Inference Sentence Examples

The inference was insulting.

The teacher asked the students to draw an inference based on the clues given in the storybook.

The pre-existence of souls is another inference from the immutability of God.

This is, however, very doubtful, and an entirely different inference is possible.

Skylar made an inference about what was in the wrapped box under the Christmas tree after picking it up to feel the weight.

This argument from a pure assumption is a confusion of sense and inference.

The deepest problem of logic is the relation of sense and inference.

The solution of the dilemma is a matter of inference.

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.

The teacher asked the students to draw an inference based on theclues given in the storybook.

After observing how the man and woman treated each other, she made an inference that they were married.

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.

It was hardly possible that he could survive such treatment; the natural inference is that he was not intended to survive it.

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.

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.

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.

Flint that while materialism requires sensationalist psychology, yet the psychology in question allows no valid inference to matter, and therefore destroys materialism.

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.

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 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.

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.

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.

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.

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 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.

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.

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.

If in this sentence he scarcely does justice to the powers of logical inference and inductive reasoning displayed in much of his work, it remains true that blind experiment - heating a substance, or treating it with some reagent, to see what would happen - was his characteristic method of inquiry.

An immediate inference was that the Daltonian " atom " must have parts which enter into combination with parts of other atoms; in other words, there must exist two orders of particles, viz.

Thus the alternative use of cope or chasuble (vestment) is allowed at the celebration of Holy Communion - an obvious compromise; of the amice, girdle (cingulum), maniple and stole there is not a word, 2 and the inference to be drawn is that these were now disused.

Thus, if any inference as to date can be drawn from ch.

There can be little doubt, however, that inference by man differs from that of the brute creation in respect of self-consciousness, and, though there can be no doubt that some animals dream, it is difficult to find evidenc 2 for the presence of ideal images in the minds of ..

Even after interviewing multiple people, the detective could not make an inference about who could be a suspect.

In the case of any crop year, if the relations which are suggested as indicating the "bulling" work of "futures" usually corresponded with "spot" prices being below the normal price of the crop year, or of what was left of the crop year, while the relations which are suggested to indicate the "bearing" work of "futures" on the whole corresponded with a relatively abnormal height of "spot," it would be a legitimate inference that "futures" were tending to smooth prices.

Joule also made experiments upon iron wires under tension, and drew the erroneous inference (which has been often quoted as if it were a demonstrated fact) that under a certain critical tension (differing for different specimens of iron but independent of the magnetizing force) magnetization would produce no effect whatever upon the dimensions of the wire.

They were met by the criticism that possibly such a development had taken place; but, as no one could show as a simple fact of observation that it had taken place, nor as a result of legitimate inference that it must have taken place, it was quite as likely that the past and present species of animals and plants had been separately created or individually brought into existence by unknown and inscrutable causes, and (it was held) the truly scientific man would refuse to occupy himself with such fancies, whilst ever continuing to concern himself with the observation and record of indisputable facts.

The fact that in the formation of the reproductive cells of the hybrid generation the material which carries the positive quality is not subdivided so as to give a half-quantity to each reproductive cell, but on the contrary is apparently distributed as an undivided whole to half only of the reproductive cells and not at all to the remainder, is the important inference from Mendel's experiments.

Whether this inference is applicable to other classes of cases than those studied by Mendel and his followers is a question which is still under investigation.

But if its dimensions be much less than the half wave-length, it can only be seen as a whole, and its parts cannot be distinctly separated, although in cases near the border line some inference may be possible, founded upon experience of what appearances are presented in various cases.

Another obvious inference from the necessary imperfection of optical images is the uselessness of attempting anything like an absolute destruction of spherical aberration.

Unfortunately we are reduced to inference and conjecture with regard both to his life and to the extent of his literary activity.

The inference that Lucretius belonged to this class is confirmed by the tone in which he addresses Gaius Memmius, a man of an eminent senatorian family, to whom the poem is dedicated.

