Grice's Logical Corpuscularism

Speranza

Was Grice a logical corpuscularian? It seems so.  After all, he  wrote  an essay, "Definite descriptions in Russell and in the   vernacular", by vernacular meaning Strawson; and while Grice agrees that   both Russell and Strawson make a 'common mistake', Grice feels he has a foot on each camp
(Russell's and Strawson's).

Grice's manoeuvre is to re-interpret what Russell saw as an entailment (and Strawson ignored)  as  an implicature.

When Myro  published  (rather posthumously published)  his "Logic" he makes much of the atomic-molecular distinction as applied  to propositions, and it's noteworthy  that Grice's claim to fame (among  logicians) was his implicatural analysis of  two-place operators, that make  up for  MOLECULAR propositions.

So a purist could  say that Grice was the greatest molecularist of all.

But surely a  molecule is composed of  corpuscules, too.

Why did Russell describe his   philosophy as a kind  of "logical atomism" and not the more correct   'corpuscularism'?

After all,  Russell just meant to endorse both a   metaphysical view and a certain  methodology for doing philosophy.

The  metaphysical view amounts to the  claim that the world consists  of a plurality of  independently existing  things exhibiting qualities and standing in relations.

But as Grice says, every school boy (at least at Clifton, which he attended) knows that.

 "There must be  more to Russell's logical  atomism."

According to logical atomism, all truths are ultimately  dependent upon a layer of atomic facts, which consist either of a simple particular exhibiting a quality, or multiple simple particulars standing in a  relation.

The  methodological view  recommends a process of conceptual  analysis, whereby one attempts to  define or reconstruct more complex notions or vocabularies in terms of simpler ones.

According to Russell, at least early on  during his  logical atomist phase, such an analysis could eventually   result in a  language containing only words representing simple  particulars, the  simple  properties and relations thereof, and  logical constants, which, despite   this limited vocabulary,
could  adequately capture all truths. Russell's   logical atomism had a profound influence on analytic philosophy,   including  Grice, if  only to criticise it.

Ideed, it is arguable that the  very name   “analytic philosophy” derives from Russell's defense of the  method of  analysis.

And while Austin used to say

i. Some like  Witters,  but Moore's MY man.

Grice could have said:

ii. Some like Witters, but Russell's MY man.

Trust Ayer, who was an 'enfant  terrible'  to attempt to trump both:

iii. Some like Witters, but  Moore and Russell  are MY men.

(vide Ayer: Russell and Moore: the  anaytical heritage"). 

Russell introduced the phrase “logical atomism” to  describe his philosophy  in  1911.

Russell's logical atomism is  perhaps best described as partly a  methodological viewpoint, and partly a  metaphysical  theory.  

Methodologically, logical atomism can be seen  as endorsement of  conceptual  analysis, understood as a two-step  process in which one attempts to   identify, for a given domain of  inquiry, set of beliefs or scientific  theory,  the minimum and  most basic concepts and vocabulary in which  the other concepts and  vocabulary of that domain can be defined or recast,  and the most general  and  basic principles from which the remainder of the  truths of the domain can be  derived or reconstructed.

Metaphysically,  logical  atomism is the view  that the world consists in a plurality of   independent and discrete entities,  which by coming together   form  facts.

According to Russell, a fact is  a  kind of complex, and  depends for its existence on the simpler  entities making it  up.

The  simplest sort of complex, an atomic fact,  was thought to consist  either of  a single individual
exhibiting a  simple quality, or of multiple    individuals standing in a simple relation.

The methodological and   metaphysical elements of  logical atomism come together in postulating the   theoretical, if not  the practical, realizability of  a fully analyzed  language,  in  which all truths could in principle be expressed in a  perspicuous  manner.

Such a “logically ideal language”, as Russell at times  called it,  would, besides logical constants,
consist only of words representing  the  constituents  of atomic facts.

And Grice says Russell is "okay" only   he misses to even THINK such a logically ideal language should invite this  or  that implicature.

Russell impertinently responded:

"Implicature  happens, so?"

In such a language, the simplest sort of  complete  sentence would  be what Russell called an “atomic  proposition”, containing a  single  predicate or verb representing  a quality or relation along with the   appropriate number of  proper names, each representing an individual. 

The  truth or  falsity of an atomic proposition would depend entirely on  a   corresponding atomic fact.

The other sentences of such a  language  would  be derived either by combining atomic propositions using   truth-functional  connectives, yielding molecular propositions, or  by  replacing constituents of a  simpler proposition by variables,  and  prefixing a universal or existential  quantifier, resulting
in general and  existential propositions. According  to the  stronger form of logical  atomism Russell at times adopted, he held  that  in such a language, "g]iven  all true atomic propositions,  together with the fact that they are all,  every other true  proposition can  theoretically be deduced by  logical   methods".

This puts the truth or falsity of atomic propositions   at  the core of
Russell's theory of truth, and hence, puts atomic facts  at the   center of
Russell's metaphysics.

Russell himself  dated his first   acceptance of logical atomism to the
vintage  year of 1899 (what Grice called  "that year of Grice") when he and
Moore 
rejected the  main tenets of the  dominant school of philosophy in  Oxford
at the time -- oddly,  since both  were at Cambridge --  (and to which both
had previously been  adherents),  the tradition  of neo-Hegelian Idealism
exemplified in works of F.H.   Bradley,  and adopted instead a  fairly
strong form
of realism. Of   their  break with idealism, Russell wrote that "Moore led
the way, but  I  followed  closely in his footsteps".

**************** WHY  NEITHER  RUSSELL NOR GRICE LIKED BRADLEY -- "MUCH"
------

Moore  published an essay  entitled “The  Nature of Judgment”, in which he

outlined his main reasons  for accepting the new  realism. It  begins with
a 
discussion of a  distinction made by Bradley  between  different notions of
idea. According  to Bradley, the  notion of idea  understood as a mental
state or mental  occurrence  is not the notion of “idea”  relevant to
logic or
to truth   understood as a relationship between our ideas and  reality.
Instead,  the  relevant notion of idea is that of a sign or symbol 
representing 
something  other than itself, or an idea understood as possessing  
meaning.
Bradley  understood meaning in terms of  "a part of the  content of an idea
cut
off,  fixed by the mind, and  considered  apart from the existence of the
sign".  Moore agreed with  Bradley  that it is not the mental occurrence
that
is  important to logic.   However, with regard to Bradley's second notion
of  “
idea”, Moore  accused  Bradley of conflating the symbol with the 
symbolized,  and rejected Bradley's view that what is symbolized is itself
a part  of 
the idea and dependent upon it. 

Moore introduces the  term  "concept" for the meaning of a symbol; for 
Moore, what it  is for different  ideas to have a common content is for
them to   
represent the same  concept. However, the concept itself is independent  of
the ideas. When we   make a judgment, typically, it is not our  ideas, or
parts of our ideas,  which  our judgment is about.  According to Moore, if
I
make an assertion,  what  I assert is  nothing about my ideas or my mental
states, but a certain   "connexion  of concepts". Moore went on to
introduce the
term  “proposition”  for  complexes of concepts such as that which would
be 
involved in a belief  or  judgment. While propositions represent  the
content
of judgments,   according to Moore,
they and their  constituents are entirely independent  from  the judging  
mind. Some propositions are true, some are not. 

For   Moore, however, truth is not a correspondence relationship  between 
propositions  and reality, as there is no difference between a  
proposition — 
understood as a  mind-independent complex — and  that  which would make it
true. The facts of the world then consist of  true  propositions,
themselves 
understood as complexes of  concepts. According to  Moore, something 
"becomes intelligible  first when it is analyzed into its  constituent 
concepts". 
Moore's "The Nature of Judgment" had a profound  influence on   Russell,
who
later heralded it as the first account of the  “new  philosophy” to  which
he
and Moore subscribed. For his own part,   Russell often described  his
dissatisfaction with the   dominant  Idealist (and largely monist)
tradition as 
primarily  having to do   with the nature and existence of relations. 

