Languages & Linguistics
Syllogism
A syllogism is a form of reasoning that consists of two premises and a conclusion. It follows a specific structure, with a major premise, a minor premise, and a conclusion. Syllogisms are used in logic and argumentation to demonstrate the validity of a conclusion based on the truth of the premises.
Written by Perlego with AI-assistance
Related key terms
1 of 5
8 Key excerpts on "Syllogism"
eBook - PDFThe Dialogical Roots of Deduction
Historical, Cognitive, and Philosophical Perspectives on Reasoning
- Catarina Dutilh Novaes(Author)
- 2020(Publication Date)
- Cambridge University Press(Publisher)
113 Aristotle’ s Syllogistic and Other Ancient Logical Traditions Rhetoric, which suggests a general, unified conception of deduction present in these different domains of application. In Striker, 2009 (emphasis added), the definition is translated as: A Syllogismos is an argument (logos) in which, (i) certain things being posited (tethentōn), (ii) something other than what was laid down (keimenōn) (iii) results by necessity (ex anagkēs sumbainei) (iv) because these things are so. By ‘because these things are so’ I mean that it results through these, and by ‘resulting through these’ I mean that no term is required from outside for the necessity to come about. A Syllogismos thus has four main features: (i) There are at least two premises which are posited. (ii) The conclusion is different from the premises. (iii) The conclusion follows necessarily from the premises. (iv) The premises imply the conclusion by themselves; they are jointly necessary and sufficient for the conclusion to be produced. 7 Each of these clauses can receive natural dialogical interpretations, pertain- ing both to dialectic and to demonstrations. 8 As Aristotle presents it in the first chapter of Prior Analytics, the distinction between dialectical and demonstra- tive Syllogisms seems to pertain exclusively to the status of the premises: if known to be true and more primary than the conclusion, then the Syllogism will be demonstrative; if merely ‘reputable’ (endoxa), then the Syllogism is dialect- ical. But with respect to the pragmatics of the two situations, there are other relevant differences. In particular, demonstrative Syllogisms used in the context of teaching will presuppose an asymmetric relationship between the interlocu- tors (teacher and pupil), whereas in a dialectical context, although questioner and answerer have different roles to play, their statuses are usually compar- able – they are peers.
eBook - PDF- Irving M. Copi, Carl Cohen, Victor Rodych, Kenneth McMahon(Authors)
- 2018(Publication Date)
- Routledge(Publisher)
More formally, we define a categorical Syllogism as a deductive argument consisting of three categorical proposi-tions that together contain exactly three terms, each of which occurs in exactly two of the constituent propositions. Syllogisms are very common, very clear, and readily testable. The system of cat-egorical Syllogisms that we will explore is powerful and deep. The seventeenth-century philosopher and mathematician Gottfried Leibniz said, of the invention of the form of Syllogisms, that it was “one of the most beautiful and also one of the most impor-tant made by the human mind.” Syllogisms are the workhorse arguments with which deductive logic, as traditionally practiced, has been made effective in writing and in controversy. It will be convenient to have an example to use as we discuss the parts and features of the Syllogism. Here is a valid standard-form categorical Syllogism that we shall use as an illustration: No heroes are cowards. Some soldiers are cowards. Therefore some soldiers are not heroes. Syllogism Any deductive argument in which a conclusion is inferred from two premises. Categorical Syllogism A deductive argument consisting of three categorical propositions that contain exactly three terms, each of which occurs in exactly two of the propositions. chapter 6 6.1 chapter 6 Categorical Syllogisms 188 To analyze such an argument accurately, it needs to be in standard form . A categorical Syllogism is said to be in standard form (as the above example is) when two things are true of it: (1) its premises and its conclusion are all standard-form categorical proposi-tions ( A , E , I , or O ); and (2) those propositions are arranged in a specified standard order . The importance of this standard form will become evident when we turn to the task of testing the validity of Syllogisms.
