Aristotelian Syllogistic Division
 

Kinds of Division

• Logical division divides a class into its subclasses
– E.g., mammals into monotremes, marsupials & placentals
– Division is useful for
• determination of exact relationships among related things
• formulation of definitions

• Other kinds of division

– Physical division divides a whole into its parts
• E.g., a complex machine into its simple mechanical parts

– Metaphysical division divides an entity into its qualities, 

• e.g.,a species into its genus & difference
– man into animality & rationality
• a substance into its attributes
– sugar into color, texture, solubility, taste, &c.
• a quality into its dimensions
– sound into pitch, timbre, volume

How to Divide

• Logical Division

– begins with a summum genus
– proceeds through intermediate genera
– ends at the infimae species
– NB: It does not continue to individuals

• The results of division should meet these criteria:

1. The subclasses of each class should be coextensive with the
original class.
2. The subclasses of each class should be mutually exclusive.
3. The subclasses of each class should be jointly exhaustive.
4. Each stage of a division should be based on a single principle.

Kinds of Classification

• Classification is the technique of inquiry in which similar individuals and classes are grouped into larger classes.
– E.g., how are steam, diesel, & gasoline engines related to one another?

Natural Classification

• Natural classification is a scheme that provides theoretical understanding of its subject matter
– E.g., classification of living things into monerans, protistans, plants, fungi and animals
• The concept “monerans” is now obsolescent because it does not provide sufficient theoretical clarity.

Artificial Classification

• Artificial classification is a scheme established merely to serve some particular human purpose
– E.g., classification of plants as crops, ornamentals, and weed

Classification and Division Compared

• The result of a classification will look like the result of a division.
• Classification begins with a individuals or small classes and works
towards a summum genus.
– i.e., it works in the direction opposite to that of division
• Classification begins with a set of apparently related things found in
the world (i.e., it is based on experience) and builds from there.
– Hence, it is well-suited to natural objects.
– But it will work with any kind of object.

Two Overly Ambitious Ideals

• Pure division
– begins with the summum genus and
– divides on the basis of a priori considerations
• i.e., it is based on logical possibility, not experience

• Dichotomous division
– divides on the basis of the presence or absence of a particular feature
• (NB: Classification can also be dichotomous.)
• Striving for these ideals
– works well with mathematical objects, &c.
– does not work well with natural objects (e.g., kinds of animals)
– guarantees a division that meets criteria (2) – (3)
– sometimes provides more insight than alternative divisions.
• But “ dichotomous division is often difficult and often impracticable”—Aristotle, Parts of Animals I.2-3
• Sometimes, class Rules notification (a bottom-up approach) is more practical.

 RULES OF DIVISION:

When we are using logical division, we need to follow certain rules. thesde are as follows:

1. One division must follow only one criteria. It must be either physical or metaphysical.
2. The division criteria must be mutually exclusive and collectively exhaustive.
3. All the parts of an entity being explained must be covered by the division.
4. No extra members must be suggested as parts of the entity explained during the process of division.

FALLACIES OF DIVISION:

 

When we fail to follow the above rules, we end up in committing the following fallacies:

1. Division by cross criteria: When we divide something by using two or more criteria at the same time, we commit this fallacy. e.g. when we divide Indians into "Hindus, Muslims, Christians, Sikh, Rich, poor, Tall, short, Fair, Dark, introverts and extroverts"; we are committing this fallacy as we are using many criteria, both of physical as well as metaphysical divisions at the same time. at the same time. 
2. Too narrow division: when we exclude some of the members from the group or some qualities of the entity being explained, we commit this fallacy. e.g. Quadrilateral into, square and rectangle. Here we exclude many other types of quadrilaterals and so the division becomes too narrow as it leaves out many other members that actually belong to this group.
3. Too wide division: when we include some members that actually do not belong to the group as we are dividing, our division becomes too wide. e.g. birds into single coloured & multi-coloured. Here, many other single coloured and multi-coloured things and beings get indicated as part of the group of bired, so it is a too wide division.

