 Dear learners, today I will take a video class for you. The unit known 6. The unit is Modern Classification of Propositions, Simple and Compound, Singular and General. Modern Classification of Propositions. Simple and Compound, Simple and Compound, Singular and Singular and General. In this unit we basically discuss Modern Analysis of Propositions, Propositions and Sentences, Modern Classification of Propositions, Simple Propositions, Compound Propositions and General Propositions. Now you will see there learners. This unit introduces you to the Modern Analysis and Classification of Propositions. Modern Logicians do not agree with the traditional definition of Propositions. They define Propositions as a statement which is either true or false but it cannot be both true and false. A proposition is not identical with sentence. Similarly, a proposition may express a fact but it is not a fact. Only indicative sentences may be judged to be either true or false. If proposition may have any number of constituents and these constituents are combined in various ways. The mode of combination expresses the logical form of proposition. Modern Logicians have classified proposition into Simple, Compound and General. Modern Logicians have classified proposition into Simple, Compound and General. Now there are learners. In Modern Logic, proposition means a statement which is said to be true or false. For example, Asako was the king of Pataniputra. 3 plus 6 is equal to 9. So Critics was a philosopher. No man is immortal. Truth or falsity can be ascribed to every one of them. Every one of them can be either true or false. But may God help us is not a proposition because the properties, truth or falsity cannot be ascribed to it. In Modern Logic, the component of a proposition that is subject and predicate are known as constituents of a proposition. Again I repeat there, learners. The components of a proposition that is subject and predicate are known as constituents of a proposition. Subject and predicate in Modern Logic known as constituents of a proposition. You see, there are learners. Truth or falsity of a proposition is called truth value. The truth value of a proposition is determined by the fact. If a proposition represents a fact as it is, then the proposition is true. Otherwise it is false. But a proposition is different from a fact. Now you see there are learners the difference between a proposition and a sentence. There is a clear difference between a proposition and a sentence. Do a proposition is expressed in the form of a sentence it is not identical with a sentence. We can point out following points as their differences. You see there learners the difference between proposition and sentence. You see a proposition may be understood as that to which the truth or falsity can be ascribed. So in case of proposition we ascribe truth and falsity. But truth and falsity cannot be ascribed to all kinds of sentences. All grammatical sentences are not propositions. Only indicative sentences can be just to be either truth or false. Indicative sentences can be said to be true or false. Indicative sentences, imperative sentences, operative sentences cannot be just to be either true or false. For example, have you ever gone to Kolkata? Then may God help us? Truth or falsity cannot be ascribed to these propositions. So they are not propositions. The same proposition may have different verbal expressions. Therefore the same proposition may be expressed by different sentences. But various sentences have a single underlying meaning which is called a proposition. Now the learners you see modern classification of proposition. Modern physicians have broadly classified the propositions into elementary propositions and non-elementary propositions. Elementary propositions are of two kinds, simple and compound propositions. And non-elementary propositions include all general propositions. Let us discuss all types of propositions. Now the learners you see what is simple propositions? A simple proposition expresses a simple fact and it cannot be analyzed into further propositions. Moreover a simple proposition makes an assertion about an individual, a person, a place, a theme, a country and so on and so forth. For example Sima is doing a course in logic. Simple propositions have four forms. You see first one is you can say that is subjectless proposition. Second one you can say subject predicate proposition. Third one you can say relational proposition. These are the examples of subjectless proposition. These propositions are also known as the explanatory propositions. The propositions such as it rains, it thunders are known as impersonal propositions. Such propositions have no logical subject. In these propositions the thinker asserts something but the statement is not fully expressed. These propositions give information and therefore they are regarded as proposition. Now the learners the second one is subject predicate proposition. A proposition which asserts that a quality or an attribute belong to something is called subject predicate proposition. For example Sima is intelligent, this paper is white. Subjects of this type of proposition is a singular term. The subject predicate type of proposition is represented as SP. It indicates subject predicate proposition. In predicate logic small letters ABC are used to symbolize individuals and capital letters ABC are used to symbolize attributes. For example Sam is intelligent the symbolic expression of this proposition is I. Sam IS means Sam is intelligent. Here the symbol I stands for intelligent and S stands for Sam. Sam is intelligent can be symbolized as I capital S small. I S means Sam is intelligent. I is capital S is small. S indicates attribute and not S indicates person and I indicates attributes that is capital letter. So it indicates Samal is intelligent. The learners now you see what is relational proposition. Relational proposition asserts a relation between two or more constituents. There are various ways to express