THE FAILURE OF FORMAL LOGIC
In order to escape the necessity of concerning itself with personality
and particular circumstances in questions of truth and error,
Intellectualism appeals to Logic, which it conceives as a purely formal
science and its impregnable citadel. This appeal, however, rests on a
number of questionable assumptions, and most of these are not avowed.
1. It assumes that forms of thought can be treated in abstraction from
their matter--in other words, that the general types of thinking are
never affected by the particular context in which they occur. Now, this
means that the question of real truth must not be raised; for, as we
have seen (Chapter V.), real truth is always an affair of particular
consequences. The result is, that as truth-claims are no longer tested,
they _all pass as true_ for Logic, and are even raised to the rank of
'absolute truths,' or are mistaken for them. For the notion of a really
('materially') true judgment which someone has chosen, made, and tested,
there is substituted that of a formally valid proposition, and in the
end Logic gets so involved in the study of 'validity' that it puts aside
altogether all real tests of truth, and becomes a game with verbal
symbols which is entirely irrelevant to scientific thinking.
2. Formal Logic assumes the right of abstracting from the whole process
of making an assertion. It presumes that the assertion has already been
made somehow. How, it does not inquire. Yet it is clear that in each
case there were concrete reasons why just _that_ assertion was preferred
to any other. These concrete reasons it makes bold to dismiss as
'psychological,' and between 'logic' and 'psychology'[F] it decrees an
absolute divorce. Where, when, why, by and to whom, an assertion was
made, is taken to be irrelevant, and put aside as 'extralogical.'
3. This convenient assumption, however, ultimately necessitates an
abstraction from meaning, though Formal Logic does not avow this openly.
Every assertion is meant to convey a certain meaning in a certain
context, and therefore its verbal 'form' has to take on its own
individual _nuance_ of meaning. What any particular form of words does
in fact mean on any particular occasion always depends upon the use of
the words in a particular context. Meaning, therefore, cannot be
depersonalized; if meanings are depersonalized, they cease to be real,
and become verbal.
Formal Logic has, in fact, mistaken _words_, which are (within the same
language) identical on all occasions, for the _thoughts_ they are
intended to express, which are varied to suit each occasion. Words alone
are tolerant of the abstract treatment Formal Logic demands. This
'science,' therefore, finally reduces to mere verbalism, distracted by
inconsistent relapses into 'psychology.'
But will this conception of Logic either work out consistently in itself
or lead to a tenable theory of scientific thinking? Emphatically not.
What is the use of a logic which (1) cannot effect the capital
distinction of all thought, that between the true and the false? (2) is
debarred by its own principles from considering the _meaning_ of any
real assertion? and (3) is thus tossed helplessly from horn to horn of
the dilemma 'either verbalism or psychology'?
We may select a few examples of this fatal dilemma.
1. In dealing with what it calls 'the meaning' of terms, propositions,
etc., Formal Logic has always to choose between the meaning of the
_words_ and the meaning of the _man_. For it is clear that words which
may be used ambiguously may on occasion leave no doubt as to their
meaning, while conversely all may become 'ambiguous' in a context. If,
therefore, the occasion is abstracted from, all forms must be treated
verbally as ambiguous formulae, which may be used in different senses.
If it is, nevertheless, attempted to deal with their actual meaning on
any given occasion, what its maker meant the words to convey must be
discovered, and the inquiry at once becomes 'psychological'--that is to
say, 'extralogical.'
2. If judgments are not to be verbal ('propositions'), but real
assertions which are actually meant, they must proceed from personal
selections, and must have been chosen from among alternative
formulations because of their superior value for their maker's purpose.
But all this is plainly an affair of psychology. So inevitable is this
that a truly formal Ideal of 'Logic' would exclude all judgment whatever
from the complete system of 'eternal' Truth. For from such a system no
part could be rightly extracted to stand alone. Such a selection could
be effected and justified only by the exigencies of a human thinker.
The impotent verbalism of the formal treatment of judgment appears in
another way when the question is raised _how_ a 'true' judgment is to be
distinguished from a 'false.' For the logician, if his public will not
accept either the relegation of this distinction to 'psychology' or the
proper formal answer that _all_ judgments are (formally) 'true' and even
'infallible,' can think of nothing better to say than that if the
'judgment' is not true it was not a 'true judgment,' but a false
'opinion' which may be abandoned to 'psychology.'[G] Apparently he is
not concerned to help men to discriminate between 'judgments' and
'opinions,' or even to show that true 'judgments' do in fact occur.
