The inference was insulting.
The pre-existence of souls is another inference from the immutability of God.
"Dusty's not here," he said, irritated by the inference that he was somehow someone to be less feared.
This is, however, very doubtful, and an entirely different inference is possible.
The teacher asked the students to draw an inference based on the clues given in the storybook.
Any further inference that the birth really took place there is matter of probability on which opinions will differ.
Any further inference that the birth really took place there is matter of probability on which opinions will differ.
By inference only, increasing complication of stomach with ruminating function superadded.
The necessary inference is that his stay at the university was short, and that only the groundwork of his education was laid there.
The necessary inference is that his stay at the university was short, and that only the groundwork of his education was laid there.
Skylar made an inference about what was in the wrapped box under the Christmas tree after picking it up to feel the weight.
It was an easy inference for the French mind that the Rhine should be the boundary throughout and the Gaul of Caesar restored.
After observing how the man and woman treated each other, she made an inference that they were married.
It was by weighing that in 1770 he proved that water is not converted into earth by distillation, for he showed that the total weight of a sealed glass vessel and the water it contained remained constant, however long the water was boiled, but that the glass vessel lost weight to an extent equal to the weight of earth produced, his inference being that the earth came from the glass, not from the water.
long, with a strong crista lateralis, which indicates a strongly developed great pectoral muscle and hence, by inference, the presence of a keel to the sternum.
Passing from Moleschott to Lyell's view of the evolution of the earth's crust and later to Darwin's theory of natural selection and environment, he reached the general inference that, not God but evolution of matter, is the cause of the order of the world; that life is a combination of matter which in favourable circumstances is spontaneously generated; that there is no vital principle, because all forces, non-vital and vital, are movements; that movement and evolution proceed from life to consciousness; that it is foolish for man to believe that the earth was made for him, in the face of the difficulties he encounters in inhabiting it; that there is no God, no final cause, no immortality, no freedom, no substance of the soul; and that mind, like light or heat, electricity or magnetism, or any other physical fact, is a movement of matter.
We may draw the inference that they formed an insignificant item in the population of a small province of the Persian Empire, and yet doubt whether they did actually refuse - alone of all the inhabitants of Palestine - to submit to the conqueror of the whole.
He found that pressure increases luminosity, so that hydrogen, for example, the flame of which in normal circumstances gives no light, burns with a luminous flame under a pressure of ten or twenty atmospheres, and the inference he drew was that the presence of solid particles is not the only factor that determines the light-giving power of a flame.
In short, from different standpoints, the three philosophical successions had devised systems which were in reality sceptical, though they had none of them recognized the sceptical inference.
But, although Protagoras and Gorgias had examined the teaching of their predecessors so far as to satisfy themselves of its futility and to draw the sceptical inference, their study of the great problem of the day was preliminary to their sophistry rather than a part of it; and, as the overthrow of philosophy was complete and the attractions of sophistry were all-powerful, the question " What is knowledge?
Since, however, Bale describes him as "ex patricio genitore natus," it is a reasonable inference (so R.
- Logic is the science of the processes of inference.
What, then, is inference ?
Some suppose that we may infer from one premise by a so-called " immediate inference."
There are as many kinds of inference as there are different ways of combining premises, and in the main three types: 1.
Analogical Inference, from particular to particular: e.g.
Inductive Inference, from particular to universal: e.g.
Deductive or Syllogistic Inference, from universal to particular, e.g.
In each of these kinds of inference there are three mental judgments capable of being expressed as above in three linguistic propositions; and the two first are the premises which are combined, while the third is the conclusion which is consequent on their combination.
Each inference contains three terms. In syllogistic inference the subject of the conclusion is the minor term, and its predicate the major term, while between these two extremes the term common to the two premises is the middle term, and the premise containing the middle and major terms is the major premise, the premise containing the middle and minor terms the minor premise.
Analogical and inductive inference alike begin with a particular premise containing one or more instances; but the former adds a particular premise to draw a particular conclusion, the latter requires a universal premise to draw a universal conclusion.
On this point both differ from inference by analogy, which proceeds entirely from particular premises to a particular conclusion.
The tone of the picture warrants the inference that 1 [W.
