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Class 11 Logic And Philosophy Chapter 8 Categorical Syllogism
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Categorical Syllogism
Chapter – 8
LOGIC & PHILOSOPHY
VERY SHORT TYPES QUESTIONS AND ANSWERS
1. Find out the correct answer :
(a) Is it true that in a immediate inference there are premises?
Ans : No, it is false.
(b) Obversion is an immediate inference. Is it true?
Ans : Yes, it is true.
(c) How many premise are required to draw a conclusion immediate inference?
Ans : Only one premise.
(d) Is it true that in a categorical syllogism there is only one middle term?
Ans : Yes, it is true.
(e) In a categorical syllogism the middle term must be distributed at least once?
Ans : Yes.
(f) Which term determine the figure of a syllogism. Ans : Middle term.
Ans :Middle term.
(g) How many valid moods are there is the third figure?
Ans : Six valid moods.
(h) ‘In the first figure the major premise must be particular proposition’- is it true?
Ans : It is false.
(i) What is the name of the predicate of the conclusion of a syllogism?
Ans : Major term.
2. Define :
(a) Conversion.
Ans : Conversion is a kind of Immediate Inference, in which there is a legitimate transposition of the subject and the predicate of a proposition.
(b) Obversion.
Ans : Obversion is a kind of Immediate Inference, in which there is a change in the quality of the given proposition, while its meaning remains unchanged.
(c) Syllogism.
Ans : A syllogism is a form of mediate deductive inference, in which the conclusion is drawn from two premises, taken jointly.
(d) Minor term.
Ans : The subject of the conclusion is called the Minor term.
(e) Middle term.
Ans : The terms which occurs is both the premises, but does not go in the conclusion is called the Middle term.
(f) Major term.
Ans : Inference is the process of passing from one or more propositi to another, which is justified by term, and the product in calli an inference.
(h) Material obversion.
Ans : Material obversion is the process of drawing obverse inference which are justified only on an examination of the matter of th À proposition.
(i) Figure of syllogism.
Ans : Figure is the form of a syllogism as determined by the position of the middle term in the premises.
(j) Mood of syllogism.
Ans : Mood has been define as the form of a syllogism, as determined by the quality and the quantity of the constituent premises.
SHORT AND LONG TYPES QUESTIONS ANSWERS
3. Answer the following :
(a) What is immediate inference ?
Ans : Immediate inference is a kind of deductive inference, in which the conclusion follows from only one premise.
(b) Can a proposition be converted simply?
Ans : A proposition can be said to be converted simply . In simple conversion, the quantity of the converse is the same as the quantity of the converted. If we can draw an A proposition from an Á proposition by conversion, in ordinary sense this is not possible., Because if the converse be an A proposition, its subject will be distributed though that term which is the predicate of the convertend, is not distributed therein. But, certain exceptional kinds of a A proposition which the subject and the predicate have the same denotation, there simply conversion of a proposition is possible.
For example : Everest is the highest mountain. (A)
The highest mountain is Everest. (A)
(c) What is material obversion?
Ans : Material obversion is the process of drawing obverse inference which are justified only on an examination of the matter of the proposition.
(d) How many propositions are there in a logical syllogism? Explain.
Ans : In a logical syllogism, there are three propositions viz., two given propositions and the proposition which is inference from the given propositions.
The inferred propositions is called the conclusion, and the two given propositions, from which the conclusion is drawn, are called the premises. The major term occurs in Major Premise and the minor term occurs in Minor Premise. In a syllogism, the major premise in given first, the minor premise comes next and last of all comes the conclusion.
(e) How many term are there in a logical syllogism? Explain.
Ans : There are three different terms in a logical syllogism, each of which occurs twice. The predicate of the conclusion is called the major term, the subject of the conclusion is called the Minor term and that term which occurs in both the premises, but does not occur in the conclusion, is called the Middle term. The Major and Minor terms are called Extermes, to distinguish them from the Middle term.
4. Distinguish between :
(a) Immediate inference and mediate inference.
Ans : Immediate Inference is a kind of deductive inference, in the conclusion follows from only one premise. For example No men are perfect No Perfect beings are men In Mediate Inference, the conclusion follows from more than proposition. The form of Mediate Inference is called ‘Syllogism’.