As the Welsh word for " bridge " is " pont," and this was taken directly from the Latin, the inference is almost conclusive that the Britons acquired their knowledge of bridges from the Romans.

Looking at the stage of culture which the Britons had probably reached, it would further be a natural inference that there was no such thing as a bridge anywhere in Britain before the Roman occupation; but, if Dion's statement is correct, it may be suggested as a possible explanation that the increased intercourse with Gaul during the hundred years that - elapsed between Julius Caesar's raids and Claudius Caesar's invasion may have led to the construction of a bridge of some kind across the Thames at this point, through the influence and under the guidance of Roman traders and engineers.

The presence of these inscriptions may perhaps lead to the inference that the vase was made in Sicily, but by Byzantine workmen.

This inference has involved him in much controversy with the ultra-Darwinians of Weismann's school, who deny the possibility of the inheritance of acquired characteristics altogether.

Dalton's idea that elements preferentially combined in equiatomic proportions had as an immediate inference that metallic oxides contained one atom of the metal to one atom of oxygen, and a simple expansion of this conception was that one atom of oxide combined with one atom of acid to form one atom of a neutral salt.

To judge only by the negative evidence of the decree of Aristoteles which records the terms of alliance of the second confederacy (below), we gather that in the later period at least of the first league's history the Athenians had interfered with the local autonomy of the allies in various ways - an inference which is confirmed by the terms of "alliance" which Athens imposed on Erythrae, Chalcis and Miletus.

As conceptions are not always present in judgment, as they are only occasional conditions, and as they are unfitted to cause beliefs or judgments, and especially judgments of existence, and as judgments both precede conceptions in sense and continue after them in inference, it follows that conceptions are not the constituents of judgment, and judgment is not a combination of conceptions.

We know nothing quantitatively of the radiations from a nebulous body; and it is quite possible that the loss of radiant energy in this early stage was very small; but it is at least as certain as any other physical inference that 17,000,000 years ago the earth itself was of its present dimensions, a comparatively old body with sea and living creatures upon it, and it is impossible to believe that the sun's radiations were wholly different; but, if they were not, they have been maintained from some other source than contraction.

To the observation of consciousness Cousin adds induction as the complement of his method, by which he means inference as to reality necessitated by the data of consciousness, and regulated by certain laws found in consciousness, viz.

It is therefore of interest to test this inference by observations at midnight in such a latitude that the distance of the sun below the horizon is no more than necessary to preclude the possibility of twilight.

General purpose inference systems, such as Prolog 's resolution refutation can be used to solve problems stated in logic.

Unfortunately, this frequency may cause inference with cell phones or cordless phones; this interference causes loud screeching noises and can be very annoying.

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.

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.

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.

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.

That Apollos visited Italy at any rate once during Paul's imprisonment in Rome is a reasonable inference from Titus iii.

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 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.

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.

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.

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.

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.

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.

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 universal by Inductio, ascendendo; 3.

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.

But we must first consider the mental analysis of inference, and this brings us to conceptual and formal logic.

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.

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.

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.

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.

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.

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.

All these are beliefs in being and existence, and this existential belief is first in sense, and afterwards transferred to 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.

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.

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.

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.

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.

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.

But this inference contains the tacit major, " What has a given colour, &c., is magnesium," and is a syllogism of recognition.

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.

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.

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.

Logic is the science of all inference, beginning from sense and ending in reason.

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.

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.

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.

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.

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.

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.

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.

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.

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.

The inference as to diversity of authorship is much more conclusive when difference of standpoint can be proved, cf.

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.

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.

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.

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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.

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.

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.

This should help finding the origin of type errors without detailed knowledge of type inference on the user side.

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.

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.

The duties of the skip will already be understood by inference.

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.

It is equally opposed to the doctrine which represents the subject itself and its state and judgments as the single immediate datum of consciousness, and all else, whether the objects of an external world or person other than the individual subject whose states are known to itself, as having a merely problematic existence resting upon analogy or other process of indirect 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.

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.

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.

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."