In short, the comprehensive genius of Bacon widened logic into a
general science of inference.
On the other hand, as Aristotle over-emphasized deduction so Bacon
over-emphasized induction by contending that it is the only process of
discovering universals (_axiomata_), which deduction only applies to
particulars. J. S. Mill in his _Logic_ pointed out this defect, and
without departing from Baconian principles remedied it by quoting
scientific examples, in which deduction, starting from inductive
principles, applies more general to less general universals, e.g. when
the more general law of gravitation is shown to include the less
general laws of planetary gravitation. Mill's logic has the great
merit of copiously exemplifying the principles of the variety of
method according to subject-matter. It teaches us that scientific
method is sometimes induction, sometimes deduction, and sometimes the
consilience of both, either by the inductive verification of previous
deductions, or by the deductive explanation of previous inductions.
It is also most interesting to notice that Aristotle saw further than
Bacon in this direction. The founder of logic anticipated the latest
logic of science, when he recognized, not only the deduction of
mathematics, but also the experience of facts followed by deductive
explanations of their causes in physics.
The consilience of empirical and deductive processes was an Aristotelian
discovery, elaborated by Mill against Bacon. On the whole, however,
Aristotle, Bacon and Mill, purged from their errors, form one empirical
school, gradually growing by adapting itself to the advance of science;
a school in which Aristotle was most influenced by Greek deductive
Mathematics, Bacon by the rise of empirical physics at the Renaissance,
and Mill by the Newtonian combination of empirical facts and
mathematical principles in the _Principia_. From studying this
succession of empirical logicians, we cannot doubt that sense, memory
and experience are the real origin of inference, analogical, inductive
and deductive. The deepest problem of logic is the relation of sense and
inference. But we must first consider the mental analysis of inference,
and this brings us to conceptual and formal logic.
Aristotle's logic has often been called formal logic; it was really a
technical logic of syllogism analysed into linguistic elements, and of
science rested on an empirical basis. At the same time his psychology,
though maintaining his empiricism, contained some seeds of conceptual
logic, and indirectly of formal logic. Intellectual development, which
according to the logic of the _Analytics_ consists of sense, memory,
experience, induction and intellect, according to the psychology of the
_De Anima_ consists of sense, imagination and intellect, and one
division of intellect is into conception of the undivided and
combination of conceptions as one (_De An._ iii. 6). The _De
Interpretatione_ opens with a reference to this psychological
distinction, implying that names represent conceptions, propositions
represent combinations of conceptions. But the same passage relegates
conceptions and their combinations to the _De Anima_, and confines the
_De Interpretatione_ to names and propositions in conformity with the
linguistic analysis which pervades the logical treatises of Aristotle,
who neither brought his psychological distinction between conceptions
and their combinations into his logic, nor advanced the combinations of
conceptions as a definition of judgment ([Greek: krisis]), nor employed
the mental distinction between conceptions and judgments as an analysis
of inference, or reasoning, or syllogism: he was no conceptual logician.
The history of logic shows that the linguistic distinction between terms
and propositions was the sole analysis of reasoning in the logical
treatises of Aristotle; that the mental distinction between conceptions
([Greek: ennoiai]) and judgments ([Greek: axiômata] in a wide sense) was
imported into logic by the Stoics; and that this mental distinction
became the logical analysis of reasoning under the authority of St
Thomas Aquinas. In his commentary on the _De Interpretatione_, St
Thomas, after citing from the _De Anima_ Aristotle's "duplex operatio
intellectus," said, "Additur autem et tertia operatio, scilicet
ratiocinandi," and concluded that, since logic is a rational science
(_rationalis scientia_), its consideration must be directed to all these
operations of reason. Hence arose conceptual logic; according to which
conception is a simple apprehension of an idea without belief in being
or not being, e.g. the idea of man or of running; judgment is a
combination of conceptions, adding being or not being, e.g. man is
running or not running; and reasoning is a combination of judgments:
conversely, there is a mental analysis of reasoning into judgments, and
judgment into conceptions, beneath the linguistic analysis of rational
discourse into propositions, and propositions into terms. Logic,
according to this new school, which has by our time become an old
school, has to co-ordinate these three operations, direct them, and,
beginning with conceptions, combine conceptions into judgments, and
judgments into inference, which thus becomes a complex combination of
conceptions, or, in modern parlance, an extension of our ideas.