For example : No perfect beings are mortal
All men are mortal
∴ No men are perfect beings.
(b) Simple conversion and conversion per accidens.
Ans : In simple conversion, the quantity of the converse is the same the quantity of the convertend, ic, to say if the convertend universal, the converse also is universal, and if the converter be particular, the converse is also particular. Thus E proposition and I propositions are converted simply.
In conversion per accidens, the quantity of the converse different from the quantity of the convertednic, the converter is universal but the converse is particular. Thus A proposition which yield I propositions as conclusion, are converted accidens.
5. Give example :
(a) Simple conversion.
Ans : No man is perfect (E)
No perfect beings are men (E)
(b) Material Obversion.
Ans : War is productive of evil
Peace is productive of good.
(c) Fallacy of Four terms.
Ans : My hand touches the table.
The table touches the floor.
My hand touches the floor.
(d) Syllogism.
Ans : All men are mortal
Socrates is a man.
Socretes is mortal.
(e) Conversion per accidens.
Ans : All men are mortal. (A)
Some mortals are men (1)
(f) Obversion-
Ans : All men are mortal (A)
No men are non-mortal
6. Short notes :
(a) Figure.
Ans : Figure is the form of a syllogism as determined by the position of the middle term in the premises.
There are four figures of syllogism :
(i) First Figure :- In the first figure, the middle term is the subject in the major premise and predicate in the minor premise.
(ii) Second Figure :- In the second figure, the middle term is the predicate in both the premises.
(iii) Third Figure :- In the third figure, the middle term is the subject in both the premises.
(iv) Fourth Figure :- In the fourth figure, the middle term is the predicate in the major premise and subject in the minor premise.
(b) Copula.
Ans : A proposition consists of three parts, viz, two terms and the sign of relation between these two terms. This sign of relation between
the subject term and the predicate term is known as the copula, The copula is sign of affirmation or denial. In the proposition “Man is mortal’, the subject term is ‘man’, the predicate term is *mortal’, while ‘is’ stands as the sign of relation constituted the copula. The copula may be affirmative or negative. But it should be in the present tense of the verb to be.
(c) Mood.
Ans : Mood has been defined as the form of syllogism, as determined by the quality and the quantity of the constituent premises. As there are four kinds of propositions and every syllogism has two premises. So, we have sixteen moods in each figure. There are all together four figures – so we have 16×4 =64 possible moods. Again, if we take the conclusion with the premises, then there are three propositions and therefore each of the 64 combinations have four forms. Thus is all the four figures, there are 64 02154 = 256 moods. But all of these moods are not valid. Only those combinations which yield valid conclusions are valid moods. In this sense, only 19 moods are valid.
(d) Middle term.
Ans : The term which occurs in both the premises, but does not occur in the conclusion, is called the Middle term. The Middle terms occurs in both the premises and the common element between them. The conclusion seeks to establish a relation between the major term and the minor term.
The middle term performs the function of an intermediary, a person who, as it were, is known to both these strangers, and brings about an introduction between these strangers. Thus in the major premise, the major terms is compared with the middle term, and in the way. ultimately in the conclusion a relation is established between the major term and the minor term. The middle term is a mediating term by which we pass from premises to conclusion.
(e) Material obversion.
Ans : Bain describes a process of inference, which is known as Material obversion. It is a process in which, “there are obverse inferences justified only on an examination of the matter of the proposition.” For example ;
Knowledge is good
Ignorance is bad.
Bain recognises that these inference are entirely different from the formal inference of obversion. None of the rules of obversion has been followed, here. In obversion, the subject of the obverse is the same as the subject of the given proposition, but in material obversion they are contraries. In obversion, the predicate of the obverse is the contradictory of the predicate of the obvertend, whereas, in material obversion the predicates are also contraries. Again, is material obversion the quality is the same, but is obversion the quality of the conclusion is the opposite of the quality of the given proposition. These inferences are not formal inferences, but material inferences based on experience and knowledge and so it is outside the scope of Deductive Logic.
(f) Fallacy of four terms.
Ans : According to the General Rule of Categorical Syllogism- every syllogism must contain three, and only three terms.’ So, we see that a syllogism consists of three terms- the major term; the minor terms and the middle term, each of which occurs twice. A violation of this rule gives rise to an error of fallacy known as the fallacy of four terms.