In  particular, Russell  took issue with the claim found in  Bradley and
others, that  the notion of  a fundamental relation  between two distinct
entities  is  incoherent.  Russell  diagnosed this belief as stemming from
a
widespread   logical   doctrine to the effect that every proposition is
logically 
of  subject-predicate  form. Russell was an ardent opponent of a  position
known  as the “doctrine of  internal relations”, which  Russell stated as
the
view  that  "every relation is   grounded in the natures of the related 
terms". Perhaps most  charitably  interpreted, this amounts to the claim 
that a's 
bearing relation R to b is  always reducible to properties held  by  a and
b
individually, or to a property  held by the complex  formed of a and  b. In
the period leading up to his  own  abandonment of idealism, Russell  was
already pursuing a research  program  involving the foundations of 
arithmetic.
This work,  along with his  earlier work on the foundations of  geometry,
had 
convinced him of the importance  of relations for  mathematics.  However,
Russell found that one category of relations, viz.,    asymmetrical
transitive
relations, resisted any such reduction to the   properties  of the relata
or
the whole formed of them. These  relations  are  especially important in
mathematics, as they are  the
sort that  generates series. 

Consider the relation of  being taller than, and  consider the fact that

iv. Shaquille O'Neal  is taller than Michael  Jordan.

It might be thought that this  relation between O'Neal and Jordan  can be
reduced to properties of  each. O'Neal has the property of being  7'2'' 
tall,
and Jordan  has the property  of being 6'6'' tall, and the  taller than  
relation in this case is reducible to their possession of  these 
properties. 
The problem, according to Russell, is that for this   reduction to hold, 
there
must be a certain relation between the  properties  themselves. This 
relation would account for the  ordering of the various  height
properties,  putting the property  of being-6'8''-tall in between  that of
being-7'2''-tall and  that  of being-6'6''-tall. This relation among  the
properties would   itself be an asymmetrical and transitive relation,  and
so the
analysis  has not  rid us of the need for taking relations as  ultimate. 
Another hypothesis  would be that there is such an entity as the   whole
composed of O'Neal and  Jordan, and that the relation between the  two  men
is
reducible to some property  of this whole. Russell's  complaint was  that
since
the whole composed of  O'Neal and Jordan  is the same as the  whole
composed of
Jordan and O'Neal, this   approach has no way to explain  what the
difference would be between  O'Neal's  being taller than Jordan and 
Jordan's being
taller than  O'Neal, as both would  seem to be reduced to the  same
composite 
entity bearing the same  quality. Russell's rejection of the   doctrine of
internal relations is  very  important for  understanding  the development
of
his atomistic doctrines in  more  than
one respect. 

Certain advocates of the claim that a  relation  must always be  grounded
in
the nature of its relata  hold that in virtue of a  relating to  b, a must 
have a  complex nature that includes its relatedness to b.   Since every 
entity presumably bears some relation to any other, the nature of  any 
entity
could arguably be described as having the same complexity as  the  universe
as
a whole (if indeed, it even makes sense on such a  picture   to  divide the
world into distinct entities at all,  as many denied).   Moreover,
according
to some within this  tradition, when we consider a,   obviously we do not
consider all  its relations to every entity, and hence grasp  a in a way
that 
falsifies the whole of what a is. This led some to the   claim  that “
analysis
is falsification”, and even to  hold that when we   judge that  a is the
father of b, and judge that a is the  son of  c,  the a in the first 
judgment is
not strictly speaking the same  a as  involved in the second judgment; 
instead, in the first we  deal only  with  a-quâ-father-of-b in the first,
and  
a-quâ-son-of-c in the  second. In contradistinction to these  views, 
Russell
adopted what he  called “the  doctrine of  external relations”, which he 
claimed “may  be expressed by 
saying that

A) relatedness does not  imply any   corresponding complexity in the relata.

B) any given entity is   a  constituent of many different complexes.

This position on  relations   allowed Russell to adopt a pluralism in which
the  world is conceived as   composed of many distinct, independent 
entities,
each of which can be  considered  in isolation from its  relations to other

things, or its  relation to the mind.   Russell claimed that this doctrine
was the  fundamental doctrine of his  realistic position, and it represents
perhaps the  most important  turning point in the development of his
logical
atomism.  Russell's  first published  account of his newfound realism came
in
the   classic The Principles of  Mathematics. Part I is dedicated largely
to a 
philosophical inquiry into  the nature of  propositions. Russell  took 
over from Moore the conception  of propositions as   mind-independent 
complexes; a true proposition was then  simply  identified by Russell  
with a fact.
However, Moore's   characterization of a proposition as a  complex of 
concepts was  largely in  keeping with traditional  Aristotelian logic in
which  all 
judgments were thought  to involve a  subject concept,  copula and
predicate
concept. Russell,  owing in  part to his own  views on relations, and in
part from his adopting  certain   doctrines stemming from Peano's symbolic
logic, sought to refine  and   improve upon this characterization. In the
terminology  introduced by   Russell, constituents of a proposition  occur 
either as
term or as  concept.  An entity occurs as term when it  can be replaced by
any other  entity and   the result would  still be a proposition, and when
it
is  one of the subjects   of  the proposition, i.e., something the 
proposition is about. An  entity  occurs as concept when it occurs 
predicatively,
i.e.,  only as part of the  assertion made about the things  occurring as 
term.
In the proposition

v. Russell is human (versus  "Russell  is humane"?)

the person Russell (the man himself) occurs as  term,  but humanity occurs
as concept.  In the proposition

vi.   Strawson orbits Grice.

Strawson and Grice occur as term, and  the   relation of orbiting occurs as
concept. Russell used  "concept" for all   those entities capable of
occurring as   concept — chiefly relations and  other  universals — and
"thing" for 
those entities such as Socrates,  Callisto and  Jupiter, that can  only
occur
as term.  While Russell  thought that only certain  entities were capable
of
occurring  as concept,  at the time, he  believed that every entity was
capable of  occurring   as  term in a proposition. In the proposition

vii. Gluttony is a big   vice.

the concept gluttony occurs as term. His argument that this  held 
generally
was that if there were some entity, E, that could not  occur as  term,
there  would  have to be a fact, i.e., a true  proposition, to  this
effect.
However, in the proposition E cannot  occur as term in a  proposition, E 
occurs
as term. Russell's  account of propositions as  complexes of  entities was
in
many  ways in keeping with his views as the  nature of complexes  and facts

during the core logical atomist period. In  particular, at both   stages he
would regard the simple truth that an  individual a stands in  the  simple
relation R to an individual b as a  complex   consisting of the individuals
a
and b and the relation  R.   However, there are a number of positions 
Russell
held in 1903   that were
abandoned in this later period; some of the more   important  were these.
He
is committed to a special kind of  propositional  constituent  called a “
denoting concept”, involved  in descriptive and quantified   propositions.
He
believes that  there was such a complex, i.e., a   proposition, consisting 
of 
a, b and R even when it is not true that a  bears  relation R to  b. He
also
believes in the reality of classes,  understood  as  aggregate  objects,
which could be constituents of  propositions.  In each case,  it is worth,
at least briefly, discussing   Russell's change of  heart. Russell
expressed
the view that grammar is  a  useful guide in  understanding  the make-up of
a  proposition, and even  that in many cases, the  make-up of  a 
proposition
corresponding to a  sentence can be understood by   determining,  for each
word of the  sentence, what entity in the  proposition is  meant by the
word.
Perhaps in  part because such  phrases as "all dogs",  "some numbers" and 
"the   queen"appear as a grammatical unit, Russell came to the  conclusion
that
they made a unified contribution to the corresponding    proposition.  B
ecause Russell believed it impossible for a finite  mind  to  grasp a
proposition of infinite complexity, however,  Russell  rejected a view 
according to
which the (false)  proposition designated  by

viii. All  numbers are  odd.

actually contains all numbers.  Similarly,  although  Russell admitted that
such a proposition as that  is  equivalent  to a  formal implication, i.e.,
a
quantified  conditional of the 
form:

ix. (x)(x  is a number ⊃ x is  odd)

