Brief Answers 1) Define Logic. What are traditional and modern definition of logic, and why they where rejected? ‘All our lives we are giving and accepting reasons. Reasons are the coin we pay for the belief we hold.’ -Edith Watson Schipper. Simply stating logic is an art and science of correct thinking or presenting it in most simple word, Logic is the study of the methods and principles used to distinguish correct reasoning from incorrect reasoning. It took birth by sole and hard work of Aristotle; that became the very mould of medieval thought; it nevertheless trained the intellect of adolescent Europe to reasoning and subtlety and constructed the terminology of modern science. It is derived from Greek word ‘logy’ or ‘logos’ which means method of every science of every discipline and every art, as reason or expression of reason in words, that is, discourse. Looking to its wide ranging alpha and omega and placing specific rules like physics or mathematics. Traditional logicians claimed logic asThe science that investigate the general principles of valid thought. They felt logic as systematic enquiry into principles that helps to disciplines thought to distinguish between correct and incorrect thinking. But it over claimed and failed as thought is not mere correct or incorrect rather it includes imagination dreaming and day dreaming, what is not a task of logician, rather it is task of psychologist. Hence it was too wide definition. To over-come this problem Cohen and Nagel performed arduous task and develop definition asThe science of implication or of valid inferences (based on such implication) But here definition went too narrow as implication is only limited unto deductive argument, while logic also includes inductive arguments. And finally it takes mould, it was been observed that no logician is bound to say my content is only true, and else false. Rather logician just gets an opportunity to practice the analysis of arguments and construct arguments. On this basis logic was defined asThe study of the form of valid argument This definition includes particularly thought related to argument, deductive as well as inductive, serving the purpose of logician. 2) Distinguish between Deductive and inductive. Ans.- Deduction is ‘nothing doubtful’ (Frege) Induction is ‘to enquire what is nature of evidence which assures us of any real existence and matter of fact, beyond the present testimony of our senses, or the records of our memory’. (D. Hume) (Traditional logicians also regarded deduction and induction as two processes of reasoning that was, inverse. Argument is classified into 1) Deductive and other 2) inductive, they can be distinguish as1) DefinitionsDeductive- When the premises of an argument claim to provide sufficient evidence for the conclusion, the argument is said to be deductive argument.
Inductive- It is an inference which claims to provide some evidence for the conclusion. 2) EvidenceDeductive provide sufficient evidence for conclusion. Inductive does not provide sufficient evidence and goes beyond premises. 3) PropertyDeductive is judged as valid or invalid Inductive is said to be true or false (Many logicians feel deductive if formally valid and inductive is materially valid) 4) Truth In deductive argument premises implies conclusion. So, if premises are true conclusion must be true. In inductive argument conclusion depends upon the soundness and probability of evidence. 5) Certainty Deductive arguments are certain. (its conclusion is beyond doubt) Inductive arguments are probable, and therefore Bennett and Baylis call them ‘empirically probable argument’. And they can be rejected on discovery of contradictory instances. 6) DerivationDeductive is derived from general to particular (though modern logician disagrees with it). Inductive is derived from particular to general. Therefore it is even called leap in dark. 7) ExampleWrite your own example. Relation of deductive and inductive and LawNot only content of law or argumentation in law related to logic, but even procedure of courts are related logic. Basically there are two types of courts Trial and Appellate, and their function is similar to that of inductive and deductive respectively. Let us analyses the function of to courtsA) Trial courtsIt has five steps1) First instance is filed here, and case is either accepted or rejected. If accepted then, 2) Documentation is made that is gathering material, evidences and argumentation. 3) Argumentation is done on previous case law and if it is not enough. 4) Then hearing take place, where a) Examination-in-chief, and b) cross-examination, takes place. 5) Judgments are given on base of observed facts. B) Appellate courtWhen plaintiff is not satisfied by trial court decision, then he appeals in higher court, and that is Appellate court. Here no argumentation is as such, no examination or cross-examination of evidence take place. Just the file of trial court is considered, and on base of it verdict is given, and if necessary reverts the case to lower authority for reconsideration on technical flaws like wrong clause may be applied or something may be overlooked etc. From the above distinction it is quite clear, that in Trial courts premises are gathered, and we observe its relevance, and conclude as the given premises have certain
similarity, so it will be continued further. Hence it is clearly seen trial courts are adapted by inductive procedure. But in Appellate court, premises is lower courts judgement and documentation, and conclusion is merely on that base, there is no comparision and further resemblance accepted, it is direct from premise conclusion is derive. So appellate courts are adapted to deductive arguments. 3) Truth and validity. Ans.“Validity of argument is sometime confused with truth of conclusion” K.T. Basantani. The discussion concerning the nature of argument makes one arrive at the question of truth and validity. Defining the truth and falsehood in logic Copi says, it ‘characterizes propositions or statements and may also be said to characterize the declarative sentences in which they are formulated’. Looking to it one may feel that truth and validity are generally dependent on each other. But, they can be distinguished as1) Truth or falsity depends on fact. (if it is fact, then it is true and fact is absent then it is false) Validity depends on form. (if the relation between premises and conclusion are implying each other, then it is valid, or else invalid) 2) To verify statement to be true or false, one has to analyze its content or subject matter. To verify valid or invalid one has to check formal relation. 3) Truth is property of induction Validity is property of deduction 4) Brief with your own example. 4) Distinguish between inference and implication. Ans.- Cohen and Nagal pointed out logic as ‘the science of valid implication’ it created need to probe into inference and implication. 1) Inference is the process of deriving conclusion on base of premises in implication conclusion is derived because there are certain relations between premises and conclusion. 2) Inference is temporal. Implication is not temporal. 3) All inferences are not implication. All implication is inferences. 4) Inference is of two types deductive and inductive. Implication is just deductive. (In an inference the thinker proceeds from the premises to the conclusion. He does so, because he believes that there is a certain relationship between the premises and the conclusion. This relation is that of Implication. The IMPLICANS is the statement (or statements) which imply some other statement. IMPLICATE is the statement which follows from the implicans. If the relation between the premises and the conclusion of an inference is that of implication, then it could not be the case that the conclusion is
false when the premises are true. This means when the premises are true, the conclusion must also be true.) Examples 5) Differentiate between form and subject matter or content? Ans.- Logic deals with forms of valid argument, so form has primary importance in logic then subject matter, it can be distinguished as followsDefinition Form means structure of argument. In other words way in which the conclusion is derived from premises. Subject matter are sentences and it’s words that make argument, it is facts of arguments Meaning Form gives general idea of how conclusion can be derived from the premises Subject matter helps us to understand what each argument wants to say. Form itself makes sense or it can be said sense of argument is given by form Subject matter gets it sense by getting a particular form, it does not make sense alone Effects on change of arguments The form remains same though argument changes (there are few form only in which argument can be made Subject matter changes from argument to argument. Testing Form can be said as valid or invalid Subject matter can be said true or false Existence Form does not have physical existence, it is recognize by way premises are connected with each other and to conclusion It has physical existence and recognized by words used in it Examples All men are mortal Socrates is man Therefore Socrates is mortal In it form is A= B, B= C ; so A=C or say deductive In it words like Socrates , is , mortal etc are subject matter 6) Proposition and sentences Proposition and sentence is closely related as a Proposition is expressed in the form of a sentence. But it is not same as a sentence. The same Proposition may be expressed by different sentences. Eg: I am an Indian. Above three sentences are from three different languages, yet they convey the same Proposition. This is because Proposition is what a sentence states, and not the words in which the statement is made.