(g) Structure of a syllogism.
Ans : A syllogism consists of three proposition, viz, two given propositions and the proposition which is inferred from the given propositions. The inferred proposition is called the conclusion and the two given propositions from which the conclusion is drawn are called the premises.
Each proposition consists of two terms. Therefore, a syllogism consists of three propositions should consist of six terms. But find that a syllogism consists of three terms, each of which occur twice.
The predicate of the conclusion is called the Major Term, the subject of the conclusion is called the Minor Term and that ter which occurs in both the premises, but does not occur in the conclusion is called the Middle term
The Middle term occurs in both the premises and in the common element between them. The conclusion seeks to establish a relation between the major term and the minor terrì. In the major premise, 7. the major term is compared with the middle term and in the minor premise, the minor term is compared with the middle term and A thereby in the conclusion a relation is established between the major and the minor term.
For example :
All men are mortal
All kings are men
∴ All kings are mortal.
The term “mortal’ is the major term, the term “kings’ is the minor term and the term ‘men’ is the middle term. The first premise ‘All men are mortal is the major premise, the second premise, ‘All kings are men’ is the minor premise. And the last proposition All kings are mortal’ is the conclusion.
The symbol M stands for the Middle term, S stands for the Minor term, and P stands for the Major term.
(h) Conversion by negation.
Ans : According to the rule ‘O’ proposition can not be converted. Some lovicians seek to convert an ‘O’ proposition, by a process of conversion by negation. They first of all reduce the ‘0’ proposition to an T proposition, by transferring the sign of negation to the predicate and then convert it. Thus –
Some S is not P.(O)
∴ Some S is not, P.(I)
∴ Some not-P is S. (I)
But the form of argument cannot be called conversion at all. Because, the conclusion is different from that of the given proposition. Again, the subject of the conclusion is not the predicate of the premise, but its contradictory.
7. Answer the following Questions :
(a) What is inference? Explain the various types of inference.
Ans : Inference is the process of passing from one or more propositions to another, which is justified by them and the product is called an inference.
Inference have been broadly divided into Deductive and Inductive. In Deductive Inference, the conclusion can not be more general than the premise or premise while in Inductive Inference, the conclusion must be more general than the premises. So in Deductive Inference we pass from the general to the particular.
For example :
All men are mortal.
All kings are men
∴ All Kings are mortal.
In Inductive Inference we pass from particular to general i.e. from ‘some’ to ‘all’.
For example :
Socrates is mortal
Kant is mortal
Sartre is mortal.
∴ All men are mortal.
(b) What is Deductive Inference? Explain its significance.
Ans : In Deductive Inference the conclusion can never be more general than the premise or premises.
For example :
All philosophers are mathematician.
Descartes is a philosopher.
∴ Descartes is a mathematician.
The significance of Deductive Inference :- The significance of Deductive Inference follows from one or more premises. The conclusion necessarily follows from the premises as the conclusion is implicitly contained in the premise. The conclusion can not be more general than the premises. Again, if the premises are true, the conclusion must also be true. The aim of Deductive Inference is to prove the formal truth and not at all concerned with the material truth of the conclusion.
(c) What is Inductive Inference? Explain its significance.
Ans : In Inductive Inference the conclusion must be more general than the premises.
For example :
Socrates is mortal.
Aristotle is mortal.
Plato is mortal
∴ All men are mortal.
Significance of Inductive Inference :- In Inductive Inference the conclusion follows from move than one premise As the conclusion is not implicitly contain in the premise, So the conclusion does not necessarily follow from the premises. The conclusion is more general than the premises i.e. the conclusion goes beyond the premises. So, the truth of the premises can not prove the truth of the conclusion. Although the conclusion can not prove the truth, yet it can help in the discovery of the truth.
(d) What are the differences between Deductive and inductive Inference.
Ans : In Deductive Inference we pass from the general to the particular. On the other hand, in Inductive Inference we pass from particular to general.
In Deductive Inference, the conclusion necessarily follows from the premises. But in Inductive Inference the conclusion do not necessarily follow from the premises.
The conclusion of the deductive inference can not be more general than the premises. But the conclusion of the Inductive Inference is always move general than the premises.
