| 单词 | middle term |
| 例句 | The border confounded racists who’d reduced the world to a basic binary but didn’t know how to slot a middle term between white and black, acceptance and opprobrium. A Tale of Racial Passing and the U.S.-Mexico Border 2016-07-20T04:00:00Z Check the middle term to see if it is equivalent to , or , and it is. College Algebra with Corequisite Support 2020-09-23T00:00:00Z The final products in the last example were trinomials because we could combine the two middle terms. Intermediate Algebra 2020-05-06T00:00:00Z The final products in the last four examples were trinomials because we could combine the two middle terms. Elementary Algebra 2020-04-22T00:00:00Z Rewrite the middle terms as a perfect square. Calculus, Volume 3 2016-03-30T00:00:00Z Then, find of the middle term, and add to both sides of the equal sign: Algebra and Trigonometry 2015-02-13T00:00:00Z A US Congressional report in October last year said that the "Indian military cannot operate effectively without Russian-supplied equipment and will continue to rely on Russian weapons systems in the near and middle term". Ukraine crisis: Could India cut its defence ties with Russia? 2022-05-12T04:00:00Z Remember, when the middle term is negative and the last term is positive, the signs in the binomials must both be negative. Intermediate Algebra 2020-05-06T00:00:00Z Split the middle term using m and n: Elementary Algebra 2020-04-22T00:00:00Z After hearing more than two hours of testimony Thursday morning, San Diego Superior Court Judge Runston Maino rejected Fisher’s motion for a new trial and sentenced Fisher to the middle term available under state law. Ex-Compton school official gets prison in sex case 2016-07-14T04:00:00Z For the middle term of the trinomial, double the product of the two terms. Algebra and Trigonometry 2015-02-13T00:00:00Z But any short and middle term strategies aimed at protecting vulnerable people and pushing back terrorist forces will only work if they go hand in hand with our long-term conversion to a new energy economy. Defeating ISIS Will Take More Than Military Action 2014-09-19T04:00:00Z Since 15 is positive and the coefficient of the middle term is negative, we use the negative factors. Intermediate Algebra 2020-05-06T00:00:00Z Let’s look first at trinomials with only the middle term negative. Elementary Algebra 2020-04-22T00:00:00Z In exposition, the progress was regular from syllogism to syllogism, great care being taken never to skip over a middle term. The Contemporary Review, Volume 36, November 1879 2012-04-25T02:01:12.830Z The middle term has an exponent that is one-half the exponent of the leading term. Algebra and Trigonometry 2015-02-13T00:00:00Z What need is there in cases of this kind to introduce a middle term between the actions of the magician and their expected effect? The Psychological Origin and the Nature of Religion 2012-04-24T02:00:19.043Z Our own life, too, is enacted in such processes; all that we call science may be regarded as parts, or middle terms, of such activities. Popular scientific lectures 2012-04-24T02:00:17.273Z The coefficient of the middle term is negative, so we use the negative factors. Elementary Algebra 2020-04-22T00:00:00Z In fact there was no possible middle term, no compromise in which the disputants could unite. A History of The Inquisition of The Middle Ages; volume II 2012-04-18T02:00:12.957Z We can solve these equations by substituting a variable for the middle term. Algebra and Trigonometry 2015-02-13T00:00:00Z In this notion we have the speculative middle term between the inner being of the Church and her historical form of manifestation. The Catholic World; Volume I, Issues 1-6 A Monthly Eclectic Magazine 2012-04-05T02:00:40.207Z The middle term of all this argument is Love. The Five Great Philosophies of Life 2012-03-09T03:00:19.413Z Since 15 is positive and the coefficient of the middle term is negative, we use the negative facotrs. Elementary Algebra 2020-04-22T00:00:00Z The first appearance is formed by the syllogism, which is based on the Logical system as starting-point, with Nature for the middle term which couples the Mind with it. Hegel's Philosophy of Mind 2012-03-07T03:00:14.327Z The middle term is double the product of the two terms. Algebra and Trigonometry 2015-02-13T00:00:00Z Accordingly, we have not yet found, in the Catholic sacramental conception, the middle term we are seeking, by which the essence of catholicity can be brought into visible manifestation. The Catholic World; Volume I, Issues 1-6 A Monthly Eclectic Magazine 2012-04-05T02:00:40.207Z If the middle term of is equal to the fourth term of find the value of x. A Review of Algebra 2012-01-11T03:00:29.300Z You have to be very careful to choose factors to make sure you get the correct sign for the middle term, too. Elementary Algebra 