, as
I said about 'belief' 'imagination'
is still
imagination no matter what and that
is inescapable.
Must get ready for work The false prophet
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