Deductive Inference is concerned with formal truth or validity truth of its constituent propositions. But Inductive Inference in concerned with material truth of its constituent propositions. Inductive Inference is related with both formal and material truth.
The conclusion of a valid Deductive Inference is always certain. But the conclusion of Inductive Inference is not alway certain, it may be probable.
But from the above differences between Deductive and Inductive Inference we see that the difference is not fundamental. The common aim of both Deductive and Inductive Inference consists in the unification of the particular and the universal into a common system. In fact, Deduction and Induction are supplementary to each other. Deduction assumes a universal proposition as one of its premises and that universal proposition is established by induction in its inductive process. Again, the universal proposition which is established in induction is verified by deduction by applying it to particular facts is its deductive process. So Deduction and Induction are not opposed to each other. But one depends upon the other and both are the two important forms of argument for the attainment of truth.
(e) What is Deductive Inference? What are the various types Deductive Inference?
Ans : In Deductive Inference the conclusion follows from one or mor than one premise.
Deductive Inference is of two types :
(i) Immediate Inference.
(ii) Mediate Inference.
(i) Immediate Inference :- Immediate Inference is a kind of Deductive Inference, in which the conclusion follows from only one premise. The chief function of Immediate Inference is to bring out the full implications of a given proposition. So, we can say that Immediate Inference certainly leads from something known to something unknown.
(ii) Mediate Inference :- In Mediate Inference, the conclusion follows from more than one proposition. There are only two premises, and the conclusion follows from them jointly. The form of mediate inference is called “Syllogism”. The conclusion of syllogism can not be more general than the premises.
(f) What is Immediate Inference? Explain the difference between Immediate and Mediate Inference?
Ans : Conversion is a kind of Immediate Inference, in which there is a legitimate transposition of the subject and the predicate of a proposition.
For example :- Converted- All men are mortal (A).
∴ Converse-Some mortal beings are men.(I)
The rules of conversion are as follows :
(i) The subject of the coinvertend becomes the predicate of the converse
(ii) The predicate of the covertend becomes the subject of the converse.
(iii) The quality of the converse is the same as that of the convertend i.e. to say, if the covertend be affirmative, the converse is affirmative, and if the convertend to Negative, the converse is negative.
(iv) No term can be distributed in the converse, unless it is distributed in the convertend.
When we apply the rules in four kinds of proposition, the converse of a proposition is an I proposition.
For example :
All men are mortal (A)
∴ Some mortals are men (1)
The converse of E proposition is-
No men are perfect (E)
∴ No perfect beings are men (E)
The Converse of I proposition is-
Some men are wise (I)
∴ Some wise beings are men (T)
The converse of O proposition- is
Some men are not intelligent (O)
∴ Some intelligent persons are not men.
| Sl. No. | Contents |
| Unit – 1 | Logic |
| Unit – 2 | Proposition |
| Terms | |
| Proposition | |
| Transformation of Ordinary Sentences to Logical Proposition | |
| Distribution of a term is a logical Proposition | |
| Modern Classification of Proposition | |
| Unit – 3 | Inference, Categorical Syllogism |
| Inference | |
| Categorical Syllogism | |
| Unit – 4 | Symbolic Logic |
| Unit – 5 | Philosophy |
| Unit – 6 | Indian Philosophy |
| Unit – 7 | Theory of Knowledge |
| Rationalism & Empiricism | |
| Pramāna: Pratyaksa and Anumana | |
| Unit – 8 | Realism and Idealism |
| Realism | |
| Idealism |
(g) What is conversion? Explain the rules of conversion.
Ans : Conversion is a kind of Immediate Inference, in which there is a predicate of a legitimate transposition of the subject and the proposition.
For example: Converting- All men are mortal (A).
∴ Converse-Some mortal beings are men (1)
The rules of conversion are as follows:
(i) The subject of the coinvertend becomes the predicate of the converse.
(ii) The predicate of the covertend becomes the subject of the converse.
(iii) The quality of the converse is the same as that of the convertend i.e. to say, if the covertend be affirmative, the converse is affirmative, and if the convertend to Negative, the converse is negative.
(iv) No term can be distributed in the converse, unless it is distributed in the convertend.
When we apply the rules in four kinds of proposition, the converse of a proposition is an I proposition.