Like Kant, he supposes that experience is concerned with sensations, distinguishes matter and form in sense, identifies time and space, eternal time and infinite space, with the formal element, and substitutes 'synthesis of sensations of touch and sight for association and inference, as the origin of our knowing such a solid material object as a bell.
This argument from a pure assumption is a confusion of sense and inference.
In no case is the evidence of the senses fallacious or mendacious; the fallacy is in the inference.
a tree, is a matter of inference.
Seen from an eminence on their surface, the inference is irresistible that these plateaus are fragments of the original tableland, trenched into segments by the formation of the longitudinal and transverse valleys.
The question arises whether this depression affected only the area of the midland valley, or extended also to the regions to the north and south; and so far as the evidence goes there is ground for the inference that, while the depression had its maximum along the line of the lowlands, it also involved some portion at least of the high grounds on either side.
He pointed to the changes wrought on domesticated organisms by the artificial selection of similar variations, and drew the inference that there must be parallel occurrences under wild nature.
The number of these "ancient originals" is not stated, nor is there any mention of the language in which they were composed; Montalvo's silence on the latter point might be taken to imply that they were in Castilian, but any such inference would be hazardous.
The inference has been generally drawn that the Phrygians belonged to a stock widespread in the countries which lie round the Aegean Sea.
Still more original and remarkable, however, was that part of his system, fully stated in his Laws of Thought, which formed a general symbolic method of logical inference.
What political aspirations were revived, what other writers were inspired by these momentous events are questions of inference.
These works, however, warrant the inference.
This formation of the Greek system (25) is only an inference from the facts yet known, for we have not sufficient information to prove it, though it seems much the simplest and most likely history.
Philo, who translated the Old Testament religion into the terms of Hellenic thought, holds as an inference from his theory of revelation that the divine Supreme Being is " supra rational," that He can be reached only through " ecstasy ", and that the oracles of God supply the material of moral and religious knowledge.
Analogy, in its power of transforming unlike and unrelated animals or unlike and unrelated parts of animals into likeness, has done such miracles that the inference of kinship is often almost irresistible.
The inference is almost irresistible that the law of gradual transformation through minute continuous change is by far the most universal; but many palaeontologists as well as zoologists and botanists hold a contrary opinion.
He brought in inference to supply the place of discredited tradition, and showed the possibility of writing history in the absence of original records.
Paschasius shrank from the logical outcome of his view, namely, that Christ's body or part of it is turned into human excrement, but Ratramnus, another monk of Corbey, in a book afterwards ascribed to Duns Scotus, drew this inference in order to discredit his antagonists, and not because he believed it himself.
The marble and graphite, as well as some other indirect evidence of life less susceptible of brief statement, have been thought by many geologists sufficient to warrant the inference that life existed before the close of the era when the Archean rocks were formed.
Induction (E7rayo.y17) and syllogism (ovXXcytcr oc), the general forms of inference, do not occur in the Rhetoric to Alexander.
He gradually became a logician out of his previous studies: out of metaphysics, for with him being is always the basis of thinking, and common principles, such as that of contradiction, are axioms of things before axioms of thought, while categories are primarily things signified by names; out of the mathematics of the Pythagoreans and the Platonists, which taught him the nature of demonstration; out of the physics, of which he imbibed the first draughts from his father, which taught him induction from sense and the modification of strict demonstration to suit facts; out of the dialectic between man and man which provided him with beautiful examples of inference in the Socratic dialogues of Xenophon and Plato; out of the rhetoric addressed to large audiences, which with dialectic called his attention to probable inferences; out of the grammar taught with rhetoric and poetics which led him to the logic of the proposition.
So can we men, not, as Plato thought, by having in our souls universal principles innate but forgotten, but by acquiring universal principles from sense, which is the origin of knowledge, arrive at judgments which are true, and true because they agree with the things which we know by sense, by inference and by science.
Intelligence is not active intellect propagating universal essence in passive intellect, but only logical inference starting from sense, and both requiring nervous body and conscious soul.
He experimented with an air-thermometer, in which the temperature was defined by measurement of the length of a column of mercury; and he pointed out that the extreme cold of such a thermometer would be that which reduced the "spring" of the air to nothing, thus being the first to recognize that the use of air as a thermometric substance led to the inference of the existence of a zero of temperature.
The two opposite processes confirm the inference that both are due to some change of race, not merely to a change of custom in the same population in a later age; for in that case the change would have been in one direction only.