We know a Proposition is either true or false. But truth and falsity arises only with regard to what declarative or indicative sentences say. Therefore, all sentences do not express propositions. Eg: 1). Thief ! 2). What Thief would trust a thief ? Truth or falsity of above sentences not possible to determine so these sentences do not express propositions. So, we can say that, every sentence does not express a Proposition. But every Proposition is in the form of a sentence. 6. Distinction between Grammatical sentence and Proposition. Ans.- In common man’s language proposition is equal to sentence. But technically speaking proposition is ‘sentence that is either true or false’. So, it is clear that all propositions can be said sentence, but all sentences are not proposition. Grammatical sentences can be distinguished by proposition in following way Grammatical sentences are of four types a) Imperative, b) Interrogative, c) exclamatory and d) assertive or indicative, while proposition is only assertive or indicative type sentence. As language changes sentence is grammatically said to be different, while on change of language makes no difference in proposition Grammatical sense of subject- predicate understanding is different from logical one; also in grammatical sentence subject-predicate can change its position, but in proposition first subject and then predicate Grammatical sentence has two divisions only viz., subject and predicate, while proposition has one more part viz. copula (and has very important function) Grammatical sentence can have multiple subject as ‘time and tide waits for no body’ but proposition has only one subject, and if there are two subjects of propositions there must be two and not one proposition Grammatical sentence can be in past, present or future tense, but logical proposition must be in present tense only Grammatical sentence can be with or without any quantity or quality, but proposition must have one quantity and one quality Grammatical sentence can be true today and false tomorrow, but propositions truth and falsity must e universal i.e. if it is true then it must be true in all time and all places Lastly grammatical sentence can be expressed incompletely, while proposition has to be complete and definite to maintain its condition of true or false of universality. For example Sentence- ‘India has congress government. (it can be true now, but in past it was false, so it is not proposition in real sense) to be proposition it must beIndia has congress government on 13th of August 2006. A sentence has a physical existence, when spoken it is sound waves. When written other hand, a Proposition is what a sentence says. The Proposition has no physical existence. The logical form of a Proposition depends upon the statement that a Proposition expresses. On the other hand, grammatical form of a sentence is determined by
various considerations. Some of them have nothing to do with giving information. Eg: Expression, "United we stand, divided we fall", emphasizes the fact that unity is strength and disunity is weakness. 7) Constituent and component Ans.- Though Proposition is the basic unit of logic, it can be analysed into its elements. However, the elements into which a Proposition is analysed have no existence apart from the Proposition. These are called constituents. So, constituents can be defined as "the Elements into which a Proposition can be analysed are called its constituents". E.g.: Seeta is beautiful girl In above Proposition, 'Seeta' 'is' 'beautiful' are constituents of given proposition. A constituent is any element of a Proposition; it can be subject, object or copula. In every Proposition there is one element which combines the other elements. This combining element is called as Component. Eg: In Proposition, RAM LOVED SITA, 'LOVED' is combining element, i.e., Component. So, without combining element, there would be no Proposition. Difference between component and constituents:1. A component is universal, while the constituents it combines can be particulars. This is the reason, constituents and component combines may be changed, yet the Proposition would be meaningful. Eg: We will change individuals combined by the component 'loved' and still Proposition will be meaningful. Mother loved Children 1. Majnu loved Laila. In these, the component (combining element) 'loved' cannot be replaced by an individual. Thus, we may say that a particular can occur as a constituent, but it cannot be a component. 2. Every Proposition is about certain content (subject matter). And constituents indicate the content of a Proposition. Since the contents of propositions differ, their constituents too differ. However, even though propositions differ in their constituents, they may have the same form. E.g.:
1. Ram is honest 2. Rahul is tall 3. Raman is clever
All these above propositions assert that an individual possess a quality. Thus, the above propositions have different constituents, the relation between the constituents is the same. 3. The form of a Proposition depends upon the way the constituents are combined. That is to say, form of a Proposition depends upon the component. However, a component is
not to be identified with the words through which it is expressed. The following propositions have different component, though in all of them the component is expressed by the same word "is". 1. John is intelligent 2. Sonu Nigham is singer 3. A peacock is a bird In the first Proposition, the component is predication. The attribute of intelligence is affirmed to John. In second Proposition, the component is membership of a class. Sonu Nigham is a member of the class of singers. In the last Proposition, the component is class inclusion. The class of Peacocks is included in the class of birds. As the components in these propositions are different, these propositions are of different forms 8) Give brief account of traditional classification of proposition? Or categorical classification of proposition? Or four fold classification of proposition? Ans.- Immanuel Kant ‘the great philosopher, under the head of relation, classified propositions, into categorical, hypothetical and disjunctive amongst them, hypothetical and disjunctive are grouped under the head of conditional propositions. This was done to distinguish categorical propositions from compound. AS the name indicates conditional propositions imposes a provision or condition on simple categorical proposition. While ccategorical merely affirms or denies some facts. Traditional classification Of proposition
Compound
Hypothetical
Categorical
Disjunctive
Let us first see compound classification; there are two types compound proposition i.e. conditional proposition. It can be defined as one in which the assertion is made subject to some expressed condition.