For example :
All men are mortal (A)
∴ Some mortals are men (1)
The converse of E proposition is
No men are perfect (E)
∴ No perfect beings are men (E)
The Converse of I proposition is
∴ Some men are wise (1)
Some wise beings are men (T)
The converse of O proposition is
Some men are not intelligent (O)
∴ Some intelligent persons are not men.
(b) What is obversion? Explain the rules of obversion.
Ans : Obversion is a kind of Immediate Inference, in which there is a a change in the quality of the given proposition, while its meaning remains unchanged.
The rules of obversion are as following :
(a) The subject of the obverse is the same as the subject of the obverted
(b) The predicate of the obverse is the contradictory of the predicate of obverted,
(c) The quality of the obverse is the opposite of the quality of the obvertend, i.e. to say, if the obvertend be affirmative the obverse is negative and if the obvertend be negative, the obverse is affirmative.
(d) The quantity of the obverse is the same as the quantity of the obvertend, i.e., if the obvertend be universal, the obverse is also universal, and if the obverted be particular, the obverse is also particular
(i) What is conversion? Explain with example the various types of conversion.
Ans : Conversion is a kind of Immediate Inference, in which there is a legitimate transposition of the subject and the predicate of a proposition.
For example : Converting-All men are mortal (A)
∴ Converse-Some mortal beings are men (1)
And add the following conversion has two types, viz. simple conversion is the same as the quantity of the convertend i.e. to say, if the convertend be universal, the converse also is universal, and if the convertend be particular, the converse is also particular.
For example :
No man is perfect (E)
∴ No perfect beings are men (I) and,
Some men are intelligent (I)
∴ Some intelligent beings are men (I)
In Conversion per accidens, the quantity of the converse in difference from the quantity of the convertend i.e., the converted is universal but the converse is particular. Thus A proposition which yield I proposition as conclusion, are converted accidens.
For example : All men are mortal (A)
∴ Some mortal beings are men (1)
(j) What is Simple Conversion? Explain the cases where A proposition is converted simply.
Ans : Simple conversion is a form of conversion where the quantity of the converse is same as the quantity of the convertend.
A proposition can be said to be converted simply. In simple conversion, the quantity of the converse is the same as the quantity of the converted. If we can draw an A proposition from an A proposition by conversion, in ordinary sense this is not possible., Because if the converse be an A proposition, its subject will be distributed though that term which is the predicate of the convertend, is not distributed therein. But, certain exceptional kinds of a A proposition which the subject and the predicate have the same denotation, there simply conversion of a proposition is possible.
For example :
Everest is the highest mountain. (A)
∴ The highest mountain is Everest. (A)
(k) What is categorical syllogism? Explain its characteristics.
Ans : A categorical syllogism is a form of mediate deductive inference which consists of three categorical propositions and the conclusion. necessarily follows from two premises taken jointly.
Characteristics :
(i) Categorical Syllogism is a form of deductive inference. So, its conclusion can not be more general than the premises.
(ii) Categorical Syllogism is a form of mediate deductive inference. So its conclusion is drawn from more than one premise.
(iii) The conclusion of a categorical syllogism is deduced from two premises only.
(iv) The conclusion of categorical syllogism must be drawn from two premises taken jointly.
(v) All the propositions of a categorical syllogism are categorical propositions.
(vi) The truth of the conclusion depends on the truth on the premises.
(l) What is syllogism? Explain the structure of a syllogism.
Ans : A syllogism is a form of mediate deductive inference, in which the conclusion is drawn from two premises taken jointly.
Structure of Syllogism :- A syllogism consists of three proposition viz., two given propositions and the proposition which is inferred from the given propositions. The inferred proposition is called the conclusion and the two given propositions from which the conclusion is drawn, are called premises.
Each proposition consists of two terms. Therefore, a syllogism, which consists of three proposition should consist of six terms. On an examination of a syllogism, however, we find that it consists not six different terms but of three terms, each of which occurs twice.
The predicate of the conclusion is called the Major Term, the subject of the conclusion is called the Minor Term and that term which occurs in both the premises, but does not occur in the conclusion is called Middle Term. The Middle term occurs in both the premises and is the common element between them. The conclusions seeks to establish a relation between the major term and the minor term.
The premises in which the major term occurs is called the Major Premise and the premise in which the minor term occurs is called the Minor Premise.