Russell  held that they are nevertheless distinct  propositions.  This was 
perhaps in part due to the difference in  grammatical   structure,  and
perhaps also because the former appears only to  be   about numbers, 
whereas the
latter is about all things,  whether numbers or  not.  Instead, Russell
thought that the  proposition corresponding to the  above   contains as a 
constituent the denoting concept all numbers.  Russell  explained  denoting
concepts
as entities which, whenever they occur 
in  a  proposition, the proposition is not about them but about   other 
entities to which  they bear a special relation. So when  the  denoting
concept
all numbers  occurs in a proposition,  the   proposition is not about the
denoting concept, but   instead about 1 and 2  and 3,  etc. Russell
abandons this
theory  in favour  of his celebrated  theory of definite and indefinite 
descriptions. What  precisely lead  Russell to become dissatisfied  with
his
earlier  theory, and the   precise nature of the  argument he gave against
denoting concepts  (and  similar   entities such as Frege's senses), are a
matter
of great    controversy, and have  given rise to a large body of secondary 
literature.  It can merely be  noted that Russell professed an  inability
to 
understand  the logical form of  propositions  about denoting concepts 
themselves, as in  the claim that  "The  present King of France is a 
denoting
concept". According to  the new  theory adopted, the proposition  expressed
by the
above  was now identified with  that expressed by a  quantified conditional

such  as the formalised version.  Similarly,  the proposition  designated by

x. Some number is odd.

was  identified with the  existentially quantified conjunction  represented

by

xi.  (∃x)(x is a number & x is odd)

Perhaps most   notoriously,  Russell argued that a proposition involving a
definite   description,  e.g.,

xii. The King of France is not  bald.

was  to be understood as  having the structure of a  certain kind of  
existential statement, in this   case:

xiii. (∃x)(x is King of France  & (y)(y is King of France  ⊃ x =  y) & x
is
not  bald)

Russell cited in favor of  these theories that  they provided  an elegant
solution to certain  philosophical puzzles. One  involves how it  is that a
proposition  can be meaningful even if it involves a  description  or other

denoting phrase that does not denote anything. Given the above account   of
the
structure of the proposition expressed by  "the King of France  is  bald",
while France and the relation of being King of   are   constituents, there
is no
constituent directly corresponding  to the  whole  phrase  "the King of
France".  The  proposition in question is false,  since there  is no value
of x 
which  would make it true. One is not  committed to a   nonexistent entity
such as the King of France  simply  in order to  understand the  make-up of
the
proposition.  Russell's   theory provides an answer to how  it is that
certain  identity   statements can be both true and informative.  On the 
above
theory, the  proposition corresponding to:

xiv. The   author of Waverly =  Scott

would be understood as having the  following   structure:

xv. (∃x)(x authored Waverly & (y)(y  authored Waverly ⊃ x  =  y) & x =
Scott)

If instead,  the proposition corresponding to  the  above was simply a  
complex consisting of the relation of  identity, Scott, and  the  author of
Waverly  himself, since the author  of Waverly simply is  Scott, the 
proposition
would  be the same as the   uninformative proposition

xvi.  Scott = Scott.

(but,  as  Grice said, "What conversational POINT could THAT have?")  By 
showing that  the actual structure of the proposition is quite a  bit 
different
from what  it appears from the grammar of the  sentence

xiv. The author of Waverly =  Scott.

Russell  believed he had shown how it might be more informative (or 
'stronger'  as Grice prefers -- The Causal Theory of Perception, 1961,
repr.   in  
WoW, Way of Words) than a trivial instance of the law  of  identity, which 

intelligent people like Grice or  Russell are  supposed to KNOW  already.
The
theory did away with  Russell's temptation to  regard grammar  as a very 
reliable  guide towards understanding the  structure or make-up of a   
proposition.  Especially important in  this regard is the notion  of an  “
incomplete
symbol”, by which Russell  understood an  expression that can be 
meaningful
in the context of its use   within a sentence, but does not by itself 
correspond to  a   constituent or unified part of the corresponding
proposition.  
According to  Russell's theory, phrases such as "the King of France,"  or 
"the
author of  the Waverly novels" were to be understood as  incomplete symbols

in this  way. The general notion of an  incomplete symbol was applied by 
Russell in  ways  beyond  the theory of descriptions, and perhaps most 
importantly,  to his  understanding of classes. Russell postulates two
types  of  
composite entities: unities and aggregates. By a unity Russell meant   a 
complex entity in which the constituent parts are arranged with  a 
definite 
structure.  A proposition was understood to be a  unity in  this sense.  By
an
aggregate, Russell means an entity  such as a class  whose  identity
conditions
are governed entirely  by what members or parts  it has, and  not by  any 
relationships between the parts. By the time  of the  publication,  with
Whitehead, of Principia Mathematica Russell's  views about  both  types of
composite entities had changed    drastically.Russell  fundamentally
conceived of a
class as the  extension of  a concept,  or as the  extension of a 
propositional function. Indeed,  in The Principles of  Mathematics  he
claims that a
class may be   defined as all the terms  satisfying  some propositional
function.
However,  Russell was  aware already at the  time of POM that the
supposition    there is always a class, understood as an  individual
entity, as  the  
extension of every propositional function, leads to   certain logical 
paradoxes. Perhaps the most famous, now called  Russell's  paradox, derived
from 
consideration of the  class, w, of all classes not members  of  themselves.

The  class w would be a member of itself if it satisfied   its  defining 
condition, i.e., if it were not a member of  itself.   (Grice was to joke
on this
calling Austin's Play Group,  to which he    belonged, as "the class of
tutors that have no  other class"). Similarly,  w  would not be a member of
itself
if  it did not satisfy its defining  condition,  i.e., if it were a member 
of itself.  Hence, both the  assumption that it is a member of  itself, and
the  assumption that it is  not, are impossible.   Another related paradox
Russell often discussed in  this regard has  since   come to be called
Cantor's
paradox. Cantor had   proven that if a class  had n members, that the
number
of   sub-classes  that can be taken from that class  is 2n, and also that 
2n >
n, even 
when n is infinite. It follows from  this  that the number of subclasses 
of
the class of all individuals, i.e.,  the  number of different classes of 
individuals, is greater   than the number of  individuals. 

Russell took this as strong  evidence that a class of individuals  could
not itself be  considered an individual. Likewise, the  number of 
subclasses
of  the class of all classes is greater  than the number of   members  in
the
class of all classes.  This Russell took to be   evidence  that there is
some
ambiguity in the notion of a class so that  the  subclasses of  the class
of
all classes would not   themselves be among  its members, as it would 
seem.
Russell spent  some time searching for a  philosophically motivated 
solution
to  such paradoxes. He tried  solutions of various sorts.  However, after 
the discovery of the theory of  descriptions, Russell  becomes  convinced
that
an expression for a class is  an incomplete symbol,  i.e.,   that while
such
an expression can occur  as part of a  meaningful sentence, it  should not
be regarded as  representing a  single entity in the corresponding 
proposition.   Russell  dubbed this approach the no-classes theory of 
classes  
because,  while it allows discourse about classes to be  meaningful,  it 
does not
posit  classes as among the  fundamental ontological  furniture of the 
world.
The precise  nature of Russell's no-classes  theory underwent  significant 

changes.

However, in the version  adopted in the first  edition  of Principia 
Mathematica, Whitehead and  Russell  believed that a statement  apparently
about a 
class could   always be reconstructed, using higher-order  quantification,
in   terms  of a statement involving its defining propositional  function. 
Russell  believed that whenever a class term of the form 

xv.   {z|ψz}

appeared in some sentence, the sentence as  a whole could be   regarded as
defined as follows:

xvi.  f({z|ψz})     =df   (∃φ)((x)(φ!x ≡ ψx) &  f(φ))

The above view can  be  paraphrased, somewhat crudely, as  the claim that
any  truth  seemingly about a  class can be  reduced to a claim about some
or
all   of its members. It   follows from this contextual definition of class
terms that the   statement to the  effect that one class A is a subset of 
another  class B is  equivalent to the  claim that whatever satisfies  the 
defining propositional  function of A also  satisfies the  defining 
propositional
function of B. Russell also  sometimes  described this as the  view that
classes are logical   constructions, not  part of the real  world, but only
the
world of  logic  (This irritated Grice -- and   Hart, "A logician's fairy 
tale"). Another way Russell expressed himself  is  by saying that  a class
is a 
logical FICTION, an expression he borrowed   from  Bentham, but never
returned. While it may seem that a class  term  is  representative of an
entity,
according to Russell, class  terms are  meaningful in  a different way. 
Classes are not  among the basic stuff  of the world; yet  it is possible
to
make  use of class terms in  significant speech, as if there  were such 
things  as classes. 