Conceptual logicians were, indeed, from the first aware that sense
supplies the data, and that judgment and therefore inference contains
belief that things are or are not. But they held, and still hold that
sensation and conception are alike mere apprehensions, and that the
belief that things are or are not arises somehow after sensation and
conception in judgment, from which it passes into inference. At first,
they were more sanguine of extracting from these unpromising beginnings
some knowledge of things beyond ideas. But at length many of them became
formal logicians, who held that logic is the investigation of formal
thinking, or consistent conception, judgment and reasoning; that it
shows how we infer formal truths of consistency without material truth
of signifying things; that, as the science of the form or process, it
must entirely abstract from the matter, or objects, of thought; and that
it does not tell us how we infer from experience. Thus has logic drifted
further and further from the real and empirical logic of Aristotle the
founder and Bacon the reformer of the science.
The great merit of conceptual logic was the demand for a mental analysis
of mental reasoning, and the direct analysis of reasoning into judgments
which are the sole premises and conclusions of reasoning and of all
mental inferences. Aristotle had fallen into the paradox of resolving a
mental act into verbal elements. The Schoolmen, however, gradually came
to realize that the result to their logic was to make it a
_sermocionalis scientia_, and to their metaphysics the danger of
nominalism. St Thomas made a great advance by making logic throughout a
_rationalis scientia_; and logicians are now agreed that reasoning
consists of judgments, discourse of propositions. This distinction is,
moreover, vital to the whole logic of inference, because we always think
all the judgments of which our inference consists, but seldom state all
the propositions by which it is expressed. We omit propositions, curtail
them, and even express a judgment by a single term, e.g. "Good!"
"Fire!". Hence the linguistic expression is not a true measure of
inference; and to say that an inference consists of two propositions
causing a third is not strictly true. But to say that it is two
judgments causing a third is always true, and the very essence of
inference, because we must think the two to conclude the third in "the
sessions of sweet silent thought." Inference, in short, consists of
actual judgments capable of being expressed in propositions.
Inference always consists of judgments. But judgment does not always
consist of conceptions. It is not a combination of conceptions; it
does not arise from conceptions, nor even at first require conception.
Sense is the origin of judgment. One who feels pained or pleased, who
feels hot or cold or resisting in touch, who tastes the flavoured, who
smells the odorous, who hears the sounding, who sees the coloured, or
is conscious, already believes that something sensible exists before
conception, before inference, and before language; and his belief is
true of the immediate object of sense, the sensible thing, e.g. the
hot felt in touch. But a belief in the existence of something is a
judgment and a categorical judgment of existence. Sense, then, outer
and inner, or sensation and consciousness, is the origin of sensory
judgments which are true categorical beliefs in the existence of
sensible things; and primary judgments are such true categorical
sensory beliefs that things exist, and neither require conception nor
are combinations of conceptions. Again, since sense is the origin of
memory and experience, memorial and experiential judgments are
categorical and existential judgments, which so far as they report
sensory judgments are always true. Finally, since sense, memory and
experience are the origin of inference, primary inference is
categorical and existential, starting from sensory, memorial and
experiential judgments as premises, and proceeding to inferential
judgments as conclusions, which are categorical and existential, and
are true, so far as they depend on sense, memory and experience.
Sense, then, is the origin of judgment; and the consequence is that
primary judgments are true, categorical and existential judgments of
sense, and primary inferences are inferences from categorical and
existential premises to categorical and existential conclusions, which
are true so far as they arise from outer and inner sense, and proceed
to things similar to sensible things. All other judgments and
inferences about existing things, or ideas, or names, whether
categorical or hypothetical, are afterthoughts, partly true and partly
false.
Sense, then, because it involves a true belief in existence is fitted
to be the origin of judgment. Conception on the other hand is the
simple apprehension of an idea, particular or universal, but without
belief that anything is or is not, and therefore is unfitted to beget
judgment. Nor could a combination of conceptions make a difference so
fundamental as that between conceiving and believing. The most that it
could do would be to cause an ideal judgment, e.g. that the idea of a
centaur is the idea of a man-horse; and even here some further origin
is needed for the addition of the copula "is."