Deduction versus Induction

We cannot fully understand the nature or role of inductive syllogism in Aristotle without situating it with respect to ordinary, “deductive” syllogism.  

Aristotle’s distinction between deductive and inductive argument is not precisely equivalent to the modern distinction.  

Contemporary authors differentiate between deduction and induction in terms of validity.  (A small group of informal logicians called “Deductivists” dispute this account.)  

According to a well-worn formula, deductive arguments are valid; inductive arguments are invalid. 

The premises in a deductive argument guarantee the truth of the conclusion: if the premises are true, the conclusion must be true.  The premises in an inductive argument provide some degree of support for the conclusion, but it is possible to have true premises and a false conclusion.  

Although some commentators attribute such views to Aristotle, this distinction between strict logical necessity and merely probable or plausible reasoning more easily maps onto the distinction Aristotle makes between scientific and rhetorical reasoning (both of which we discuss below).  

Aristotle views inductive syllogism as scientific (as opposed to rhetorical) induction and therefore as a more rigorous form of inductive argument.

We can best understand what this amounts to by a careful comparison of a deductive and an inductive syllogism on the same topic.  

If we reconstruct, along Aristotelian lines, a deduction on the longevity of bileless animals, the argument would presumably run: All bileless animals are long-lived; all men, horses, mules, and so forth, are bileless animals; therefore, all men, horses, mules, and so forth, are long-lived.  

Defining the terms in this syllogism as: Subject Term, S=men, horses, mules, and so forth; Predicate Term, P=long-lived animals; Middle Term, M=bileless animals, we can represent this metaphysically correct inference as:  Major Premise: All M are P.  Minor Premise: All S are M.  Conclusion: Therefore all S are P.  (Barbara.)  

As we already have seen, the corresponding induction runs: All men, horses, mules, and so forth, are long-lived; all men, horses, mules, and so forth, are bileless animals; therefore, all bileless animals are long-lived.  Using the same definition of terms, we are left with:  Major Premise: All S are P.  Minor Premise: All S are M (convertible to All M are S).  Conclusion: Therefore, all M are P.  (Converted to Barbara.)  

The difference between these two inferences is the difference between deductive and inductive argument in Aristotle.

Clearly, Aristotelian and modern treatments of these issues diverge.  As we have already indicated, in the modern formalism, one automatically defines subject, predicate, and middle terms of a syllogism according to their placement in the argument.  

For Aristotle, the terms in a rigorous syllogism have a metaphysical significance as well.  In our correctly formulated deductive-inductive pair, S represents individual species and/or the individuals that make up those species (men, horses, mules, and so forth); M represents the deep nature of these things (bilelessness), and P represents the property that necessarily attaches to that nature (longevity).  Here then is the fundamental difference between Aristotelian deduction and induction in a nutshell.  

In deduction, we prove that a property (P) belongs to individual species (S) because it possesses a certain nature (M); in induction, we prove that a property (P) belongs to a nature (M) because it belongs to individual species (S).  Expressed formally, deduction proves that the subject term (S) is associated with a predicate term (P) by means of the middle term (M); induction proves that the middle term (M) is associated with the predicate term (P) by means of the subject term (S).  

Aristotle does not claim that inductive syllogism is invalid but that the terms in an induction have been rearranged.  In deduction, the middle term joins the two extremes (the subject and predicate terms); in induction, one extreme, the subject term, acts as the middle term, joining the true middle term with the other extreme.  This is what Aristotle means when he maintains that in induction one uses a subject term to argue to a middle term.  

Formally, with respect to the arrangement of terms, the subject term becomes the “middle term” in the argument.

Aristotle distinguishes then between induction and deduction in three different ways.  First, induction moves from particulars to a universal, whereas deduction moves from a universal to particulars.  The bileless induction moves from particular species to a universal nature; the bileless deduction moves from a universal nature to particular species.  Second, induction moves from observation to language (that is, from sense perception to propositions), whereas deduction moves from language to language (from propositions to a new proposition).  

