Syllogism Sentence Examples

These two kinds of syllogism are synthesis and analysis in the ancient sense.

When Aristotle called syllogism X6yos, he meant that it is a combination of premises involving a conclusion of necessity.

Nevertheless, deduction or syllogism is not independent of the other processes of inference.

On the one hand, having reduced categorical judgments to an existential form, Brentano proposes to reform the syllogism, with the results that it must contain four terms, of which two are opposed and two appear twice; that, when it is negative, both premises are negative; and that, when it is affirmative, one premise, at least, is negative.

Sigwart does not indeed shrink from this and greater absurdities; he reduces the first figure to the modus ponens and the second to the modus tollens of the hypothetical syllogism, and then, finding no place for the third figure, denies that it can infer necessity; whereas it really infers the necessary consequence of particular conclusions.

He holds - on grounds of fact and science - to the mechanical orderliness of nature, but claims that the Weltanschauung thus suggested may be reinterpreted in view of those undying human aspirations which MacTaggart dismisses to instant execution (unless they can dress themselves in syllogism).

He is, perhaps, most suggestive in his emendations of the syllogism.

The first adumbration was forced upon him in the former work by his theory of opposition; the complete appearance in the latter work by his theory of syllogism.

Hence, without his saying it in so many words, Aristotle's logic perforce became a logic of deductive reasoning, or syllogism.

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.

But the crowning absurdity is that, if all universals were hypothetical, Barbara in the first figure would become a purely hypothetical syllogism - a consequence which seems innocent enough until we remember that all universal affirmative conclusions in all sciences would with their premises dissolve into mere hypothesis.

But in a hypothetical syllogism of the ordinary mixed type, the first or hypothetical premise is a conditional belief, e.g.

But even Sigwart's errors are outdone by Lotze, who not only reduces " Every NI is P " so " If S is M, S is P," but proceeds to reduce this hypothetical to the disjunctive, " If S is NI, S is P L or P 2 or 1 33, " and finds fault with the Aristotelian syllogism because it contents itself with inferring " S is P " without showing what P. Now there are occasions when we want to reason in this disjunctive manner, to consider whether S is I n or P 2 or P 3, and to conclude that " S is a particular P "; but ordinarily all we want to know is that " S is P "; e.g.

Quasi-syllogisms. - Besides reconstructions of the syllogistic fabric, we find in recent logic attempts to extend the figures of the syllogism beyond the syllogistic rules.

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.

But to say from these premises, " God and metal are similar in what is signified by the middle term," is a mere repetition of the premises; to say, further, that " Gold may be a metal " is a non-sequitur, because, the middle being undistributed, the logical conclusion is the contingent "Gold may or may not be a metal," which leaves the question quite open, and therefore there is no syllogism.

Wundt, who is again followed by Bosanquet, also supposes another syllogism in the third figure, under the title of "Inference by Connexion."

The moment we stir a step further with Wundt in the direction of a more general conclusion (ein allgemeinerer Satz), we cannot infer from the premises the conclusion desired by Wundt, "Metals and fusible are connected "; nor can we infer " All metals are fusible, " nor "Metals are fusible," nor "Metals may be fusible," nor "All metals may be fusible," nor any assertory conclusion, determinate or indeterminate, but the indifferent contingent, "All metals may or may not be fusible," which leaves the question undecided, so that there is no syllogism.

What they really are in the inferences proposed by Wundt is not premises for syllogism, but data for induction parading as syllogism.

Erdmann propose new moods of syllogism with convertible premises, containing definitions and equations.

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.

Yet such is the passion for one type that from Aristotle's time till now constant attempts have been made to reduce induction to syllogism.

Whately, on the other hand, proposed an inductive syllogism with the major suppressed, that is, instead of the minor premise above, he supposed a major premise, " Whatever belongs to A, B, C magnets belongs to all."

Reduction he defines as " the framing of possible premises for given propositions, or the construction of a syllogism when the conclusion and one premise is given."

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.

This is like Aristotle's inductive syllogism in the arrangement of terms; but, while on the one hand Aristotle did not, like Wundt, confuse it with the third figure, on the other hand Wundt does not, like Aristotle, suppose it to be practicable to get inductive data so wide as the convertible premise, " All S is M, and all M is S," which would at once establish the conclusion, " All M is P."

Wundt's point is that the conclusion of the inductive syllogism is neither so much as all, nor so little as some, but rather the indeterminate "M and P are connected."