So far from being a cause, conception is not even a condition of all
judgments; a sensation of hot is sufficient evidence that hot exists,
before the idea of hot is either present or wanted. Conception is,
however, a condition of a memorial judgment: in order to remember
being hot, we require an idea of hot. Memory, however, is not that
idea, but involves a judgment that there previously existed the hot
now represented by the idea, which is about the sensible thing beyond
the conceived idea; and the cause of this memorial judgment is past
sense and present memory. So sense, memory and experience, the sum of
sense and memory, though requiring conception, are the causes of the
experiential judgment that there exist and have existed many similar,
sensible things, and these sensory, memorial and experiential
judgments about the existence of past and present sensible things
beyond conceived ideas become the particular premises of primary
inference. Starting from them, inference is enabled to draw
conclusions which are inferential judgments about the existence of
things similar to sensible things beyond conceived ideas. In rising,
however, from particular to universal inference, induction, as we have
seen, adds to its particular premise, S is P, a universal premise,
every M is similar to S, in order to infer the universal conclusion,
every M is P. This universal premise requires a universal conception
of a class or whole number of similar particulars, as a condition. But
the premise is not that conception; it is a belief that there is a
whole number of particulars similar to those already experienced. The
generalization of a class is not, as the conceptual logic assumes, the
abstraction of a general idea, but an inference from the analogy of a
whole individual thing, e.g. a whole man, to a whole number of similar
individuals, e.g. the whole of men. The general idea of all men or the
combination that the idea of all men is similar to the idea of
particular men would not be enough; the universal premise that all men
in fact are similar to those who have died is required to induce the
universal conclusion that all men in fact die. Universal inference
thus requires particular and universal conceptions as its condition;
but, so far as it arises from sense, memory, experience, and involves
generalization, it consists of judgments which do not consist of
conceptions, but are beliefs in things existing beyond conception.
Inference then, so far as it starts from categorical and existential
premises, causes conclusions, or inferential judgments, which require
conceptions, but are categorical and existential judgments beyond
conception. Moreover, as it becomes more deductive, and causes
conclusions further from sensory experience, these inferential
judgments become causes of inferential conceptions. For example, from
the evidence of molar changes due to the obvious parts of bodies,
science first comes to believe in molecular changes due to
imperceptible particles, and then tries to conceive the ideas of
particles, molecules, atoms, electrons. The conceptual logic supposes
that conception always precedes judgment; but the truth is that
sensory judgment begins and inferential judgment ends by preceding
conception. The supposed triple order--conception, judgment,
reasoning--is defective and false. The real order is sensation and
sensory judgment, conception, memory and memorial judgment, experience
and experiential judgment, inference, inferential judgment,
inferential conception. This is not all: inferential conceptions are
inadequate, and finally fail. They are often symbolical; that is, we
conceive one thing only by another like it, e.g. atoms by minute
bodies not nearly small enough. Often the symbol is not like. What
idea can the physicist form of intraspatial ether? What believer in
God pretends to conceive Him as He really is? We believe many things
that we cannot conceive; as Mill said, the inconceivable is not the
incredible; and the point of science is not what we can conceive but
what we should believe on evidence. Conception is the weakest,
judgment the strongest power of man's mind. Sense before conception is
the original cause of judgment; and inference from sense enables
judgment to continue after conception ceases. Finally, as there is
judgment without conception, so there is conception without judgment.
We often say "I understand, but do not decide." But this suspension of
judgment is a highly refined act, unfitted to the beginning of
thought. Conception begins as a condition of memory, and after a long
continuous process of inference ends in mere ideation. The conceptual
logic has made the mistake of making ideation a stage in thought prior
to judgment.
It was natural enough that the originators of conceptual logic, seeing
that judgments can be expressed by propositions, and conceptions by
terms, should fall into the error of supposing that, as propositions
consist of terms, so judgments consist of conceptions, and that there
is a triple mental order--conception, judgment, reasoning--parallel to
the triple linguistic order--term, proposition, discourse. They
overlooked the fact that man thinks long before he speaks, makes
judgments which he does not express at all, or expresses them by
interjections, names and phrases, before he uses regular propositions,
and that he does not begin by conceiving and naming, and then proceed
to believing and proposing. Feeling and sensation, involving believing
or judging, come before conception and language. As conceptions are
not always present in judgment, as they are only occasional
conditions, and as they are unfitted to cause beliefs or judgments,
and especially judgments of existence, and as judgments both precede
conceptions in sense and continue after them in inference, it follows
that conceptions are not the constituents of judgment, and judgment is
not a combination of conceptions. Is there then any analysis of
judgment? Paradoxical as it may sound, the truth seems to be that
primary judgment, beginning as it does with the simplest feeling and
sensation, is not a combination of two mental elements into one, but
is a division of one sensible thing into the thing itself and its
existence and the belief that it is determined as existing, e.g. that
hot exists, cold exists, the pained exists, the pleased exists. Such a
judgment has a cause, namely sense, but no mental elements.
