[lit-ideas] Re: Logical Corpuscularism

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  • Date: Mon, 21 Sep 2015 05:50:15 -0400

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
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
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

of classes of like cardinality, and then showing how apparent discourse
about “classes” could be replaced by higher-order quantification,
made it possible to see how it is that there could be truths of
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

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
terms of particular sensations: i.e., bits of colour (Russell predates
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
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
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,
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
could be discarded from the minimum vocabulary needed for physics or

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

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

Wherever possible, logical constructions are to be substituted for

Rival philosophies that postulate an ego or mind as an entity distinct
from its mental states involve inferring the existence of an entity that
directly be found in experience.

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

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
view that classes are logical fictions, results in the view that minds
physical objects too are logical fictions, or not parts of the basic
building blocks of reality. Instead, all truths about such purported
turn out instead to be analyzable as truths about sensible particulars
their relations to one another.

This is in keeping with the general metaphysical outlook of logical

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

The slogan was applied within his analyses in mathematics as well.
that sometimes a series of rational numbers converges towards a limit
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

species of mathematical entity not already known to exist.

Complaining that the method of postulating what we want has the

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
regarded as logical premises from which the original body of knowledge
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
and accept, than many of the logical premises from which it is derived.

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

The reason for accepting an axiom, as for accepting any other
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,
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
body of knowledge or set of data (Cfr. Paul, "Is there a problem about
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
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

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

this room at this moment”.

In this case, the truth or falsity of this statement may seem obvious,
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,
something to be a person, for a person to be in a room, what a moment is,

In this case, it might seem that the ordinary language statement is
sufficiently vague that there is likely no one precise or unambiguous
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,
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
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
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
classes of sensible particulars related to each other in ways
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
will be far more doubtful than the truth of the vague assertion with
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
qualities and stand in relations to one another.

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

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
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
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

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
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

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

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

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

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

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
if you suppose that it must be a fact that there is not such a complex,
such a fact would itself seem to be a negative fact.

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

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

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

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

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
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
although he admitted a certain amount of uncertainty as to their precise

Likewise, Russell also posited existence facts, those facts
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
fact, and a negative existence fact could be described as a general

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
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
propositions that report a belief, desire or other propositional

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

views regarding the nature of judgment, belief and representation

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,
and b are all relata.

At other points, he considered more complicated analyses in which

amount to the possession of certain psychological states bearing causal
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
Russell spoke of, must be regarded as utterly simple and devoid of

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

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

"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

"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

"Every simple entity is an atom."

Elsewhere Russell speaks of “logical atomism” as involving the view
you can get down in theory, if not in practice, to ultimate simples, out
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
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

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

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
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

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

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
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
with the
meaning of every simple symbol making it up.

Russell at times suggested that we are only directly acquainted with

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

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
complex without being aware that it is complex and without being
with its constituents.

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

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
it is possible that, uncharacteristically, he held this belief without
argumentation. In admitting that it is possible that analysis could go
infinitum, Russell claimed that "I do not think it is true, but it is a
that one might argue, certainly".

In “Logical Atomism”, Russell admits that "by greater logical skill,
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
lectures on logical atomism, he claimed that the things he is going to
in those lectures are mainly "my own personal opinions and I do not
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
combating the widespread arguments of others that the notion of a
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
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
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
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
is advanced by discovering constituents of it, even if these
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
more basic notions, this is a philosophical advance, even if these
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
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

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

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
as "atomic", even if the facts corresponding to them cannot be regarded
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
since they are divisible) making up the world of facts, or even the
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
relative, not absolute simplicity.

Another important issue often discussed in connection with logical
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
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
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
it as
a open possibility makes it seem that he would not consider it a
feature of an atomic proposition that it must be independent from all
others, or a central tenet of logical atomism generally that atomic
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
any other and does not depend upon anything else for the logical
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

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

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

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

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

Russell saw himself as denying the view that when a bears R to b, there
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
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

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
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
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
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
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
-- 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" 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.

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