1)
Hypothetical Proposition- It is one which presents a condition together with some consequences which follows from it. In other words it is ‘if-then’ sentence. For e.g.- If ram scores 95 in logic, then he will be awarded scholarship It does not refer to any actual instance; it only states on fulfillment of condition, result will follow. In hypothetical proposition there are two propositions, antecedent i.e. which states the condition and consequent which expresses consequence. So, hypothetical proposition is like- If antecedent then consequent
2)
Disjunctive proposition- It is one which states alternatives. In other words it is ‘either – or’ sentence. For e.g.- Either ram will go to Dubai or Hongkong. Each part of condition expressed here that is part before or and after or is called disjunct. In this example proposition is mutually exclusive, but there are some proposition like ‘Reyan will pass in logic or English’. Infact he can pass in both the subjects. So, Keynes calls it non-exclusive proposition, whereas, atleast one disjunct has to be true (and it means if both are true then also there is no problem
3)
Categorical proposition- It either affirms or denies a predicate of the subject absolutely. There is no condition and it is single, simple and nuclear sentence. If any sentence occurs with and then according to traditional logician, they are two proposition and must be segregated to give logical form.
There is a peculiarity in this proposition as it states about assertion of predicate relation with subject, it must state quantity and quality of the proposition as well. So, logician states that every proposition has one quantity and one quality. Whereasa) Quantity- It means reference of number of subject; rather it is to individual, complete class/group or part of the group. Hence there are three types of quantity
Universal- It refers to whole class. For e.g. – All Maharashtrian are Indian
Particular- It refers not only some, but everything that comes under 1 to 99.99. For e.g. – Some student are smarts.
Singular- It asserts about one single individual by using proper name or designation or pointing him out. For e.g. Logic Professor of D.Y. Patil
Law College is orator. But logicians classify it under universal proposition and states only two type b) Quality- It indicates that whether predicate is affirmed or denied by subject. In other words subject has any relation with predicate or not is indicated by quality. There are two type of quality
Affirmative- It means subject has relation with predicate. For e.g. ‘Some roses are red’. It indicates some roses exists that has quality of redness.
Negative- it is just opposite of affirmative i.e. denies the relation of subject and predicate. For e.g.
Looking to the whole aspect one quantity and one quality makes up 4- fold classification of categorical propositions asUniversal Affirmative (A) - In it some thing is affirmed of the whole subject. Looking to word Affirmo (affirmative) first vowel is adopted for its symbol i.e. ‘A’. It is affirmative sentence, with prefix ‘all’. E.g. – ‘All lions are animals’ Symbolized as SaP. Universal Negative (E) - In it something is denied of the whole subject. On base of word Nego (negative) first vowel is taken as its symbol i.e. ‘E’. It starts with prefix ‘No’. E.g.- No men is bird. Symbolised as SeP. Particular Affirmative (I)- In it predicate affirm part of the subject. It is symbolized by second vowel from word ‘affirmo’ i.e. ‘I’. It starts with prefix ‘some’. E.g. – Some roses are red. Symbolized as SiP. Particular Negative- In it predicate denies part of the subject. It is symbolized by second vowel of nego i.e. ‘O’. It starts with prefix ‘some’ and with copula ‘not’ is attached. E.g. – Some roses are not red. Symbolized as SoP. Using symbol ‘s’ for subject and ‘p’ for predicate, we can represent this proposition in following wayUniversal Affirmative (A) - All S is P Universal Negative (E) - No S is P Particular Affirmative (I) - Some S is P Particular Negative (O) - Some S is not P While singular affirmative and singular negative proposition can be A and E
9) Give in details opposition of proposition and distinguish between mediate and immediate inferences? Or give account of Contradiction, contrary, sub-contrary and subaltern. Ans. Immediate and Mediate Inferences:Traditionally, deductive inferences have been classified into immediate and mediate In an immediate inference we proceed from one given proposition (the premise) to another proposition (the conclusion) without requiring anything further for drawing the conclusion. In other words one can say that in immediate inference one proposition is sufficient from drawing the conclusion. In mediate inference conclusion is drawn from two or more proposition taken together. Mediate inferences are generally divided into
Syllogism
Reduction
Immediate inferences are generally divided into
Opposition of proposition
Educations
Opposition of proposition: - The term Opposition is used for the relation between two propositions having the same subject and the same predicate, but differing either in quantity or in quality or in both. The traditional logicians applied the doctrine of opposition of propositions to the four kinds of categorical proposition. Taking ‘A’ ‘E’ ‘I’ ‘O’ propositions in combination, four kinds of oppositions are possible. These are 1)
Contradictory Opposition:- Contradictory opposition is the relation between two propositions which differ both in quantity and quality (keeping subject and predicate same). It is the relation between ‘A’ and ‘O’ proposition. e.g. L.F.A. – All men are mortal is contradictory to L. F. O. – Some men are not mortal Same relation is showed by propositions ‘E’ and ‘I’ as e.g. L.F.E – No men are mortal is contradictory to L.F.I. – Some men are mortal
2)
Contrary Opposition – Contrary opposition is the relation between two universal propositions differing in quality (keeping subject and predicate same). It is the relation between ‘A’ and ‘E’ propositions. e.g. L.F.A – All flowers are white is contrary to L.F. E. – No flowers are white
3)
Sub contrary Opposition – Sub contrary opposition is the relation between two particulars propositions differing in quality (keeping subject and predicate same). Sub Contrary is the relation between ‘I’ and ‘O’ propositions. E.g. L.F.I- Some servants are loyal is sub contrary to L.F. O. Some servants are not loyal.