The bileless induction is really a way of demonstrating how observations of bileless animals lead to (propositional) knowledge about longevity; the bileless deduction demonstrates how (propositional) knowledge of a universal nature leads (propositional) knowledge about particular species. 

Third, induction identifies or explains a nature, whereas deduction applies or demonstrates a nature.  The bileless induction provides an explanation of the nature of particular species: it is of the nature of bileless organisms to possess a long life.  The bileless deduction applies that finding to particular species; once we know that it is of the nature of bileless organisms to possess a long life, we can demonstrate or put on display the property of longevity as it pertains to particular species.

One final point needs clarification.  The logical form of the inductive syllogism, after the convertibility maneuver, is the same as the deductive syllogism.  In this sense, induction and deduction possess the same (final) logical form.  

But, of course, in order to successfully perform an induction, one has to know that convertibility is possible, and this requires an act of intelligence which is able to discern the metaphysical realities between things out in the world.  We discuss this issue under non-discursive reasoning below.

Laws of Thought

During the 18th, 19th, and early 20th Century, scholars who saw themselves as carrying on the Aristotelian and Medieval tradition in logic, often pointed to the “laws of thought” as the basis of all logic.  One still encounters this approach in textbook accounts of informal logic.  The usual list of logical laws (or logical first principles) includes three axioms: the law of identity, the law of non-contradiction, and the law of excluded middle.  (Some authors include a law of sufficient reason, that every event or claim must have a sufficient reason or explanation, and so forth.)  It would be a gross simplification to argue that these ideas derive exclusively from Aristotle or to suggest (as some authors seem to imply) that he self-consciously presented a theory uniquely derived from these three laws.  The idea is rather that Aristotle’s theory presupposes these principles and/or that he discusses or alludes to them somewhere in his work.  Traditional logicians did not regard them as abstruse or esoteric doctrines but as manifestly obvious principles that require assent for logical discourse to be possible.

The law of identity could be summarized as the patently unremarkable but seemingly inescapable notion that things must be, of course, identical with themselves.  Expressed symbolically: “A is A,” where A is an individual, a species, or a genus.  Although Aristotle never explicitly enunciates this law, he does observe, in the Metaphysics, that “the fact that a thing is itself is [the only] answer to all such questions as why the man is man, or the musician musical.” This suggests that he does accept, unsurprisingly, the perfectly obvious idea that things are themselves.  If, however, identical things must possess identical attributes, this opens the door to various logical maneuvers.  One can, for example, substitute equivalent terms for one another and, even more portentously, one can arrive at some conception of analogy and induction.  Aristotle writes, “all water is said to be . . .  the same as all water  . . .  because of a certain likeness.” If water is water, then by the law of identity, anything we discover to be water must possess the same water-properties.

Aristotle provides several formulations of the law of non-contradiction, the idea that logically correct propositions cannot affirm and deny the same thing:

“It is impossible for anyone to believe the same thing to be and not be.” 

“The same attribute cannot at the same time belong and not belong to the same subject in the same respect.”

“The most indisputable of all beliefs is that contradictory statements are not at the same time true.”

Symbolically, the law of non-contradiction is sometimes represented as “not (A and not A).”

The law of excluded middle can be summarized as the idea that every proposition must be either true or false, not both and not neither.  In Aristotle’s words, “It is necessary for the affirmation or the negation to be true or false.”  Symbolically, we can represent the law of excluded middle as an exclusive disjunction: “A is true or A is false,” where only one alternative holds.  Because every proposition must be true or false, it does not follow, of course, that we can know if a particular proposition is true or false.

Despite perennial challenges to these so-called laws (by intuitionists, dialetheists, and others), Aristotelians inevitably claim that such counterarguments hinge on some unresolved ambiguity (equivocation), on a conflation of what we know with what is actually the case, on a false or static account of identity, or on some other failure to fully grasp the implications of what one is saying.