A class is thus portrayed by Russell  as a  mere façon de parler, or 
convenient way of speaking about  all or some of the  entities satisfying 
some 
propositional  function. During the period in  which Russell was  working
on 
Principia Mathematica,
Russell also radically  revised his   former realism about propositions 
understood as mind  independent   complexes. The motivations for the change
are
a  matter of some   controversy, but there  are at least two  possible
sources. The first  is  that in addition to the logical  paradoxes
concerning the  
existence of classes,  Russell was  aware of certain paradoxes stemming
from 
the  assumption  that  propositions could be understood as individual  
entities.  By Cantor's  theorem, there must be more classes  of 
propositions than
propositions.  However, for every class  of  propositions, m, it is
possible to generate  a distinct  proposition, such  as the proposition
that every
proposition in m  is  true, in violation of  Cantor's theorem.

Unlike the other  paradoxes  mentioned above, a  version of this paradox
can
be  reformulated even if talk of  classes  is replaced by talk of  their 
defining propositional functions.  

Russell  was also aware of certain contingent paradoxes involving 
propositions,  such as the Liar paradox formulated involving a person S, 
whose  only 
assertion at time t is the proposition All propositions  asserted by S  at 
time t are false. Given the success of the rejection of   classes as 
ultimate
entities in resolving the paradoxes of  classes,  Russell was motivated  to
see if a similar solution to  these paradoxes  could be had by rejecting 
propositions as  singular entities. Another set  of considerations pushing 
Russell  towards the rejection of his former view  of propositions is more 

straightforwardly metaphysical. According to his  earlier view, and  that 
of
Moore, a proposition was understood as a mind   independent complex.

The constituents of the complex are the  actual  entities involved, and 
hence, as we have seen, when a  proposition is true,  it is the same entity
as a
fact or state of  affairs. However, because some  propositions are false,
this view of  propositions   posits objective  falsehoods. The false 
proposition that

xvii. Venus orbits  Neptune.

is thought  to be a complex containing Venus and Neptune the  planets, as
well as  the relation of orbiting, with the relation occurring as a 
relation, 
i.e., as relating Venus to Neptune. However, it seems natural to   suppose
that the relation of orbiting could  only unite Venus and  Neptune  into a
complex, if in fact, Venus orbits Neptune.  

Hence, the  presence of such falsehoods is itself out of sorts  with 
common
sense. 

Worse, as Russell explained, positing  the existence of objective 
falsehoods in addition to objective truths  makes the difference between
truth  and
falsehood  inexplicable,  as both become irreducible properties of 
propositions, and we  are  left without an explanation for the privileged  
metaphysical 
status of truth over  falsehood. Whatever his  primary  motivation, Russell
abandons any  commitment to objective  falsehoods, and  restructured his
ontology of facts, and  adopted  a new Tarski-type  correspondence theory
of
truth (also endorsed by  Grice  just to oppose  Strawson's naive
performative
'ditto'  theory of 'true').

In the  terminology of the new theory,  "proposition" was used not for an
objective  metaphysical complex, but  simply for an interpreted declarative

sentence,  an item of  language. Propositions are thought to be true or
false
depending on   their correspondence, or lack thereof, with facts. In the
Introduction  to   Principia Mathematica, as part of his explanation of
ramified 
type-theory,   Whitehead Russell described various notions of  truth
applicable to  different  types of propositions of different  complexity.

Grice  made fun of this when he used the  example

xviii. My neighbour's  three-year-old child understands  Russell's Theory
of

Types.

("Unbelievable, but hardly  logically contradictory" -- the  implicature 
was that only  Russell understood his own theory of types). The  simplest
propositions  in the language of Principia Mathematica are what Russell 
there
called  “elementary propositions”, which take forms such as “a has  
quality  q”
, “a has relation [in intension] R to b”, or “a and b and c stand   in 
relation S”. Such propositions consist of a simple  predicate,  
representing
either a  quality or a relation,  and a number of proper names. 

According to Russell, such a  proposition is true when there is a  
corresponding fact or  complex, composed of the entities named by the 
predicate  and 
proper names related to each other in the appropriate way.  E.g., 

xix. a has relation R to b.

is true if there exists a   corresponding complex in which the entity a is
related by the relation R to  the  entity b. If there is no corresponding
complex, then the  proposition is   false. Russell dubbed the notion of
truth 
applicable to elementary   propositions
first truth. This  notion of truth serves as the ground for a  hierarchy of
different  notions of truth applicable to different types of  propositions 
depending on   their complexity. A proposition such as  

xx. (x)(x has quality q).

which involves a first-order   quantifier, has (or lacks) second truth 
depending on whether its  instances  have first truth.

In this case

xx. (x)(x has  quality  q)

would be true if every proposition got by replacing the  "x" in "x  has 
quality q" with the proper name of an individual  has first  truth.

A  proposition involving the simplest kind of  second-order  quantifier,
i.e., a  quantifier using a variable for  predicative  propositional
functions of
the  lowest type,  would have or lack third  truth depending on whether its

allowable  substitution instances have  second or lower truth. 

Because any statement apparently about a class of  individuals  involves
this
sort of higher-order quantification, the truth or   falsity of such a
proposition  will ultimately depend on the truth  or  falsity of various
elementary 
propositions about  its  members.

Although Russell did not use "logical  atomism"  in the  Introduction to
Principia Mathematica, in many ways it   represents the  first work of
Whitehead's
and Russell's atomist  period.

Whitehead  and Russell there explicitly endorsed the view  that the
universe

consists of objects having various qualities  and standing in various  
relations.

Propositions that  assert that an object has a quality, or  that  multiple
objects  stand in a certain relation, were given a  privileged place in 
the 
theory, and explanation was given as to how  more complicated  truths, 
including
truths about classes, depend on the  truth  of such simple propositions.

Russell's work over the next two   decades consisted largely in refining
and

expanding upon this  picture  of the world.

Although Russell changed his  mind on a  great number  of philosophical
issues throughout his career, one of  the  most stable  elements in his
views is
the endorsement of  a certain methodology  for  approaching philosophy.

Indeed, it  could be argued to be the most  continuous and unifying feature
 
of Russell's philosophical  work.

Russell employed the  methodology self-consciously, and gave only  slightly

differing  descriptions of this methodology in works  throughout his  
career.

Understanding this methodology is  particularly important  for 
understanding
his logical atomism, as well  as what he  meant by  “analysis”.

The methodology consists of a two  phase  process.

The  first phase is dubbed the analytic phase   (although it should be
noted
that  sometimes Russell used  "analysis”  for the whole procedure.

One begins with a certain  theory, doctrine or  collection of beliefs which

is taken to be  more or less correct, but  is taken to be in certain
regards

vague,  imprecise, disunified, overly  complex or in some other way
confused 
or  puzzling.

The aim in  the first phase is to work  backwards from these beliefs, taken

as a  kind of data”, to a  certain minimal stock of undefined concepts and 
general   principles which might be thought to underlie the original  body
of 
knowledge. 

The second phase, which Russell described  as  the constructive or 
synthetic
phase, consists in rebuilding  or  reconstructing the original body of 
knowledge in terms of the  results  of the first phase.

More specifically, in the synthetic  phase, one  defines those elements of 
the original conceptual  framework and  vocabulary of the discipline in
terms of
the minimum  vocabulary  identified in the first phrase, and derives or 
deduces  the main tenets  of the original theory from the basic  principles
or
general  truths one  arrives at after  analysis.

As a result of such a process, the   system of  beliefs with which one
began
takes on a new form in which   connections  between various concepts it
uses
are made clear, the   logical interrelations  between various theses of the
theory are   clarified, and vague or unclear aspects  of the original 
terminology 
are eliminated.