But as Mr Stone well puts it, " It would not be a necessary inference [from Dr Hort's opinion] that there ought to be no ministry in the Christian Church."
But by this noumenal will he did not mean a divine will similar to our rational desire, a will in which an inference and desire of a desirable end and means produces our rational action.
It becomes necessary, therefore, to determine how far Fechner derived his psychophysics from experience, how far from fallacies of inference, from his romantic imagination and from his theosophic metaphysics, which indeed coloured his whole book on psychophysics.
Now, Kant and his followers start from this second and narrower meaning, and usually narrow it still more by assuming that what appears to the senses is as mental as the sensation, being undistinguishable from it or from the idea of it, and that an appearance is a mental idea(Vorstellung) of sense; and then they conclude that we can know by inference nothing but such mental appearances, actual and possible, and therefore nothing beyond sensory experience.
the farther side of the moon, which is known to exist only by inference.
In either case, the effective power of inference, which makes us rational beings, is gone.
1908) as well as in his psychological work on the Analysis of Sensations (Beitrage zur Analyse der Empfindungen, 1886), we find two main causes, both psychological and epistemological; namely, his views on sense and on inference.
Secondly, his theory of inference contains the admission that we infer beyond sensations: he remarks that the space of the geometer is beyond space-sensations, and the time of the physicist does not coincide with time-sensations, because it uses measurements such as the rotation of the earth and the vibrations of the pendulum.
But by inference beyond sense he does not mean a process of concluding from sensible things to similar things, e.g.
Inference, according to him, is merely mental completion of sensations; and this mental completion has two characteristics: it only forms ideas, and it proceeds by an " economy of thought."
As a matter of fact, this characteristic differentiates experience from inference.
By inference we know that things, such as the farther side of the moon, which neither are, nor have been, nor can be, present to an experiencing subject on the earth, nevertheless exist.
It may well be that impulsive feeling is the beginning of mind; but then the order of mind is feeling, sense, inference, will, which instead of first is last, and implies the others.
If judgment is an analysis of an aggregate idea into subject and predicate, it follows, as he says, that " as judgment is an immediate, so is inference a mediate, reference of the members of any aggregate of ideas to one another " (System der Philosophie, 66, first ed.).
Hence, according to Wundt, the world we know is still unitary experience, distinguished, not separated, into subject and object, aggregates of ideas analysed by judgment and combined by inference, an object of idea elaborated into causes and substances by logical thinking, at most a world of our ideas composed out of our sensations, and arranged under our categories of our understanding by our inner wills, or a world of our ideating wills; but nothing else.
If knowledge is experience of ideas distinguished by inner will of apperception into subject and object in inseparable connexion, if the starting-point is ideas, if judgment is analysis of an aggregate idea, if inference is a mediate reference of the members of an aggregate of ideas to one another, then, as Wundt says, all we can know, and all reason can logically infer from such data, is in our ideas, and consciousness without an object of idea is an abstraction; so that reason, in transcending experience, can show the necessity of ideas and " ideals," but infer no corresponding reality beyond, whether in nature, or in Man, or in God.
Having thus confused contradiction and difference, independence and solitariness, experience and inference, Bradley is able to deduce finally that reality is not different substances, experienced and inferred, as Aristotle thought it, but is one absolute super-personal experience, to which the socalled plurality of things, including all bodies, all souls, and even a personal God, is appearance - an appearance, as ordinarily understood, self-contradictory, but, as appearing to one spiritual reality, somehow reconciled.
He hardly has a formal theory of inference, but implies throughout that it only transcends perceptions, and perceptual realities or phenomena, in order to conclude with ideas, not facts.
Two psychological errors, among many others, constantly meet us in the history of idealism - the arbitrary hypothesis of a sense of sensations, or of ideas, and the intolerable neglect of logical inference.
Logical inference from sense is a process from sensible to insensible existence.
only one lip pressing; by inference from touch I infer that it is reciprocally pressing another body similar to my other bodily member, i.e.
another body similar to my other lip. On this theory, then, founded on the conscious facts of double and single pressure in touch, and on the logic of inference, we have at once a reason for our knowledge of external bodies, and an explanation of the early appearance of that knowledge.
Having thus begun by touch and tactile inference, we confirm and extend our inferences of bodies in Nature by using the rest of the senses.