3. Inference involves Formal Logic in a host of difficulties.
_(a)_ If it is not to be a verbal manipulation of phrases whose coming
together is not inquired into, it must be a connected train of thought.
But such a connection of thoughts cannot be conceived or understood
without reference to the purpose of a reasoner, who _selects_ what he
requires from the totality of 'truths.' If, then, 'Logic' has merely to
contemplate this eternal and immutable system of truth in its integrity,
and forbids all selection from it for a merely human purpose, how can it
either justify, or even understand, the drawing of any inference
whatever?
(_b_) Formal Logic clearly will not quail before the charge of
uselessness. But on its own principles it ought to be consistent. But by
this test also, when it is rigorously judged by it, it fails completely.
Its inconsistencies are many and incurable. It cannot even be consistent
in its theory of the simplest fundamentals. It is found upon some
occasions to define judgment as that which may be _either_ true _or_
false; and upon others as that which is 'true' (formally)--_i.e._, it
cannot decide whether or not to ignore the existence of error.
(_c_) The Formal view of inference regards it as a 'paradox.' An
inference is required on the one hand to supply fresh information, and
on the other to follow rigorously from its premisses; it must, in a
word, exhibit both _novelty_ and _necessity_. It would seem, however,
that if our inference genuinely had imparted new knowledge, the event
must be merely psychological; for how can any process or event perturb,
or add to, the completed totality of truth in itself? On the other hand,
if the 'necessity' of the operation be taken seriously, the 'inference'
becomes illusory; for if the conclusion inferred is already contained
in the premisses, what sense is there in the purely verbal process of
drawing it out?
(_d_) Most glaringly inadequate of all, however, is the Formal doctrine
of 'Proof' contained in its theory of the Syllogism. A Formal or verbal
syllogism depends essentially on the ability of its Middle Term to
connect the terms in its conclusion. If, however, the Middle Term has
not _the same_ meaning in the two premisses, the syllogism breaks in
two, and no 'valid' conclusion can be reached. Now, whether in fact any
particular Middle Term bears the same meaning in any actual reasoning
Formal Logic has debarred itself from inquiring, by deciding that actual
meaning was 'psychological.' It has to be content, therefore, with an
identity _in the word_ employed for its Middle, But this evidence may
always fail; for when two premisses which are (in general) 'true' are
brought together for the purpose of drawing a particular conclusion, a
glaring falsehood may result. _E.g._, it would in general be granted
that 'iron sinks in water,' yet it does not follow that because 'this
ship is iron' it will 'sink in water,' Hence syllogistic 'proof' seems
quite devoid of the 'cogency' it claimed. After a conclusion has been
'demonstrated' _it has still to come true in fact_. This flaw in the
Syllogism was first pointed out by Mr. Alfred Sidgwick.
(_e_) The formal Syllogism, moreover, conceals another formal flaw. An
infinite regress lurks in its bosom. For if its premisses are disputed,
they must in turn be 'proved.' Four fresh premisses are needed, and if
these again are challenged, the number of true premisses needed to prove
the first conclusion goes on doubling at every step _ad infinitum_. The
only way to stop the process that occurred to logicians was an appeal to
the 'self-evident' truth of 'intuitions'; but this has been shown to be
argumentatively worthless. From this difficulty the pragmatist alone
escapes, by assuming his premisses _provisionally_ and arguing
_forwards_, in order to test them by their consequences. If the deduced
conclusion can be verified in fact, the premisses grow more assured.
Thus every real inference is an experiment, and 'proof' is an affair of
continuous trial and verification--not an infinite falling back upon an
elusive 'certainty,' but an infinite reaching forwards towards a fuller
consummation.