Moreover, the procedure also  provides opportunities  for the application
of

Occam's razor, as it  calls for the elimination  of unnecessary or
redundant

aspects of a  theory.

Concepts or  assumptions giving rise to paradoxes or  conundrums or other 
problems  within a theory are often found to  be wholly unnecessary or
capable
of   being supplanted by  something less problematic.

Another advantage is  that the  procedure arranges its results as a
deductive
system, and hence   invites and facilitates the discovery of new  results.

Examples  of  this general procedure can be found throughout  Russell's 
writings, and  Russell also credits others with having achieved  similar 
successes. 

Russell's work in mathematical logic  provides perhaps the  most  obvious
example of his utilization of  such a procedure. It is also an   excellent
example of Russell's  contention that analysis proceeds in stages. 

Russell saw his own  work as the next step is a series of successes  
beginning with  the work of Cantor, Dedekind and Weierstrass.

Prior  to the work of  these figures, mathematics employed a number of  
concepts,number,  magnitude, series, limit, infinity, function, continuity,

etc.,  
without a full understanding of the precise definition of each   concept,
nor
how  they related to one another.

By  introducing  precise definitions of such  notions, these thinkers 
exposed 
ambiguities (e.g., such as with the word   "infinite"), revealed 
interrelations between certain of them, and  eliminated  dubious notions 
that had
previously caused  confusion and paradoxes (such as  those  involved with
the notion 
of an infinitesimal).

Russell saw the next  step forward in the  analysis of mathematics in the 
work of Peano and  his associates,  who not only attempted to explain how
many  
mathematical  notions could be arithmetized, i.e., defined and proven in 
terms  of  arithmetic, but had also identified, in the case of  arithmetic,

three
basic  concepts (zero, successor, and natural number)   and five basic
principles (the  Peano axioms), from which the rest  of  arithmetic was
thought to be
derivable.

Russell  described the next  advance as taking place in the work  of Frege.


According to the  conception of number found in Frege, a  number  can be
regarded as an  equivalence class consisting of  those classes whose 
members can
be put  in 1-1 correspondence  with any other member of the class.

According to  Russell, this  conception allowed the primitives of Peano's 
analysis to  be  defined fully in terms of the notion of a class, along
with 
other   logical notions such as identity, quantification, negation  and the

conditional. 

Similarly, Frege's work showed how  the basic  principles of Peano's 
analysis could be derived from  logical axioms  alone.

However, Frege's analysis was not in all  ways successful, as the  notion
of

a class or the extension of a  concept which Frege included  as a logically

primitive notion  lead to certain contradictions. 

In this regard, Russell saw his  own analysis of mathematics  (largely 
developed independently  from Frege) as an improvement, with  its more
austere  
analysis that eliminates even the notion of a class  as a primitive  idea,
and 
thereby eliminates the  contradictions.

When Grice delivered his lecture, "Definte descriptions in Russell and in 
the vernacular" he was being polemical. He knew that he was regarded as the 
'head' (as it were) of Oxford ordinary language philosophy, and Russell was
in  the "Antipodes" (metaphorically). So, Grice's point was that even if
you are an  Oxford ordinary philosopher (as his tutee Strawson was) you can be
wrong. And  Grice's place in the history of philosophy was, he thought, to
identify this  manoeuvre that simply ignored the distinction (which he
thought crucial) between  implication and implicature. This he did via 'analysis'
of the conceptual type. 

It was clearly a part of Russell's view in that in  conducting an  analysis

of a domain such as mathematics (for it is clear that  definite
descriptions also occur elsewhere), and reducing  its primitive  conceptual
apparatus  and unproven premises to a minimum,  one is  not merely reducing
the
vocabulary of  a certain theory, but   also showing a way of reducing the
metaphysical  commitments of  the  theory.

In first showing that numbers such as 1, 2, etc.,  could be  defined in
terms

of classes of like cardinality, and then  showing how  apparent discourse
about  “classes” could be replaced  by higher-order  quantification,
Russell
made it  possible to  see how it is that there  could be truths of
arithmetic 
without  presupposing that the numbers  constitute a special  category of
abstract entity.

Numbers are placed  in the  category of “logical fictions” or “logical 
constructions” along   with all other classes.

Russell's work from the  period after  the  publication with Whitehead of
Principia Mathematica shows   applications  of this general philosophical
approach to  non-mathematical domains. 

In particular, his work over the next  two decades shows concern with  the 
attempt to provide analyses  of the notions of knowledge, space,  time, 
experience, matter and  causation.

When Russell applied  his analytic methodology to  sciences such as
physics,

again the goal  was to arrive at a  minimum vocabulary required for the
science in   question, as well  as a set of basic premises and general
truths from
which  the   rest of the science can be derived.

However, according to the   views developed by Russell in the mid-1910s, 
many of the  fundamental  notions in physics were thought to be analyzable
in  
terms of  particular sensations: i.e., bits of colour (Russell predates 
the
idea   of 'fifty shades of grey' -- even though he implicates  that 'grey'
is "no 
colour") auditory notes, or other simple parts  of sensation, and their 
qualities  and relations.

Russell  called such sensations, when  actually experienced, “sense”. In  
particular, Russell believed that  the notion of a physical thing could  be

replaced, or analyzed in terms  of, the notion of a series of  classes of
sensible  particulars each  bearing to one another  certain relations of
continuity, 
resemblance,  and perhaps  certain other relations relevant to the
formulation of  the  laws  of physics.

Other physical notions such as that of a point of    space, or an instance
of
time, could be conceived in terms of  classes  of  sensible particulars and
their spatial and  temporal  relations.

Later,  after abandoning the view that  perception is  fundamentally
relational, and  accepting a form of  William James's  neutral monism,
Russell
similarly came to   believe that the notion of a  conscious mind could be
analyzed in 
terms of  various percepts,  experiences and sensations related to  each
other by  psychological  laws.

Hence, Russell came to  the view point, matter,  instant, mind,  and the
like
could be  discarded from the minimum vocabulary  needed for  physics or 
psychology.

Instead, such words could be systematically   translated into a language
only
containing words representing  certain  qualities and relations between
sensible    particulars.

Throughout these analyses, Russell put into practice  a   slogan he stated
as
follows.

Wherever possible,  logical constructions  are to be substituted for
inferred 
entities.

Rival philosophies that  postulate an ego or mind as  an entity distinct 
from its mental states  involve inferring the  existence of an entity that
cannot
directly be found  in  experience.

Something similar can be said about philosophies that   take matter to be
an

entity distinct from sensible appearances,  lying  behind them and inferred
from  them.

Combining  Russell's  suggestions that talk of minds or physical objects is
 
to be analyzed  in terms of classes of sensible particulars with his 
general
view  that  classes are logical fictions, results in  the view that minds
and 
physical  objects too are logical  fictions, or not parts of the basic 
building blocks of  reality.  Instead, all truths about such purported 
entities
turn out instead  to  be analyzable as truths about sensible  particulars
and 
their relations to one  another.

This is in  keeping with  the general metaphysical outlook of logical 
atomism. 

We  also have here a fairly severe application of Occam's razor.   

The slogan was applied within his analyses in mathematics as  well.  
Noting
that sometimes a series of rational numbers  converges towards a  limit 
which
is not itself specifiable as  a rational, some philosophers  of mathematics

thought that one  should postulate an irrational number  as a limit.

Russell claimed  that rather than postulating entities in  such a case, an 

irrational number should simply be defined as a class  of rational  numbers

without a rational upper bound. Russell preferred  to  reconstruct talk of 
irrationals this way rather than infer or   postulate the existence of a
new

species of mathematical entity  not  already known to exist.

Complaining that the method of  postulating what  we want has the
advantages

of theft over honest  toil.

In  conducting an analysis of mathematics, or  indeed, of  any other domain

of thought, Russell was clear that although the   results of analysis  can
be
regarded as logical premises from which  the original  body of  knowledge
can
in principle be derived,  epistemologically speaking, the   pre-analyzed
beliefs are more  fundamental.

For example, in  mathematics, a belief such as 

xxi. 2 + 2 = 4.

is  epistemologically more certain, and  psychologically easier to
understand
and  accept, than many of the  logical premises from which it is derived.  