He agrees with Jevons in calling this second syllogism analytical deduction, and with Jevons and Sigwart in calling it hypothetical deduction.

Hence induction cannot be reduced to Aristotle's inductive syllogism, because experience cannot give the convertible premise, " Every S is M, and every M is S "; that "All A, B, C are magnets " is, but that " All magnets are A, B, C " is not, a fact of experience.

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

It is not syllogism in the form of Aristotle's or Wundt's inductive syllogism, because, though starting only from some particulars, it concludes with a universal; it is not syllogism in the form called inverse deduction by Jevons, reduction by Sigwart, inductive method by Wundt, because it often uses particular facts of causation to infer universal laws of causation; it is not syllogism in the form of Mill's syllogism from a belief in uniformity of nature, because few men have believed in uniformity, but all have induced from particulars to universals.

Bacon alone was right in altogether opposing induction to syllogism, and in finding inductive rules for the inductive process from particular instances of presence, absence in similar circumstances, and comparison.

There are, as we have seen (ad init.), three types - syllogism, induction and analogy.

Bradley seems to suppose that the major premise of a syllogism must be explicit, or else is nothing at all.

But it is often thought without being expressed, and to judge the syllogism by its mere explicit expression is to commit an ignoratio elenchi; for it has been known all along that we express less than we think, and the very purpose of syllogistic logic is to analyse the whole thought necessary to the conclusion.

Aristotle, however, treats it as a dialectical rival to syllogism, and it influenced Galilei and Bacon in their views of inference after the Renaissance.

Plato's division is nevertheless neither syllogism nor exclusiva.

It is not syllogism because it is based on the disjunctive, not on the hypothetical relation, and so extends horizontally where syllogism strikes vertically downward.

Again it is not syllogism because it is necessarily and finally dialectical.

This is embodied in the group of treatises later known as the Organon 7 and culminates in the theory of syllogism and of.

In the well-known sentences with which the Organon closes 8 Aristotle has been supposed to lay claim to the discovery of the principle of syllogism.

In the course of inquiry into the formal consequences from probable premises, the principle of mediation or linking was so laid bare that the advance to the analytic determination of the species and varieties of syllogism was natural.

It is in the Topics, further, that we clearly have a first treatment of syllogism as formal implication, with the suggestion that advance must be made to a view of its use for material implication from true and necessary principles.

In any case, however, definition, syllogism, induction all invited further determination, especially if they were to take their place in a doctrine of truth or knowledge.

Again, so long as we keep to the syllogism as complete in itself and without reference to its place in the great structure of knowledge, the nerve of proof cannot be conceived in other than a formal manner.

The forms of syllogism, however, are tracked successfully through their figures, i.e.

Syllogism already defined 1 becomes through exhibition in its valid forms clear in its principle.

Syllogism must indeed be objective, i.e.

Syllogism as formula for the exhibition of truth attained, and construction or what not as the instrumental process by which we reach the truth, have with writers since Hegel and Herbart tended to fall apart.

In the Posterior Analytics the syllogism is brought into decisive connexion with the real by being set within a system in which its function is that of material implication Posterior from principles which are primary, immediate and Analytics.

Of a non-self-subsistent or attributive conception definition in its highest attainable form is a recasting of the syllogism, in which it was shown that the attribute was grounded in the substance or self-subsistent subject of which it is.

In the scientific syllogism the interposition of the earth is the middle term, the cause or " because " (Sairt.), the residue of the definition is conclusion.

In the aporematic treatment of the relation of definition and syllogism identical as to one form and in one view, distinct as to another form and in another view, much of Aristotle's discussion consists.

The advance from syllogism as formal implication is a notable one.

The planets are near, and we know it by their not twinkling, 2 but science must conceive their nearness as the cause of their not twinkling and make the Arius in the real order the middle term of its syllogism.

Thirdly we have the limiting cases of this in the inductive syllogism 5ui 7riu'mw, 7 a syllogism in the third figure concluding universally, and yet valid because the copula expresses equivalence, and in analogy 8 in which, it has been well said, instances are weighed and not counted.

The Aristotelian theory of the universal of science as secure from dependence on its instances and the theory of linking in syllogism remain a heritage for all later logic, whether accepted in precisely Aristotle's formula or no.

The major premise of syllogism, says the Pyrrhonist, is established inductively from the particular ' 'Errt4 opcc. = " in " as in i raywyi 7, inductio, and - 40pa = - ferentia, as in 8eoopa, differentia.