Afterwards come judgments of complex sense, e.g. that the existing hot
is burning or becoming more or less hot, &c. Thus there is a
combination of sensations causing the judgment; but the judgment is
still a division of the sensible thing into itself and its being, and
a belief that it is so determined. Afterwards follow judgments arising
from more complex causes, e.g. memory, experience, inference. But
however complicated these mental causes, there still remain these
points common to all judgment:--(1) The mental causes of judgment are
sense, memory, experience and inference; while conception is a
condition of some judgments. (2) A judgment is not a combination
either of its causes or of its conditions, e.g. it is not a
combination of sensations any more than of ideas. (3) A judgment is a
unitary mental act, dividing not itself but its object into the object
itself and itself as determined, and signifying that it is so
determined. (4) A primary judgment is a judgment that a sensible thing
is determined as existing; but later judgments are concerned with
either existing things, or with ideas, or with words, and signify that
they are determined in all sorts of ways. (5) When a judgment is
expressed by a proposition, the proposition expresses the results of
the division by two terms, subject and predicate, and by the copula
that what is signified by the subject is what is signified by the
predicate; and the proposition is a combination of the two terms; e.g.
border war is evil. (6) A complex judgment is a combination of two
judgments, and may be copulative, e.g. you and I are men, or
hypothetical, or disjunctive, &c.
Empirical logic, the logic of Aristotle and Bacon, is on the right way.
It is the business of the logician to find the causes of the judgments
which form the premises and the conclusions of inference, reasoning and
science. What knowledge do we get by sense, memory and experience, the
first mental causes of judgment? What is judgment, and what its various
kinds? What is inference, how does it proceed by combining judgments as
premises to cause judgments as conclusions, and what are its various
kinds? How does inference draw conclusions more or less probable up to
moral certainty? How does it by the aid of identification convert
probable into necessary conclusions, which become necessary principles
of demonstration? How is categorical succeeded by conditional inference?
What is scientific method as a system of inferences about definite
subjects? How does inference become the source of error and fallacy? How
does the whole process from sense to inference discover the real truth
of judgments, which are true so far as they signify things known by
sense, memory, experience and inference? These are the fundamental
questions of the science of inference. Conceptual logic, on the other
hand, is false from the start. It is not the first business of logic to
direct us how to form conceptions signified by terms, because sense is a
prior cause of judgment and inference. It is not the second business of
logic to direct us how out of conceptions to form judgments signified by
propositions, because the real causes of judgments are sense, memory,
experience and inference. It is, however, the main business of logic to
direct us how out of judgments to form inferences signified by
discourse; and this is the one point which conceptual logic has
contributed to the science of inference. But why spoil the further
mental analysis of inference by supposing that conceptions are
constituents of judgment and therefore of inference, which thus becomes
merely a complex combination of conceptions, an extension of ideas? The
mistake has been to convert three operations of mind into three
processes in a fixed order--conception, judgment, inference. Conception
and judgment are decisions: inference alone is a process, from decisions
to decision, from judgments to judgment. Sense, not conception, is the
origin of judgment. Inference is the process which from judgments about
sensible things proceeds to judgments about things similar to sensible
things. Though some conceptions are its conditions and some judgments
its causes, inference itself in its conclusions causes many more
judgments and conceptions. Finally, inference is an extension, not of
ideas, but of beliefs, at first about existing things, afterwards about
ideas, and even about words; about anything in short about which we
think, in what is too fancifully called "the universe of discourse."