This is not to forget that the five senses are not our whole stock or to confine inference to body.
The common tenet of the whole school is that without inference we immediately perceive the external world, at all events as a resisting something external to our organism.
Finally, as touch perceives reciprocal pressure within, and tactile inference infers it without, touch is the primary evidence of the senses which is the foundation and logical ground of our belief in Nature as a system of pressing bodies.
a desire of food, is effect, not cause, of a previous belief that there is such a thing, and of a present inference that it may again be realized.
Moreover, when the belief pr inference is uncertain, need even in the shape of desire is not in itself a foundation of belief in the thing desired: to need a dinner is not to believe in getting it; and, as Aristotle said, " there is a wish for impossibilities."
Inference from sense is the one condition of all belief in anything beyond oneself, whether it be Nature, or Authority, or God; and it is the one condition of all needs, which are not mere feelings, but desires of things.
This turf wall is certainly older than the stone wall, and, as our ancient writers mention two wall-builders, Hadrian and Septimius Severus, the natural inference is that Hadrian built his wall of turf and Severus reconstructed it in stone.
Yet it was perhaps, like those named by Origen, only an inference from the epistle itself, as if a "word of exhortation" (xiii.
That Apollos visited Italy at any rate once during Paul's imprisonment in Rome is a reasonable inference from Titus iii.
p. 115 seq.); but we must be careful not to draw the inference that Phoenicia itself had any such magistrates.
All the original records of the order until after 1416 have perished, and consequently the question depends for its settlement not on direct testimony but on inference from circumstances.
He took the same course soon afterwards with four other papers, two of which - "On the quantity of acids, bases and salts in different varieties of salts" and "On a new and easy method of analysing sugar," contain his discovery, regarded by him as second in importance only to the atomic theory, that certain anhydrous salts when dissolved in water cause no increase in its volume, his inference being that the "salt enters into the pores of the water."
This inference is made from (4) taken along with (2).
Pathos and indignation, subtlety and simplicity, personal appeal and political reasoning, were the alternate weapons with which she fought against all odds of evidence or inference, and disputed step by step every inch of debatahle ground.
The majority of medieval writers on the subject state that Mark was a Levite; but this is probably no more than an inference from his supposed relationship to Barnabas.
The various amounts of these needed in different cases have to be adjusted by the gardener, according to the nature of the plant, its " habit" or general mode of growth in its native country, and the influence to which it is there subjected, as also in accordance with the purposes for which it is to be cultivated, &c. It is but rarely that direct information on all these points can be obtained; but inference from previous experience, especially with regard to allied forms, will go far to supply such deficiencies.
We do not know, except by inference, to what studies he especially devoted himself.
The perception of relations, which, according to him, is the essence of cognition, the demonstrative character which he thinks attaches to our inference of God's existence, the intuitive knowledge of self, are doctrines incapable of being brought into harmony with the view of mind and its development which is the keynote of his general theory.
For a complete treatment of this portion of the theory of knowledge, there require to be taken into consideration at least the following points: (a) the exact nature and significance of the space and time relations in our experience, (b) the mode in which the primary data, facts or principles, of mathematical cognition are obtained, (c) the nature, extent and certainty of such data, in themselves and with reference to the concrete material of experience, (d) the principle of inference from the data, however obtained.
For Philo lays stress upon the weakness of the analogical argument, points out that the demand for an ultimate cause is no more satisfied by thought than by nature itself, shows that the argument from design cannot warrant the inference of a perfect or infinite or even of a single deity, and finally, carrying out his principles to the full extent, maintains that, as we have no experience of the origin of the world, no argument from experience can carry us to its origin, and that the apparent marks of design in the structure of animals are only results from the conditions of their actual existence.
Cleanthes's view is, therefore, an hypothesis, and in no sense an inference.
It is a reasonable inference from this statement that the thesmothetae had previously sat together apart from the superior archons and that it was only after Solon that collegiate responsibility began.
His inference of the existence, between Mercury and the sun, of an appreciable quantity of circulating matter (Comptes rendus, 1859, ii.
Such an inference is, however, clearly at variance with the whole doctrine of sin, repentance and the atonement, as also with that of eternal reward and punishment, which postulates a real measure of human responsibility.
Hence conjecture, or at least inference, must always enter largely into any estimate of Pascal, except a purely literary one.
This may represent local tradition or may be an inference from i Cor.
I) and other later writers; but it is possible that it is merely an inference from the epistle..
This he remarks in explanation of the order of his version in some places, which he feels may strike his friend Gaudentius as unusual, the inference being that the other edition was the better-known one, although it lacked "the transformation of Simon" (i.e.
The tone of the picture warrants the inference that 1 [W.
The inference is that, shortly after the compiling of this Alfredian chronicle, a copy of it was sent to some northern monastery, probably Ripon, where it was expanded in the way indicated.
The inference is that the "fatigue substances" generated in the muscle fibres in the course of their prolonged contraction injure and paralyse the motor end plates, which are places of synapsis between nerve cell and muscle cell, even earlier than they harm the contractility of the muscle fibres themselves.
That in man the excitable foci of the motor field are islanded in excitable surface similarly and even more extensively, was a natural inference, but it had its chief basis in the observations on the orang, now known to be erroneous.
Moreover, the reactions seem to follow the sense impressions with such fatality, that, as an inference, absence of will-power to control them or suppress them is suggested.
His main result is that God is infinite, and as such, incomprehensible; that his attributes of goodness, knowledge and power are credited to him only by inference from their effects; that this inference is logically valid and sufficient for human thought.
Indefatigable in sifting original documents, Aubigne had amassed a wealth of authentic information; but his desire to give in all cases a full and graphic picture, assisted by a vivid imagination, betrayed him into excess of detail concerning minor events, and in a few cases into filling up a narrative by inference from later conditions.
Hence we may redivide inference into particular inference by analogy and universal inference by induction and deduction.
Universal inference is what we call reasoning; and its two species are very closely connected, because universal conclusions of induction become universal premises of deduction.
Indeed, we often induce in order to deduce, ascending from particular to universal and descending from universal to particular in one act as it were; so that we may proceed either directly from particular to particular by analogical inference, or indirectly from particular through universal to particular by an inductivedeductive inference which might be called " perduction."
The three processes of inference, though different from one another, rest on a common principle of similarity of which each is a different application.
Analogical inference requires that one particular is similar to another, induction that a whole number or class is similar to its particular instances, deduction that each particular is similar to the whole number or class.
Not that these inferences require us to believe, or assume, or premise or formulate this principle either in general, or in its applied forms: the premises are all that any inference needs the mind to assume.
Thus the very principle of inference by similarity requires it to be a combination of premises in order to draw a conclusion.
For this reason it has been elevated by some logicians above all other inferences, and for this very same reason attacked by others as no inference at all.
The truth is that, though the premises contain the conclusion, neither premise alone contains it, and a man who knows both but does not combine them does not draw the conclusion; it is the synthesis of the two premises which at once contains the conclusion and advances our knowledge; and as syllogism consists, not indeed in the discovery, but essentially in the synthesis of two premises, it is an inference and an advance on each premise and on both taken separately.
Inference in general is a combination of premises to cause a conclusion; deduction is such a combination as to compel a conclusion involved in the combination, and following from the premises of necessity.
Nevertheless, deduction or syllogism is not independent of the other processes of inference.
It is not the primary inference of its own premises, but constantly converts analogical and inductive conclusions into its particular and universal premises.
Analogical inference in its turn is as closely allied with induction.
In this case, analogical inference has led to induction, as induction to deduction.
Further, analogical inference from particular to particular suggests inductivedeductive inference from particular through universal to particular.
In fact, analogical, inductive and deductive inferences, though different processes of combining premises to cause different conclusions, are so similar and related, so united in principle and interdependent, so consolidated into a system of inference, that they cannot be completely investigated apart, but together constitute a single subject of science.
This science of inference in general is logic.
Logic, however, did not begin as a science of all inference.
Rather it began as a science of reasoning (Xbyos), of syllogism (vvXXoycvA6s), of deductive inference.
24) we owe the triple distinction into inference from particular to particular (irapf16ecy i ug, example, or what we call " analogy "), inference from particular to universal (i raywy17, induction), and inference from universal to particular (ouXXoyco-Os, syllogism, or deduction).
But he thought that inferences other than syllogism are imperfect; that analogical inference is rhetorical induction; and that induction, through the necessary preliminary of syllogism and the sole process of ascent from sense, memory and experience to the principles of science, is itself neither reasoning nor science.
To be perfect he thought that all inference must be reduced to syllogism of the first figure, which he regarded as the specially scientific inference.
On the other hand, the demonstrations of mathematical sciences of his time, and the logical forms of deduction evinced in Plato's dialogues, provided him with admirable examples of deduction, which is also the inference most capable of analysis.
Nevertheless, the wider question remained for logic: what is the nature of all inference, and the special form of each of its three main processes?
Some have devoted themselves to induction from sense and experience and widened logic till it has become a general science of inference and scientific method.
Beneath deductive logic, in the logic of Aristotle and the canonic of the Epicureans, there already lay the basis of empirical logic: sensory experience is the origin of all inference and science.
The ministration to intellect or reason, aided by the negative elimination by means of contradictory instances of whatever in the instances is not always present, absent and varying with the given subject investigated, and finally by the positive inference that whatever in the instances is always present, absent and varying with the subject is its essential cause.
Inference from particular to particular by Experientia Literata, in piano; 2.
Inference from particular to universal by Inductio, ascendendo; 3.
Inference from universal to particular by Syllogism, descendendo.
In short, the comprehensive genius of Bacon widened logic into a general science of inference.
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.
But the same passage relegates conceptions and their combinations to the De Anima, and confines the De Inter pretatione 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 (Kcp16cs), nor employed the mental distinction between conceptions and judgments as an analysis of inference, or reasoning, or syllogism: he was no conceptual logician.
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.
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.
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.
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.
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.
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.
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.
The real order is sensation and sensory judgment, conception, memory and memorial judgment, experience and experiential judgment, inference, inferential judgment, inferential conception.
Sense before conception is the original cause of judgment; and inference from sense enables judgment to continue after conception ceases.
Conception begins as a condition of memory, and after a long continuous process of inference ends in mere ideation.
memory, experience, inference.
But however complicated these mental causes, there still remain these points common to all judgment: - (i) The mental causes of judgment are sense, memory, experience and inference; while conception is a condition of some judgments.
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 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 is categorical succeeded by conditional inference?
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.
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.
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.
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.
Again, the science of inference has for its subject the form, or processes, of thought, but not its matter or objects.
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.
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.
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.
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.
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.
But we are also conscious of the processes of the operation of inference.
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.
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.
- 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.
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.
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.
pressure existed: afterwards come judgments of memory after inference, e.g.
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.
Inference, no doubt, is closely involved with conception.
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.
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 smiliar 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.
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.
Besides inference of existence there is inference of non-existence, of things inconsistent with the objects of primary judgments.
- Aristotle, by distinguishing affirmative and negative, particular and universal, made the fourfold classification of judgments, A, E, I and 0, 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.
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 inference, a particular is an example of a universal which in its turn may become a particular example of a higher universal.
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.
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.
- The false views of judgment, which we have been examining, have led to false views of inference.
On the other hand, if on the plan of Sigwart categorical universals were reducible to hypotheticals, the same inference would be a pure hypothetical syllogism, thus: If anything is a man it is mortal.
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.
The last supposed syllogism, namely, that having two affirmative premises and entailing an undistributed middle in the second figure, is accepted by Wundt under the title "Inference by Comparison" (Vergleichungsschluss), and is supposed by him to be useful for abstraction and subsidiary to induction, and by Bosanquet to be useful for analogy.
Wundt, who is again followed by Bosanquet, also supposes another syllogism in the third figure, under the title of "Inference by Connexion."
Indeed, it is the very essence of a convertible judgment to think it in both orders, and especially to think it in the order necessary to an inference from it.
It is the same with all the recent attempts to extend the syllogism beyond its rules, which are not liable to exceptions, because they follow from the nature of syllogistic inference from universal to particular.
To give the name of syllogism to inferences which infringe the general rules against undistributed middle, illicit process, two negative premises, non-sequitur from negative to affirmative, and the introduction of what is not in the premises into the conclusion, and which consequently infringe the special rules against affirmative conclusions in the second figure, and against universal conclusions in the third figure, is to open the door to fallacy, and at best to confuse the syllogism with other kinds of inference, without enabling us to understand any one kind.
No distinction is more vital in the logic of inference in general and of scientific inference in particular; and yet none has been so little understood, because, though analysis is the more usual order of discovery, synthesis is that of instruction, and therefore, by becoming more familiar, tends to replace and obscure the previous analysis.
All M is P. Proceeding from one order to the other, by converting one of the premises, and substituting the conclusion as premise for the other premise, so as to deduce the latter as conclusion, is what he calls circular inference; and he remarked that the process is fallacious unless it contains propositions which are convertible, as in mathematical equations.
There is indeed a sense in which all inference is from ground to consequence, because it is from logical ground (principium cognoscendi) to logical consequence.
Lastly, Wundt's view is an interesting piece of eclecticism, for he supposes that induction begins in the form of Aristotle's inductive syllogism, S-P, S-M, M-P, and becomes an inductive method in the form of Jevons's inverse deduction, or hypothetical deduction, or analysis, M-P, S-M, S-P. In detail, he supposes that, while an " inference by comparison," which he erroneously calls an affirmative syllogism in the second figure, is preliminary to induction, a second " inference by connexion," which he erroneously calls a syllogism in the third figure with an indeterminate conclusion, is the inductive syllogism itself.
M-P; because, though both end in a universal conclusion, the limits of experience prevent induction from such inference as: Every experienced magnet attracts iron.
particular magnets attracing iron are the origin of an inference that all do; in hypothetical deduction, the universal is the evidence by which we explain the given particulars, as when we suppose undulating aether to explain the facts of heat and light.
The fact is that the uniformity of nature stands to induction as the axioms of syllogism do to syllogism; they are not premises, but conditions of inference, which ordinary men use spontaneously, as was pointed out in Physical Realism, and afterwards in Venn's Empirical Logic. The axiom of contradiction is not a major premise of a judgment: the dictum de omni et nullo is not a major premise of a syllogism: the principle of uniformity is not a major premise of an induction.
Thus Whewell mistook Kepler's inference that Mars moves in an ellipse for an induction, though it required the combination of Tycho's and Kepler's observations, as a minor, with the laws of conic sections discovered by the Greeks, as a major, premise.
For example, the inference from the similarity between solar spectra and the spectra of various gases on the earth to the existence of similar gases in the sun, is called by him an induction; but it really is an analytical deduction from effect to cause, thus: Such and such spectra are effects of various gases.
But this inference contains the tacit major, " What has a given colour, &c., is magnesium," and is a syllogism of recognition.
This view makes inference easy: induction is all over before it begins; for, according to Bradley, " every one of the instances is already a universal proposition; and it is not a particular fact or phenomenon at all," so that the moment you observe that this magnet attracts iron, you ipso facto know that every magnet does so, and all that remains for deduction is to identify a second magnet as the same with the first, and conclude that it attracts iron.
Hence also induction is a real process, because, when we know that this individual magnet attracts iron, we are very far from knowing that all alike do so similarly; and the question of inductive logic, how we get from some similars to all similars, remains, as before, a difficulty, but not to be solved by the fallacy that inference is identification.
But when he goes on to propose, as a complete independent inference, " A is to the right of B, B is to the right of C, therefore A is to the right of C," he confuses two different operations.
When A, B and C are objects of sense, their relative positions are matters, not of inference, but of observation; when they are not, there is an inference, but a syllogistic inference with a major premise, induced from previous observations, " whenever of three things the first is to the right of the second, and the second to the right of the third, the first is to the right of the third."
As Aristotle puts it, the syllogism is directed " not to the outer, but to the inner discourse," or as we should say, not to the expression but to the thought, not to the proposition but to the judgment, and to the inference not verbally but mentally.
Inference is a deeper thinking process from judgments to judgment, which only occasionally and partially emerges in the linguistic process from propositions to proposition.
We may now then reassert two points about inference against Bradley's logic: the first, that it is a process from similar to similar, and not a process of identification, because two different things are not at all the same thing; the second, that it is the mental process from judgments to judgment rather than the linguistic process from propositions to proposition, because, besides the judgments expressed in propositions, it requires judgments which are not always expressed, and are sometimes even unconscious.
Our third point is that, as a process of judgments, inference is a process of concluding from two beliefs in being to another belief in being, and not an ideal construction, because a judgment does not always require ideas, but is always a belief about things, existing or not.
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