INDUCTION:

Induction is a type of inference where we go from known to unknown or from less general to more general. Here, from the things that are known, we say something about things that are not known. This is the reason why in induction we always say something more than what we already know of. So, Induction, a form of argument in which the premises give grounds for the conclusion but do not make it certain. Induction is contrasted with deduction, in which true premises imply a definite conclusion, the conclusion of Induction is always probable. The probability rate changes as per strength of evidence. Unlike deductive arguments, inductive reasoning allows for the possibility that the conclusion is false, even if all of the premises are true. 

Induction is of two types, perfect and imperfect. Perfect induction takes support of deduction in later stages to establish a certain conclusion, while imperfect induction does not do this.

There are two main types of imperfect induction. they are, Simple enumeration and Analogy. 

Simple enumeration is a method of arriving at a generalization on the basis of uniform uncontradicted observation of something. This conclusion can be disproved by observing just one single contrary instance. Yet, the conclusion by simple enumeration is highly probable when the number of observed instances is really high. But if one is arriving at a conclusion on the basis of very limited observation, the conclusion is less probable and hence, it is termed as hasty generalization or illicit generalization.

Analogy is a type of imperfect induction where we are comparing two things, persons, groups or classes. while doing so, we observe some similarities and on the basis of these, we infer some further similarity, as we find an additional quality in one of the two compared things, persons, groups or classes. Here, if the observed similarities are relevant to the additional quality, then our conclusion is likely to be true and we may say that Analogy is good Analogy. But if the observed qualities are not relevant to the additional quality, then our conclusion about predicting the additional similarity is not likely to be true, so, we say that such an analogy is Bad Analogy.

In law, we need to use simple enumeration and Analogy to infer things from circumstantial evidence. Of them analogy is more useful in legal matters. Also, while using precedent law, we use analogy to indicate the support of past decided cases  in our matter.

When we see a person following some pattern of behavior or thinking or actions, while talking of the Modus Operandi of that person, we are using simple enumeration as we talk of the generalized pattern of behavior of that person. This is the method followed by criminal investigators quite often. They determine the Modus Operandi of a criminal to find out the criminal and / or to track the criminals. This is a very common practice used by the police in registering the crime record of certain criminals while maintaining their files.

While contesting any matter, the lawyers use analogy in arguing about similar matters, or actions done by an individual in similar situations, to infer about the truth of the statement given by any witness. For example, if it is shown that the witness had reacted in a particular way in the past in similar situations, or has reacted in a particular way in similar situation created in court, then, one can infer that he must have reacted exactly in same way when the actual event had happened that the witness was witnessing. This type of inference adds to the weight-age in argument in court.

Similarly, when we are arguing any matter, we may come across previously decided matters of same type in the same court, or higher court or another court. We use the citation of these matters as case law or precedent law to lead the judge to the conclusion we want, and the procedure of inductive argument that we use in this type of matter is of analogy. This is why is is said that Analogy is of great use in legal arguments.

University question papers compiled:

1.                   Answer the following questions in one or two sentences :-        20

1.                   Define ‘connotation’ and ‘denotation’ of a term.     (April 10)

2.                   Define ‘free’ and ‘bound’ variable.            (April 10)

3.                   Define ‘private nuisance’ as discussed in the law of courts.          (April 10)

4.                   Define “medical intervention.” (May 11)

5.                   Define “ Primary Induction “(May 11)

6.                   Define “Implications’ and ‘Implicate’. (May 11)

7.                   Define Analogy. (Oct 11)

8.                   Define immediate inference. Name 2 kinds of immediate inference.(Oct 11)

9.                   Define Nuisance. (March 2012)

10.               Define Physician.          (Oct 11)

11.               Define Positive and Negative terms. (May 09)

12.               Define Secondary Induction. (March 2012)

13.               Define terminally ill. (May 09)

14.               Define the law of Identity and the law of contradiction. (May 09)

15.               Distinguish between mediate and immediate inference.     (April 10)

16.               Distinguish between proposition and judgment. (May 11)

17.               Explain the meaning of denotation of a term. (March 2012)

18.               Give an example of deductive argument. (March 2012)

19.               Give any one definition of logic. (April 10)

20.               How is the constituent different from component? (May 11)

21.               Identify the inference involved in the following inference, giving reasons: The rich are lucky. Hence the poor are unlucky. (May 09)