4)
Subaltern Opposition - Subaltern opposition is the relation between two propositions having same quality but differing in quantity (keeping subject and predicate same). ‘A’ and ‘I’ propositions, have this relation. e.g. L. F.A. – All boys are naughty is subaltern to L.F. I. – Some boys are naughty Even ‘E’ and ‘O’s propositions share this relation e.g. L.F.E. – No boys are naughty is subalterns to L.F. O. – Some boys are not naughty The four forms of opposition can be traditionally represented by diagram. This diagram is called the square of opposition of proposition. It is:
The relations of oppositions are the basis of some elementary inferences i.e. given truth or falsity of any propositions, we can see which of the opposed propositions will be true which is false and which is doubtful. 1) Two contradictory propositions can neither be true together nor false together. If one is true, the other will be false and if one is false other has to be true. 2) Two contraries can never be true together, but they may both be false. 3) Sub Contraries can not be false together, but they may both be true. 4) It is the relation between universal and particular proposition so if universal is true particular will be true but when particular is true universal can true. Similarly, when universal is false, particular can be false, and particular is false, universal has to be false Opposition of Singular Proposition Keynes points out that in case of singular proposition, we can not g beyond single denial, so opposition between singular propositions is to be called contradictory opposition. 10) Give account of failure of traditional logic? What are the reasons for failure of traditional classification of proposition? Compare between traditional and modern classification? Ans.- ‘time and tide waits for no men’, every moment there is progress, in this tide logic is no exception. From Aristotelian logic to modern logic i.e. symbolic or mathematical logic it is revolution. Yet, it cannot be said that two are unconnected and mutually exclusive. The symbolic logic makes use of heavy technical symbols and minimum use of language is development of traditional logic. Basson and O’Connor, “that modern symbolic logic is a development of concepts and techniques which were implicit in the work of Aristotle”. Let us mark distinct point of modern logic as stated by C.I. Lewis, there are three pointsa) The use of ideogram (i.e. signs like x or?) or signs which directly stands for concepts, instead of phonogram (or written words ‘multiplication’ or ‘question marks’) which directly stands for sound and indirectly for concepts. b) The deductive method. By positing the truth of certain elementary statements we can derive indefinite rules,
c) The use of variable having a definite range of significance. Distinction can be brought out as follows1) DefinitionAristotle finds logic as tool to prove his theories, so finds it as ‘science which investigates general principles of thought’; while modern logician cite word thought as too vague, and simplifies it as ‘logic is form of valid argument’. 2) Form If we take close perusal of both logic, then it will be found that both depends on form and both believes in truth or falsity by virtue of its form; but traditional believes in truth n falsity of proposition n stress on form as particular way of writing the proposition called as A,E,I,O; while modern logicians advances as logic has concern with validity, so if we deduce it into symbols as mathematics does then also analysis will be possible and easy to generalize. So they gave technical symbols. 3) Classification of propositions
Traditional logician simple classify proposition into simple and compound, while modern logician extends as simple, compound and general.
Traditional finds simple as categorical i.e. subject-predicate type, while modern finds these are only quantity representing proposition, and classify them under general i.e. quantification. At same time modern logicians believe simple proposition as nuclear statements, and term them as subjectless, subject-predicate (individual), class-membership and Relational. Compound for tradition are conditional and that to hypothetical and disjunctive only, while modern enhances as negation, conjunction, disjunctive, implication (what is hypothetical for traditional), and Bi-conditional.
4) Parts of proposition Traditional logicians observe three parts of propositions, viz., subject, predicate and copula; and modern logician says it to be constituent and component. Whereas constituent is same as subject-predicate (though it indicate something more then subject and predicate), and component is copula. 5) Tense
Traditional logician believes in present tense and specially recommends that copula must be present tense verb ‘to be’ so ‘is or are’ is mandatory to add. While modern accept all tense. 6) Symbols In traditional logic there are only 4 symbols viz. A,E, I, O; while modern logic give technically give symbols to each type of sentence as for conjunction ‘.’ (dot), or disjunctive ‘v’ (wedge) etc, beside it for singular sentence like ‘Ram is wise’ it is symbolized as ‘Wr’, and for quantity special signs are used as for universal ‘x’ and existential ‘эx’. 7) Predication Traditional logician finds function of copula as expressing relation of subject with predicate is of class inclusion or exclusion, while in modern logic copula i.e. component ‘is’ combine constituent in three waysa) For class inclusion or exclusion b) To indicate membership c) To indicate predication as attribute to individual or class. 8) QuantificationTraditional logicians say ‘all’ as universal and symbolize as ‘A’ or so, but in modern it is directly given symbol as of universal and existential and of implication and conjunction respectively. 9) Way of Proof In traditional form it was judged on base of deductive or inductive type, while in modern logic special deductive rules and truth tables are device that help us to derive validity even for long stanzas and proof. Failure of Traditional classification(as it is mentioned in earlier there is hardly any difference) but yet traditional logic has many drawback as1. Short come in analysesTraditional logician analyses only assertive proposition as proposition and also strictly ask to consider proposition as ‘ Subject Predicate n forces even compound proposition to reduce to such form. But in reality there are many sentences and expression in different ways and when reduce loses its weightage. 2. Proposition classificationThey distinguish compound as only hypothetical or disjunctive proposition and miss out conjunction or bi-conditional and so. 3. Symbolic shortcomewhile stating symbol for any statement with ‘all’ is symbolize as ‘A’ or so. And it fails to show sign of quantity and relation between subject and predicate 4. Partial precision Traditional people fails to recognize importance of partial in its fullest sense they consider it just as partial class inclusion or exclusion, but in fact in modern sense it gets it value by stating ‘ existential denotes atleast once’
5. SubjectIn traditional subjectless has no existence, even proposition like ‘no one is immortal’ has any stand in tradition This is the reason where traditional logic fails. 11) Give modern classification of proposition? Give brief on Simple/compound proposition? Ans.- We have seen traditional classification as simple and compound proposition. We see it is modern Logic. Simple proposition we may define Simple proposition are one which does not contain any other proposition as its component. e.g.