Experience is appealed to as fruitful where the formal employment of syllogism is barren.

Rather a scientific process, which as experiential may be called inductive, but which is in other regards deductive as syllogism, is set up in constrast to syllogism YvI.

The syllogism is ineffective, belonging to argumentation, and constraining assent where what we want is control of things.

It is in virtue of this view of derived or mediate knowledge that Descartes speaks of the (subsumptive) syllogism as " of avail rather in the communication of what we already know."

Syllogism is not the synthesis which together with analysis goes to constitute the new instrument of science.

Syllogism is simply summation of propositions, its function being communication merely.

As to syllogism specifically, Locke in a passage, 8 which has an obviously Cartesian ring, lays down four stages or degrees of reasoning, and points o ut that syllogism serves us in but one of these, and that not the all-important one of finding the intermediate ideas.

He is prepared readily to " own that all right reasoning may be reduced to Aristotle's forms of syllogism," yet holds that " a man knows first, and then he is able to prove syllogistically."

This point of departure is noteworthy, as also is the treatment of the inductive syllogism as one in which the middle term is resoluble into a group or series (Reihe).

Syllogism is no instrumental method by which we compose our knowledge, but an ideal to the form of which it should be brought.

The psychologist and the formal logician do indeed join hands in the denial of a real movement of thought in syllogism.

In the stage, however, of his process in which he is concerned with the notion are to be found concept, judgment, syllogism.

It is, of course, the rhythm of the syllogism that attracts him.

The concept goes out from or utters itself in judgment to return to an enhanced unity in syllogism.

Ueberweg (System § Ioi) is, on the whole, justified in exclaiming that Hegel's rehabilitation of syllogism " did but slight service to the Aristotelian theory of syllogism," yet his treatment of syllogism must be regarded as an acute contribution to logical criticism in the technical sense.

Hegel's logic as a whole, however, stands and falls not with his thoughts on syllogism, but with the claim made for the dialectical method that it exhibits logic in its integral unity with metaphysic, the thought-process as the self-revelation of the Idea.

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.

The first were the speculative or logical philosophers, who construe the universe ex analogia hominis, and not ex analogia mundi, who fashion nature according to preconceived ideas, and who employ in their investigations syllogism and abstract reasoning.

Hitherto the mode of demonstration had been by the syllogism; but the syllogism is, in many respects, an incompetent weapon.

For a syllogism consists of propositions, propositions of words, and words are the symbols of notions.

This is clear from the use he makes of the Vindemiatio, from certain hints as to the testing of axioms, from his admission of the syllogism into physical reasoning, and from what he calls Experientia Literata.

In physics you wisely note, and therein I agree with you, that after the notions of the first class and the axioms concerning them have been by induction well made out and defined, syllogism may be applied safely; only it must be restrained from leaping at once to the most general notions, and progress must be made through a fit succession of steps."

In logic he is reported to have agreed with Eusebius, Iamblichus and Porphyry in asserting the validity of the second and third figures of the syllogism.

From simple judgments they proceeded to compound judgments, and declared the hypothetical syllogism to be the normal type of reason, of which the categorical syllogism is an abbreviation.

There is no evidence from Galen's own works that he did make this addition to the doctrines of syllogism, and the remarkable passage quoted by Minoides Minas from a Greek commentator on the Analytics, referring the fourth figure to Galen, clearly shows that the addition did not, as generally supposed, rest on a new principle, but was merely an amplification or alteration of the indirect moods of the first figure already noted by Theophrastus and the earlier Peripatetics.

Thus they amplified - the Aristotelian logic by the theory of the hypothetical and disjunctive syllogism, and added to the first figure of the categorical syllogism the five moods out of which the fourth figure was afterwards constructed.

This contains a reprint of the First Notions, an elaborate development of his doctrine of the syllogism, and of the numerical definite syllogism, together with chapters of great interest on probability, induction, old logical terms and fallacies.

There followed at intervals, in the years 1850, 1858,1860 and 1863, a series of four elaborate memoirs on the "Syllogism," printed in volumes ix.

We cannot, however, find that he has furnished any substantial principles for its determination; indeed, he hardly seems to have formed a distinct general idea of the practical syllogism by which he conceives it to be effected.'

The whole doctrine of judgment, syllogism and method is a mixture of Aristotelian and Ramist notions.

Owing largely to the simplicity and symmetry of the syllogism it has been a commonplace of logic to make the syllogistic form the type of all thought.

