Chapter IV: Front Matter (4)

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.

GENERAL TENDENCIES OF MODERN LOGIC

There are several grounds for hope in the logic of our day. In the first place, it tends to take up an intermediate position between the extremes of Kant and Hegel. It does not, with the former, regard logic as purely formal in the sense of abstracting thought from being, nor does it follow the latter in amalgamating metaphysics with logic by identifying being with thought. Secondly, it does not content itself with the mere formulae of thinking, but pushes forward to theories of method, knowledge and science; and it is a hopeful sign to find this epistemological spirit, to which England was accustomed by Mill, animating German logicians such as Lotze, Dühring, Schuppe, Sigwart and Wundt. Thirdly, there is a determination to reveal the psychological basis of logical processes, and not merely to describe them as they are in adult reasoning, but to explain also how they arise from simpler mental operations and primarily from sense. This attempt is connected with the psychological turn given to recent philosophy by Wundt and others, and is dangerous only so far as psychology itself is hypothetical. Unfortunately, however, these merits are usually connected with a less admirable characteristic--contempt for tradition, Writing his preface to his second edition in 1888, Sigwart says: "Important works have appeared by Lotze, Schuppe, Wundt and Bradley, to name only the most eminent; and all start from the conception which has guided this attempt. That is, logic is grounded by them, not upon an effete tradition but upon a new investigation of thought as it actually is in its psychological foundations, in its significance for knowledge, and its actual operation in scientific methods." How strange! The spirit of every one of the three reforms above enumerated is an unconscious return to Aristotle's _Organon_. Aristotle's was a logic which steered, as Trendelenburg has shown, between Kantian formalism and Hegelian metaphysics; it was a logic which in the Analytics investigated the syllogism as a means to understanding knowledge and science: it was a logic which, starting from the psychological foundations of sense, memory and experience, built up the logical structure of induction and deduction on the profoundly Aristotelian principle that "there is no process from universals without induction, and none by induction without sense." Wundt's comprehensive view that logic looks backwards to psychology and forward to epistemology was hundreds of years ago one of the many discoveries of Aristotle.

JUDGMENT

1. _Judgment and Conception._--The emphasis now laid on judgment, the recovery from Hume's confusion of beliefs with ideas and the association of ideas, and the distinction of the mental act of judging from its verbal expression in a proposition, are all healthy signs in recent logic. The most fundamental question, before proceeding to the investigation of inference, is not what we say but what we think in making the judgments which, whether we express them in propositions or not, are both the premises and the conclusion of inference; and, as this question has been diligently studied of late, but has been variously answered, it will be well to give a list of the more important theories of judgment as follows:--

a. It expresses a relation between the content of two ideas, not a
relation of these ideas (Lotze).

b. It is consciousness concerning the objective validity of a
subjective combination of ideas, i.e. whether between the
corresponding objective elements an analogous combination exists
(Ueberweg).

c. It is the synthesis of ideas into unity and consciousness of their
objective validity, not in the sense of agreement with external
reality but in the sense of the logical necessity of their synthesis
(Sigwart).

d. It is the analysis of an aggregate idea (_Gesammtvorstellung_) into
subject and predicate; based on a previous association of ideas, on
relating and comparing, and on the apperceptive synthesis of an
aggregate idea in consequence; but itself consisting in an
apperceptive analysis of that aggregate idea; and requiring will in
the form of apperception or attention (Wundt).

e. It requires an idea, because every object is conceived as well as
recognized or denied; but it is itself an assertion of actual fact,
every perception counts for a judgment, and every categorical is
changeable into an existential judgment without change of sense
(Brentano, who derives his theory from Mill except that he denies the
necessity of a combination of ideas, and reduces a categorical to an
existential judgment).

f. It is a decision of the validity of an idea requiring will
(Bergmann, following Brentano).

g. Judgment (_Urtheil_) expresses that two ideas belong together:
"by-judgment" (_Beurtheilung_) is the reaction of will expressing the
validity or invalidity of the combination of ideas (Windelband,
following Bergmann, but distinguishing the decision of validity from
the judgment).

h. Judgment is consciousness of the identity or difference and of the
causal relations of the given; naming the actual combinations of the
data, but also requiring a priori categories of the understanding, the
notions of identity, difference and causality, as principles of
thought or laws, to combine the plurality of the given into a unity
(Schuppe).

i. Judgment is the act which refers an ideal content recognized as
such to a reality beyond the act, predicating an idea of a reality, a
what of a that; so that the subject is reality and the predicate the
meaning of an idea, while the judgment refers the idea to reality by
an identity of content (Bradley and Bosanquet).

k. Judgment is an assertion of reality, requiring comparison and ideas
which render it directly expressible in words (Hobhouse, mainly
following Bradley).