The symbol M stands for the middle term, S stands for the Mini term and P stands for the Major term.
(m) What is middle term? Explain the function of a middle ten in a categorical syllogism.
Ans : The term which occurs in both te premises, but does not occur the conclusion is called the Middle Term.
Function of the Middle Term :- The Middle Term occurs i both the premises and is the common element between them, The conclusion seeks to establish a relation between the major term and the minor term which to begin with are, as it were, strangers to each other. The middle term performs the function of an intermediary, a person who, as it were, is known to both these strangers and bring about an introduction between these strangers.
But for this common friend, the major term and the minor term would remain strangers to each other for all time. In the major premise, the major term is compared with the middle term and in the minor premise the minor term is compared with the middle term and ultimately in the conclusion a relation is established between the major term and the minor term.
The middle term is thus a mediating term with which other terms are compared and is thus means by which we pass from premises to conclusion. The middle term having performed its function of bringing the extremes together, drops out from the conclusion Thus we reach the conclusion in a Syllogism by means of the Middle term.
(n) What is Figure? Explain with examples the various kinds of figure.
Ans : Figure is the form of a syllogism as determined by the position of the middle term in the premises. There are four possible arrangements of the middle term in the two premises and therefore, there are four figures of syllogism.
First figure :- In the first figure, the middle term is the subject in the major premise, and these predicate in the minor premise ;
thus,
MP All men are mortal
SM All kings are men
∴ SP All kings are mortal
Second figure :- In the second figure, the middle term is the predicate in both the premises; thus,
PM No perfect beings are mortal S
M All men are mortal
∴ SP No men are perfect beings
Third figure :- In the third figure, the middle term is the subject in both the premises; thus,
MP All men are rational
MS All men are mortal
∴ SP Some mortals are rational.
Fourth figure :- In the fourth figure, the middle term is the predicate in the major premise and the subject in the minor; thus
PM All men are animals
MS All animals are mortal
∴ SP Some mortals are men.
(o) What is mood? How many valid moods are there in all the four figures? Explain.
Ans : Mood has been defined as the form of a syllogism, as determined by the quality and the quantity of the constituent premises. There are 19 valid moods in all the four figures. We know that, there are four kinds of proposition A, E, I and O and a syllogism has got two premises. SO we have sixteen possible moods. As there are four figures- so we have 16 x 4 = 64 possible moods. Each of 64 combinations mentioned above may have four forms.
Thus, in thus sense there are 64×4=256 moods in all the four figures. But there are some logicians, who use the word ‘Mood’ in a highly restricted sense to mean only valid moods i.e. those combinations which yeild valid conclusion. So there are only 19 valid moods in all the four figures, if we taken into account the premises only.
8. Test the following :
(i) He must be coward, for he is dishonest and all cowards are dishonest.
Ans : Logical Forms :- All cowards are dishonest (A)
He is dishonest (A)
∴ He is a person who must be coward (A)
The given argument is fallacious. According to the rule of syllogism “middle term must be distributed at least once in the premises.” But here the middle term remains undistributed in both the premises as affirmative propositions do not distribute their predicate. So the argument involves “The Fallacy of Undistributed Middle.”
(ii) Only the Naiyayikas are philosophers. Since he is not aNaiyayika, he is not a philosopher.
Ans : Logical Form :- All philosophers are Naiyayikas (A)
He is not a Naiyayika (E)
∴ He is not a philosopher (E)
One premise being negative, the conclusion be negative. If we draw a E proposition in the conclusion, no syllogistic rule is violated, because the middle termin debuted in the common are also distributed in the respective premises Thalive its conclusion in the second time the name of the valid is Camesties.
(iii) An elephant han four legs. The table to his four les Therefore the table is also an elephant.
Ans : Logical Form :- All clephant has tou leyn (A)
The table is that which has fou leyn (A)
∴ The table is an elephant (A)
The above argument is invalid. Il involves “The Fallacy of Ambiguous Middle” Because the word ‘le’ which appears to be the middle term in both the premies has different aching, In the major promise the meaning of ley, an organ of a living being” but in the minor promiso the meaning of lexisland of a non living being”
(iv) Every man commits suicide, every man in rational. Therefore all rational beings commits suicide.