22.               Identify types of inference involved & test its validity: A politician is a man. Hence we can conclude that good politician is good man. (April 10)

23.               Indentify the type of inference in following:   “All cars are vehicles .   All Indian cars are Indian Vehicles.” (March 2012)

24.               Name kinds of simple proposition according to modern logic. (Oct 11)

25.               Name the kinds of compound proposition according to modern logicians. (May 11)

26.               Name three laws of thought and define any one of them. (April 10)

27.               Name two limitations of ostensive definition.        (April 10)

28.               Reduce the following statement to logical form “Ramanuja was a great mathematician”. (March 2012)

29.               State any two characteristics of a proposition?     (Oct 11)

30.               State the Law of Excluded Middle. (March 2012) . (May 2011)

31.               Symbolize the statement as per Modern classification ‘Samson is not weak’.  (March 2012)

32.               What are catagorematic and   syncategorematic words? (May 11)

33.               What are necessary and contingent propositions? (Oct 11)

34.               What is ‘Fundamentum divisionis’?          (Oct 11)

35.               What is a deductive argument? Give one example.           (May 09)

36.               What is a proposition? State one characteristic of a proposition. (May 09)

37.               What is a relational proposition? Give an example. (May 09)

38.               What is a singular term? Give one example. (May 09)

39.               What is division by dichotomy?  (May 11)

40.               What is induction? Define secondary induction. (May 09)

41.               What is meant by ‘induction’?     (April 10)

42.               What is meant by ‘universe of discourse’? Give an example          (Oct 11)

43.               What is meant by “subjective connotation”?         (Oct 11)

44.               What is meant by obversion? (May 11)

45.               What is mediate inference? Give one example. (March 2012)

46.               What is Primary induction?         (Oct 11)

47.               What is propositional function? (May 09)

48.               What is sound argument?           (March 2012)

49.               When is an inductive inference said to be a ‘good’ one? (April 10)

 

2.                   Write short notes on any four of the following :-                         20

1.                   Coercion and misrepresentation as per the Indian Contract Act (May 09)

2.                   Connotation (May 09)

3.                   Contrary and Contradictory terms (Oct 11)

4.                   Conversion (May 09)

5.                   Deductive arguments (Oct 11)

6.                   Distribution of terms in A and O propositions (Oct 11)

7.                   Division by dichotomy (April 10)

8.                   Extensive definition (May 11)

9.                   Fallacy of too narrow and too wide definitions (May 09)

10.               Form and Content. (May 11)

11.               Fraud and undue influence as per the Indian Contract Act (April 10)

12.               Industry according to Labour Law. (May 11)

13.               Influence by Added Determinants and Inference by Complex Conception. (May 11)

14.               Lexical and stipulative definitions (Oct 11)

15.               Material observation       (April 10)

16.               Opposition of singular propositions (May 09)

17.               Physical and Metaphysical division. (May 11)

18.               Propositional function and proposition (Oct 11)

19.               Proposition, Fact and Judgment (April 10)

20.               Public Nuisance (Oct 11)

21.               Salient features of Simple Enumeration (April 10)

22.               Subject less and class-membership propositions (May 09)

23.               Sentence and Proposition. (May 11)

24.               Two rules and fallacies of a per genus et differentia definition (April 10)

3.                   Solve any two questions from a, b, c :-                                       12

(a)   Do as directed:

(i) Identify the following compound proposition and construct a truth table for it: - In case there is an earthquake, there will be destruction.