These theories are of varying value in proportion to their proximity to Aristotle's point that predication is about things, and to Mill's point that judgments and propositions are about things, not about ideas. The essence of judgment is belief that something is (or is not) determined, either as existing (e.g. "I am," "A centaur is not") or as something in particular (e.g. "I am a man," "I am not a monkey"). Neither Mill, however, nor any of the later logicians whose theories we have quoted, has been able quite to detach judgment from conception; they all suppose that an idea, or ideas, is a condition of all judgment. But judgment starts from sensation (_Empfindung_) and feeling (_Gefühl_), and not from idea (_Vorstellung_). When I feel pleased or pained, or when I use my senses to perceive a pressure, a temperature, a flavour, an odour, a colour, a sound, or when I am conscious of feeling and perceiving, I cannot resist the belief that something sensible is present; and this belief that something exists is already a judgment, a judgment of existence, and, so far as it is limited to sense without inference, a true judgment. It is a matter of words whether or not we should call this sensory belief a judgment; but it is no matter of choice to the logician, who regards all the constituents of inference as judgments; for the fundamental constituents are sensory beliefs, which are therefore judgments in the logical sense. Sense is the evidence of inference; directly of analogical and inductive, directly or indirectly of deductive, inference; and therefore, if logic refuses to include sensory beliefs among judgments, it will omit the fundamental constituents of inference, inference will no longer consist of judgments but of sensory beliefs plus judgments, and the second part of logic, the logic of judgment, the purpose of which is to investigate the constituents of inference, will be like _Hamlet_ without the prince of Denmark. If, on the other hand, all the constituents of inference are judgments, there are judgments of sense; and the evidence of the senses means that a judgment of sense is true, while a judgment of inference is true so far as it is directly or indirectly concluded from judgments of sense. Now a sensory judgment, e.g. that a sensible pressure is existing, is explained by none of the foregoing theories, because it requires nothing but sensation and belief. It requires no will, but is usually involuntary, for the stimulus forces one's attention, which is not always voluntary; not all judgment then requires will, as Wundt supposes. It requires no reference to reality beyond the sensible pressure, because it is merely a belief that this exists without inference of the external stimulus or any inference at all: not all judgment then requires the reference of subjective to objective supposed by Ueberweg, or the consciousness of logical necessity supposed by Sigwart. It requires in addition to the belief that something exists, no consideration as to whether the belief itself be true, because a man who feels pressure believes in the thing without further question about the belief: not all judgment then requires a decision of validity, as Bergmann supposes. It requires nothing beyond the sensation and belief in the given existence of the given pressure: not all judgment then requires categories of understanding, or notions of identity, difference and causality, or even of existence, such as Schuppe supposes. It requires no comparison in order to express it in words, for a judgment need not be expressed, and a sensory judgment of pressure is an irresistible belief that a real pressure exists, without waiting for words, or for a comparison which is wanted not to make a sensation a judgment, but to turn a judgment into language: not all judgment then requires comparison with a view to its expression, as supposed by Hobhouse. Lastly, all the authors of the above-quoted theories err in supposing that all judgment requires conception; for even Mill thinks a combination of ideas necessary, and Brentano, who comes still nearer to the nature of sensory judgment when he says, "Every perception counts for a judgment," yet thinks that an idea is necessary at the same time in order to understand the thing judged. In reality, the sensation and the belief are sufficient; when I feel a sensible pressure, I cannot help believing in its reality, and therefore judging that it is real, without any _tertium quid_--an idea of pressure, or of existence or of pressure existing--intervening between the sensation and the belief. Only after sensation has ceased does an idea, or representation of what is not presented, become necessary as a substitute for a sensation and as a condition not of the first judgment that there is, but of a second judgment that there was, something sensible. Otherwise there would be no judgment of sensible fact, for the first sensation would not give it, and the idea following the sensation would be still farther off. The sensory judgment then, which is nothing but a belief that at the moment of sense something sensible exists, is a proof that not all judgment requires conception, or synthesis or analysis of ideas, or decision about the content, or about the validity, of ideas, or reference of an ideal content to reality, as commonly, though variously, supposed in the logic of our day.