1) Taj Mahal is beautiful 2) Rekha was actress.
Above statements are simple propositions. A simple proposition cannot be analysed into it other proposition i.e. constituents of simple proposition are not proposition. The simple proposition makes an assertion about an individual (or individuals) There are four kinds of simple propositions are as A) Subjectless propositions B) Subject – predicate propositions C) Relational propositions. D) Class – membership propositions. 1) Subjectless Propositions – This is the first and simplest kind of simple proposition in which statement is not fully expressed by thinker. Generally subjectless propositions are either exclamatory or impersonal propositions. It rains In above examples first proposition is an exclamatory proposition as it gives information about fire. The second subjectless proposition is impersonal proposition which has grammatical subject but not logical subject.
2) Subject Predicate propositions: A subject
Predicate proposition states that an
individual possesses a quality or an attribute. As individual is singular term, subject of this kind of proposition is singular. e.g.
1) Shivaji was a king 2) Abhijit is a singer 3) Soloman was wise.
All above propositions assert an attribute about as individual. The form of subject predicate proposition is symbolically represented as S-P is it ‘S’ stands for subject and ‘P’ stands for the predicate which is an attribute. 3) Relational Propositions: A relational proposition asserts a relation between two or more constituents. The constituents between which a relation is asserted are called terms of relation. These terms of relation can not be called subject and predicate. All of them are subjects of relation which can be minimum two e.g. Ram loved Sita. In it two subjects are ‘Ram and Sita’ and their relation is shown by loved. In relational propositions the relation proceeds from something to something else. This is called sense or direction of relation. The term from which the relation proceeds is called referent. The term to which the relation proceeds is called relation. One can indicate the sense or direction of relation may be indicated by an arrow. e.g. defeated Rama
Rawana Same proposition can be expressed by using symbols as ‘a’ will be
for referent and ‘arrow’ for relation and ‘D’ will be for showing. The relation of defeated. In it ‘a’ and ‘v’ are small letters and ‘D’ will be capital letter. The symbolization will be a D v stands for ‘Ravana’ and ‘D’ stands for Defeated. The direction or sense of relation is indicated by the order in which the small letters ‘x’ ‘y’ etc. ‘o’ ‘v’ etc. occur. The letter which occurs first is referent and that which comes next is the relation. 4) Class – membership proposition: A class membership proposition asserts that as individual is a member of ‘a’ class
e.g.
Amitabh is a hero. Sonu Nigam is a singer. Urmila is an actress.
Above are class – membership propositions as Amitabh is included in class of heros. Sonu Nigam in class of singers and so on. Class membership proposition is symbolized as aεf In if, letter ‘a’ stands for any individual and the letter ‘F’ for any class. The sign ‘E’ (called epsilon) stands for class membership. The letter which stands for the individual is a small letter (small ‘a’ is used above). The letter which stands for class is a capital letter (capital ’F’ used above). In the symbolic representation of class membership proposition, epsilon (E) is a component. Even when the individual and the class change the relationship of ‘class membership’ remains the same. a εH In it ‘a’ stands for individual Amitabh. ‘H’ stands for class of heros. And E this sign shows the class membership. Distinction between subject predicate proposition and class membership proposition. Explanation of class – membership will be same as above subject predicate proposition though assert something about an individual, it asserts a quality. And when we say an individual possesses a certain quality, we emphasise the cannotative aspect. Compound proposition and its kinds – Compound proposition can be defined as the proposition which contains another proposition (or propositions) as a component is called compound proposition (or compound statement) e.g. Rahul is handsome and Tall In above proposition there are two propositions as its components they are 1) Rahul is handsome 2) Rahul is Tall. So above given example is of compound proposition. There are five types of compound propositions. 1) Negative propositions.
2) Conjunctive propositions 3) Disjunctive propositions 4) Implicative propositions. 5) Equivalent propositions. 1) Negative Propositions – when any proposition is denied or negated, we get a negative proposition. And it is denoted by word not: e.g.
1) This flower is not white 2) Train is not fast. 3) I will have neither tea nor coffee In third proposition there are two negated propositions as
I will not have tea I will not have coffee. So negative proposition can be express negation of two (or more) proposition. In logic it has been denoted by symbol ‘~’ (curl) or (tilde) so when ‘N’ comes before any proposition, then the proposition is negated e.g. Rose is not white. We can symbolize this proposition as
~N When ‘W’ stands for ‘Rose is white’ A negative proposition is false, it its component is true. It is true when its component is false. e.g.