(Oct 11)

(ii) Construct a truth table for the following proposition. State its kind “if and only if you have merit, you will get admission.”            (April 10)

(iii) With the help of quantifiers, symbolise the following modern general propositions:-

1)                   Many lawyers are unsuccessful (Lx, Ux).(Oct 11)

2)                   Many politicians are not punctual ( Px, Nx)(April 10)

3)                   No scientist is dogmatic (Sx, Dx).           (Oct 11)

4)                   Planets move in an elliptical orbit (Px, Ex)           (April 10)

5)                   Tigers exist (Tx) (April 10)

(b) Reduce following sentences to logical form and identify and name disturbed term or terms, giving reasons:-

1.                   Birds fly. (April 10)

2.                   Few patients are courageous. (Oct 11)

3.                   Many dreams turn into realities (Oct 11)

4.                   Monkeys have a tail (Oct 11)

5.                   Never is a man perfect. (April 10)

6.                   Not all your wishes will be fulfilled.(April 10)

(c)     Answer the following questions, reducing sentences to logical form wherever required:-

(i)                   What is the sub alternate of “Natural calamities can never be controlled by man”?   (Oct 11)

(ii)                 What is the contradictory of “India lost the match against South Africa”?    (Oct 11)

(iii)                What inference by converse relation can be drawn from “Deepak is junior to Dilip”? (Oct 11)

(iv)               What is the Material Obversion of “Metals expand when heated”?  (Oct 11)

Attempt any two sub-questions a, b, or c :

a)                   Reduce the following to logic form and identify and name the distributed term or terms, giving reasons :

i)                     Never is a man perfect.  (April 10)

ii)                   Not all your wishes will be fulfilled.          (April 10)

iii)                  Birds fly.           (April 10)

b)                      

i)                     Construct a truth table for the following proposition. State its kind “if and only if you have merit, you will get admission.”            (April 10)

ii)                   With the help of quantifiers, symbolize the following modern general propositions :

(1)                 Tigers exist (Tx)            (April 10)

(2)                 Planets move in an elliptical orbit (Px, Ex)           (April 10)

(3)                 Many politicians are not punctual ( Px, Nx)          (April 10)

c)                    

i)                     Identify the definitions involved, giving reasons :-

(1)                 Sloth means laziness     (April 10)

(2)                 Animal means cats, dogs, monkeys, donkeys etc.           (April 10)

(3)                 For Mill, cause is a sum total of positive and negative conditions taken together which are invariably   precedent to the effect.               (April 10)

 ii)                   Identify the kind of division involved, giving reasons :-

(1)                  Manage into seed, skin, pulp.    (April 10)

(2)                 Educational Institutions into Universities and Colleges.     (April 10)

(3)                 Schools into aided, unaided, primary and secondary.        (April 10)

Solve any two sub-questions: 1, 2 or 3 :-

(a)                  Using the suggested notation, identify and symbolize the following general propositions with the appropriate quantifiers :

(i)                   All students do not take interest in studies. (Sx, Ix) (May 09)

(ii)                 Some gujratis are not dectors. (Gx, Dx). (May 09)

(b)                 Identify and construct a truth table for the following propositions:

(i)                   If today is Sunday, college is closed. (May 09)

(ii)                 The guests enjoyed the party and they left at night. (May 09)

(c)                 State the logical form and the truth values of the following propositions assuming the given proposition to be false.

(i)                   The sub alternate of “All rich girls are beautiful” (May 09)

(ii)                 The contrary of “No elephants are tiny” (May 09)

(iii)                The contradictory of “Some cases are complicated” (May 09)

3. Attempt any 2 questions from “A”,“B”or“C”:-                                  12

A) Reduce the following statements to logical form and name the term that is distributed:-

i) Any son is younger than his father (May 11)

II) Roses are always pink

III) Some people cannot climb Mount Everest. 

B) i) Indentify the following proposition and construct a truth table for it.

     He is both a singer as well as a dancer.

   ii) Indentify and symbolize the following simple proposition as per modern logicians:-

       1) A rose is fragrant

       2) Lokamanya Tilak was a freedom fighter.