The distinction of moods is according to the quantity or quality of the propositions of the syllogism (universal, particular, affirmative, negative, in all the possible combinations).

A syllogism must contain three and three terms only.

The general criticism of the syllogism as a means of discovering truth is that it is a petitio principii, or begging of the question.

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.

The term syllogism has been extended to cover certain forms of ratiocination which are not based on categorical propositions.

It has been defined as a syllogism in Fig.

The Inductive Syllogism, like the deductive, is first systematized by Aristotle, who described it as o E brawl/Cis ovXXoycaµos.

Discussions of the syllogism will be found in all textbooks on Logic, and the more elaborate syllogistic forms are discussed in the article Logic.

In logic Avicenna starts from distinguishing between the isolated concept and the judgment or assertion; from which two primitive elements of knowledge there is artificially generated a complete and scientific knowledge by the two processes of definition and syllogism.

Accordingly, the expositors of religious metaphysics, Ghazal" included, are the enemies of true religion, because they make it a mere matter of syllogism.

But average human nature does not take kindly to a syllogism, and theology had ceased to have any appreciable influence on popular religion.

The adjective "hypothetical" is used in the same sense, both loosely in contradistinction to "real" or "actual," and technically in the phrases "hypothetical judgment" and "hypothetical syllogism."

Let me explain why, in simple terms using a classical syllogism (or formal argument ).

Comparing this finding to a legal standard creates a syllogism.

Chapter Two considers the normative syllogism, a formalization of the process of (deductively) applying law to facts.

This type of argument is called syllogism and dates back to ancient Greece.

Hence it does not follow, by disjunctive syllogism, that H1 is true.

That this process has a valid logical structure can be seen when we notice that it takes the form of an inverted syllogism.

Bailey replied to his critics in a Letter to a Philosopher (1843), &c. In 1851 he published Theory of Reasoning (2nd ed., 1852), a discussion of the nature of inference, and an able criticism of the functions and value of the syllogism.

Aristotle apparently intended, or at all events has given logicians in general the impression, that he intended to analyse syllogism into propositions as premises, and premise into names as terms. His logic therefore exhibits the curious paradox of being an analysis of mental reasoning into linguistic elements.

More particularly "argument" means a synopsis of the contents of a book, the outline of a novel, play, &c. In logic it is used for the middle term in a syllogism, and for many species of fallacies, such as the argumentum ad hominem, ad baculum, &c. '(see' Fallacy).

This so-called syllogism has been much criticized by modern logicians on various grounds (see LoGic).

Let me explain why, in simple terms using a classical syllogism (or formal argument).

Demonstrative syllogism gives us the most certain knowledge, and is the part of logic toward which the other parts are directed.

Moreover, the study of analogical and inductive inference is necessary to that of the syllogism itself, because they discover the premises of syllogism.

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.

Bacon, like Aristotle, was anticipated in this or that point; but, as Aristotle was the first to construct a system of deduction in the syllogism and its three figures, so Bacon was the first to construct a system of induction in three ministrations, in which the requisites of induction, hitherto recognized only in sporadic hints, were combined for the first time in one logic of induction.

Aristotle's logic has often been called formal logic; it was really a technical logic of syllogism analysed into linguistic elements, and of science rested on an empirical basis.

The formal thinking of syllogism alone is merely necessary consequence; but when its premises are necessary principles, its conclusions are not only necessary consequents but also necessary truths.

It is not necessary in every proposition, but it is necessary in the arrangement of a syllogism, to extricate the terms of its propositions from the copula; e.g.

In acquiring scientific knowledge, syllogism cannot start from universals without induction, nor induction acquire universals without sense.

In this way the Presocratics and Sophists, and still more Socrates and Plato, threw out hints on sense and reason, on inferential processes and scientific methods which may be called anticipations of logic. But Aristotle was the first to conceive of reasoning itself as a definite subject of a special science, which he called analytics or analytic science, specially designed to analyse syllogism and especially demonstrative syllogism, or science, and to be in fact a science of sciences.

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.

Accordingly, the syllogism appeared to him to be the rational process (wet X6yov), and the demonstrative syllogism fran inductively discovered principles to be science (Eirurrr7un).

Aristotle's analysis of the syllogism showed man how to advance by combining his thoughts in trains of deductive reasoning.

In the Analytics he took the final step of originating the logical analysis of the proposition as premise into subject and predicate as terms mediated by the copula, and analysed the syllogism into these elements.

But he laid too much stress on reasoning as syllogism or deduction, and on deductive science; and he laid too much stress on the linguistic analysis of rational discourse into proposition and terms. These two defects remain ingrained in technical logic to this day.

The science of inference again rightly emphasizes the formal thinking of the syllogism in which the combination of premises involves the conclusion.

Hence the manner in which induction aided by identification discovers necessary principles must be studied by the logician in order to decide when the syllogism can really arrive at necessary conclusions.

False Views of Syllogism arising from False Views of Judg- ment.

But as yet he had only glimpses of a logical method which should invigorate the syllogism by the co-operation of ancient geometry and modern algebra.

Whately defined it as "a conditional syllogism with two or more antecedents in the major and a disjunctive minor."

Logic falls, according to Ramus, into two parts - invention (treating of the notion and definition) and judgment (comprising the judgment proper, syllogism and method).

So also he might add the appendix to the Sophistical Elenchi, long after he had written that book, and perhaps, to judge from its being a general claim to have discovered the syllogism, when the founder of logic had more or less realized that he had written a number of connected treatises on reasoning.

In analysing the syllogism, he first says that a premiss is an affirmative or negative sentence, and then that a term is that into which a premiss is dissolved, i.e.

Because the crossing of terms in a syllogism requires it.

In the syllogism " Every man is mortal and Socrates is a man," if in the minor premiss the copula " is " were not disengaged from the predicate " man," there would not be one middle term " man " in the two premisses.

Example (7rapabayma) is not called rhetorical induction, and consideration (EVBuµnya) is not called rhetorical syllogism, as they are in the Rhetoric, and in the Analytics.

Induction (E7rayo.y17) and syllogism (ovXXcytcr oc), the general forms of inference, do not occur in the Rhetoric to Alexander.

We cannot write a history of the varied origin of logic, beyond putting the rudimentary logic of the proposition in the De Interpretatione before the less rudimentary theory of categories as significant names capable of becoming predicates in the Categories, and before the maturer analysis of the syllogism in the Analytics.

As he says at the end of the Sophistical Elenchi on the syllogism, he had no predecessor, but took pains and laboured a long time in investigating it.

He got so far as gradually to write short discourses and long treatises, which we, not he, now arrange in the order of the Categories or names; the De Interpretatione on propositions; the Analytics, Prior on syllogism, Posterior on scientific syllogism; the Topics on dialectical syllogism; the Sophistici Elenchi on eristical or sophistical syllogism; and, except that he had hardly a logic of induction, he covered the ground.

Logically regarded, the origin of all teaching and learning of an intellectual kind is a process of induction (Enraywyi) from particulars to universal, and of syllogism (ovXXoyco-p5s) from universal to further particulars; induction, whenever it starts from sense, becomes the origin of scientific knowledge (bruiriran); while there is also a third process of example (1rapaSeiyµa) from particular to particular, which produces only persuasion.

At the same time, there are three species of syllogism, scientific, dialectical and eristical or sophistical; and in consequence there are different ways of acquiring premisses.

Nor does the process of acquiring the premisses of eristical syllogism, which is fallacious either in its premisses or in its process, differ, except that, when the premisses are fallacious, the dialectical interrogations must be such as to cause this fallacy.

Hence, as science and dialectic are different, so scientific induction and syllogism must be distinguished from dialectical induction and syllogism.

But it is by a different process of sense, memory, experience, induction, intelligence, syllogism, that science becomes knowledge of real causes, of real effects, and especially of real essences from which follow real consequences, not beyond, but belonging to real substances.

Otherwise, logical ground remains logical ground, as in any noncausal syllogism, such as the familiar one from " All men are mortal," which causes me to know that I shall die, without telling me the cause of death.

Under the head of notion are considered, firstly, the subjective forms of conception, judgment and syllogism; secondly, their realization in objects as mechanically, chemically or teleologically constituted; and thirdly, the idea first of life, and next of science, as the complete interpenetration of thought and objectivity.

Thus in the example of syllogism given above, " border-war between Thebes and Athens " is the minor term, " evil " the major term, and " border-war " the middle term.

Deduction or syllogism is superior to analogy and induction in combining premises so as to involve or contain the conclusion.

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.

As again the synthesis contains or involves the conclusion, syllogism has the advantage of compelling assent to the consequences of the premises.

Rather it began as a science of reasoning (Xbyos), of syllogism (vvXXoycvA6s), of deductive inference.

As then the reasoning of the syllogism was the main problem of Aristotle's logic, what was his analysis of it?