Indeed, Russell  believed that the results obtained through the  process 
of 
analysis obtain their epistemic warrant inductively from  the evident 
truth
of  their logical consequences.

The reason for   accepting an axiom, as for accepting any other 
proposition,
is  always  largely inductive, namely that many propositions which  are 
nearly  indubitable can be deduced from it, and that no equally  plausible
way  is 
known by which these propositions could be  true if the axiom were false,
and 
nothing which is plausibly false  can be deduced from it.

It is  perhaps for these reasons that  Russell believed that the process of


philosophical analysis should  always begin with beliefs the truth of which

are  not in  question, i.e., which are nearly indubitable.

When  Russell  spoke  about the general philosophical methodology described
 
here, he usually had in  mind applying the process of analysis to  an 
entire
body of knowledge or set of  data (Cfr. Paul, "Is  there a  problem about
sense
data" and its attending   implicature: "No, in spite  of Russell -- Grice
suggests that the  implicature is  "RUSSELL is the  problem.").

In fact, Russell  advocated usually to begin with the  uncontroversial 
doctrine of  a certain science, such as mathematics or  physics, largely 
because 
he held that these theories are the most  likely to  be true, or at least
nearly  true, and hence make the most   appropriate place to begin the
process of 
analysis.

Russell  did  on occasion also speak of analyzing a particular  proposition

of  ordinary life. One example he gave is “There are a number of   people
in

this room at this moment”.

In this case, the truth or  falsity   of this statement may seem obvious,
but
exactly what  its truth would involve  is  rather obscure.

The process of  analysis in this case would  consist in attempting to make 
the  proposition clear by defining what  it is for something to be a room, 
for 
something to be a person, for a  person to be in a room,  what a moment is,
etc.

In this case, it  might seem that the  ordinary language statement is 
sufficiently vague  that there is  likely no one precise or unambiguous 
proposition
that   represents the correct analysis of the proposition.

In a way, this  is  right.

However, this does not mean that analysis would be  worthless. 

Russell was explicit that the goal of analysis is not  to unpack what  is 
psychologically intended by an ordinary  statement such as the  previous
example,  nor what a person would  be thinking when he or she  utters it.

The point rather is simply  to begin with a certain obvious,  but rough and

vague statement,  and find a replacement for it in a more  precise,
unified,
and   minimal idiom.

On Russell's view,  vagueness is a feature of  language, not  of the world.
In vague  language, there is no  one-one relation between  propositions and
facts,  so that a vague  statement could be considered verified  by any one
of a 
range  of different facts.

However, in a properly analyzed  proposition,  there is a clear isomorphism

between the structure of the   proposition and the structure of the fact
that 
would make it   true.

Hence a precise and analyzed proposition is capable of being  true  in one 
and only one way.

In analyzing a proposition  such as 

xxii. There are a number of people in this room at  this  moment.

one might obtain a precise statement which would  require for its  truth
that
there is a certain class of sensible  particulars related to each  other in
a very  definite way  constituting the presence of a room, and  certain
other
classes  of  sensible particulars related to each other in  ways 
constituting
people, and that  the sensible particulars in  the  latter classes bear
certain definite relations  to those in  the first  class of particulars.

Obviously, nothing like this is  clearly in the  mind of a person who would

ordinarily use the  original expression. 

It is clear to see in this case that a very  specific state of things  is 
required for the truth of the  analyzed proposition, and hence the  truth
of
it 
will be far  more doubtful than the truth of the vague  assertion with
which 
one  began the process.

As Russell put the  point, the  point of philosophy is  to start with
something so simple as  not  to seem worth stating, and to end with 
something so 
paradoxical  that no one will believe it.

As we have seen,   the primary  metaphysical thesis of Russell's atomism is
the view that  the world   consists of many independent entities that
exhibit 
qualities and stand  in  relations to one another.

On this  picture, the simplest sort of  fact or  complex consists either of

a
single individual or particular  bearing a quality,  or a  number of
individuals bearing a relation to  one another. 

Relations can be divided into various categories depending  on how  many 
relata they involve: a binary or dyadic relation involves   two relata
(e.g., a
is  to the left of b); a triadic relation  (e.g., a  is between b and c)
involves  three relata and so on. 

Russell  at times used the word “relation” in a broad sense so as  to
include   qualities, which could be considered as monadic  relations, i.e.,
relations  that  only involve one relatum. 

The quality of being white,  involved, e.g., in the fact that a is  white, 
could then, in this  broader sense, also be considered a  relation.

At the  time of  Principia Mathematica, complexes in  Russell's and
Whitehead's ontology   were all described as taking  the form of n
individuals entering
into an  n-adic  relation. 

We will give, they write, the name of a complex  to any such object  as "a
in
the relation R to b" or "a having the quality q"  or "a  and b and c
standing in  relation S."

Broadly speaking, a   complex is anything which occurs in the universe and
is
not   simple.

Russell believes that an elementary proposition consisting of  a  single 
predicate representing an n-place relation along with n  names  of
individuals is
true if it corresponds to a complex. 

An elementary  proposition is false if there is no corresponding  complex.

Russell there  gave no indication that he believed in any  other sorts of 
complexes or  truth-makers for any other sorts of  propositions.

Indeed, he held that a  quantified proposition is  made true not by a
single

complex, but by  many.

If φx is an  elementary judgment it is true when it points to  a  correspond
ing  complex.

But (x).φx does not point to a single  corresponding  complex.

Te corresponding complexes are as numerous as the  possible  values of  x.

Soon after Principia Mathematica, Russell  became  convinced that this 
picture -- which he shared with Whitehead  --  was "too simplistic" ("to me

if not
to Whitehead, an otherwise  very  smart professor").

Thus, in the “Philosophy of Logical  Atomism” lectures  Russell  described
a
more complicated  framework.

In the new  terminology, an atomic fact is was  introduced for the simplest

kind of  fact, i.e., one in which n  particulars enter into an n-adic 
relation. 

Russell uses  "atomic proposition" for a proposition  consisting  only of a

predicate for an n-place relation, along with n proper  names  for 
particulars.

Hence, such propositions could take such forms   as 

“F(a)”, “R(a, b)”, “S(a, b, c)”

An atomic  proposition  is true  when it corresponds to a positive atomic 
fact. 

However, Russell no  longer conceived of falsity as  simply lacking  a
corresponding fact.

Russell now believes that  some facts are  negative, i.e., that if “R(a, b)”

is false, there is  such a fact as a's not  bearing relation R to b.

Since  the  proposition “R(a, b)” is  affirmative, and the corresponding
fact  is  negative, “R(a, b)” is  false, and, equivalently, its negation  “
not-R(a, b)” is  true. 

Russell's rationale for endorsing  negative facts was somewhat  
complicated.

However, one might  object that on his earlier view,  according to which  “
R(a, b)” is  false because it lacks a corresponding  complex, is only 
plausible 
if you suppose that it must be a fact that  there  is not such a complex,
and
such  a fact would itself seem to be  a  negative fact.

Russell later abandoned  the view that  qualities and  relations can occur
in
a complex as themselves  the  relata to another  relation, as in priority
implies  diversity.

Russell  now held  the view that whenever a  proposition apparently
involves
a relation or   quality occurring  as logical subject, it is capable of
being
analyzed into  a   form in which the relation or quality occurs
predicatively. 

For  example,

xxiii. Prriority implies  diversity.

might be analyzed  as:

xxiv. (x)(y)(x is prior to  y ⊃ x is not  y)

Russell uses  "molecular proposition" for  those propositions that are 
compounded  using truth-function  operators.

Examples would   include:

F(a) & R(a,  b)” and “R(a, b) ∨ R(b, a)

According  to  Russell, it is  unnecessary to suppose that there exists any
special  sort of  fact  corresponding to molecular propositions.

The  truth-value  of a molecular proposition could be entirely derivative
on

the  truth-values of its constituents.

Hence, if

xxv. F(a)   &  R(a,b)

is true, ultimately it is made true by two  atomic  facts, the fact  that a
has property F and the fact that a  bears R to  b, and not by a single 
conjunctive  fact.