     3) The book is under the table.

c) Point out the relation of the second proposition to the first proposition in the following pairs of propositions :-

i) Some physicists are mathematicians.

  All mathematicians are physicists.

ii) All criminals are to be punished

    Some criminals are not be punished .

iii) Some students are lazy

    Some students are not lazy

iv) No saints are pious.

    All saints are pious .

v) China is not a democratic country.

   China is democratic country .

Vi) Some vegetarians are those who enjoy good health.

     No vegetarian are those who enjoy good health.

Solve any Two sub questions : A, B or C:   (March 2012)

A) Reduce the following sentences to logical form and indentify and name the

 terms distributed                                                                                                                          6

i) Not always Brain and beauty found together .

II) None of the Pigs are intelligent .

III) Many big cities have sky scrapers.

B)  I) Symbolize the following general propositions with quantifiers :                                            3

1) No Tiger have wings ( Tx  Wx)

2) A few hospitals have good facilities (Hx, Fx)

3) Every child is innocent (Cx, Ix)

II) Do as directed:                                                                                                                          3

1) State the material obverse relation of

 “ Men are strong . “

2) What is inference by converse relation of

‘ X is younger than Y’

3) What is the observe of

‘Some eggs are rotten ‘ 

C) I) Draw the square of opposition of propositions .                                                                          2

    II) Point out the relation of second proposition to the first proposition                                               4

        In the following pairs of proposition :-

1) No Britishers are Arabs.

   Some Britishers are not Arabs.

2) Some flowers are fragrant

    Some flowers are not Fragrant.

3) All tigers are ferocious

    No tigers are ferocious

4) No riots are desirable

    Some riots are desirable.

4.   Question (f) is compulsory attempt any 3 from rest :-                        48

a)                   What is Logical Division? State and explain the four processes which are not considered to be logical division.(Oct 11)

b)                   Explain with examples the square of opposition of propositions.(Oct 11)

c)                   What is Simple Enumeration? State its characteristics and value.(Oct 11)

d)                   What is Eduction? Explain with examples how conversion and obversion is applied to A,E,I,O propositions?(Oct 11)

e)                   Explain any two of the following concept :-

(i)                   A definition in figurative and obscure language.   (Oct 11)

(ii)                 Fraud as per Indian Contract Act.            (Oct 11)

(iii)                Truth and Validity of an argument.           (Oct 11)

(iv)               “Medical intervention” and “terminally ill”   (Oct 11)

               (f)  Identical the kind of simple or compound proposition and     represent its symbolic form:-

(i)                   Churchill was not a journalist, but the Prime Minister of England.   (Oct 11)

(ii)                 Neither x nor y can play cricket.  (Oct 11)

(iii)                This sheet of ice is thin. (Oct 11)

(iv)               An honest man hates corruption. (Oct 11)

(v)                 Picasso was a painter.   (Oct 11)

(vi)               If and only if he influence, he will get the job. (Oct 11)

4:  Question ‘f’ is compulsory, attempt any three from rest :-        48

a)                   Name the different kinds of simple and compound propositions according to modern logicians. Write examples and truth tables discuss any three kinds of compound propositions. (April 10)

b)                   Distinguish between inductive and deductive reasoning and explain in detail their value in a court of law.     (April 10)

c)                   Outline the main features of a good analogy with the help of examples. Explain the value of analogical reasoning in law.            (April 10)

d)                   Give an example and define singular proposition as per traditional logicians. With suitable examples explain the 4 fold classifications of propositions and the principle of quantity and quality.      (April 10)

e)                   State and explain the rules of logical division. Name the four process which are not considered to be logical division.            (April 10)

f)                     

(i)                   Give the contrary of ‘All rabbits are very fast runners’.      (April 10)

(ii)                 State the sub alternate and contradictory of ‘No television stars are chartered accountants’. (April 10)

(iii)                If ‘some toys are not suitable for little children’ is true, then give its relation to and truth of ‘some toys are suitable for little children. (April 10)

(iv)               Reduce the sentence to logical form and state its obverse and converse “Every equilateral triangle is an equiangular triangle. (April 10)

(v)                 Reduce the following sentence to logical form and draw the square of opposition in relation to it and write down each of the relations in proper logical form.’ Several judges resigned in protest’.     (April 10)

4:   Part ‘a’ is compulsory, attempt any 3 from the remaining :-      48

a)                    State whether the following statements are True or False, giving reasons :- (May 09)

(i)                   “Animals into those which live on land and those which live in water” is an example of too wide division.