A monkey has a tail is true
Then its negation A monkey does not have a tail is false. 2) Conjunctive proposition – A conjunctive proposition is a compound proposition formed by combining any two propositions with the (truth functional) connective ‘and’ what the conjunction ‘and’ does is to form a single proposition by combining two propositions e.g. Sarita is intelligent and beautiful. The above proposition is conjunctive proposition as the given single statement conjoins two propositions as 1) Sarita is intelligent 2) Sarita is beautiful
The components of a conjunctive proposition are called conjuncts. Propositional connective conjunctive propositions is ‘ . ’ (dot) e.g. Ramesh is intelligent and hardworking This proposition will be symbolized as I. H in which ‘I’ stands for Ramesh is intelligent and ‘H’ stands for Ramesh is hardworking. A conjunctive proposition is true if and only if both the conjuncts are true even if one of the conjuncts is false, it is false. 3) Disjunctive proposition: a disjunctive proposition is compound proposition in which the word either or combines two propositions. The components of disjunctive propositions are called disjuncts (or alternatives) Disjunction may be used in two senses 1) Inclusive sense (weak) – when both The disjuncts can be true disjunction is said to be used in inclusive sense. e.g. Sonu Nigam either singer or an actress. 2) Exclusive sense (strong) – When one disjunct is true and the other false, disjunction is said to be used in exclusive sense e.g. Sonu is either handsome or ugly But to find out whether injunction is used in disjunction sense or of disjunctive sense one has to see the content of proposition and as logic is formal science and does not deals with content but form of proposition. So in logic disjunctive propositions are interpreted in the inclusive sense. Propositional connective for disjunctive propositions is V (wedge) e.g. Either I will have tea or coffee It will be symbolised as T
v
C
Where ‘T’ stands for ‘I will have tea and ‘C’ stands for I will have coffee. A disjunctive proposition will be false if and only if both the alternatives are false. 4) Implicative (or conditional) proposition – An Implicative proposition is a compound proposition in which two propositions are combined by words if then.
In an implicative proposition the component proposition between the word ‘if’ and the worked ‘then’ is called the antecedent (or implicans) and the component proposition which follows the word ‘then’ is called the consequent (or the implicate) e.g. If he is guilty then he will be punished. In above example he is guilty is antecedent and he will be punished is consequent. Prepositional connective for implicate proposition is ‘s’ (horse shoe) e.g.
If he is guilty then he will be punished will be symbolized as
Y כ P Where ‘Y’ stands for he is guilty and ‘p’ stands if he will be punished. An implicative proposition is false if and one if. The antecedent is true and the consequent is false. 5) Equivalent (or bi-conditional) propositions An equivalent proposition is a compound proposition in which two component propositions materially imply each others. The prepositional connective material equivalence is symbolized as ‘Ξ’ (triple bar) or (two headed arrow). e.g. If and only if an animal is mammal then it breastfeeds its young ones. It will be symbolised as m Ξ y or m y in which ‘M’ stands for an animal is mammal and ‘Y’ stands for it breastfeeds its young ones. An equivalent Proposition is true if both the components have the same truth value. General Propositions Apart from simple and compound propositions, modern logic, recognizes general propositions so a general proposition can be defined as a proposition that makes an assertion out a class or classes. These propositions show connection between two properties. These propositions consider properties (characteristics) apart from the individual things which have these properties. That is why the proposition (A) ‘All fairies are beautiful’ would be true even if there were no fairies. On the other hand, the proposition (I) ‘some singers are actors’ asserts that there exists at least one individual who possess the property of being a singer and being an
actor from this we can know universal proposition does not imply existence but a particular proposition does. Distinction between general proposition and class membership proposition In a class membership proposition an individual is asserted to be a member of a certain class. This shows, one of the constituents of a class-membership proposition is an individual, while. The other constituent is of a class. On the other hand all constituents of a general proposition are classes. General propositions assert relation between two classes and they are about properties and not about the individuals which possess these properties. Distinction between general proposition from simple and compound proposition. Simple propositions contain a particular as a constituent i.e. one of the constituents of a simple proposition is an individual. e.g.
1) Rahul is smart 2) Shivaji defeated Afzal Khan General propositions contain universal as its constituents.
e.g. all Indians are helpful. In above proposition Indians and helpful are universals. Compound propositions are farmed by combining other propositions while general proposition is a single statement and it cannot be analysed into propositions. 12) What is purpose of definition? Definitions are required for making communication possible as well as clear. These functions can be analysis into five purpose of definition. These are 1) To increase vocabulary :- By explaining the meaning of new words, definition increases vocabulary one way of varifying the meaning of a word is by using it. But sometimes the context does not rarify the meaning. In such case, the meaning has to be deliberately explained deliberate explanation of meaning involves definition e.g. lady explains her friend that she is on her family way. If expression
family way the lady has to define it. They will define it as family way means she is pregnant. The above example shows that definition of new words increase vocabulary. 2) To eliminate ambiguity: In every day many words which are many a time equivocal, ambiguous or vague. An equivocal word is one which can be interpreted in two or more ways usually, this causes no trouble. By this there meaning become clear from the context. e.g. The word ‘bat’ is equivocal. Its one meaning is ‘animal’ and the other meaning is ‘an instrument’ by which game of cricket is played. So When I say ‘Sachin’s bat weights more than Saurav’s then everyone will understand what I am referring to thus, in the case of equivocal words no difficulty arises. There bare, words whose meaning does not become clear from the context such words are said to be ambiguous. E.g. Industry should be encouraged. In above example, we are not sure whether ‘industry’ means ‘hard work’ or ‘industrial organization’. This is due to ambiguity of the word ‘industry’. In such cases, definition plays vital roles as is serves the purpose of eliminating ambiguity. 3) To reduce vagueness of words: A word is vague when the type of things to which is applies is not definite which many a time leads to differences of opinion. Definitions help in resolving differences by reducing the vagueness e.g. cashew should be considered what a fruit or a vegetable? This confusion can be resolved by resolving vagueness of terms. 4) To explain word theoretically- This is especially applicable to the world of science or discovery where they come in touch with new words and they not only need special definition, but also some technical explanation. It is also, required in field of law to interpret statute. For e.g.- ‘robbery’ is defined by the ‘Federal Bureau of Investigation’ as “the taking, or attempted taking, of anything of value from one person by another, in which the offender uses force or the threat of violence”.