Ans : Logical Form :- All men are persons who commit suicide (A)
All men are rational
∴ All rational beings are persons who commit suicide
The abovo argument is invalid. According to the rule of syllogism “No term can be distributed in the conclusion unless it is distributed in the premises, “Here the minor term “rational” has been distributed in the conclusion as a subject of universal proposition, which is undistributed in the minor premise as a predicate of an affirmative proposition. So the argument involves the Fallacy of Illicit Minor.
(v) Gold is precious than silver, silver is precious than ini therefore gold is precious than iron.
Ans : Logical Form :- Gold is precious than silver (A)
Silver is precious than iron (A)
∴ Gold is precious than iron (A)
The above argument is invalid. According to the general rule syllogism “Every syllogism must contain only three terms.” here we have got tour different terms-
(a) Gold
(b) Precious than silver
(c) Silver
(d) Precious than iron
So, it involves “The Fallacy of Tour Terms.”
(vi) Aristotle is not Plato. Plato is a philosopher. Therefore Aristotle is not a philosopher.
Ans : Logical Form :- Aristotle is not Plato. (E)
Plato is a philosopher (A)
∴ Aristotle is not a philosopher (E)
The above argument is invalid. According to the general rule syllogism “No term can be distributed in the conclusion unless is distributed in the premises.” But here the minor ten “philosopher” has been distributed in the conclusion as a predictor of negative proposition, which is undistributed in the min premise as a predicate of affirmative proposition. So it involve “The Fallacy of Illicit Minor.”
(vii) He will get the job, for he is a player and only the eligible for the job.
Ans : Logical Form :- All persons eligible for the post are players. (A)
He is a player. (A)
∴ He is a person who will get the job. (A)
The given argument is fallacious. According to the general rule of syllogism-“the middle term must be distributed at least once in the premises.” But here the middle term “player’ remains undistributed in both the premises. As both the premises are affirmation propositions, which do not distribute their predicate. So, the argument involves the fallacy of undistributed middle.
(vii) God creates man, man creates sin hence God creates sin.
Ans : Logical Form :- All men are persons who created sin (A).
God is one who created man (A).
∴ God is one who created sin (A).
The given argument is fallacious. According to the general rule of syllogism- every syllogism must contain three and only three terms. But here we get four different terms-
(i) Man.
(ii) Persons who created sin.
(iii) God.
(iv) One who created man.
So, the argument involves the Fallacy of Four Terms.
(ix) He must be a philosopher, because he is honest and all philosophers are honest.
Ans : Logical form :- All philosophers are honest (A)
He is honest. (A)
∴ He is a person who must be a philosopher. (A)
The given argument is invalid. According to the rule of syllogism “middle term must be distributed at least once in the premises.” But here the middle term ‘honest remains undistributed in both the premises as affirmative propositions do not distribute their predicate. So the argument involves “The fallacy of Undistributed Middle.”
(x) He must be intelligent, for he is straight forward and only the straight forward are intelligent.
Ans : Logical Form :- All intelligent persons are straight forward. (A)
He is straight forward (A).
∴ He is a person who must be intelligent.
The above argument is invalid. According to the rule of syllogism “middle term must be distributed at least once in the premises.” But here the middle term “straight forward” is undistributed in both the premises. Because both the premises are affirmative proposition which distributes subject only and the position of the middle term is predicate in both the premises. So it involves “The Fallacy of Undistributed Middle”.
(xi) All men are not industries but he is industrious. So, not be a man.
Ans : Logical Form :- Some men are not industrious (O)
He is industrious (A)
∴ He is not a man (E)
The above argument is invalid. According to the general rule of syllogism – “no term can be distributed in the premises.” Here the major term “men” has become distributed in the conclusion as it is E proposition. Which distributes both subject and predicate. But the same term was undistributed in the major premise as it is proposition, which distributes predicate term only and not the subject. So it involves the Fallacy of Illicit Major.
9. State three general rules of syllogism.
Ans : Three general rules of syllogism are as follows :
(i) Every syllogism must contain three and only three terms.
(ii) Every syllogism must contain only three propositions.
(iii) The middle term must be distributed at least once in the premises .
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In science inference is one of the ways of knowing the truth, Logic must be made as one of the core or compelsory subjects for science students
Logic should be included as a core or compelsary subject for our science stydents