eBook - ePub- John Neville Keynes(Author)
- 2019(Publication Date)
- Perlego(Publisher)
This is, however, nothing more than a convention. The order of the premisses in no way affects the validity of a Syllogism, and has indeed no logical significance, though in certain cases it may be of some rhetorical importance. Jevons (Principles of Science, 6, § 14) argues that the cogency of a Syllogism is more clearly recognisable when the minor premiss is stated first. But it is doubtful whether any general rule of this kind can be laid down. In favour of the traditional order, it is to be said that in what is usually regarded as the typical Syllogism (All M is P, All S is M, therefore, All S is P) there is a philosophical ground for stating the major premiss first, since that premiss gives the general rule, of which the minor premiss enables us to make a particular application. 199. The Rules of the Syllogism.—The rules of the categorical Syllogism as usually stated are as follows:— (1) Every Syllogism contains three and only three terms. (2) Every Syllogism consists of three and only three propositions. These two so-called rules are not properly speaking rules for the validity of an argument. They simply serve to define the Syllogism as a particular form of argument. A reasoning which does not fulfil these conditions may be formally valid, but we do not call it a Syllogism. 307 The four rules that follow 288 are really rules in the sense that if, when we have got the reasoning into the form of a Syllogism, they are not fulfilled, then the reasoning is invalid. 308 307 For example, B is greater than C, A is greater than B, therefore, A is greater than C. Here is a valid reasoning which consists of three propositions. But it contains more than three terms; for the predicate of the second premiss is “greater than B,” while the subject of the first premiss is “B.” It is, therefore, as it stands, not a Syllogism
eBook - ePubHuman Reasoning
The Psychology Of Deduction
- Ruth M.J. Byrne, Jonathan St.B.T. Evans, Stephen E. Newstead(Authors)
- 2019(Publication Date)
- Psychology Press(Publisher)
A comment is in order about the terminology used to describe Syllogisms. Traditionally, the first premise is the one containing the predicate of the conclusion, the second premise the one containing the subject, and only conclusions going from subject to predicate are allowed. Thus an AI1 Syllogism has the first premise in mood A, the second in mood I and is in figure 1. Traditionally, one would also have had to specify the mood of the conclusion, but in order to allow for open-ended Syllogisms where no conclusion is indicated, we will frequently exclude the conclusion from our notation. Most of the research up until the last decade used this terminology, and it is the one adopted here. However, Johnson-Laird and his colleagues (e.g. Johnson-Laird & Bara, 1984) have adopted a different way of describing Syllogisms, based on the fact that they allow conclusions in both directions, and conclusions going from the predicate term to the subject term can alter the figure of the Syllogism. This leads to some problems in comparing the results of different studies. Johnson-Laird talks, for example, of an AB-BC Syllogism, which means that the first premise contains the items A and B, in that order, while the second contains B and C in that order. Such a Syllogism does not fall automatically into one of the classical figures, since conclusions going from both A to C and from C to A are permitted. The comparisons in this chapter are based on the fact that, assuming conclusions going from A to C, then Johnson-Laird’s AB–BC figure is the classical figure 1 with the premises reversed; AB–CB is figure 2 with reversed premises; BA–BC is figure 3 with reversed premises; and BA–CB is figure 4 with reversed premises.THE PSYCHOLOGY OF SyllogismSMost people, when they have it explained to them, will accept the validity of the logic underlying Syllogisms. However, when actually confronted by exercises in syllogistic reasoning, people make a large number of errors. Not that this is a recent phenomenon; the fact that students over the ages have had to learn by rote the valid Syllogisms suggests that our forebears did not find the task any easier than we do. Much research in psychology over the past century has sought to understand the source of such errors.
- Alexander Of Aphrodisias, Ian Mueller(Authors)
- 2014(Publication Date)
- Bloomsbury Academic(Publisher)
Translation 123 things through the three terms, refuting i n this way and estab-lishing i n that (if dealing w i t h t r u t h then on the basis of things which have been listed as truly holding and i f i n dialectical Syllogisms on the basis of premisses which are i n accordance w i t h opinion)]. What he says is this. The path and method to producing Syllogisms is the same i n every science and art i n which something proper to i t is demonstrated through Syllogisms, if, indeed, every Syllogism comes from the examinations which have been described. For the previously described method and path is necessary for a philosopher, a doctor, a 35 rhetor, a music theorist, and anyone who produces Syllogisms. For the 331,1 discovery of premisses for a Syllogism comes through this method. For everyone who produces Syllogisms should examine the consequents of the things which the Syllogism is about and their antecedents and the things which do not hold of them and select as many of these as possible; and he should be well supplied w i t h them and have them 5 ready at hand. He says, 'For i n the case of each of the terms one should look at the things which hold of them and the things of which they hold' so that for each of the terms we w i l l seek both its consequents and its antecedents - and we w i l l not select only the consequents of one and the antecedents of the other. The words 'and investigate these things through the three terms ...' are equivalent to 'and combine these 10 things i n the three terms from which the Syllogism results, refuting i n one way and establishing i n another'.
eBook - PDF- E. Wright(Author)
- 2005(Publication Date)
- Palgrave Macmillan(Publisher)
As for the logical 'must', that is an example of what happens to agreements about fears and desires when for fun we take fear and desire out of the equation. A clue to this lies in the logicians being unable to avoid using words like 'satisfies' as they trace their deductive patterns in a situation where nothing is satisfying anybody. The fact that logicians and mathematicians cannot resist using aesthetic terms like 'beautiful' for the structures and proofs that are created is more evidence that their activities are an elevated form of play. This is why it is foreign to the spirit of pure logic to quarrel with the Syllogism for ignoring the acquisition of knowledge. For example, in the Syllogism All men are mortal. Socrates is a man. Therefore, Socrates is mortal it is de rigueur not to ask how we arrived at the truth of the universal proposition 'All men are mortal' if we had not already examined Socrates and found he was mortal, for he is obviously included in 'All men'. If logic is not only timeless, so is its supposed 'knowledge'. Of course it is the case that all logic is tautology, as is so often said, for, since we are supposed to be in perfect agreement, logic can say nothing of any point to anyone! As soon as we try to transfer logical relationships into our active language, they have to fall back on our mutual trust just as any other feature of our utterances to each other has to. The Greeks, early on, detected in everyday argument a feature they called the 'enthymeme', which was any syllogistic reasoning that depended on a premise but which was not openly expressed. Christopher Lyle Johnstone in the Encyclopedia of Rhetoric gives a clear and simple example: Imagine a public meeting at which an election will be held for the office of city treasurer.
eBook - ePub- G W F Hegel(Author)
- 2014(Publication Date)
- Taylor & Francis(Publisher)
Or to put it otherwise the subject obtains through the conclusion a predicate as a consequence; but the major premiss already contains this conclusion within it; therefore the major premiss is not correct on its own account, or is not an immediate, presupposed judgement, but already presupposes the conclusion whose ground it was supposed to be. In the favourite perfect Syllogismml: All men are mortal Now Gaius is a man Therefore Gaius is mortal, the major premiss is correct only because and in so far as the conclusion is correct ; if Gaius should chance to be not mortal, the major premiss would not be correct. The proposition which was supposed to be the conclusion must already be immediately correct on its own account, because otherwise the major premiss could not embrace all individuals; before the major premiss can pass as correct, there is the prior question whether the conclusion itself may not be an instance against it. In the case of the Syllogism of existence we found from the Notion of the Syllogism that the premisses, as immediate, contradicted the conclusion, that is to say the mediation demanded by the Notion of the Syllogism, and that the first Syllogism therefore presupposed others and conversely these others presupposed it. In the Syllogism of reflection, this is posited in the Syllogism itself, namely, that the major premiss presupposes its conclusion, in that the former contains that connexion of the individual with a predicate which is supposed to appear only as conclusion. What, then, we really have here may be expressed in the first instance by saying that the Syllogism of reflection is only an external, empty show of syllogizing —hence that the essence of this syllogizing rests on subjective individuality and that therefore this latter constitutes the middle term and is to be posited as such—the individuality that is individuality as such and possesses universality only externally
eBook - ePub- John Buridan, Stephen Read(Authors)
- 2014(Publication Date)
- Fordham University Press(Publisher)
Moreover, sometimes the direct [term] is distributed and not the oblique nor the combination of the direct and the oblique, but the oblique retains determinate supposition, namely, if it precedes the distributive sign, for example, in saying, “Of [some] human any ass whatever is running.” For it does not follow, “Of [some] human any ass whatever is running, so any human whatever’s ass is running.” But in the said proposition the term “ass” is not distributed straightforwardly, but restricted by the term “human” suppositing determinately. So it does not follow, “Of [some] human any ass is running, Brownie is an ass, so Brownie is running.” Similarly, because the whole combination is not distributed, it does not follow, “Of [some] human any ass is running, the bishop’s ass is [some] human’s ass, so the bishop’s ass is running,” because the bishop’s ass is perhaps lying in the stable and Socrates is the human whose every ass is running. So in this case, if we wish to include in a Syllogism what is distributed in the proposition in question, we must form a minor premise in which a relative of identity is adjoined to the term “human” so that the middle is understood to hold of the same thing in the premises. For example, it does follow, “Of [some] human any ass is running, the bishop’s ass is an ass of that human, so the bishop’s ass is running.” For in this way the rule is preserved by which affirmative Syllogisms were said to hold.This [concludes] what is set down in the first chapter. [p. 100] Chapter 2: The Syllogistic Extremes and Middle Now in the second chapter, we take it that sometimes in syllogizing with oblique [terms] it is not necessary that the syllogistic extreme or the syllogistic middle is the extreme of either premise.For I call the extremes of the Syllogism what are inferred in the conclusion to be linked by the fact that each is linked with the middle in the premises, and I call the extremes of the premises their subjects and predicates.So I say that the syllogistic middle is sometimes neither the subject nor the predicate of the major premise but part of the subject or predicate; and similarly, [sometimes] neither of the extremes is the subject or predicate either in the premises or in the conclusion. For example, here is a good Syllogism: “Some human [it is] every horse [he or she] is seeing; Brownie is a horse, so some human [it is] Brownie [he or she] is seeing.”22
Index pages curate the most relevant extracts from our library of academic textbooks. They’ve been created using an in-house natural language model (NLM), each adding context and meaning to key research topics.