5) To influence attitude- Lastly, but not least, it is very important aspect, certain words when define it resolves the conflicts, and bring peace. It occurs just because the attitude of person is changed towards the meaning of the term. Definition that produces effect to influence attitude is called persuasive definition. 13) What are different types of definition? Show its relation with law? Definition is the explanation of the meaning of a word phrase or symbol (i.e. non vertical symbol) What is defined may be the name of concept or class, or it may be a symbol. Definitions consist of two parts. These are 1) What is defined is called definiendum 2) The words in which it is defined, is called definiens. e.g. Bachelor means unmarried man. In above example ‘bachelor’ is definiendum and ‘unmarried man’ is definien. When definition is given the definiendum is placed to the left, and definien to the right. The definition should be stated thus, X means Y. Here ‘X’ is the definiendum, ‘Y’ is define and the word ‘means’ indicates that the statement is a definition. Relativity of definition- Definition is relative i.e. it can change from person to person. The release, the same word may have to be defined differently for different persons. e.g. The definition of soft drink as ‘a carbonated non toxicating beverage is appropriate and good definition but a common man wick fend it cult to understand. So the word which is easy for scientist to understand may not be lean to common man. This is the recon, the need of definition arises, to make, understand the unknown word and the purpose of defining served only if the given definition is clear to the receiver of definition. Distinction between Real and Nominal Definitions: Traditional logicians believed that we define things but, modern logicians believed that words have meaning things do not. So it is necessary to define both the views.
1) Real Definition: - A definition which notifications to state the nature of a thing is called real definition. This is view was put forth by traditional logicians. 2) Nominal Definitions: - A nominal definitions explains the meaning of a word, phrase or symbol. This view was put forth by modern logicians. They believed some words are not names of real things. So we cannot state them essential nature e.g. fairy unicorn ghost. Technical terms of a science do not name real objects e.g. evaporation They believed real definition can be given if the nature of a thing was to remain fixed and if we could know it, but we do not know what the essential nature of it is. As modern logicians put forth nominal definitions, there are two categories which are on basis of method of definition. 3) Type/Kinds of Definition :- On the basis of the method of defining terms, we get four main kinds of definitions these are:1) Ostensive definition 2) Extensive Definition 3) Bi verbal definition 4) Per genus et differentia definition From another point of view, definitions may be classified into denotative and connotative definitions. A denotative definition indicates the things to which the definiendum applies. A Connotative definition states properties in above four types first two are denotative and later two are connotative. 1) Ostensive definition: - An Ostensive consists in pointing out an object to which the definiendum applies ostensive definition of chain would be pointing out one or more chairs. Ostensive definition is the best method of defining words in certain cases. It is the first (or primary) method of explaining meanings of new words. Ostensive definitions are absolutely necessary for defining those words which are names of sensations and desires. And very useful to learn new words and corresponding objects even it is useful in learning language.
Limitations:1) An object has many qualities. By ostensive definition one is not sure of which quality has been pointed out e.g. If one wants do define word ‘dog’ ostensively. From the gesture it may not be clear whether the word means colour or body structure of the animal 2) We cannot define things ostensive-ly which are not real e.g. ghost fairy etc. 3) Scientific concepts are not possible to define ostensive e.g. gravitation. 2) Extensive definition: Extensive definition explains shows a word is to be applied and it consists in giving examples of the definiendum. Such, examples, can be given in two ways. Examples of individual objects, (included in the class) to which the word applies e.g. Bombay, Madras. Examples of suit-classes to which the word applies bangles (ornaments) one can give a satisfactory extensive definition when the definiendum applies to limited number of objects. 1) Biverbal definition – Biverbal definition is the explanation of the meaning of, one word by another word or of one phrase by another phrase when they house the same meaning. e.g. valour means courage In above example, word velour and courage have same meaning so one word can be used to explain the other. Biverbal definition of a phrase will consist in explaining its meaning by another phrase. e.g. To think better of the matter means to give it further consideration. In above example defines has the same meaning as the definiendum. 4) Definition per genus et differentia- Certain words are names of classes. Members of a class have certain qualities in common. When a definition states this, this definition is called analytical definition. The most commonly used definition in this regard is definition. There are two more definition based on usage of term, this are-
5. Stipulative definition 6. Lexical definition 5. Stipulative definition- The definition that arises from deliberate assignment of a meaning is properly called stipulative. It is needed if any novel term is formed or tentative explanation is given or poet uses its liberty to express any term or many a time it can be used as code to pass secret messages. It is referred as nominal definition or verbal definition. E.g.- ‘Black Beauty’ in general it may mean ‘beautiful girl with sharp feature, but with dark skin’, yet in reality it is stipulated by poet Wordsworth as ‘black horsess’ It is stipulative till it becomes popular, or gets it place in dictionary. Then it becomes ‘lexical’. 6. Lexical definition- It is said to be popular or dictionary meaning or utmost reported meaning. It does not give definiendum a meaning, it hitherto lacked but reports a meaning of the definiendum already has. It is referred many a time as ‘real’. When any term that can be stipulative and becomes popular, it becomes lexical. This normally occur with scientific term, or newly derived term. For example‘mobile’ this word was used earlier for moving, then when instrument of communication was device that was used to communicate even while moving was term ‘mobile’ and now everyone is familiar with word ‘mobile’. Beside this one more additional definition can be given, that is, 7. Précising definition- It is definition that reduces vagueness of the term. As stipulative and lexical serves to reduce ambiguity, while this definition is to reduce vagueness. It means that terms which has borderline meaning that means, such a meaning that it can be interpreted as per the individual intends; for such case some limits or appropriate meaning should be fixed, to avoid the conflict in understanding. It is conceptual instrument of wide and powerful use. In appellate courts, for example, are obliged to draw conceptual lines, making some common terms more precise, they commonly give reasons for the refinements introduce. Now, a special section is there in courts for ‘definitions’ to give the special interpretation of the statute. For e.g.- ‘robbery’ is defined by the ‘Federal Bureau of
Investigation’ as “the taking, or attempted taking, of anything of value from one person by another, in which the offender uses force or the threat of violence”. 14) What are rules of traditional definition? Ans. Traditional logician believes that there can be no other definition else then ‘Per genus et differentia’. They not only believe it to be ‘the definition’, but also prescribes some strict rule for defining it and they are as follows1) A definition should state the essential attributes of the speciesIn other words it must not be too narrow or too broad. For e.g.- If in today scenario, if we consider scientists definition of planets and then state that there are nine planets then it is too wide Or if we say ‘man as animal (only)’ then it is too narrow definition In reality definition must state the essential feature completely and avoid extra features, redundant feature or some accidental i.e. that quality r feature it is some time seen in observed thing. 2) It must not be synonyms or circular in definitionAny definition if it has same meaning or twisted meaning, and given in circular way its purpose itself fails. For e.g. Synonyms- Bachelor is unmarried person Circular – This person is murderer because he has weapon And he has weapon so he is murderer. 3) A definition must not be figurative or obscureAny definition must not give complex or perplexed meaning otherwise individual will not get it meaning and term will be vague for e.g. Figurative- ‘Envelop is coffin of letter’ Obscure- ‘anesthesia is sophoric’ 4) A definition must not be negative where it can be affirmativeDefinition must state what it means rather then what it cannot be. If we just say that what it cannot be, one may not be able to derive the perfect meaning. Same case occurred in defining God in Vedas. According to Vedas definition God is ‘not like human, not like tree, not like demon, not like air …’ then lastly question comes then god is like what?
