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.
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.
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.
a tree, is a matter of inference.
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.
This argument from a pure assumption is a confusion of sense and inference.
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.
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.
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.
In no case is the evidence of the senses fallacious or mendacious; the fallacy is in the inference.
There are as many kinds of inference as there are different ways of combining premises, and in the main three types: 1.
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.
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.
But by inference beyond sense he does not mean a process of concluding from sensible things to similar things, e.g.
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.
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."
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.
These works, however, warrant the inference.
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."
All we aspire to add is that, in order to attain to real truth, we must proceed gradually from sense, memory and experience through analogical particular inference, to inductive and deductive universal inference or reasoning.
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.
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.
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.
If, for example, judgment were an analysis of an aggregate idea as Wundt supposes, it would certainly be true with him to conclude that " as judgment is an immediate, inference is a mediate, reference of the members of an aggregate of ideas to one another."
But really a judgment is a belief that something, existing, or thinkable, or nameable or what not, is (or is not) determined; and inference is a process from and to such beliefs in being.
Hence the fallacy of those who, like Bosanquet, or like Paulsen in his Einleitung in die Philosophie, represent the realistic theory of inference as if it meant that knowledge starts from ideas and then infers that ideas are copies of things, and who then object, rightly enough, that we could not in that case compare the copy with the original, but only be able to infer from idea to idea.
But there is another realism which holds that inference is a process neither from ideas to ideas, nor from ideas to things, but from beliefs to beliefs, from judgments about things in the premises to judgments about similar things in the conclusion.
Logical inference never goes through the impossible process of premising nothing but ideas, and concluding that ideas are copies of things.
Inference then, though it is accompanied by ideas, is not an ideal construction, nor a process from idea to idea, nor a process from idea to thing, but a process from direct to indirect beliefs in things, and originally in existing things.
These are the limits within which logical inference works, because its nature essentially consists in proceeding from two judgments to another about similar things, existing or not.
judgment is always true of its sensible object, inferential judgments are not always true, but are true so far as they are logically inferred, however indirectly, from sense; and knowledge consists of sense, memory after sense and logical inference from sense, which, we must remember, is not merely the outer sense of our five senses, but also the inner sense of ourselves as conscious thinking persons.
A judgment is true whenever it is a belief that a thing is determined as it is known to be by sense, or by memory after sense, or by inference from sense, however indirect the inference may be, and even when in the form of inference of non-existence it extends consequently from primary to secondary judgments.
Consequently, as knowledge is attainable by sense, memory and inference, truth is also attainable, because, though we cannot test what we know by something else, we can test what we judge and assert by what we know.
Not that all inference is knowledge, but it is sometimes.
The aim of logic in general is to find the laws of all inference, which, so far as it obeys those laws, is always consistent, but is true or false according to its data as well as its consistency; and the aim of the special logic of knowledge is to find the laws of direct and indirect inferences from sense, because as sense produces sensory judgments which are always true of the sensible things actually perceived, inference from sense produces inferential judgments which, so far as they are consequent on sensory judgments, are always true of things similar to sensible things, by the very consistency of inference, or, as we say, by parity of reasoning.
Logic is the science of all inference, beginning from sense and ending in reason.
Hughes, The Theory of Inference (London, 1894); E.
And it sets forth a dialectic with a twofold movement, towards differentiation and integration severally, which amounts to a formulation of inference.
Aristotle, however, treats it as a dialectical rival to syllogism, and it influenced Galilei and Bacon in their views of inference after the Renaissance.
If we add to this logic of " idea," judgment and inference, a doctrine of categories in the modern sense of the word which makes the Theaetetus, in which it first occurs, a forerunner of Kant's Critique of Pure Reason, we have clearly a very significant contribution to logic even in technical regard.
The two are complementary, and the reinstatement of the disjunctive judgment to the more honourable role in inference has been made by so notable a modern logician as Lotze.
(e) Back of Plato's illustration and explanation of predication and dialectical inference there lies not only the question of their metaphysical grounding in the interconnexion of ideas, but that of their epistemological resu presuppositions.
of the fact that in one sense to go beyond what is in the premises is fallacy, Problem of while in another sense not to go beyond them is futility, Inference.
They are not to be used as premises but as immanent laws of thought, save only when an inference from true or admitted premises and correct in form is challenged.
Even inference, though apparently not a classical word, throws back to the Stoic name for a conclusion.'
Along the same lines is their use of the hypothetical form for the universal judgment, and their treatment of the hypothetical form as the typical form of inference.
Yet, in falling back, with a difference, upon the atomism of Democritus, Epicurus had to face some questions of logic. In the inference from phenomena to further phenomena positive verification must be insisted on.
In the inference from phenomena to their non-phenomenal causes, the atoms with their inaccessibility to sense, a different canon of validity obtains, that of non-contradiction.'
He distinguishes too between the inference to combination of atoms as universal cause, and inference to special causes beyond the range of sense.
1 Locke's logic comprises, amid much else, a theory of general terms 2 and of definition, a view of syllogism 3 and a declaration as to the possibility of inference from particular to particular,4 a distinction between propositions which are certain but trifling, and those which add to our knowledge though uncertain, and a doctrine of mathematical certainty.
It follows consistently enough that inference is from particular to particular.
Even so the inference to the a priori ground of its necessity is, it has been often pointed out, subject to the limitation inherent in any process of reduction, in any regress, that is, from conditionate to condition, viz.
From the judgment viewed as hypothetical we pass by affirmation of the antecedent or denial of the consequent to inference.
Inference, curiously enough, falls under the technical side of dialectic concerned with knowledge in process or becoming, a line of cleavage which Ueberweg has rightly characterized as constituting a rift within Schleiermacher's parallelism.
3 As to inference, finally, the ideal of the articulation of the universe of discourse, as it is for complete knowledge, when its disjunctions have been thoroughly followed out and it is exhaustively determined, carried the day with him against the view that the organon for gaining knowledge is syllogism.
Schleiermacher's separation of inference from judgment and his attribution of the power to knowledge in process cannot find acceptance with Lotze.
The detail, too, of the whole discussion is rich in suggestion, and subsequent logiciansUeberweg himself perhaps, Lotze certainly in his genetic scale of types of judgment and inference, Professor Bosanquet notably in his systematic development of " the morphology of knowledge," and others - have with reason exploited it.
The view of inference with which he complements it is only less satisfactory because of a failure to distinguish the principle of nexus in syllogism from its traditional formulation and rules, and because he is hampered by the intractability which he finds in certain forms of relational construction.
It is to Lotze, however, that he owes most in the characteristic feature of his logic, viz., the systematic development of the types of judgment, and inference from less adequate to more adequate forms. His fundamental continuity with Bradley may be illustrated by his definition of inference.
" Inference is the indirect reference to reality of differences within a universal, by means of the exhibition of this universal in differences directly referred to reality."
It is found by these methods that the behaviour of superheated vapours closely resembles that of noncondensible gases, and it is a fair inference that similar behaviour would be observed up to the saturation-point if surface condensation could be avoided.
While Dahomey furnishes this elaborate example of the modern worship of a god in the embodiment of a serpent, elsewhere we find either less organic types, or the persistence and survival of cults whose original form can only be reconstructed by inference.
5) Aristotle quotes the statement that Thales attributed to water a divine intelligence, and criticizes it as an inference from later speculations.
Barisch was shown to have been careless in the performance of his duties, and to have disregarded instructions; and the inference is that he conveyed the infection to his mouth, and so to the lungs, from the bacteriological specimens or inoculated animals.
It may well contain some true supplements to the original text, derived from local tradition or happy inference - a few perhaps from a written source used by Luke.
The statement of the scholiast is evidently a mere inference from the patronymic form of the word.
The inference seems a fair one, that the author of the law was really unknown.
Muller, for instance, maintained the view of Wolf on this point, while he strenuously combated the inference which Wolf drew from it.
These differences bear out the inference that the Odyssey is of a later age.
Possibly the poet may have been of British descent, though the inference is not certain, as British names may sometimes have been given to English children.
This throws a new light on the question, and from it the inference at once follows, that the forms are the permanent causes or substances underlying all visible phenomena, which are merely manifestations of their activity.
Least of all does the historical evidence at our disposal justify the inference that the civilization of north Galatia, during the 1st century A.D., was Romano-Gallic rather than Hellenic; for, as the coins and inscriptions indicate, the Anatolian culture which predominated throughout the province did not exclude the infusion either of Greek religious conceptions or of the Greek language.
The hypothesis that a saying of Jesus is loosely added here to an Old Testament citation is very forced, and the inference is that by the time the author wrote, Luke's gospel was reckoned as This would be explicable if Luke could be assumed to have been the author, in whole or part, of the pastorals.
The inference in all cases passes beyond the field of experience; that it does so may be and has been advanced as a conclusive objection against it.
We may waive his other statement that Papias was "a hearer of John," owing to the possibility of a false inference in this case.
The negative evidence afforded in the account of his establishment suggests the inference that, like Lucilius and Horace, Juvenal had no personal experience of either the cares or the softening influence of family life.
The inference is not expressly drawn, though it becomes perfectly clear from his refutation of William Whiston's curious counter theory that there were in the original Hebrew scriptures prophecies which were literally fulfilled in the New Testament, but had been expunged at an early date by Jewish scribes.
Here again the inference is that the Latin treatises printed from the 15th century onwards as the work of Geber are not authentic, regarded as translations of the Arabic author Jaber, always supposing that the Arabic MSS.
Thus it is a fair inference to draw from the shortness of the list in the opening words of the Lalita Vistara, as compared with that in the first sections of the Saddharma Pundarika, that the latter work is much the younger of the two, a conclusion supported also by other considerations.
18 the omission of all reference to the restoration, in 20 B.C., of the standards taken at Carrhae seems to justify the inference that the passage was written before that date.
(B) In heteroscopic divination the process is rather one of inference from external facts.
The inference to be deduced from the foregoing is plainly this, that even in large-bodied, small-winged insects and birds the wing-surface is greatly in excess, the surplus wing area supplying Not, FIG.
He makes no mention of the Great De- claration, but as in several places he makes Simon speak in the first person, the inference is that he is quoting from it, though perhaps not verbatim.
Human bones and objects of human manufacture have been found in such geological relation to the remains of fossil species of elephant, rhinoceros, hyena, bear, &c., as to lead to the distinct inference that man already existed at a remote period in localities where these mammalia are now and have long been extinct.
The inference that these tribes represent the stage of culture before the invention of pottery is confirmed by the absence of buried fragments of pottery in the districts they inhabit.
Mind, as studied by the psychologist - mind as a mere fact or phenomenon - grounds no inference to anything beyond itself.
The continuous spectrum leads to no inference, except that of the temperature of the central globe; but the multitude of dark lines by which it is crossed reveal the elements composing pe ct rum o the truly gaseous cloaks which enclose it.
The first really adequate determinations of solar parallax were those of Sir David Gill, measured by inference from the apparent diurnal shift of Mars among the stars as the earth turned diurnally upon its axis; the observations were made at the island of Ascension in 1878.
By testing the beam with the scale-pans attached and equal weights in the pans, and noting carefully the position which it takes up; and then interchanging the scale-pans, &c., and again noting the position which the beam takes up, a correct inference can be drawn as to the causes of error; and if after slightly altering or adjusting the knife-edges and scale-pans in the direction indicated by the experiment, the operation is repeated, any required degree of accuracy may be ob - tained by successive approximations.
The same criticism applies equally to the inference of an absolute cause from the two limited forces which he names self and not-self.
Immediate spontaneous apperception may seize this supreme reality; but to vindicate it by reflection as an inference on the principle of causality is impossible.
Late in 1847 De Morgan published his principal logical treatise, called Formal Logic, or the Calculus of Inference, Necessary and Probable.
Newton he entertained a confident belief in Providence, founded not on any tenuous inference, but on personal feeling.
But the inference which he draws from this silence of the historical books is manifestly a precarious one at best.
But this inference is by no means a necessary one.
Of course, we might seek to infer an unwritten tradition of Christ's words; but without pedantic ultra-Protestant devotion to written scripture, one may distrust on scientific grounds the attempt to reconstruct tradition by a process of inference.
The Articles of the Church of England (19, 26) speak of the visible Church, but unless by inference do not assert a Church invisible.
All Isaac D'Israeli's children were born into the Jewish communion, in which, however, they were not to grow up. It is a reasonable inference from Isaac's character that he was never at ease in the ritual of Judaism.
Investigation of the foundation of inductive inference was resumed by Hume where Locke left it.
The stamens of the wheat plant may frequently be seen protruding beyond the glumes, and their position might lead to the inference that cross-fertilization was the rule; but on closer examination it will be found that the anthers are empty or nearly so, and that they are not protruded till after they have deposited the pollen upon the stigma.
The fact that men give different answers to moral problems which seem similar in character, or even the mere fact that men disregard, when they act immorally, the dictates and implicit principles of the moral consciousness is certain sooner or later to produce the desire either, on the one hand, to justify immoral action by casting doubt upon the authority of the moral consciousness and the validity of its principles, or, on the other hand, to justify particular moral judgments either by (the only valid method) an analysis of the moral principle involved in the judgment and a demonstration of its universal acceptation, or by some attempted proof that the particular moral judgment is arrived at by a process of inference from some universal conception of the Supreme Good or the Final End from which all particular duties or virtues may be deduced.
But this much may be said by way of delimitation of the scope of ethics: however complicated and involved its arguments and processes of inference may become, the facts from which they start and the conclusions to which they point are such as the moral consciousness alone can understand or warrant.
Of their contrasted principles we may perhaps say that, while Aristippus took the most obvious logical step for reducing the teaching of Socrates to clear dogmatic unity, Antisthenes certainly drew the most natural inference from the Socratic life.
That man was " naturally " a social animal Aristotle had already taught; that all rational beings, in the unity of the reason that is common to all, form naturally one community with a common law was (as we saw) an immediate inference from the Stoic conception of the universe as a whole.
It should be observed that Plotinus himself is still too Platonic to hold that the absolute mortification of natural bodily appetites is required for purifying the soul; but this ascetic inference was drawn to the fullest extent by his disciple Porphyry.
It is assumed that divine commands have been implicitly given for all occasions of life, and that they are to be ascertained in particular cases by interpretation of the general rules obtained from texts of scripture, and by inference from scriptural examples.
But when this inference was developed in the teaching of Pelagius, it was repudiated as heretical by the church, under the powerful leadership of Augustine (354-430); and the doctrine of man's.
With Price, again, he holds that rightness of intention and motive is not only an indispensable condition or element of the rightness of an action, but actually the sole determinant of its moral worth; but with more philosophical consistency he draws the inference - of which the English moralist does not seem to have dreamt - that there can be no separate rational principles for determining the " material " rightness of conduct, as distinct from its " formal " rightness; and therefore that all rules of duty, so far as universally binding, must admit of being exhibited as applications of the one general principle that duty ought to be done for duty's sake.
The legitimate inference which should follow would be the denial of the validity of those moral laws which have hitherto been regarded as absolute in character, and the substitution for all customary moral terms of an entirely new set based upon biological considerations.
But it is precisely this, the only logical inference, which most evolutionary philosophers are unwilling to draw.
It seems a fair inference that Salvian had divested himself of all his property in favour of that society and sent his relative to Lerins for assistance (Ep. i., with which compare Ad eccles.
It has been conjectured that Salvian paid a visit to Carthage; but this is a mere inference based on the minute details he gives of the state of this city just before its fall (De gub.
This result was traced by Z011ner to the general irregularity of the lunar surface, and the inference was drawn that the average slope of the lunar elevation amounts to 47°.
Corresponding to this observed fact was the inference that the action of the planets might in some way influence the moon's motion.
The logic, which contains at least one praiseworthy portion, a sketch of the history of the science, is divided into theory of right apprehension (bene imaginari), theory of right judgment (bene proponere), theory of right inference (bene colligere), theory of right method (bene ordinare).
But the context alone can determine the question; and that is often so ambiguous that a sure inference is impossible.
warrants no such inference.
The inference as to diversity of authorship is much more conclusive when difference of standpoint can be proved, cf.
- This argument is the simplest form of "mediate" inference, i.e.
No inference can be made from two negative premises.
The " whole " (omne) of the dictum, the major term, ceases to be taken in extension, and becomes intensive or connotative, and the inference consists in subsuming the minor under (bringing it into connexion with) the major.
It remains true that in fact the conclusion is contained in the premises - this is essential to the validity of the syllogism - but the inference is a real one because it brings out and shows the necessity of a conclusion which was not before in our minds.
A further inference (c) from a comparison of I Sam.
It is true that stone implements of palaeolithic and neolithic types are found sporadically in the Nile valley, Somaliland, on the Zambezi, in Cape Colony and the northern portions of the Congo Free State, as well as in Algeria and Tunisia; but the localities are far too few and too widely separated to warrant the inference that they are to be in any way connected.
It might be inferred, therefore, and the inference is proved by facts, that truly oceanic islands have no indigenous fauna of earthworms, but are inhabited by forms which are identical with those of neighbouring continents, and doubtless, therefore, accidentally introduced.
The fact that the light widens out toward the sun leads to the inference that it entirely surrounds the sun.
A transparent atmosphere and clear horizon are necessary, conditions which can best be secured on a mountain top. The visibility of a light corresponding to the inference was shown by Simon Newcomb, by observations at the top of the Brienzer Rothorn, in 1905.
Now it may be taken as admitted that the book of Esther was written in Persia, or by one who had lived in Persia, and not earlier than the 3rd century B.C. If now there is real weight in the points of contact between this story and the Arabian Nights - and the points of difference cannot be held to outweigh the resemblances between two legends, each of which is necessarily so far removed from the hypothetical common source - the inference is important for both stories.
Nor would it be a strained inference from much that he said, to believe that he hoped and expected that in the " crisis " he foresaw, when democracy should have caused the ruin of the country, a new government might be formed that should approximate to his own ideals.'
It is certain, however, that the finer-grained rocks are richest in alumina, and in combined water; hence the inference is clear that kaolin or some other hydrous aluminium silicate is the dominating constituent.
Some clays, however, such as fireclays, contain very little potash or soda, while they are rich in alumina; and it is a fair inference that hydrated aluminous silicates, such as kaolin, are well represented in these rocks.
The most probable inference, however, is that these settlements were not built to avoid the danger of inundation, but represent a survival of the ordinary lake dwelling.
The inference was insulting - especially so since he had been throwing the money at her ever since they met.
"Our father â€“ and Andre â€“ would've wanted us to stay together," Kris said in a hushed tone, wounded by his brother's inference.
Bayesian inference for stochastic kinetic models using a diffusion approximation.
Earlier studies have used Bayesian inference under simplifying assumptions.
The concept of a fair bet has no relevance to statistical inference in science.
The content addressed includes data analysis, correlation, the normal distribution, statistical inference and tests (including the chi-square and t-tests ).
defeasible consequence would have a wider scope of application than a merely epistemological theory of inference.
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equivocal response or a late response could allow the civil court to draw an adverse inference.
fuzzy inference will result in confidence factors (MV's) assigned to each outcome in the rule base.
Those facts certainly do not constitute logical proof of the defendant's guilt, which is the standard Popper sets for inductive inference.
We see from this that the inference engine is the interpreter for a very high-level language.
inaccuracywith specific inaccuracies in the article other than the central inference of improper conduct I would make the following points.
inductive inference is the most widely used technique for machine learning.
Possession of nuclear weapons may indeed justify an inference of preparedness to use them.
That claim would seem at most to license the very different inference that we cannot tell whether they tell the truth or lie.
We use Bayesian networks (BN) to perform probabilistic inference.
Such a method is that founded on inductive inference.
Conference on Nonparametric inference and Probability with Applications to Science, Ann Arbor, Michigan (September 2005 ).
The model's regime probabilities provide an optimal statistical inference of the turning point of the European business cycle.
A new Monte Carlo Markov chain method has the capacity to perform Bayesian phylogenetic inference in a relaxed clock framework.
inference algorithms for Comparative Genomics.
inference rules to permit the inclusion of optional matter in any resulting commands.
inference mechanism used.
inference steps will lead to a value for the goal being found.
This should help finding the origin of type errors without detailed knowledge of type inference on the user side.
inferential transitions in virtue of their form involves having tacit knowledge of a rule of inference.
propagated upwards in the inference network.
General purpose inference systems, such as Prolog's resolution refutation can be used to solve problems stated in logic.
Although Merhige adamantly rebukes the inference that he has constructed a rather revisionist vampire film, he has indeed crafted simply that.
Records of theatrical performances in Elizabethan times are so scanty that no inference can be drawn from them.
statistical inference in science.
Aristotelian syllogisms constituted the deductive schemas for logical inference and were relatively uncontroversial.
That the 8-hour and 6-hour waves, though small near midsummer, represent more than mere accidental irregularities, seems a safe inference from the regularity apparent in the annual variation of their phase angles.
It was hardly possible that he could survive such treatment; the natural inference is that he was not intended to survive it.
It is commonly supposed that by jactus lapidum Fitzstephen meant the game of bowls, but though it is possible that round stones may sometimes have been employed in an early variety of the game - and there is a record of iron bowls being used, though at a much later date, on festive occasions at Nairn, - nevertheless the inference seems unwarranted.
Since his writings are read more easily than Chaucer's, the inference is plain - that he was more effectual as a maker of our present English.
The discovery in the island of a number of gold ornaments belonging to the latest period of Mycenaean art suggests the inference that the Mycenaean culture held its own in Aegina for some generations after the Dorian conquest of Argos and Lacedaemon (see A.
This inference is supported by the date of the building of the 200 triremes "for the war against Aegina" on the advice of Themistocles, which is given in the Constitutionof Athens as 483-482 B.C. (Herod.
But against this inference the following considerations may be advanced: (1) Man does distinguish himself from his body; (2) he is conscious of his personal identity through all the changes of his body; (3) in the exercise of his will he knows himself not controlled by but controlling his body; (4) his consciousness warrants his denying the absolute identification of himself and his body.
The date of his birth depends upon an inference based on the statement of Cicero (De senectute, xiv.
The new phrase indicates that we are to approach the thought of God through a study of religious beliefs phy of and practices; " theism " tended to make God a purely scientific inference from the facts of nature.
Sometimes it will be found that free will is asserted as an assured fact, as a datum, and so as a ground of inference to God.
of reliable inference.
They incline to the Design Argument and Analogy - to the Cosmological argument (with other elements in a subordinate place) and proof by inference - to the Ontological argument.
Flint that while materialism requires sensationalist psychology, yet the psychology in question allows no valid inference to matter, and therefore destroys materialism.
The inference seemed unwarrantable.
David Hume, following up Berkeley's leading suggestion, pointed out that the inference to God is as precarious as the inference to matter, and that the assertion of a continuous or immaterial mind in man also goes beyond the immediate facts.
The inference that organized bodies are due to an intelligent cause is only reached by the " Method of Agreement " - a full J.
It is an obvious inference that if a small quantity of a substance can affect the development of an entire organ it probably acts after the manner of an enzyme.
The leader in speculative philosophy is Immanuel Kant, though he includes many agnostic elements, and draws the inference (which some things in the letter of Butler might seem to warrant) that the essence of Christianity is an ethical theism.
As far as pure science goes, the inference from science in favour of materialism has visibly lost much of its plausibility, and Protestant apologists would probably be prepared to accept in advance all verified discoveries as belonging to a different region from that of faith.
This, however, is rather a matter of inference from the cessation of all mention of them in local records than from any definite evidence of their extirpation.
In doctrine the church has been from the first contentious for believers' baptism, holding that nowhere in the New Testament can be found any authority even by inference, precept or example for the baptism of infants.
But it seems a fair inference from a passage of Michael Psellus (Diophantus, ed.
At least this seems a fair inference from Eurip. Alc., 75, 76, 101 -104.
The pre-existence of souls is another inference from the immutability of God, although Origen also deduced it from the nature of the soul, which as a spiritual potency must be eternal.
In later times both the orthodox and the Arians appealed to his teaching, both with a certain plausibility; but the inference of Arius, that an imparted divinity must be divinity in the second degree, Origen did not draw.
The inference was inevitable that, as German affairs were about to be profitably exploited by France in the bargains then beginning at Rastatt, she must throw her chief energies into the Egyptian expedition.