Not, however, that all judgment is sensory: after the first judgments of sense follow judgments of memory, and memory requires ideas. Yet memory is not mere conception, as Aristotle, and Mill after him, have perceived. To remember, we must have a present idea; but we must also have a belief that the thing, of which the idea is a representation, was (or was not) determined; and this belief is the memorial judgment. Originally such judgments arise from sensory judgments followed by ideas, and are judgments of memory after sense that something sensible existed, e.g. pressure existed: afterwards come judgments of memory after inference, e.g. Caesar was murdered. Finally, most judgments are inferential. These are conclusions which primarily are inferred from sensory and memorial judgments; and so far as inference starts from sense of something sensible in the present, and from memory after sense of something sensible in the past, and concludes similar things, inferential judgments are indirect beliefs in being and in existence beyond ideas. When from the sensible pressures between the parts of my mouth, which I feel and remember and judge that they exist and have existed, I infer another similar pressure (e.g. of the food which presses and is pressed by my mouth in eating), the inferential judgment with which I conclude is a belief that the latter exists as well as the former (e.g. the pressure of food without as well as the sensible pressures within). Inference, no doubt, is closely involved with conception. So far as it depends on memory, an inferential judgment presupposes memorial ideas in its data; and so far as it infers universal classes and laws, it produces general ideas. But even so the part played by conception is quite subordinate to that of belief. In the first place, the remembered datum, from which an inference of pressure starts, is not the conceived idea, but the belief that the sensible pressure existed. Secondly, the conclusion in which it ends is not the general idea of a class, but the belief that a class, represented by a general idea, exists, and is (or is not) otherwise determined (e.g. that things pressing and pressed exist and move). Two things are certain about inferential judgment: one, that when inference is based on sense and memory, inferential judgment starts from a combination of sensory and memorial judgment, both of which are beliefs that things exist; the other, that in consequence inferential judgment is a belief that similar things exist. There are thus three primary judgments: judgments of sense, of memory after sense, and of inference from sense. All these are beliefs in being and existence, and this existential belief is first in sense, and afterwards transferred to memory and inference. Moreover, it is transferred in the same irresistible way: frequently we cannot help either feeling pressure, or remembering it, or inferring it; and as there are involuntary sensation and attention, so there are involuntary memory and inference. Again, in a primary judgment existence need not be expressed; but if expressed, it may be expressed either by the predicate, e.g. "I exist," or by the subject, e.g. "I who exist think." There are indeed differences between primary judgments, in that the sensory is a belief in present, the memorial in past, and the inferential in present, past and future existence. But these differences in detail do not alter the main point that all these are beliefs in the existing, in the real as opposed to the ideal, in actual things which are not ideas. In short, a primary judgment is a belief in something existing apart from our idea of it; and not because we have an idea of it, or by comparing an idea with, or referring an idea to, reality; but because we have a sensation of it, or a memory of it or an inference of it. Sensation, not conception, is the origin of judgment.

2. _Different Significations of Being in different Kinds of Judgment._--As Aristotle remarked both in the _De Interpretatione_ and in the _Sophistici Elenchi_, "not-being is thinkable" does not mean "not-being exists." In the latter treatise he added that it is a _fallacia a dicto secundum quid ad dictum simpliciter_ to argue from the former to the latter; "for," as he says, "it is not the same thing to be something and to exist absolutely." Without realizing their debt to tradition, Herbart, Mill and recently Sigwart, have repeated Aristotle's separation of the copula from the verb of existence, as if it were a modern discovery that "is" is not the same as "exists." It may be added that they do not quite realize what the copula exactly signifies: it does not signify existence, but it does signify a fact, namely, that something is (or is not) determined, either absolutely in a categorical judgment, or conditionally in a conditional judgment. Now we have seen that all primary judgments signify more than this fact; they are also beliefs in the existence of the thing signified by the subject. But, in the first place, primary judgments signify this existence never by the copula, but sometimes by the predicate, and sometimes by the subject; and, secondly, it does not follow that all judgments whatever signify existence. Besides inference of existence there is inference of non-existence, of things inconsistent with the objects of primary judgments. Hence secondary judgments, which no longer contain a belief that the thing exists, e.g. the judgment, "not-being is thinkable," cited by Aristotle; the judgment, "A square circle is impossible," cited by Herbart; the judgment, "A centaur is a fiction of the poets," cited by Mill. These secondary judgments of non-existence are partly like and partly unlike primary judgments of existence. They resemble them in that they are beliefs in being signified by the copula. They are beliefs in things of a sort; for, after all, ideas and names are things; their objects, even though non-existent, are at all events things conceivable or nameable; and therefore we are able to make judgments that things, non-existent but conceivable or nameable, are (or are not) determined in a particular manner. Thus the judgment about a centaur is the belief, "A conceivable centaur is a fiction of the poets," and the judgment about a square circle is the belief, "A so-called square circle is an impossibility." But, though beliefs that things of some sort are (or are not) determined, these secondary judgments fall short of primary judgments of existence. Whereas in a primary judgment there is a further belief, signified by subject or predicate, that the thing is an existing thing in the sense of being a real thing (e.g. a man), different from the idea of it as well as from the name for it; in a secondary judgment there is no further belief that the thing has any existence beyond the idea (e.g. a centaur), or even beyond the name (e.g. a square circle): though the idea or name exists, there is no belief that anything represented by idea or name exists. Starting, then, from this fundamental distinction between judgments of existence and judgments of non-existence, we may hope to steer our way between two extreme views which emanate from two important thinkers, each of whom has produced a flourishing school of psychological logic.