2020-04-22T00:00:00Z In the process of reasoning the situation is analyzed; some particular feature of it is abstracted and made the middle term in an inference. John Dewey's logical theory 2011-11-28T03:00:21.547Z The middle term drops out, resulting in a difference of squares. Algebra and Trigonometry 2015-02-13T00:00:00Z How often have I, in thought, linked these two graves together, striving to find a middle term or point of meeting for them both! From the Oak to the Olive A Plain record of a Pleasant Journey 2011-11-26T03:00:12.337Z The sum of two numbers x and y is 5, and the sum of the two middle terms in the expansion of is equal to the sum of the first and last terms. A Review of Algebra 2012-01-11T03:00:29.300Z Notice: We listed both 1, −5 and − 1, 5 to make sure we got the sign of the middle term correct. Elementary Algebra 2020-04-22T00:00:00Z But is it only in such moments that we deliberately resolve a situation into its elements, and abstract an 'essence' to serve as a middle term in inference? John Dewey's logical theory 2011-11-28T03:00:21.547Z No. The difference of squares occurs because the opposite signs of the binomials cause the middle terms to disappear. Algebra and Trigonometry 2015-02-13T00:00:00Z A thing is either A or non-A; there is no middle term. The life and teaching of Karl Marx 2011-09-03T02:00:19.203Z They jump the middle terms of their syllogisms, it is true, and assume premises to which the world has not yet arrived; but time stamps their deductions as invincible.'* A Logic Of Facts Or, Every-day Reasoning 2011-07-22T02:00:18.543Z It is very important to make sure you choose the factor pair that results in the correct sign of the middle term. Elementary Algebra 2020-04-22T00:00:00Z But in Summer, having reached the middle term of their annual life, they pause in their appointed course, and then, if ever, taste the nourishment they take in, and “enjoy the air they breathe.” Mirror of the Months 2011-05-21T02:00:10.227Z In the middle term, which assumes that a volition is an effect, the point in dispute is taken for granted, the whole question is completely begged. An Examination of President Edwards' Inquiry into the Freedom of the Will 2011-04-14T02:00:52.727Z Or, according to our example, the earth is either a solid body, or, if it is not solid, it is no earth; there is no middle term. The life and teaching of Karl Marx 2011-09-03T02:00:19.203Z The Sorites uses several middle terms by which the predicate of the last proposition is connected with the first subject. A Logic Of Facts Or, Every-day Reasoning 2011-07-22T02:00:18.543Z When the middle term is negative and the last term is positive, the signs in the binomials must both be negative. Elementary Algebra 2020-04-22T00:00:00Z However, the good old man77 would not try a new middle term, and made no further attempt to prove me a heretic. The Condition of Catholics Under James I. 2011-03-09T03:00:42.087Z It is clear, then, that there is no difference between profit-making in its mildest form, speculation in its opprobrious sense as the middle term, and gambling as the ultimate, except in degree. Cannibals all! or, Slaves without masters 2011-03-06T03:00:21.020Z Socialism is either revolutionary, or not Socialism at all; there is no middle term. The life and teaching of Karl Marx 2011-09-03T02:00:19.203Z It is in order to prove faulty generality in a middle term that the Condition has to be employed. The Sarva-Darsana-Samgraha Review of the Different Systems of Hindu Philosophy Then check the middle term—is it twice the product, 2ab? Elementary Algebra 2020-04-22T00:00:00Z He there says: "It is possible to obtain what is the right result from a syllogism, which is incorrect, but not by an argument which is right, for the middle term is wrong." Dante. An essay. To which is added a translation of De Monarchia. By the use of such symbols propositions could be reduced to the form of equations, and the syllogistic conclusion from two premises was obtained by eliminating the middle term according to ordinary algebraic rules. Encyclopaedia Britannica, 11th Edition, Volume 4, Slice 2 "Bohemia" to "Borgia, Francis" Humility is that line of conduct which is a mean between overbearing pride on the one hand and abject servility on the other, as economy is the middle term between extravagance and avarice. Arabian Wisdom If your definition of a condition be correct, surely a pretended condition which fulfils your definition can always be found even in the case of a valid middle term. The Sarva-Darsana-Samgraha Review of the Different Systems of Hindu Philosophy The sign of the middle term determines which pattern we will use. Elementary Algebra 2020-04-22T00:00:00Z As he sat near the leading counsel in a cause, he seemed a kind of middle term between the lawyer and the jury. Jack Hinton The Guardsman But, if we are