relations. We may use the verbs drink, love, enemy, heart or words greater than smaller than etc. to express various relations. For example the lecturer teaches a course in English. He owes me 5 rupees for a bag. So in a relational proposition the relation proceeds from something to something else. This is called a direction or sense of relation. The term from which the relation proceeds is called a referent and the term to which the relation proceeds is called a rhythm. So in case of relational proposition we find the direction of relation where we find the relationship between referent and rhythm. In the above example which we already mentioned the lecturer teaches a course in English. Here the lecturer is a referent and the term a course in English is a relatum. Therefore their learners in relational proposition we find relatum and relatum and what? Relatum and referent. Now you see their learners what is class membership proposition. So class membership proposition asserts that an individual is a member of a class. For example Shibaji is a hero, Rabindranath Thakur is a poet, Gurgenstein is a philosopher. This class membership proposition is symbolically expressed as R-E-P. It is R-E-P-E indicates the relations you see belongs to. So this class membership proposition is symbolically expressed as R belongs to P. So you see here R stands for Rabindranath Thakur and P stands for a class of poet. In symbolic logic the capital letters A, B, C are used to symbolize the class and small letters A, B, C are used to symbolize to individual. So this is all about class membership proposition. Now their learners you see what is compound proposition. So you see their learners compound proposition contains two or more simple propositions as these components. For example Socrates was philosopher and Russell was a mathematician. This proposition is a single proposition. Simple propositions are combined by various ways to form a compound proposition. It means that compound proposition provides two or more simple propositions. Now you see compound proposition again is of four kinds their learners. Compound proposition again of four kinds one is conjunctive proposition. Second one is disjunctive proposition. Third one is alternative proposition and fourth one is implicative proposition. So these are the four kinds of compound proposition. Now you see what is conjunctive proposition. Now you see what is conjunctive proposition. So the compound proposition in which two or more simple propositions are combined by the word N is known as conjunctive proposition. Suppose you see Manmohan Singh is the Prime Minister of India and Barack Obama is the President of USA. This conjunctive proposition is symbolically expressed as P.Q. When two simple propositions are combined by the word N then it is known as conjunctive proposition. Here we use the symbol N it is written as dot P dot Q. Now you see what is disjunctive proposition. Now dear learners the compound proposition in which two propositions are combined into one by the word or either or in the inclusive sense is called disjunctive proposition. In the inclusive sense for example either logic is interesting subject or it is a scoring subject. Logic is interesting subject or it is a scoring subject. The components of disjunctive propositions are presented in the form of disjuncts. This disjunctive proposition may be symbolically represented symbolically stated as P.H.Q. P implies or P indicates that logic is interesting either logic is interesting or it is a scoring subject. So both these propositions are joined by the symbol P.H. This P.H.Q. it indicates the disjunctive proposition like either logic is interesting either logic is interesting or it is scoring. Now dear learners you see the third one that is alternative proposition. So this is very very important one. You see the compound proposition in which two propositions are combined into one by the word or either or in exclusive sense not in inclusive sense is called alternative proposition as for example the man is either literate or illiterate. It indicates that the two propositions cannot be true in the same time. That's why it is used in the exclusive sense. P alternate Q either man is literate or illiterate either man is rich or poor. In this exclusive sense we use the symbol that alternate we use. So you see their learners here P and Q stand for two alternative and the symbol the latino art stands for or in this exclusive sense not in inclusive sense. The meaning of or in its exclusive sense can be expressed as P alternate art Q dot negation P dot Q. Now you see their learners the fourth one that is implicative proposition implicative proposition. The compound proposition in which the two simple propositions are combined by the word if then is called an implicative proposition. For example if rain comes then the price of food grains will rise. If rain comes then the price of food grain will rise. The component proposition which follows if is called the antecedent or the implicance. And the component proposition which follows then is called the consequent or the implicate. So in case of implicative proposition we find two parts one is called antecedent that is implicance and the another is called consequent that is also called as implicate. It in an implicative proposition one component proposition implies the other the proposition which implies the other is implicance and the proposition which is implied that is consequent part it is called as implicate. Now their learners so this is all about compound propositions. Now we will discuss what is general proposition. Now you see their learners general propositions are non-compound propositions. They are all about classes such propositions either affirm or deny the existence of proposition the existence of something or a property of the whole universe and the relation between two classes. So there are three kinds of general propositions their learners first one is existential general propositions. Existential