Formal logic has arisen out of the narrowness of conceptual logic. The
science of inference no doubt has to deal primarily with formal truth or
the consistency of premises and conclusion. But as all truth, real as
well as formal, is consistent, formal rules of consistency become real
rules of truth, when the premises are true and the consistent conclusion
is therefore true. The science of inference again rightly emphasizes the
formal thinking of the syllogism in which the combination of premises
involves the conclusion. But the combinations of premises in analogical
and inductive inference, although the combination does not involve the
conclusion, yet causes us to infer it, and in so similar a way that the
science of inference is not complete without investigating all the
combinations which characterize different kinds of inference. The
question of logic is how we infer in fact, as well as perfectly; and we
cannot understand inference unless we consider inferences of probability
of all kinds. Moreover, the study of analogical and inductive inference
is necessary to that of the syllogism itself, because they discover the
premises of syllogism. The formal thinking of syllogism alone is merely
necessary consequence; but when its premises are necessary principles,
its conclusions are not only necessary consequents but also necessary
truths. Hence the manner in which induction aided by identification
discovers necessary principles must be studied by the logician in order
to decide when the syllogism can really arrive at necessary conclusions.
Again, the science of inference has for its subject the form, or
processes, of thought, but not its matter or objects. But it does not
follow that it can investigate the former without the latter. Formal
logicians say that, if they had to consider the matter, they must either
consider all things, which would be impossible, or select some, which
would be arbitrary. But there is an intermediate alternative, which is
neither impossible nor arbitrary; namely, to consider the general
distinctions and principles of all things; and without this general
consideration of the matter the logician cannot know the form of
thought, which consists in drawing inferences about things on these
general principles. Lastly, the science of inference is not indeed the
science of sensation, memory and experience, but at the same time it is
the science of using those mental operations as data of inference; and,
if logic does not show how analogical and inductive inferences directly,
and deductive inferences indirectly, arise from experience, it becomes a
science of mere thinking without knowledge.
Logic is related to all the sciences, because it considers the common
inferences and varying methods used in investigating different subjects.
But it is most closely related to the sciences of metaphysics and
psychology, which form with it a triad of sciences. Metaphysics is the
science of being in general, and therefore of the things which become
objects apprehended by our minds. Psychology is the science of mind in
general, and therefore of the mental operations, of which inference is
one. Logic is the science of the processes of inference. These three
sciences, of the objects of mind, of the operations of mind, of the
processes used in the inferences of mind, are differently, but closely
related, so that they are constantly confused. The real point is their
interdependence, which is so intimate that one sign of great philosophy
is a consistent metaphysics, psychology and logic. If the world of
things is _known_ to be partly material and partly mental, then the mind
must have powers of sense and inference enabling it to know these
things, and there must be processes of inference carrying us from and
beyond the sensible to the insensible world of matter and mind. If the
whole world of things is matter, operations and processes of mind are
themselves material. If the whole world of things is mind, operations
and processes of mind have only to recognize their like all the world
over. It is clear then that a man's metaphysics and psychology must
colour his logic. It is accordingly necessary to the logician to know
beforehand the general distinctions and principles of things in
metaphysics, and the mental operations of sense, conception, memory and
experience in psychology, so as to discover the processes of inference
from experience about things in logic.
The interdependence of this triad of sciences has sometimes led to their
confusion. Hegel, having identified being with thought, merged
metaphysics in logic. But he divided logic into objective and
subjective, and thus practically confessed that there is one science of
the objects and another of the processes of thought. Psychologists,
seeing that inference is a mental operation, often extemporize a theory
of inference to the neglect of logic. But we have a double consciousness
of inference. We are conscious of it as one operation among many, and of
its omnipresence, so to speak, to all the rest. But we are also
conscious of the processes of the operation of inference. To a certain
extent this second consciousness applies to other operations: for
example, we are conscious of the process of association by which various
mental causes recall ideas in the imagination. But how little does the
psychologist know about the association of ideas, compared with what the
logician has discovered about the processes of inference! The fact is
that our primary consciousness of all mental operations is hardly equal
to our secondary consciousness of the processes of the one operation of
inference from premises to conclusions permeating long trains and
pervading whole sciences. This elaborate consciousness of inferential
process is the justification of logic as a distinct science, and is the
first step in its method. But it is not the whole method of logic, which
also and rightly considers the mental process necessary to language,
without substituting linguistic for mental distinctions.
Nor are consciousness and linguistic analysis all the instruments of the
logician. Logic has to consider the things we know, the minds by which
we know them from sense, memory and experience to inference, and the
sciences which systematize and extend our knowledge of things; and
having considered these facts, the logician must make such a science of
inference as will explain the power and the poverty of human knowledge.