However Russell's  attitude with regard to quantified   propositions had
changed. 

He no longer believed that the truth  of a  general proposition  could be
reduced simply to the facts or  complexes making its  instances  true.

Russell argued that the  truth of the general proposition   “(x).R(x, b)”
could not consist  entirely of the various atomic facts that  a  bears R to
b, b 
bears R to b,c bears R to b, ….

It also  requires the   truth that there are no other individuals besides
a,
b,  c, etc., i.e.,  no other  atomic facts of the relevant form.

Hence,  Russell  concluded that there  is a special category of facts he
calls   general facts that account for the truth  of quantified 
propositions, 
although he admitted a certain amount of  uncertainty  as to their  precise
nature.

Likewise, Russell  also posited existence  facts,  those facts
corresponding
to the  truth of existentially quantified   propositions, such as 

xxvi. (∃x)R(x, b)

In the case of general  and existence  facts, Russell did not think it 
coherent to make  distinctions  between positive and negative facts. 

Indeed, a  negative  general fact could simply be described as an 
existence
fact,  and  a negative existence fact could be described as a general 
fact. 


For example, the falsity of the general proposition

xxvii.  All  birds fly.

amounts to the fact that there exist birds that do  not fly,  and the
falsity
of the existential proposition 

xxviii. There are  unicorns.

amounts to the general fact  that everything is not a unicorn. 

Obviously, however, the truth or  falsity of a general or existence  
proposition is not wholly  independent of its instances.

In addition  to  the sorts of  facts discussed above, Russell raised the
question as  to whether  a  special sort of fact is required corresponding
to  
propositions that report a  belief, desire or other propositional  
attitude.

Russell's views on this matter changed over different  periods,  as his own

views regarding the nature of judgment,  belief and  representation
matured.

Moreover, in some works he left  it as a open  question as to whether one 
need presuppose a  distinct kind of logical  form in these cases.

At times,   however, Russell believed that the  fact that S believes that a
bears R  to b  amounts to the holding of a  multiple relation in which S,
a, 
R
and b are all  relata.

At  other points, he  considered more complicated analyses in which 
beliefs

amount to  the possession of certain psychological states bearing  causal 
or 
other relationships to the objects they are about, or the  tendencies  of 
believers to behave in certain ways.

Depending on  how  such phenomena are  analyzed, it is certainly not clear
that they   require any new species of  fact.

Russell's use of "atomic  fact",  and indeed the very title of  “logical
atomism” suggest  that the  constituents of atomic facts, the logical 
atoms, 
Russell spoke of,  must be regarded as utterly simple and devoid  of 
complexity.

In  that case, the particulars, qualities  and relations  making up atomic 
facts constitute the fundamental  level of reality to which all  other 
aspects
of reality are  ultimately reducible.

This attitude is  confirmed especially in  Russell's early logical atomist 
writings. 

"The  philosophy I espouse is analytic, because it claims that  one  must 
discover the simple elements of which complexes are composed, and   that 
complexes presuppose simples, whereas simples do not   presuppose 
complexes."

"I believe there are simple beings in  the  universe, and that these beings

have relations in virtue of  which  complex beings are composed."

"Any time a bears the relation  R to b there  is a complex "a in relation R

to b.""

"You  will note that this  philosophy is the philosophy of logical  
atomism."

"Every simple  entity is an atom."

Elsewhere  Russell speaks of  “logical atomism”  as involving the view
that 
you can get down in theory, if not  in  practice, to ultimate  simples, out
of
which the world is built, and  that  those  simples have a kind of reality
not belonging to anything   else.

However, it has been questioned whether Russell had   sufficient 
argumentation for thinking that there are such simple   beings.

In the  abstract, there are two sorts of arguments  Russell  could have
given
for the  existence of simples, a  priori arguments, or  empirical arguments
(cf. Pears  1985, 4ff). 

An a priori  argument might proceed from the very   understanding of
complexity: what  is complex presupposes parts. 

Russell wrote: "I confess it seems obvious  to me (as it did  Leibniz) that

what is complex must be composed of  simples,  though the number of
constituents  may be   infinite."

However, if construed as an argument, this does not seem  very  convincing.

It seems at least logically possible that while a  complex  may have parts,

its parts might themselves be complex,  and their parts  might also be
complex,  and so on, ad infinitum. 

Indeed,  Russell himself later came to admit that one could not  know
simply

on  the basis of something being complex that it must  be composed of  
simples.

Another sort of a priori argument  might stem from  conceptions  regarding
the nature of analysis. 

As analysis  proceeds, one reaches more primitive notions, and it  might be

thought  that the process must terminate at a stage in  which the remaining


vocabulary is indefinable because the entities  involved are absolutely 
simple,  and hence, cannot be construed  as logical constructions built 
out
of
anything  more  primitive.

Russell did at some points  describe his logical atoms  as reached at "the 
limit of analysis" or  "the final residue in  analysis".

However, even during the height of his  logical atomist  period, Russell 
admitted that it is possible that  "analysis  could go on forever", and
that

complex things might be  capable of  analysis "ad infinitum". Grice liked
that 
when he thought  he  would write: "From Genesis to Revelations: a new
foundations  for   metaphysics". Unfortunately, it remained an
unpublication.

One   might  argue for simples as the basis of an empirical argument; i.e.,
 
one might claim  to have completed the process of analysis and to  have 
reduced all sorts of  truths down to certain entities that  can be known 
in
some
way or another to be  simple. Russell is  sometimes interpreted  as having
reasoned in this way.  

According to Russell's well  known principle of acquaintance  in 
epistemology, in order to  understand a proposition, one must  be
acquainted
with  the
meaning of  every simple symbol making  it up.

Russell at times suggested that we are  only directly  acquainted with
sense

data, and their properties and  relations,  and perhaps with our own 
selves.

It might be thought  that  these entities are simple, and must  constitute
the terminus of   analysis.

However, Russell was explicit that sense data can  themselves  be complex, 
and that he knew of no reason to suppose  that we cannot be  acquainted
with
a 
complex without being  aware that it is complex and  without being
acquainted
with   its constituents.

Indeed, Russell  eventually came to the conclusion  that nothing can ever
be

known to be  simple.

While there is  significant evidence that Russell did   believe in the
existence  of simple entities in the early phases of his  logical  atomist 
period,
it is possible that, uncharacteristically, he  held this  belief  without
argumentation. In admitting that it is  possible  that analysis could go 
on
ad
infinitum, Russell claimed that   "I do not think it is true, but it is a 
thing
that one might  argue,  certainly".

In “Logical Atomism”, Russell  admits that  "by greater  logical skill,
the
need for assuming them, i.e.  simples,  can be  avoided.

This attitude may explain in part  why it is that at the   outset of his
1918
lectures on logical  atomism, he claimed that the   things he is going to
say
in  those lectures are mainly "my own   personal opinions and I do not 
claim
that they are more than that". (He  knew  most people  thought the opinions
were Witters's).

It may  have been  that  Russell was interested not so much in establishing
 
definitively that there are  any absolutely simple entities, but  rather 
in
combating the widespread arguments  of others that the  notion of a 
simple,
independent entity is incoherent, and  only  the whole of the  universe is
fundamentally real.

According to  Russell, such attitudes  are customarily traced to a wrong
view 
about relations.

In arguing  for the doctrine of "external  relations",  Russell was
attempting  simply to render a world of  simple entities coherent  again.

As his  career progressed,  Russell becomes more and more prone to 
emphasize 
that what  is important for his philosophical outlook is not absolute   
simplicity, but only relative simplicity.

Thus, in response to   criticism about his notion of simplicity, Russell 
writes: "as  for  “abstract analysis in search of the simple’ and
elemental, 
that  is a  more important matter."

To begin with, "simple"  must NOT be taken in an  absolute way.

"Simpler" would be a better  word.

Of course,  Russell should be glad  to reach the  absolutely simple, but he
did not  believe that that is within   his capacity.

What he did maintain is  that, whenever anything is  complex, out 
knowledge
is advanced by  discovering constituents  of it, even if these 
constituents
themselves  are still complex. 