(ii)                 The division of sewing machine into needle, wheel, belt, bobbin, is an example of verbal division.

(iii)                The division of Hindus into rich, poor, tall, and short is too wide definition.

(iv)               “Planet means Jupiter, Mars, Venus, Pluto” is a biverbal definition.

(v)                  “Agony means pain” is an example of a stipulative definition.

(vi)               “That chairs broken” is an example of an ostensive definition.

State and explain with examples the condition of a sound analogy. Explain the value of analogy in law. (May 09)

Define opposition. With the help of examples explain the square of opposition. (May 09)

Distinguish between inductive and deductive inference . How are they useful in law? (May 09

What is meant by distribution of a term? Explain with the help of Venn diagrams and examples the distribution of terms in A, E, I, O propositions. (May 09)

What is logical division? Explain the rules and fallacies of logical division. (May 09)

                                OR

What is per genus at differentiam definition? Explain with examples rules and fallacies of per genus at differentiam definition            (May 09)

4)  Question Number “4f” is Compulsory. attempt any 3 from rest      48

   

a) Distinguish between inductive and deductive arguments with the help of examples. Explain the use of these two kinds of arguments in Court of Law . (May 11)

b) Define a categorical proposition . What is meant by “distribution” of  a term ?

  Explain with the examples and Vinn diagrams, the distribution of terms in A, E, I, O propositions.

c) Outline the features of a good analogy . How is analogy related to Law?

d) State and explain the rules and fallacies of logical division giving suitable examples.

e) What is meant by “Education”? Discuss in detail the rules of obversion and the two types of conversion. Illustrate your answer with examples.

f) Identify the following modern definitions:-                                                                                6

i)  Look at the beautiful painting

ii) “ Between the devil and the deep sea “ means “ to be caught between two difficulties.”

iii) According to home “ Causation is nothing more than invariable sequence. “

iv) Flowers means roses, lilies, astors, lotuses etc.

v) Man is national animal.

vi) A palette means a board on which an artist mixes his colors .

Identify fallacies of per genus at differentitiam definitions in following examples:-                    6

i) Money is the honey of life

ii) Taxies are means of transport

iii) Man is rational animal who has studied logic

iv) Hue means colour 

v) Solid means not in form of gas or liquid.

vi) A judge is one who performs the functions of a judge.

4: Question “4f” is Compulsory.attempt any 3 from rest                      48   

a) Explain with examples the traditional Fourfold classification of propositions

   and the principles of Quality and Quantity of propositions. (March 2012)

b)  What is compound proposition ? State various kinds of compound propositions with examples and construct   truth-table for them .

c) What is definition ? What are the purposes of definition ? Explain with examples.

d) Define ‘ Logical Division ‘ and ‘ Division by Dichotomy’ .  Give an example of Division by Dichotomy and state its advantages and disadvantages  .

e) State the Characteristics of Simple Enumeration and evaluate critically the process of simple enumeration with examples.

f)

 i) Indentify the fallacies involved in the following definitions ; giving reasons :        6

1) A bachelor is a young unmarried male.

2) A lecturer who has tongue in your ear and faith in your patience.

3) Music is food for soul.

     ii) Indentify the fallacies of logical division, in the following given reasons :          6

1) Sportsmen into cricketers, hockey-players, foot-ballers  and chess-players.

2) Cars into sports cars, expensive cars and small cars.

3) Doctors into allopathic and Ayurvedic.