content to regard drama as a middle term between poetry and prose, he, with the two poets just named, must be appointed to the first place in it among modern authors. A Short History of French Literature Then come sudden, sharp conclusions; but for middle term there is none: "These things require no proof." Priests, Women, and Families If the middle term, as thus restricted, is still found in the minor term, the argument is valid; if not, it fails. The Sarva-Darsana-Samgraha Review of the Different Systems of Hindu Philosophy See if the middle term fits the pattern of a perfect square trinomial. Elementary Algebra 2020-04-22T00:00:00Z In logic, conversion is one of three chief methods of immediate inference by which a conclusion is obtained directly from a single premise without the intervention of another premise or middle term. Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 3 "Convention" to "Copyright" In whatever form, abstract or concrete, the predication is made of the middle term, it is applicable in the same form to that which is contained in the middle term. Logic, Inductive and Deductive We cannot all of us go farming in Colorado; and there is yet a middle term, which combines the medical benefits of the new system with the moral drawbacks of the old. The Works of Robert Louis Stevenson - Swanston Edition Vol. XXII (of 25) Juvenilia and Other Papers If we can prove that she still keeps to her old diet, of course our amended middle term will still prove B to be dark, but not otherwise. The Sarva-Darsana-Samgraha Review of the Different Systems of Hindu Philosophy And the sign of the middle term of the trinomial factor is the opposite of the sign in the original binomial. Elementary Algebra 2020-04-22T00:00:00Z The syllogistic figures are determined by the position of the middle term. Analysis of Mr. Mill's System of Logic The middle term is only an example of the minor. Logic, Inductive and Deductive But to accept the middle term, to be content with a half-gift, to flicker awhile and to burn out—never for an hour, never since I was born, has satisfied the appetite of my ambition.” The Works of Robert Louis Stevenson - Swanston Edition Vol. 5 (of 25) When you deny the existence of any object on the ground of its not being perceived, you yourself admit an inference of which non-perception is the middle term. The Sarva-Darsana-Samgraha Review of the Different Systems of Hindu Philosophy The middle term of the Binomial Squares Pattern, 2ab , is twice the product of the two terms of the binomial. Elementary Algebra 2020-04-22T00:00:00Z The middle term is not present, the disputants do not in fact use the same language. Essays in English Literature, 1780-1860 “Men” is the middle term, “are mortal” the major term, and “Socrates,” the minor term. English: Composition and Literature These generally resolve themselves into having more than three terms to the syllogism, either avowedly, or in the covert mode of an undistributed middle term, or an illicit process of one of the two extremes. A System Of Logic, Ratiocinative And Inductive Nor can you retort, "Well, let this then be our middle term;" for you cannot establish it as a real fact. The Sarva-Darsana-Samgraha Review of the Different Systems of Hindu Philosophy The middle term is predicate in both premises. Buchanan's Journal of Man, September 1887 Volume 1, Number 8 Let us see what middle term we can find between them. Essays in English Literature, 1780-1860 The middle term, in this case “animal,” must be “distributed;” some statement must be made of all animals. English: Composition and Literature Such a fallacy could not indeed be even exhibited in strict logical form, which would preclude even the attempt at it, since it has two middle terms in sound as well as sense. A System Of Logic, Ratiocinative And Inductive The upádhi or "condition" limits a too general middle term; it is defined as "that which always accompanies the major term, but does not always accompany the middle." The Sarva-Darsana-Samgraha Review of the Different Systems of Hindu Philosophy These attributes are collected around the object as a centre of interest, and it is now the middle term. Buchanan's Journal of Man, September 1887 Volume 1, Number 8 It flies off at once from experience and particulars to the highest and most general propositions, and from these descends, by the use of middle terms, to axioms of lower generality. Encyclopaedia Britannica, 11th Edition, Volume 3, Part 1, Slice 1 "Austria, Lower" to "Bacon" The middle term is found in both the premises, but not in the conclusion. English: Composition and Literature A is the minor term, C the major, B the middle term. A System Of Logic, Ratiocinative And Inductive The premiss which contains the middleterm and the major term is called the major premiss; that which contains the middle