On the one hand, early in the 19th century Herbart started the view that a categorical judgment is never a judgment of existence, but always hypothetical; on the other hand, in the latter part of the century Brentano started the view that all categorical judgments are existential. The truth lies between these contraries. The view of Herbart and his school is contradicted by our primary judgments of and from sense, in which we cannot help believing existence; and it gives an inadequate account even of our secondary judgments in which we no longer indeed believe existence, but do frequently believe that a non-existent thing is (or is not) somehow determined unconditionally. It is true, as Herbart says, that the judgment, "A square circle is an impossibility," does not contain the belief, "A square circle is existent"; but when he goes on to argue that it means, "If a square circle is thought, the conception of impossibility must be added in thought," he falls into a _non-sequitur_. To be categorical, a judgment does not require a belief in existence, but only that something, existent or not, is (or is not) determined; and there are two quite different attitudes of mind even to a non-existent thing, such as a square circle, namely, unconditional and conditional belief. The judgment, "A non-existent but so-called square circle is an impossibility," is an unconditional, or categorical judgment of non-existence, quite different from any hypothetical judgment, which depends on the conditions "if it is thought," or "if it exists," or any other "if." On the other hand, the view of Brentano and his school is contradicted by these very categorical judgments of non-existence; and while it applies only to categorical judgments of existence, it does so inadequately. To begin with the latter objection, Brentano proposed to change the four Aristotelian forms of judgment, A, E, I, O, into the following existential forms:--

A. "There is not an immortal man."
E. "There is not a live stone."
I. "There is a sick man."
O. "There is an unlearned man."

This reconstruction, which merges subject and predicate in one expression, in order to combine it with the verb of existence, is repeated in similar proposals of recent English logicians. Venn, in his _Symbolic Logic_, proposes the four forms, xy = 0, xy = 0, xy> 0, xy> 0 (where y means "not-y"), but only as alternative to the ordinary forms. Bradley says that "'S-P is real' attributes S-P, directly or indirectly, to the ultimate reality," and agrees with Brentano that "'is' never stands for anything but 'exists'"; while Bosanquet, who follows Bradley, goes so far as to define a categorical judgment as "that which affirms the existence of its subject, or, in other words, asserts a fact." Now it is true that our primary judgments do contain a belief in existence; but they do not all contain it in the same way, but are beliefs sometimes that something is determined as existing, and sometimes that something existing is particularly determined. Brentano's forms do not express such a judgment of existence, as "All existing men are mortal": nor does Bradley's form, "Reality includes S-P." Metaphysically, all realities are parts of one ultimate reality; but logically, even philosophers think more often only of finite realities, existing men, dogs, horses, &c.; and children know that their parents exist long before they apprehend ultimate reality. The normal form, then, of a judgment of existence is either "S is a real P," or "A real S is P." Hence the reconstruction of all categorical judgments by merging subject and predicate, either on Brentano's or on Bradley's plan, is a misrepresentation even of normal categorical judgments of existence. Secondly, it is much more a misrepresentation of categorical judgments of non-existence. No existential form suits a judgment such as "A centaur is a fiction," when we do not believe that there is a centaur, or that reality includes a centaur. As Mill pointed out, it cannot be implied that a centaur exists, since the very thing asserted is that the thing has no real existence. In a correspondence with Mill, Brentano rejoined that the centaur exists in imagination; Bradley says, "inside our heads." According to one, then, the judgment becomes "There is an imaginary centaur"; according to the other "Reality includes an imaginary centaur." The rejoinder, however, though partly true, is not to the point. The idea of the centaur does exist in our imagination, and inside our heads, and the name of it in our mouths. But the point is that the centaur conceived and named does not exist beyond the idea of it and the name for it; it is not, like a man, a real thing which is neither the idea of it nor the name for it. No amount of subtlety will remove the difference between a categorical judgment of existence, e.g. "An existing man is mortal," and a categorical judgment of non-existence, e.g. "A conceivable centaur is a fiction," because in the former we believe and mean that the thing exists beyond the idea, and in the latter we do not. If, contrary to usage, we choose to call the latter a judgment of existence, there is no use in quarrelling about words; but we must insist that new terms must in that case be invented to express so fundamental a difference as that between judgments about real men and judgments about ideal centaurs. So long, however, as we use words in the natural sense, and call the former judgments of existence, and the latter judgments of non-existence, then "is" will not be, as Bradley supposes, the same as "exists," for we use "is" in both judgments, but "exists" only in the first kind. Bosanquet's definition of a categorical judgment contains a similar confusion. To assert a fact and to affirm the existence of a subject are not, as he makes out, the same thing: a judgment often asserts a fact and denies existence in the same breath, e.g. "Jupiter is non-existent." Here, as usual in logic, tradition is better than innovation. All categorical judgment is an unconditional belief in the fact, signified by the copula, that a thing of some sort is (or is not) determined; but some categorical judgments are also beliefs that the thing is an existing thing, signified either by the subject or by the predicate, while others are not beliefs that the thing exists at all, but are only beliefs in something conceivable, or nameable, or in something or other, without particularizing what. Judgment then always signifies being, but not always existence.

3. _Particular and Universal Judgments._--Aristotle, by distinguishing affirmative and negative, particular and universal, made the fourfold classification of judgments, A, E, I and O, the foundation both of opposition and of inference. With regard to inference, he remarked that a universal judgment means by "all," not every individual we know, but every individual absolutely, so that, when it becomes a major premise, we know therein every individual universally, not individually, and often do not know a given individual individually until we add a minor premise in a syllogism. Whereas, then, a particular judgment is a belief that some, a universal judgment is a belief that all, the individuals of a kind or total of similar individuals, are similarly determined, whether they are known or unknown individuals. Now, as we have already seen, what is signified by the subject may be existing or not, and in either case a judgment remains categorical so long as it is a belief without conditions. Thus, "Some existing men are poets," "All existing men are mortal," "Some conceivable centaurs are human in their forequarters," "All conceivable centaurs are equine in their hindquarters," are all categorical judgments, while the two first are also categorical judgments of existence. Nevertheless these obvious applications of Aristotelian traditions have been recently challenged, especially by Sigwart, who holds in his _Logic_ (secs. 27, 36) that, while a particular is a categorical judgment of existence, a universal is hypothetical, on the ground that it does not refer to a definite number of individuals, or to individuals at all, but rather to general ideas, and that the appropriate form of "all M is P" is "if anything is M it is P." This view, which has influenced not only German but also English logicians, such as Venn, Bradley and Bosanquet, destroys the fabric of inference, and reduces scientific laws to mere hypotheses. In reality, however, particular and universal judgments are too closely connected to have such different imports. In opposition, a categorical particular is the contradictory of a universal, which is also categorical, not hypothetical, e.g., "not all M is P" is the contradictory of "all M is P," not of "if anything is M it is P." In inference, a particular is an example of a universal which in its turn may become a particular example of a higher universal. For instance, in the history of mechanics it was first inferred from some that all terrestrial bodies gravitate, and then from these as some that all ponderable bodies, terrestrial and celestial, gravitate. How absurd to suppose that here we pass from a particular categorical to a universal hypothetical, and then treat this very conclusion as a particular categorical to pass to a higher universal hypothetical! Sigwart, indeed, is deceived both about particulars and universals. On the one hand, some particulars are not judgments of existence, e.g. "some imaginary deities are goddesses"; on the other hand, some universals are not judgments of non-existence, e.g. "every existing man is mortal." Neither kind is always a judgment of existence, but each is sometimes the one and sometimes the other. In no case is a universal hypothetical, unless we think it under a condition; for in a universal judgment about the non-existing, e.g. about all conceivable centaurs, we do not think, "If anything is a centaur," because we do not believe that there are any; and in a universal judgment about the existent, e.g. about all existing men, we do not think, "If anything is a man," because we believe that there is a whole class of men existing at different times and places. The cause of Sigwart's error is his misconception of "all." So far as he follows Aristotle in saying that "all" does not mean a definite number of individuals he is right; but when he says that we mean no individuals at all he deserts Aristotle and goes wrong. By "all" we mean every individual whatever of a kind; and when from the experience of sense and memory we start with particular judgments of existence, and infer universal judgments of existence and scientific laws, we further mean those existing individuals which we have experienced, and every individual whatever of the kind which exists. We mean neither a definite number of individuals, nor yet an infinite number, but an incalculable number, whether experienced or inferred to exist. We do not mean existing here and now, nor yet out of time and place, but at any time and place (_semper et ubique_)--past, present and future being treated as simply existing, by what logicians used to call _suppositio naturalis_. We mean then by "all existing" every similar individual whatever, whenever, and wherever existing. Hence Sigwart is right in saying that "All bodies are extended" means "Whatever is a body is extended," but wrong in identifying this form with "If anything is a body it is extended." "Whatever" is not "if anything." For the same reason it is erroneous to confuse "all existing" with a general idea. Nor does the use of abstract ideas and terms make any difference. When Bosanquet says that in "Heat is a mode of motion" there is no reference to individual objects, but "a pure hypothetical form which absolutely neglects the existence of objects," he falls far short of expressing the nature of this scientific judgment, for in his _Theory of Heat_ Clerk Maxwell describes it as "believing heat as it exists in a hot body to be in the form of kinetic energy." As Bacon would say, it is a belief that all individual bodies _qua_ hot are individually but similarly moving in their particles. When, again, Bradley and Bosanquet speak of the universal as if it always meant one ideal content referred to reality, they forget that in universal judgments of existence, such as "All men existing are mortal," we believe that every individually existing man dies his own death individually, though similarly to other men; and that we are thinking neither of ideas nor of reality; but of all existent individual men being individually but similarly determined. A universal is indeed one whole; but it is one whole of many similars, which are not the same with one another. This is indeed the very essence of distribution, that a universal is predicable, not singly or collectively, but severally and similarly of each and every individual of a kind, or total of similar individuals. So also the essence of a universal judgment is that every individual of the kind is severally but similarly determined. Finally, a universal judgment is often existential; but whether it is so or not it remains categorical, so long as it introduces no hypothetical antecedent about the existence of the thing signified by the subject. It is true that even in universal judgments of existence there is often a hypothetical element; for example, "All men are mortal" contains a doubt whether every man whatever, whenever and wherever existing, must die. But this is only a doubt whether all the things signified by the subject are similarly determined as signified by the predicate, and not a doubt whether there are such things at all. Hence the hypothetical element is not a hypothetical antecedent "If anything is a man," but an uncertain conclusion that "All existing men are mortal." In other words, a categorical universal is often problematic, but a problematic is not the same as a hypothetical judgment.

4. _The Judgment and the Proposition._--Judgment in general is the mental act of believing that something is (or is not) determined. A proposition is the consequent verbal expression of such a belief, and consists in asserting that the thing as signified by the subject is (or is not) determined as signified by the predicate. But the expression is not necessary. Sensation irresistibly produces a judgment of existence without needing language. Children think long before they speak; and indeed, as mere vocal sounds are not speech, and as the apprehension that a word signifies a thing is a judgment, judgment is originally not an effect, but a cause of significant language. At any rate, even when we have learnt to speak, we do not express all we think, as we may see not only from the fewness of words known to a child, but also from our own adult consciousness. The principle of thought is to judge enough to conclude. The principle of language is to speak only so far as to understand and be understood. Hence speech is only a curtailed expression of thought. Sometimes we express a whole judgment by one word, e.g. "Fire!" or by a phrase, e.g. "What a fire!" and only usually by a proposition. But even the normal proposition in the syllogistic form _tertii adjacentis_, with subject, predicate and copula, is seldom a complete expression of the judgment. The consequence is that the proposition, being different from a judgment arising after a judgment, and remaining an imperfect copy of judgment, is only a superficial evidence of its real nature. Fortunately, we have more profound evidences, and at least three evidences in all: the linguistic expression of belief in the proposition; the consciousness of what we mentally believe; and the analysis of reasoning, which shows what we must believe, and have believed, as data for inference. In these ways we find that a judgment is both different from, and more than, a proposition. But recent logicians, although they perceive the difference, nevertheless tend to make the proposition the measure of the judgment. This makes them omit sensory judgments, and count only those which require ideas, and even general ideas expressed in general terms. Sigwart, for example, gives as instances of our most elementary judgments, "This is Socrates," "This is snow"--beliefs in things existing beyond ourselves which require considerable inferences from many previous judgments of sense and memory. Worse still, logicians seem unable to keep the judgment apart from the proposition. Herbart says that the judgment "A is B" does not contain the usually added thought that A is, because there is no statement of A's existence; as if the statement mattered to the thought. So Sigwart, in order to reduce universals to hypotheticals, while admitting that existence is usually thought, argues that it is not stated in the universal judgment; so also Bosanquet. But in the judgment the point is not what we state, but what we think; and so long as the existence of A is added in thought, the judgment in question must contain the thought that A exists as well as that A is B, and therefore is a judgment that something is determined both as existing and in a particular manner. The statement only affects the proposition; and whenever we believe the existence of the thing, the belief in existence is part of the judgment thought, whether it is part of the proposition stated or not.

Here Sir William Hamilton did a real service to logic in pointing out
that "Logic postulates to be allowed to state explicitly in language
all that is implicitly contained in the thought." Not that men should
or can carry this logical postulate out in ordinary life; but it is
necessary in the logical analysis of judgments, and yet logicians
neglect it. This is why they confuse the categorical and the universal
with the hypothetical. Taking the carelessly expressed propositions of
ordinary life, they do not perceive that similar judgments are often
differently expressed, e.g. "I, being a man, am mortal," and "If I am
a man, I am mortal"; and conversely, that different judgments are
often similarly expressed. In ordinary life we may say, "All men are
mortal," "All centaurs are figments," "All square circles are
impossibilities," "All candidates arriving five minutes late are
fined" (the last proposition being an example of the identification of
categorical with hypothetical in Keynes's _Formal Logic_). But of
these universal propositions the first imperfectly expresses a
categorical belief in existing things, the second in thinkable things,
and the third in nameable things, while the fourth is a slipshod
categorical expression of the hypothetical belief, "If any candidates
arrive late they are fined." The four judgments are different, and
therefore logically the propositions fully expressing them are also
different. The judgment, then, is the measure of the proposition, not
the proposition the measure of the judgment. On the other hand, we may
go too far in the opposite direction, as Hamilton did in proposing the
universal quantification of the predicate. If the quantity of the
predicate were always thought, it ought logically to be always stated.
But we only sometimes think it. Usually we leave the predicate
indefinite, because, as long as the thing in question is (or is not)
determined, it does not matter about other things, and it is vain for
us to try to think all things at once. It is remarkable that in
_Barbara_, and therefore in many scientific deductions, to think the
quantity of the predicate is not to the point either in the premises
or in the conclusion; so that to quantify the propositions, as
Hamilton proposes, would be to express more than a rational man thinks
and judges. In judgments, and therefore in propositions, indefinite
predicates are the rule, quantified predicates the exception.
Consequently, A E I O are the normal propositions with indefinite
predicates; whereas propositions with quantified predicates are only
occasional forms, which we should use whenever we require to think the
quantity of the predicate, e.g. (1) in conversion, when we must think
that all men are some animals, in order to judge that some animals are
men; (2) in syllogisms of the 3rd figure, when the predicate of the
minor premise must be particularly quantified in thought in order to
become the particularly quantified subject of the conclusion; (3) in
identical propositions including definitions, where we must think both
that 1 + 1 are 2 and 2 are 1 + 1. But the normal judgment, and
therefore the normal proposition, do not require the quantity of the
predicate. It follows also that the normal judgment is not an
equation. The symbol of equality (=) is not the same as the copula
(is); it means "is equal to," where "equal to" is part of the
predicate, leaving "is" as the copula. Now, in all judgment we think
"is," but in few judgments predicate "equal to." In quantitative
judgments we may think x = y, or, as Boole proposes, x = vy = (0/0)y
or, as Jevons proposes, x = xy, or, as Venn proposes, x which is not y
= 0; and equational symbolic logic is useful whenever we think in this
quantitative way. But it is a byway of thought. In most judgments all
we believe is that x is (or is not) y, that a thing is (or is not)
determined, and that the thing signified by the subject is a thing
signified by the predicate, but not that it is the only thing, or
equal to everything signified by the predicate. The symbolic logic,
which confuses "is" with "is equal to," having introduced a particular
kind of predicate into the copula, falls into the mistake of reducing
all predication to the one category of the quantitative; whereas it is
more often in the substantial, e.g. "I am a man," not "I am equal to a
man," or in the qualitative, e.g. "I am white," not "I am equal to
white," or in the relative, e.g. "I am born in sin," not "I am equal
to born in sin." Predication, as Aristotle saw, is as various as the
categories of being. Finally, the great difficulty of the logic of
judgment is to find the mental act behind the linguistic expression,
to ascribe to it exactly what is thought, neither more nor less, and
to apply the judgment thought to the logical proposition, without
expecting to find it in ordinary propositions. Beneath Hamilton's
postulate there is a deeper principle of logic--_A rational being
thinks only to the point, and speaks only to understand and be
understood_.

INFERENCE

The nature and analysis of inference have been so fully treated in the Introduction that here we may content ourselves with some points of detail.

1. _False Views of Syllogism arising from False Views of Judgment._--The false views of judgment, which we have been examining, have led to false views of inference. On the one hand, having reduced categorical judgments to an existential form, Brentano proposes to reform the syllogism, with the results that it must contain four terms, of which two are opposed and two appear twice; that, when it is negative, both premises are negative; and that, when it is affirmative, one premise, at least, is negative. In order to infer the universal affirmative that every professor is mortal because he is a man, Brentano's existential syllogism would run as follows:--

There is not a not-mortal man.
There is not a not-human professor.
:. There is not a non-mortal professor.

On the other hand, if on the plan of Sigwart categorical universals were reducible to hypothetical, the same inference would be a pure hypothetical syllogism, thus:--

If anything is a man it is mortal.
If anything is a professor it is a man.
:. If anything is a professor it is mortal.

But both these unnatural forms, which are certainly not analyses of any conscious process of categorical reasoning, break down at once, because they cannot explain those moods in the third figure, e.g. _Darapti_, which reason from universal premises to a particular conclusion. Thus, in order to infer that some wise men are good from the example of professors, Brentano's syllogism would be the following _non-sequitur_:--

There is not a not-good professor.
There is not a not-wise professor.
There is a wise good (_non-sequitur_).

So Sigwart's syllogism would be the following _non-sequitur_:--

If anything is a professor, it is good.
If anything is a professor, it is wise.
Something wise is good (_non-sequitur_).

But as by the admission of both logicians these reconstructions of _Darapti_ are illogical, it follows that their respective reductions of categorical universals to existentials and hypotheticals are false, because they do not explain an actual inference. Sigwart does not indeed shrink from this and greater absurdities; he reduces the first figure to the _modus ponens_ and the second to the _modus tollens_ of the hypothetical syllogism, and then, finding no place for the third figure, denies that it can infer necessity; whereas it really infers the necessary consequence of particular conclusions. But the crowning absurdity is that, if all universals were hypothetical, _Barbara_ in the first figure would become a purely hypothetical syllogism--a consequence which seems innocent enough until we remember that all universal affirmative conclusions in all sciences would with their premises dissolve into mere hypothesis. No logic can be sound which leads to the following analysis:--

If anything is a body it is extended.
If anything is a planet it is a body.
:. If anything is a planet it is extended.

Sigwart, indeed, has missed the essential difference between the categorical and the hypothetical construction of syllogisms. In a categorical syllogism of the first figure, the major premise, "Every M whatever is P," is a universal, which we believe on account of previous evidence without any condition about the thing signified by the subject M, which we simply believe sometimes to be existent (e.g. "Every man existent"), and sometimes not (e.g., "Every centaur conceivable"); and the minor premise, "S is M," establishes no part of the major, but adds the evidence of a particular not thought of in the major at all. But in a hypothetical syllogism of the ordinary mixed type, the first or hypothetical premise is a conditional belief, e.g. "If anything is M it is P," containing a hypothetical antecedent, "If anything is M," which is sometimes a hypothesis of existence (e.g. "If anything is an angel"), and sometimes a hypothesis of fact (e.g. "If an existing man is wise"); and the second premise or assumption, "Something is M," establishes part of the first, namely, the hypothetical antecedent, whether as regards existence (e.g. "Something is an angel"), or as regards fact (e.g. "This existing man is wise"). These very different relations of premises are obliterated by Sigwart's false reduction of categorical universals to hypotheticals. But even Sigwart's errors are outdone by Lotze, who not only reduces "Every M is P" so "If S is M, S is P," but proceeds to reduce this hypothetical to the disjunctive, "If S is M, S is P¹ or P² or P³," and finds fault with the Aristotelian syllogism because it contents itself with inferring "S is P" without showing what P. Now there are occasions when we want to reason in this disjunctive manner, to consider whether S is P¹ or P² or P³, and to conclude that "S is a particular P"; but ordinarily all we want to know is that "S is P"; e.g. in arithmetic, that 2 + 2 are 4, not any particular 4, and in life that all our contemporaries must die, without enumerating all their particular sorts of deaths. Lotze's mistake is the same as that of Hamilton about the quantification of the predicate, and that of those symbolists who held that reasoning ought always to exhaust all alternatives by equations. It is the mistake of exaggerating exceptional into normal forms of thought, and ignoring the principle that a rational being thinks only to the point.

2. _Quasi-syllogisms._--Besides reconstructions of the syllogistic fabric, we find in recent logic attempts to extend the figures of the syllogism beyond the syllogistic rules. An old error that we may have a valid syllogism from merely negative premises (_ex omnibus negativis_), long ago answered by Alexander and Boethius, is now revived by Lotze, Jevons and Bradley, who do not perceive that the supposed second negative is really an affirmative containing a "not" which can only be carried through the syllogism by separating it from the copula and attaching it to one of the extremes, thus:--

The just are not unhappy (_negative_).
The just are not-recognized (_affirmative_).
:. Some not-recognized are not unhappy (_negative_).

Here the minor being the infinite term "not-recognized" in the conclusion, must be the same term also in the minor premise. Schuppe, however, who is a fertile creator of quasi-syllogisms, has managed to invent some examples from two negative premises of a different kind:--

(1) | (2) | (3)
No M is P. | No M is P. | No P is M.
S is not P. | S is not M. | S is not M.
:. Neither S nor M | :. S may be P. | :. S may be P.
is P. | |

But (1) concludes with a mere repetition, (2) and (3) with a contingent "may be," which, as Aristotle says, also "may not be," and therefore _nihil certo colligitur_. The same answer applies to Schuppe's supposed syllogisms from two particular premises:--