general proposition and second one is one predicate general proposition. Second one is one predicate general proposition and third one is general proposition general proposition asserting relations between asserting relations between two classes. First one is existential general proposition, second one is one predicate general proposition and third one is general proposition asserting relations between two classes. Now their learners now you see what is existential general propositions. An existential proposition directly affirms or denies the existence of something. For example tiger exist in predicate logic the tiger exist can be symbolized by using existential propositions such we can Ex in predicate logic we symbolize the tiger exist as ex as dx is indicates that tigers exist. Then one predicate general propositions you see one predicate general propositions either affirm or deny a property or an attribute about the whole universe for example everything is mortal nothing is permanent. The first proposition is symbolized as you see one predicate general proposition everything is mortal we can symbolize as x dx is indicates that everything is mortal and the second proposition is also implies nothing is permanent. Nothing is permanent means you can say x implies px nothing is permanent it indicates that in predicate logic we symbolize like that we use the universal quantifier x for all and we use the symbol that ex for existential quantifier means tigers exist. Now you see their learners general propositions asserting relationship between two classes. Here you see this proposition states that one class is wholly or partially included in or exclusive from another class. So here we find all the four propositions of A, E, I, O all lions are animals no man is perfect and some students are clever some philosophers are not scientists. Here the traditional categorical propositions you see traditional categorical propositions A, E, I, O is there. Means general propositions asserting relationship between two classes here all lions are animals all lions are animals then no man is perfect then some students are clever some students are clever and some philosophers are not scientists some philosophers are not scientists so these are four categorical propositions which are included in general propositions asserting relationship between two relations between the two classes. The traditional categorical propositions belong to this category so you see we can symbolize here above the four examples like all lions are animals we can symbolize here x that is universal quantifier Lx implies Ex all lions are animals we symbolize in this way then X no man is perfect X Mx implies not Px this implies that no man is perfect then here also we use universal quantifier but in case of i propositions i categorical propositions some students are clever we use existential quantifier means some students are clever this is dot not Mx some students are clever then you see some philosophers are not scientists here also we use existential quantifier then some philosophers are not clever we use we symbolize in this way the four types of categorical propositions A, E, I, O so you see it means that given any X if X is a lion then X is mortal that the X is if it means that given any X if X is a lion then X is animal then you see again the next one given any X if X is a man then X is not perfect the third one it means that there is at least one X such that X is a student and X is clever and fourth one is that there is at least one X such that X is a philosopher and X is not scientist so this is all about the modern classification of propositions simple and compound singular and general now after going through this unit now there are some highlighting points I would like to give for you and that highlighting points you see proposition is the basic point of logical unit of logical thinking by proposition we mean any statement which must be either true and false a proposition is expressed in the form of a sentence but it is not identical with a sentence similarly the truth or falsity of a proposition is determined by the fact but a proposition is different from a fact only indicative sentences can be regarded as propositions because they can be just to be either true or false they are learners unlike traditional propositions unlike traditional logicians modern logicians do not accept that every proposition must be expressed in the same logical form that is subject copula and predicate according to modern logicians there are innumerable kinds of propositions there are some drawbacks of the traditional classification of proposition though traditional logicians try to express all type of propositions in the same logical form fundamentally they are different in their logical structures therefore there seems to arise some confusion in their classification of proposition in order to get rid of the defects and limitations of traditional classification of proposition modern logicians attempt to present their classification scientifically according to modern logicians there are three kinds of propositions simple compound and general a simple propositions contains only one statement on the other hand and compound proposition contains two or more simple propositions and general propositions are about classes now they are learners this is all about the summary of this unit modern classification of proposition simple compound and general in order to understand the unit in a very lucid manner you have to study some books and that books are you take logic in formal symbolic and inductive that is written by Sanda Sakramoti and another very important book introduction to logic written by I. M. Kopi, Kohen and Karl and Kohen another very important book modern elementary logic written by Susan Alstabing and very important one that is logic written by Ossockard and Ankush Sawant so I think they are learners you have understood the unit 6 modern classification of propositions simple compound and general thank you