15) Define ‘simple enumeration’. Explain the main features and value of either ‘simple enumeration’. And also, give its application in Law. - Simple Enumeration is a generalization that is supported by positive instances and no contrary instances that has been observed. Simple Enumeration: Main features of Simple enumeration: i.
ii.
iii.
iv.
Uniform (or uncontradicted) experience: Simple enumeration is based on the belief that what is true of observed is considered to be true of unobserved. For example, we see few elephants to be grey, and state that all elephants are grey. And we continue our belief of ‘elephants to be grey’ until we get any contradictory experience, like stating ‘elephant can be white (or any other colour)’. By such opposite experience only we can say that ‘all elephant cannot be grey’. So, very essential feature is uncontradicted experience. Belief in uniformity of nature: One can give any statement for all, only by considering that what is true uptill now will continue ahead also. And one can believe so, only due to belief in uniformity in nature. Since, nature shows the pattern of uniformity, which give us the idea of uniformity ahead. Degree of probability: Simple enumeration is based on the observation, as much more number of samples observed, more the definite-ness of the conclusion. In other word more strong belief in conclusion, and lesser the experience less confidence in the conclusion, and more the chance of contradictory result. No scientific analysis: Simple enumeration never means scientific analysis, it purely depend on external observation. As we never try to see why elephant is grey? Is there any organ or chemical or any molecule in elephant which presents elephant colour grey? Rather we just see the external colour to be grey that is common in many and conclude that ‘all elephant are grey’.
Value of Simple enumeration: i. ii.
Wider experience: Value of simple enumeration can only be effective on the wider experience as by such experience we can assure the fact to remain same ahead. Resemblance: While observing one need to check the resemblance of observation with what we need to conclude. As observing colour in elephant is possible, but if we say crying of owl is bad omen, then there is no relation between crying of owl and bad or good omen.
Application of Simple enumeration in Law: Simple enumeration has immense value in the observation and generalization in science, but equally it carries value in law. As all the cases in court stand on the base of evidences, as much more the evidence and their statement, so do we believe in the strength of case, and get the judgement accordingly. It is one of the essential elements in Jeomatrics. 16) Define ‘Analogy’. Explain the main features and value of either ‘analogy’. - Analogy is defined as an argument from particular resemblance to further resemblance. Main features of Analogy:
i.
ii.
iii.
Relevant resemblance: Comparison has its effect if the compared factor has relevance with conclusion. For example if we compare two boys having same locality, same culture, same birthday, same school and same friend circle. So, if one finds that first boy is smart, it does not make second boy intelligent. As the factors what we were comparing has no relvance with intelligence. Common characterisitics must be sufficient and difference ignorable: When one compare earth with moon wherein both have light, water, soil and environment which give us sufficient reason to believe that there can be life on the moon. But, if we compare it with mercury as both are planet, both have light of sun and both are round. So, there must be life on mercury than one can immediately realize that we are missing important difference about environment in which life can survive and heavy heat on mercury in which it is not possible for any life to survive. Hence, comparision must have sufficient reason to believe conclusion and difference must never be important. One must not conclude more than necessary: When we compare between the 2 boys as having same locality, same culture, same birthday, same school, same friend circle and have same IQ and EQ. Hence, one got 96%, so 2nd must also get 96% only. Herein we are accepting more than required and our conclusion will lead to error. So one must conclude the minimum.
Value of Analogy: i. Total positive analogy: All characteristics known as well as unknown in whom two (or more) things resemble are the total positive analogy. ii.
Known positive analogy: The known between two things are the known positive analogy.
iii.
Total negative analogy: All the characteristics (known as well as unknown) in which things differ constitute the total negative analogy.
iv.
Known negative analogy:The known differences between two things constitute the known negative analogy. To determine the value of analogy, though these four concepts are used but for us it is not possible to know all the resemblances, even not all differences. We can know only some of them. So while judging the probability of an argument from analogy, we have to depend upon the known positive analogy and the known negative analogy. Thus,When the known positive analogy (resemblances) consists of important properties, the conclusion of analogy has a high degree of probability. That is to say to derive at conclusion, when we consider important properties of two things which resemble with each other, then the analogy has high degree of probabilities: In case of analogy of earth and mars, resemblances are atmosphere water.
Application of Analogy in Law: Analogy has immense importance in law in following two ways:
i.
Circumstantial evidence: In law of court especially in case of crime when one does not have eye-witness than in such case judgement is taken and given on the base of the circumstances. In evidence act circumstantial evidence has got special clause that is on the base of given facts one can conclude that in similar condition one can commit a particular kind of crime, and if same condition has been prevalent in present case than by circumstantial evidence person can be considered guilty.
ii.
Precedent: Precedent is the previously decided pivot case. On finding that present case is similar to the precedent (i.e. earlier case) then judgement what is applicable that time is also applicable in present case also. Hence, the analogy is important in both the above cases.
f) Explain any two of the following concept:
