Защо пък Ръсел да "измисля рел. св-ва"?
Той не работи с тях, поне на мен не ми е известно, доколкото съм го чел до около 1920 г. /още съм по средата на четенето му/.
Ръсел бачка с т.нар. теория за "външни" отношения-те, отношенията играят в неговия свят ролята на идеите в Платоновия космос. Те не са нито психически, нито физически, а в същото време са общи, са логически.
С извинение за дългия цитат, ето резюме от схващанията на Ръсел със самите негови думи за отношенията, от гл. 2 "Логиката като същност на философията" на "Нашето знание за външния свят":
Here the traditional logic failed completely: it believed that there was only
one form of simple proposition (i.e. of proposition
not stating a relation between two or more other
propositions), namely, the form which ascribes a
predicate to a subject. This is the appropriate form
in assigning the qualities of a given thing we may
say "this thing is round, and red, and so on." Grammar
favours this form, but philosophically it is so far
from universal that it is not even very common. If
we say" this thing is bigger than that," we are not
assigning a mere quality of
"this," but a relation of
"this" and "that." We might express the same
fact by saying"
that thing is smaller than this," where
grammatically the subject is changed. Thus propositions
stating that two things have a certain relation
have a different form from subject-predicate propositions,
and the failure to perceive this difference or
to allow for it has been the source of many errors in
traditional metaphysics.
The belief or unconscious conviction that all propo
LOGIC AS THE ESSENCE OF PHILOSOPHY 55
sitions are of the subject-predicate form in other
words : that every fact consists in some thing having
some quality has rendered most philosophers incapable
of giving any account of the world of science and daily
life. If they had been honestly anxious to give such
an account, they would probably have discovered
their error very quickly ; but most of them were less
anxious to understand the world of science and daily
life, than to convict it of unreality in the interests
of a super-sensible "real" world. Belief in the
unreality of the world of sense arises with irresistible
force in certain moods moods which, I imagine, have
some simple physiological basis, but are none the
less powerfully persuasive. The conviction born of
these moods is the source of most mysticism and
of most metaphysics. When the emotional intensity of
such a mood subsides, a man who is in the habit of
reasoning will search for logical reasons in favour
of the belief which he finds in himself. But since the
belief already exists, he will be very hospitable to any
reason that suggests itself. The paradoxes apparently
proved by his logic are reallythe paradoxes of mysticism,
and are the goal which he feds his logic must reach
if it is to be in accordance with insight. It is in this
way that logic has been pursued by those of the great
philosophers who were mystics notably Plato, Spinoza,
and Hegel. But since they usually took for granted
the supposed insight of the mystic emotion, their
logical doctrines were presented with a certain dryness,
and were believed by their disciples to be quite independent
of the sudden jl.nnTnTjna.fifm from which they
sprang. Nevertheless their origin dung to them, and
they remained to borrow a useful word from Mr.
Santayana
"malicious" in regard to the world of
science and common sense. It is only so that we
56 SCIENTIFIC METHOD IN PHILOSOPHY
can account for the complacency with which philosophers
have accepted the inconsistence of their
doctrines with all the common and scientific facts
which seem best established and most worthy of belief.
The logic of mysticism shows, as is natural, the
defects which are inherent in anything malicious.
While the mystic mood is dominant, the need of logic
is not felt ; as the mood fades, the impulse to logic
reasserts itself, but with a desire to retain the vanishing
insight, or at least to prove that it was insight, and
that what seems to contradict it is illusion. The logic
which thus arises is not quite disinterested or candid,
and is inspired by a certain hatred of the daily world
to which it is to be applied. Such an attitude naturally
does not tend to the best results. Everyone knows
that to read an author simply in order to refute him
is not the way to understand him ; and to read the
book of Nature with a conviction that it is all illusion
is just as unlikely to lead to understanding. If our
logic is to find the common world intelligible, it must
not be hostile, but must be inspired by a genuine
acceptance such as is not usually to be found among
metaphysicians.
Traditional logic, since it holds that all propositions
have the subject-predicate form, is unable to admit
the reality of relations : all relations, it maintains,
must be reduced to properties of the apparently related
terms. There are many ways of refuting this opinion ;
one of the easiest is derived from the consideration
of what are called
"asymmetrical "relations. In
order to explain this, I will first explain two independent
ways of classifying relations
Some relations, when they hold between A and B,
also hold between B and A. Such, for example, is
the relation
"brother or sister." If A is a brother or
LOGIC AS THE ESSENCE OF PHILOSOPHY 57
sister of B thsn B is a brother or sister of A. Such
again is any kind of similarity, say similarity of colour.