(_f_) So long as the logician regards his premisses not as hypotheses to
be tested, but as established truths, he must condemn the Syllogism as a
formal fallacy. It is inevitably a _petitio principii_. If the argument
'All men are mortal; Smith is a man, therefore Smith is mortal,' means
that we know, before drawing our inference, that literally all men are
mortal, we must already have discovered that Smith is mortal; if we did
not know beforehand that Smith is mortal, we were not justified in
stating that _all_ men are mortal. Nor is it an escape to interpret 'All
men are mortal' to mean that immortals are excluded from 'man' by
definition. For then the question is merely begged in the minor premiss.
That 'Smith is a man' cannot be asserted without assuming that he is
mortal. If, lastly, 'All men are mortal' be taken to state a law of
nature conjoining inseparably mortality and humanity, the logician
either already knows that Smith is rightly classed under the species
'man,' and so subject to its mortality, or else he _assumes_ this. But
how does he know Smith is not like Elijah or Tithonus, a peculiar case,
to which for some reason the law does not apply? Will he declare it to
be 'intuitively certain' that whatever is called, or looks like, a case
of a 'law' _ipso facto_ becomes one?
The logician's analysis of reasoning, then, breaks down. In whichever
way he interprets the Syllogism it is revealed as either a superfluity
or a fallacy: it is never a 'formally valid inference' that can compel
assent. But common sense is undismayed by the pragmatist's discovery
that if the Syllogism is to have any sense its premisses _must_ be taken
as disputable; for, unlike Formal Logic, it has perceived that men do
not reason about what they think they know for certain, but about
matters in dispute.
4. It is not necessary to dwell at length on the futility of the formal
notion of Induction. Formal Induction presupposes that enough particular
instances have been collected to establish a general rule; but in actual
practice inductions always repose, not on indiscriminate observation,
but on a _selection of relevant instances_, and never claim to be based
upon an _exhaustive_ knowledge of particulars. Hence _in form_ the most
satisfactory induction is always incomplete, and differs in no wise from
a bad one. 'All bodies fall to the ground' is an induction which has
worked. 'All swans are white' broke down when black swans were
discovered in Australia. The validity of an induction, then, is not a
question of form.
The necessity for such selection no intellectualist theory of Induction
has understood. All have aimed at exhaustiveness, and imagined that if
it could be attained, inductive reasoning would be rendered sound, and
not impossible. Their ideal 'cause' was the totality of reality,
identified with its 'effect,' in a meaningless tautology. Nothing but
voluntarism can enable logicians to see that our actual procedure in
knowing is the reverse of this, that causal explanation is the
_analysis_ of a continuum, and that 'phenomena,' 'events,' 'effects,'
and 'causes' are all creations of our selective attention; that in
selecting them we run a risk of analyzing falsely, and that if we do,
our 'inductions' will be worthless. But whether they are right or wrong,
valuable or not, real reasoning from 'facts' can never be a 'formally
valid' process.
We are thus brought to see the hollowness of the contention that 'Pure
Reason' can ignore its psychological context and dehumanize itself. A
thought, to be thought at all, must seem _worth_ thinking to someone, it
must convey the meaning he intends, it must be true in his eyes and
relevant to his purposes in the situation in which it arises--_i.e._, it
must have a motive, a value, a meaning, a purpose, a context, and be
selected from a greater whole for its relevance to these. None of these
features does intellectualist logic deign to recognize. For if truth is
absolute and not relative, it is all or nothing. Yet no actual thinking
has such transcendent aims. It is content with selections relative to a
concrete situation. If it were permissible to diversify a
debate--_e.g._, about the authorship of the _Odyssey_--by an irruption
of undisputed truths--_e.g._, a recitation of the multiplication
table--how would it be possible to distinguish a philosopher from a
lunatic?
Formal Logic is either a perennial source of errors about real thinking,
or at best an aimless dissection of a _caput mortuum--i.e._, of the
verbal husks of dead thoughts, whose value Formal Logic could neither
establish nor apprehend, A real Logic, therefore, would most anxiously
avoid all the initial abstractions which have reduced Formal Logic to
such impotence, and would abandon the insane attempt to eliminate the
thinker from the theory of thought.
FOOTNOTES:
[Footnote F: The descriptive science of thought, in its concrete
actuality in different minds.]
[Footnote G: The most popular contribution which Oxford makes just now
to the theory of Error is, 'A judgment which is erroneous is not really
a judgment.' So when a professor 'judges' he is infallible--by
definition!]