term and the minor term is called the minor premiss. A System Of Logic, Ratiocinative And Inductive (Vol. 1 of 2) We may liken it to unconscious reasoning, if we are not afraid of the seeming contradiction of this expression which supposes a logical operation without consciousness of the middle term. Essay on the Creative Imagination There is perhaps a middle term between elementary and "real" mathematics; that is the mathematics that is the handmaid of physics, and leads us on to the natural sciences. The School and the World The emotion is meant to spring from the creed, and it is meant to be the middle term between the creed and the conduct. Expositions of Holy Scripture Ephesians; Epistles of St. Peter and St. John As there can be but three terms, the major and minor terms must each be found in one, and only one, of the premises, together with the middle term which is in them both. A System Of Logic, Ratiocinative And Inductive Thus, without solution of continuity, we start with matter in the atom, and end with matter in the mass; sky-matter being the middle term of the series of transformations. Fragments of science, V. 1-2 Contiguity itself, which is usually only repetition, becomes the source of unforeseen relations, thanks to the elimination of the middle term. Essay on the Creative Imagination Cybele stands as a middle term half-way between these dark forms and the Greek or Roman. The Posthumous Works of Thomas De Quincey, Vol. 1 But so many suppliants miss the middle term, and therefore the gladness is wanting. My Daily Meditation for the Circling Year The premise which contains the middle term and the major term is called the major premise; that which contains the middle term and the minor term is called the minor premise. A System Of Logic, Ratiocinative And Inductive Who has not learnt from such examples what is a major, what a middle term, and what the minor or conclusion? Blackwood's Edinburgh Magazine, No. CCCXXXVI. October, 1843. Vol. LIV. In the paper in which I explain my symbols—which are altogether different from Ploucquet's—there is found "Erase the symbols of the middle term; the remaining symbols show the inference." A Budget of Paradoxes, Volume I "Thinking a thing out" involves precisely this introduction of connecting links, or "middle terms," between what is immediately given or suggested and what necessarily, though by no means obviously, follows. Human Traits and their Social Significance When the Prefect reasons that all fools are poets, therefore all poets are fools, he has no middle term at all; that is, no class of which poets and fools are both members. The Short-story When the middle term is the predicate in both premises, the syllogism belongs to the second figure; when it is the subject in both, to the third. A System Of Logic, Ratiocinative And Inductive There is no middle term or state between the two.... Fifteen Chapters of Autobiography To which is added, with a mark of exclamation at the end, "but in analyzing the syllogism, there is a middle term, and a predicate too, in each of the lines!" A Budget of Paradoxes, Volume I Science is systematized knowing, and is a middle term, or stands and functionates mediatorially between Impression or Nature and Expression or Art. Continental Monthly , Vol. 5, No. 6, June, 1864 Devoted to Literature and National Policy The aim of his logic is represented as having been the devising of rules for the discovery of syllogistic middle terms; this system for aiding slow-witted persons became known as the pons asinorum. Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary" In the fourth figure the middle term is the subject of the minor premise and the predicate of the major. A System Of Logic, Ratiocinative And Inductive Whately says, "The pun is evidently in most instances a mock argument founded on a palpable equivocation of the middle term—and others in like manner will be found to correspond to the respective fallacies." History of English Humour, Vol. 2 It was his pet notion that I did not understand the commonest principles of logic, that I did not always know the difference between the middle term of a syllogism and its conclusion. A Budget of Paradoxes, Volume I For shrewdness consists in easily finding the middle term for demonstrations, as stated in Poster. i, 34. Summa Theologica, Part II-II (Secunda Secundae) Translated by Fathers of the English Dominican Province The three concepts involved in the syllogism are known as the major, the minor, and the middle term. Ontario Normal School Manuals: Science of Education Both these premises of Mr. Spencer's syllogism I am able to assent to, but in different senses of the middle term. A System Of Logic, Ratiocinative And Inductive We require that the middle term, as used in one premise, should necessarily overlap the same term as used in the other, so