According to Russell, analysis proceeds in  stages. 

When analysis shows the terminology and presuppositions of one   stage of 
analysis to be definable, or logically constructible,  in  terms of simpler
and 
more basic notions, this is a  philosophical  advance, even if these
notions
are  themselves  further analyzable. 

As Russell says, the only drawback to a  language which is not yet  fully 
analyzed is that in it, one  cannot speak of anything more  fundamental
than
those  objects,  properties or relations that are named  at that level.

Russell   summarized his position as  follows:

If the world is composed of  simples —  i.e., of things,  qualities and
relations that are  devoid of structure — not only  all  our knowledge but
all that 
of omniscience could be expressed by means  of  words denoting  these
simples.

We could distinguish in the world  a stuff   (to use William James's word)
and a structure.

The  stuff would  consist of all the simples denoted by names, while the  
structure  would depend on relations and qualities for which our  minimum  
vocabulary would have words.

This conception can be  applied  without assuming that there is anything 
absolutely simple.  

We can define as relatively simple whatever we do not  know to  be 
complex.

Results obtained using the concept of relative   simplicity  will still be
true if complexity is afterward found,  provided we have   abstained from
asserting absolute  simplicity.

At a given stage  of  analysis, a certain class of  sentences may be
labeled
as "atomic",  even if the  facts  corresponding to them cannot be regarded
as
built of   fundamental  ontological atoms.

Thus, Russell's logical atomism is  a  mere commitment  to conceptual
analysis as a method coupled  with a  rejection of idealistic  monism,
rather than a 
pretense to have  discovered the genuine metaphysical atoms  (or 
corpuscules,
since they  are divisible) making up the world of  facts, or even  the
belief
that  such a discovery is  possible.

Indeed, Russell continued  to use  "logical atomism"  to describe his
philosophy in later years of his   career, during  the period in which he
stressed
relative, not absolute    simplicity.

Another important issue often discussed in connection   with  logical
atomism
worth discussing in greater detail is  the  supposition that  atomic
propositions are logically  independent of each  other, or that the truth 
or falsity
of  any one atomic proposition does  not logically imply or necessitate  
the
truth or falsity of any other  atomic proposition.

Russell  writes: 

Perhaps one atomic  fact may sometimes be capable of  being inferred from 
another, though  Russell did not believe this  to be the case; but in any
case
it  cannot  be inferred from  premises no one of which is an atomic fact.

Thus   Russell  expresses doubt about the existence of any relations of 
logical   dependence between atomic propositions, but the fact that he 
left
it  as
a open  possibility makes it seem that he would not consider   it a
defining
feature of an  atomic proposition that it must be   independent from all
others, or a central  tenet of logical  atomism  generally that atomic
facts
are
independent from  one   another.

Russell does often speak about the constituents  of atomic  facts  as
independently existing entities.

He  writes for  example that each particular has its being independently 
of 
any other  and does not depend upon anything else for the  logical
possibility
of   its existence.

One possible  interpretation would be to take Russell  as  holding that any

atomic fact involving a certain group of  particulars is   logically
independent of an atomic fact involving a  distinct group  of  particulars,
even if the
two facts involve the same   quality or  relation.

To use an example favoured by Grice (he  used  to ask his  children's
playmates):

Can a sweater be  green and  red all over? No  stripes allowed.

He was amused by  how  anti-corpuscularian his children's  playmates could 
be.

The  propositions

xxix. a is red.

xxx. a is  green.

do not seem  to be independent from one another: from the  truth of one the

falsity  of the other can seemingly be inferred. 

However, the weakened version of  the independence principle, on  which
only

atomic facts involving  different particulars are  independent, does not
entail  that it is  possible that "a is red"  and "a is green" may both be 
true.

Russell  saw himself as  denying the view that when a bears R to b,  there
is 
some  part of a's nature as an entity that involves its relatedness to   b.


It might be thought that Russell's doctrine of external relations  
committed
him at least to certain principles regarding the modal status  of  atomic
facts  (if not the independence principle). 

According to  certain ways of  defining the phrase, what it  means for a
relation to  be internal is that it is a  relation  that its relata could
not fail
to  have; an external relation is  one its  relata could possibly not have.


Russell then might  be seen as committed to the view that atomic facts 
(all

of which  involve particulars standing in relations, in the broad  sense 
above)  are always contingent.

While this does not   directly bear on the question  of their independence,
it would   nevertheless commit Russell to certain tenets  regarding the 
modal 
features of atomic facts.

Atomic propositions are  of  the  simplest possible forms, and there is
certainly nothing  in their forms  that  would suggest any logical
connection to, 
or incompatibility with,  other atomic   propositions.

Perhaps the most illuminating remarks to  be found  in  Russell's work that
would lead one to expect complete  logical  independence among  ATOMIC
propositions involve the claims he   made about how it is that one 
recognizes a
certain class of  purported  entities as “logical constructions”, and  the

recommendations he gives  about analyzing propositions involving  them. 

Prior to conceptual  analysis, two propositions may  appear to be 
logically
incompatible  atomic propositions. 

However, Russell explains  that the  logical  necessities involved in cases such as these are due to the   nature of  material objects, points and instants as logical  constructions.

At a certain point in time, a physical object  might be regarded as  a class of sensible particulars bearing certain  resemblance relations  to one another occupying a continuous region  of space.

It is  therefore  impossible by  definition for the same physical object to occupy wholly distinct   locations at the same time.

When  analyzed, such propositions   as:

xxxi. O1 is located at p1 at  t1.

are revealed as having  a much  more complicated logical form,  and hence may have logical  consequences not  evident before conceptual  analysis.

We do not have here any reason to  think that  truly  atomic propositions, those containing names of genuine   particulars and  their relations, are not always  independent.

Russell's  logical  atomism  had significant influence on the works of the logical  positivist   tradition, as exemplified in the works of Ayer, whom Grice  calls an  'infant  terrible of Oxford philosophy'.

Grice   confessed that, having been born "on the wrong side of the tracks" was  never invited to the All Souls Play Group meetings on Thursday evenings  that  Ayer and Austin attended, and where they discussed  "Russell and cricket" ("not  necessarily in that order").

Especially, the  notion of a “logical   construction” was important for how such thinkers  conceived of the nature  of  ordinary objects, see, e.g., Ayer, or when  Grice said:

xxxii. The self is a logical construction.

While much of the work of the so-called “ordinary language” school of philosophy   centered in Oxford in the 1940s and 1950s and beyond can also been  seen  largely as a critical response to views of Russell (see, e.g., Austin,  'Sense and Sensibilia', Warnock, 'Metaphysics in Logic',   Urmson,
'Philosophical  analysis), trust Grice to be an Oxonian   dissident who loved Russell ("in  parts").
Abstracting away  from Russell's  particular examples of proposed  analyses in terms of  sensible  particulars, the general framework of Russell's corpuscular  picture  of the world, which consists of a plurality of entities that have qualities and enter into relations, remains one to which many philosophers  are attracted.


REFERENCES:

Bostock,  D.   Logical Atomism, Oxford: Oxford University Press.

Grice, H. P.    Definite descriptions in Russell and in the vernacular.

Hochberg, H.   Thought, Fact and Reference: The Origins and Ontology of Logical Atomism,  Minneapolis: University of Minnesota Press.

Landini,  Gregory, Russell's Hidden  Substitutional Theory, Oxford: Oxford University Press --

Linsky,  Bernard, The Metaphysics of Logical   Atomism.

Livingston, P. Russellian  Atomism, Philosophical Investigations, 24

Lycan, William, Logical Atomism and Ontological  Atoms, Synthese, 46.

Pears, D. F., Introduction to  B.  Russell,  The Philosophy of Logical Atomism, Chicago: Open Court.
Simons, P.  Logical Atomism.

Skyrms, B. Logical Atoms and  Combinatorial  Possibility, The Journal of Philosophy, 90 --

Urmson,  J. O., Philosophical Analysis: Its  Development Between the Two World Wars, Oxford:  Clarendon Press.

Warnock,  G.J., "Metaphysics in  Logic, Proceedings  of the Aristotelian Society, 51.