Any kind of dissimilarity is also of this kind : if the
colour of A is unlike the colour of B, then the colour of
B is unlike the colour of A. Relations of this sort are
called symmetrical. Thus a relation is symmetrical
if, whenever it holds between A and B, it also holds
between B and A.
All relations that are not symmetrical are called
non-symmetrical. Thus "
brother
"is ncni-syimnetrical,
because, if A is a brother of B, it may happen that
B is a sister of A.
A relation is called asymmetrical when, if it holds
between A and B, it never holds between B and A.
Thus husband, father, grandfather, etc., are asymmetrical
relations. So are before, after, greater, above,
to the right of, etc. All the relations that give rise to
series are of this kind.
Classification into symmetrical, asymmetrical and
merely non-symmetrical relations is the first of the
two classifications we had to consider. The second
is into transitive, intransitive, and merely non-transitive
relations, which are defined as follows.
A relation is said to be transitive, if, whenever it
holds between A and B and also between B and C,
it holds between A and C. Thus before, after, greater,
above are transitive, All relations giving rise to series
are transitive, but so are many others. The transitive
relations just mentioned were asymmetrical, but
many transitive relations are symmetrical for instance,
equality in any respect, exact identity of colour, being
equally numerous (as applied to collections), and
so on.
A relation is said to be non-transitive whenever it
is not transitive. Thus "
brother
"is non-transitive,
58 SCIENTIFIC METHOD IN PHILOSOPHY
because a brother of one's brother may be oneself.
All kinds of dissimilarity are non-transitive.
A relation is said to be intransitive when, if A has the
relation to B, and B to C, A never has it to C. Thus
"father
"is intransitive. So is such a relation as
"one inch taller
"or" one year later."
Let us now, in the light of this classification, return
to the question whether all relations can be reduced
to predications.
In the case of symmetrical relations i.e. relations
which, if they hold between A and B, also hold between
B and A some kind of plausibility can be given to
this doctrine. A symmetrical relation which is
transitive, such as equality, can be regarded as expressing
possession of some common property, while one
which is not transitive, such as inequality, can be
regarded as expressing possession of different properties.
But when we come to asymmetrical relations, such as
before and after, greater and less, etc., the attempt
to reduce them to properties becomes obviously
impossible. When, for example, two things are merely
known to be unequal, without our knowing which
is greater, we may say that the inequality results
from their having different magnitudes, because
inequality is a symmetrical relation ; but to say that
when one thing is greater than another, and not merely
unequal to it, that means that they have different
magnitudes, is formally incapable of explaining the
facts. For if the other thing had been greater than
the one, the magnitudes would also have been different,
though the fact to be explained would not have been
the same. Thus mere difference of magnitude is not all
that is involved, since, if it were, there would be no
difference between one thing being greater than another,
and the other being greater than the one. We shall
LOGIC AS THE ESSENCE OF PHILOSOPHY 59
have to say that the one magnitude is greater than
the other, and thus we shall have failed to get rid of
the relation
"greater." In short, both possession of
the same property and possession of different properties
are symmetrical relations, and therefore cannot account
for the existence of asymmetrical relations.
Asymmetrical relations are involved in all series
in space and time, greater and less, whole and part,
and many others of the most important characteristics
of the actual world. All these aspects, therefore, the
logic which reduces everything to subjects and predicates
is compelled to condemn as error and mere
appearance. To those whose logic is not malicious,
such a wholesale condemnation appears impossible.
And in fact there is no reason except prejudice, so far
as I can discover, for denying the reality of relations.
When once their reality is admitted, all kgical grounds
for supposing the world of sense to be illusory disappear.
If this is to be supposed, it must be frankly and simply
on the ground of mystic insight unsupported by
argument. It is impossible to argue against what
professes to be insight, so long as it does not argue in
its own favour. As logicians, therefore, we may
admit the possibility of the mystic's world, while yet,
so long as we do not have his insight, we must continue
to study the everyday world with which we are
familiar. But when he contends that our world is
impossible, then our logic is ready to repel his attack.
And the first step in creating the logic which is to
perform this service is the recognition of the reality of
relations.
Relations which have two terms are only one kind
of relations. A relation may have three terms, or four,
or any number. Relations of two terms, being the
simplest, have received more attention than the
60 SCIENTIFIC METHOD IN PHILOSOPHY
others, and have generally been alone considered by
philosophers, both those who accepted and those
who denied the reality of relations. But other relations
have their importance, and are indispensable in the
solution of certain problems. Jealousy, for example,
is a relation between three people. Professor Royce
mentions the relation
"giving"
: when A gives B
to C, that is a relation of three terms.1 When a man
says to his wife :
" My dear, I wish you could induce
Angelina to accept Edwin," his wish constitutes a
relation between four people, himself, his wife, Angelina,
and Edwin. Thus such relations are by no means
recondite or rare. But in order to explain exactly
how they differ from relations of two terms, we must
embark upon a classification of the logical forms of
facts, which is the first business of logic, and the
business in which the traditional logic has been most
deficient.
The existing world consists of many things with
many qualities and relations. A complete description
of the existing world would require not only a catalogue
of the things, but also a mention of all their qualities
and relations. We should have to know not only this
that, and the other thing, but also which was red,
which yellow, which was earlier than which, which was
which between two others, and so on. When I speak
of a "fact," I do not mean one of the simple things
in the world ; I mean that a certain thing has a certain
quality, or that certain things have a certain relation.
Thus, for example, I should not call Napoleon a fact,
but I should call it a fact that he was ambitious, or
that he married Josephine. Now a fact, in this sense,
is never simple, but always has two or more constituents.
When it simply assigns a quality to a thing,
Encyclopedia of the Philosophical Sciences, vol. i. p. 97.
LOGIC AS THE ESSENCE OF PHILOSOPHY 61
it has only two constituents, the thing and the quality.
When it consists of a relation between two things,
it has three constituents, the things and the relation.
When it consists of a relation between three things,
it has four constituents, and so on. The constituents
of facts, in the sense in which we are using the
word "fact," are not other facts, but are things
and qualities or relations. When we say that there
are relations of more than two terms, we mean that
there are single facts consisting of a single relation
and more than two things. I do not mean that
one relation of two terms may hold between A and
B, and also between A and C, as, for example, a
man is the son of his father and also the son of his
mother. This constitutes two distinct facts: if we
choose to treat it as one fact, it is a fact which has
facts for its constituents. But the facts I am speaking
of have no facts among their constituents, but only
things and relations. For example, when A is jealous
of B on account of C, there is only one fact, involving
three people ; there are not two instances of jealousy,
but only one. It is in such cases that I speak of a
relation of three terms, where the simplest possible
fact in which the relation occurs is one involving three
things in addition to the relation. And the same
applies to relations of four terms or five or any other
number. All such relations must be admitted in
our inventory of the logical forms of facts : two facts
involving the same number of things have the same
form, and two which involve different numbers of
things have different forms.
Given any fact, there is an assertion which expresses
the fact. The fact itself is objective, and independent
of our thought or opinion about it ; but the assertion
is something which involves thought, and may be
62 SCIENTIFIC METHOD IN PHILOSOPHY
either true or false. An assertion may be positive or
negative : we may assert that Charles I was executed,
or that he did not die in his bed. A negative assertion
may be said to be a denial. Given a form of words
which must be either true or false, such as
"Charles I
died in his bed," we may either assert or deny this
form of words : in the one case we have a positive
assertion, in the other a negative one. A form of
words which must be either true or false I shall call
a proposition. Thus a proposition is the same as what
may be significantly asserted or denied. A proposition
which expresses what we have called a fact, i.e. which,
when asserted, asserts that a certain thing has a
certain quality, or that certain things have a certain
relation, will be called an atomic proposition, because,
as we shall see immediately, there are other propositions
into which atomic propositions enter in a way analogous
to that in which atoms enter into molecules. Atomic
propositions, although, like facts, they may have any
one of an infinite number of forms, are only one kind
of propositions. All other kinds are more complicated.
In order to preserve the parallelism in language
as regards facts and propositions, we shall give the name
"atomic facts"
to the facts we have hitherto been
considering. Thus atomic facts are what determine
whether atomic propositions are to be asserted or
denied.
Whether an atomic proposition, such as "this is
red," or "this is before that," is to be asserted or
denied can only be known empirically.