as to furnish common ground for comparing the other terms. Logic Deductive and Inductive This, as we have seen, was the idea then current in the East, that it is possible to find some middle term between the creature and the highest deity. The Arian Controversy Now the names given to God are derived from His effects; consequently, in demonstrating the existence of God from His effects, we may take for the middle term the meaning of the word "God". Summa Theologica, Part I (Prima Pars) From the Complete American Edition Here the middle term of the syllogism seems to disappear. Ontario Normal School Manuals: Science of Education It was to find a middle term between these opposing motives that Nelson's diplomacy was exerted. The Life of Nelson, Volume 2 The Embodiment of the Sea Power of Great Britain Hence I have defined the middle term as 'that term common to both premises by means of which the other terms are compared.' Logic Deductive and Inductive She tried to find some middle term; it was not a separation from the Church, but a 'secession;' which looks very like a distinction without a difference. The English Church in the Eighteenth Century Now it is manifest that the knowledge of a conclusion depends on all the preceding middle terms not only in the new acquisition of knowledge, but also as regards the keeping of the knowledge acquired. Summa Theologica, Part I (Prima Pars) From the Complete American Edition But this implies a middle term, which could be expressed thus: Gasoline will remove stains; This is a stain; ∴ Gasoline will remove this. Ontario Normal School Manuals: Science of Education But suppose, that, instead of our needing the least circulating medium of any nation, from the circumstance before mentioned, we should place ourselves in the middle term of the calculation, to wit, at thirty-five millions. Memoir, Correspondence, And Miscellanies, From The Papers Of Thomas Jefferson, Volume 4 The fourth Canon required that the middle term should be given distributed, or in its whole extent, at least once, in order to afford sure ground of comparison for the others. Logic Deductive and Inductive Of these three only one can be the middle term. The Art of Public Speaking In ourselves we find many intellectual actions which are ordered according to the order of cause and effect; as when we gradually arrive at one conclusion by many middle terms. Summa Theologica, Part I (Prima Pars) From the Complete American Edition He therefore himself sees no middle term whatsoever, and therefore prefers, of what he sees, the individual: this is the only thing distinct and sensible that has been advocated. The Works of the Right Honourable Edmund Burke, Vol. 07 (of 12) Though not much passed the middle term of life, he seemed prematurely stricken with old age. Jack Sheppard A Romance Or the middle term may be subject of both premises, as in the third of the above examples; and this is called the Third Figure. Logic Deductive and Inductive The middle term for the rest of France is about nine hundred inhabitants to the same admeasurement. The Works of the Right Honourable Edmund Burke, Vol. 03 (of 12) That we should love ours is a sort of middle term between treason and insanity. The Open Secret of Ireland Art, in a word, is a middle term between reason and the senses. Sketches and Studies in Italy and Greece, First Series Feeling does not compound its differences with middle terms. Tragic Sense Of Life Or, finally, the middle term may be predicate of the major premise, and subject of the minor, as in the fourth example given above; and this is the Fourth Figure. Logic Deductive and Inductive From a general, or a particular and a general, the ruling both of the former and the latter is to be according to the middle term, i.e., the one which is particularized. Hebraic Literature; Translations from the Talmud, Midrashim and Kabbala In the logic of Kultur there seems to be a huge gap in the reasoning of the middle terms. New York Times, Current History, Vol 1, Issue 1 From the Beginning to March, 1915 With Index So physic is in a middle term between natural history and metaphysic; for natural history describes the variety of things, physic the variable or respective causes, and metaphysic the fixed and constant causes. The World's Greatest Books — Volume 13 — Religion and Philosophy You have committed the fallacy of the undistributed middle term, if you care to know the proper name for it. Mr. Isaacs There is no difficulty, if one bears in mind that Figure is determined by the position of the middle term. Logic Deductive and Inductive Still to attend it is rather discreditable; it is a middle term between the highly meritorious practice of going to early Mass, and the scandalous one of never going at all.' Correspondence & Conversations of Alexis de Tocqueville with Nassau William Senior from 1834 to 1859, Volume 2 He was the man made for the time—precisely the middle term between the reign of the nobility and the reign of the populace. Blackwood's Edinburgh Magazine — Volume 55, No. 339, January, 1844 The middle term of the syllogism must be distributed at least once in the premises. The Making of Arguments Democracy is contained in the triple statement that men are born free, equal, and in brotherhood; and in this formula it is the middle term that is cardinal, and the root of all. Heart of Man For else neither premise will distribute the middle term. Logic Deductive and Inductive The conjunction is an ellipse, because it is the middle term between two members of the sentence which are the extremes; it recalls what has just been said, and indicates what is to come. Delsarte System of Oratory Both the Bertillon system and the English fingerprint system involve a process of reasoning in which the middle term is undistributed. The Mystery of 31 New Inn If it were not thus distributed or taken universally, the two premises might refer to separate parts of the middle term, and so there would be no meeting ground on which to form the conclusion. The Making of Arguments In this case the middle term is birds, and the major premise, All hawks are birds, does not make a statement which applies to all birds. Composition-Rhetoric The Third Figure, again, furnishes in Darapti and Felapton, the most natural forms of stating arguments in which the middle term is singular: Socrates was truthful; Socrates was a Greek: ∴ Some Greek was truthful. Logic Deductive and Inductive Some men it calls good, others it calls evil, but it has no middle term. The Teaching of Jesus He is such a master of English, so judicious in the use of middle terms,—so shrewd a fencer altogether,—that even his timidity cannot make him other than a formidable opponent. The Atlantic Monthly, Volume 06, No. 34, August, 1860 In other words, if both the major term and the minor term lie outside the middle term, the syllogism gives us no means of knowing what their relation is to each other. The Making of Arguments If the major premise does not make a statement about every member of the class denoted by the middle term. c. Composition-Rhetoric Surely, if distinction of Figure be recognised at all, the Fourth Figure is scientifically necessary, because it is inevitably generated by an analysis of the possible positions of the middle term. Logic Deductive and Inductive In the description of Antioch, it is not easy to define a middle term between her ancient magnificence, under the successors of Alexander and Augustus, and the modern aspect of Turkish desolation. History of the Decline and Fall of the Roman Empire — Volume 5 Wolfgang Goethe, in 1798, forgetting the juvenile period, during which he had dared to raise a hymn to Gothic architecture, now began seriously to seek a middle term between beauty and expression. Aesthetic as Science of Expression and General Linguistic For him there doubtless were no middle terms. Cæsar or Nothing If the major premise does not make a statement about every member of the class denoted by the middle term, the conclusion may not be valid even though the premises are true. Composition-Rhetoric III. the middle term is subject of both premises; so that, to reduce its Moods to the First Figure, it may be enough to convert the minor premise. Logic Deductive and Inductive In Bosanquet's more technical language: "A man is the middle term between content and expression." A Study of Poetry No. He is young, and fit for work, whereas I am past the middle term of life. Fountains in the Sand Rambles Among the Oases of Tunisia Mark is in most cases the middle term which unites the other two. The Gospels in the Second Century An Examination of the Critical Part of a Work Entitled 'Supernatural Religion' It might not be wholly fanciful to call music a sort of middle term between the two other arts. Play-Making A Manual of Craftsmanship This also follows from the function of the middle term. Logic Deductive and Inductive For this end the syllogism was introduced, which descends from the universal to the particular, by deduction,--connecting the general with the special by means of a middle term which is common to both. Beacon Lights of History, Volume 05 The Middle Ages Such syllogisms as those just treated of, if syllogisms they are to be called, have a major and a middle term visible to the eye, but appear to be destitute of a minor. Deductive Logic Ah, there you err; he knows no middle term. The Poems of Emma Lazarus, Volume 1 "It will make me simply ill—I could never describe to you," said Miriam, with her face aglow, "what it is to me to hear some silly man drone away with an undistributed middle term." Pointed Roofs Pilgrimage, Volume 1 For, again, if both premises be affirmative, they only distribute one term, the subject of the universal premise, and this must be the middle term. Logic Deductive and Inductive He therefore himself sees no middle term whatsoever, and therefore prefers of what he sees the individual; this is the only thing distinct and sensible that has been advocated. Thoughts on the Present Discontents, and Speeches, etc. Why is it sufficient to distribute the middle term once only? Deductive Logic Baireuth is but a weak middle term; and there are disagreements on it. History of Friedrich II of Prussia — Volume 07 The English constitution has no middle term, and the French no extremes, and each in its way denies the Divine Trinity, the original basis and type of the syllogism. The American Republic : constitution, tendencies and destiny If we write— All authors are vain; Cicero is a statesman— there are four terms and no middle term, and therefore there is no proof. Logic Deductive and Inductive SOCRATES: And that there is no third or middle term between discretion and indiscretion? Alcibiades II If the middle term be twice distributed, what mood and figure are possible? Deductive Logic The meaning of the words that 'solid bodies are always connected by two middle terms' or mean proportionals has been much disputed. Timaeus For this end the syllogism was introduced, which descends from the universal to the particular, by deduction,—connecting the general with the special by means of a middle term which is common to both. Beacon Lights of History Suppose we are given, the premises—All P is M, and All S is M—the middle term is undistributed. Logic Deductive and Inductive It is, however, to the middle term that an ambiguity most frequently attaches. Deductive Logic This is evident also on inspection by counting the number of middle terms. Deductive Logic In both the same series of means, or middle terms, is employed, the difference lying in the extremes that are compared with one another through them. Deductive Logic Prove that if the conclusion be universal, the middle term can only be distributed once in the premisses. Deductive Logic When the middle term is subject in both premisses, we are said to have the Third Figure. Deductive Logic But Rule 3 requires that this one term should be the middle term. Deductive Logic Here the middle term is altered in the minor premiss to the destruction of the argument. Deductive Logic When the middle term is subject in the major and predicate in the minor, we are said to have the First Figure. Deductive Logic When the middle term is predicate in the major premiss and subject in the minor, we are said to have the Fourth Figure. Deductive Logic Therefore the middle term must be the predicate and is consequently undistributed. Deductive Logic But when the middle term is subject in the major and predicate in the minor premiss, we have what is called the first figure. Deductive Logic Prove that 'Brass is not a metal,' using as your middle term 'compound body.' Deductive Logic In order therefore that the middle term may be distributed, it must be subject in the major premiss, since that also is an A proposition. Deductive Logic In both it is necessary, if we are to obtain the first figure, that the position of the middle term should be changed in one premiss. Deductive Logic The middle term being predicate in both premisses, one or other must be negative; else there would be undistributed middle. Deductive Logic This must be the middle term by Rule 3. Deductive Logic When the middle term is distributed in both premisses, what must be the quantity of the conclusion? Deductive Logic Since the minor premiss is affirmative, the middle term, which is its predicate, is undistributed there. Deductive Logic In the premisses each of the two terms is compared separately with the middle term; and in the conclusion they are compared with one another. Deductive Logic There are four possible varieties of figure in a syllogism, as may be seen by considering the positions that can be occupied by the middle term in the premisses. Deductive Logic For as there are only two terms in each premiss, the position occupied by the middle term necessarily determines that of the others. Deductive Logic It is apparent from the position of the middle term that the constructive conjunctive must fall into the first figure and the destructive conjunctive into the second. Deductive Logic When the middle term is predicate in both premisses, we are said to have the Second Figure. Deductive Logic An immediate inference is so called because it is effected without the intervention of a middle term, which is required in mediate inference. Deductive Logic Now II premisses do not distribute any term at all, and therefore the middle term cannot be distributed, which would violate Rule 3. Deductive Logic |
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