CHAPTER 2 TERMS

2. TERMS

a) Meaning of Terms- Connotation and Denotation of terms- Positive and Negative terms, Contrary and Contradictory terms.
b) Distinctions between – Proposition and Sentence, Proposition and Judgment, Proposition and Fact, Constituent and Component.

c) Distribution of terms- for universal, particular, affirmative and negative terms.

The TERM is a word that is independently used in logical arguments and term is word that can stand on its own and express a meaning. Naturally, all words cannot become terms. Let us see the meaning and types and classification of terms in details:

a) Meaning of Terms- Connotation and Denotation of terms- Positive and Negative terms, Contrary and Contradictory terms.

Term is a “Word” that can stand on its own and so can become a subject or predicate of proposition in logic. We know that “Word” is a meaningful combination of alphabets.

Words are classified into two types on the basis of their function of expressing or enhancing the meaning. The types of words are, categormatic & syntacategormatic.

Let us see the definitions of the types of words:

Catergormatic are the words that can express some meaning or their own, so, they can be used as terms in any proposition.

Syncategormatic are the supporting words that are used to connect or enhance the catergormatic words. i.e. Terms.

The syncategormatic words cannot express any meaning on their own, so they do not become Terms. Only categormatic words have capacity to become terms.

Any word or term differs in its meaning as per its use. Some times a word has one dictionary meaning, but is used in a different sense. This time, if we do not understand the correct meaning, we may get confused. So, we must note that the Terms have Two senses, on the basis of the meaning indicated by them. These senses are called Connotation & Denotation.

Let us see these types in details:

Connotation indicates the meaning of a word accepted by Custom or Community. Connotation is a commonly understood association that a word or phrase carries, in addition to the explicit or literal meaning of that word or phrase that is called its Denotation. Connotation is either positive or negative.

Denotation indicates the Technical Meaning of a word accepted & listed in a Dictionary. Denotation is the transition of a sign to its meaning that dictionaries try to define.

Sometimes, denotation is contracted to connotation. e.g. “You are brilliant” in sarcastic way means, “You are an Idiot!” So its Connotation becomes opposite to its Denotation, i.e. actual meanings.

The terms are seen to indicate two things, quality and quantity. Quality indicates the presence or absence of things stated while quantity indicates number of group member that possess that quality.

The terms indicate either the presence or absence of something. According to their function, they are classified in to positive and negative.

Let us see how:

Positive Term is the term which affirms some thing or quality in Something.

Negative Term is the term which denies something or quality in something.

The positive and negativeness of a term is called its quality.

The terms indicate either one individual, or a small part of group indicated by the word or the whole group indicated by the word. According to the number of individuals indicated in the term, we have singular, particular and universal terms.

Let us see how:

A singular term is a term that speaks something about one single individual person, thing or entity. The fact stated here can be either positive or negative.

A particular term is a term that speaks about a small part of the group indicated by a term. The thing spoken can be either positive or negative.

A universal term is a term that speaks about the entire group indicated by it. This statement can be either positive or negative.

The singularity, particularness or universalness of a term is called its quantity.

Generally we find that in subject predicate class membership propositions that are used in inferences, the predicate term is always universal, and we check the quantity of the subject term to classify the proposition.

On the basis of the quality and quantity indicated in terms, the terms are classified into three more types. These classifications depend on the difference in quality, or quantity or both. When only the quality is different, the terms are called contrary, when only quantity is different, the terms are called sub-alternate and when both the quality and quantity is different, the terms are called contradictory.

Let us see this classification in details:

Contrary Terms are the Terms that have the same quantity. Generally, the contrary relationship indicated the relation between two Universal terms. If the terms that are same in quantity and differ in quality, but are Particular, the relationship is called sub–contrary. In short, contrary relation exhibits the pairs of terms that are same in quantity and different in quality.

Sub alternate or sub altern terms are the terms that have the same quality but different quantity. This means, when a pair of affirmative or negative terms has one universal and one particular term, the pair indicates a sub altern relationship. This means, the universal affirmative and particular affirmative terms indicate a sub altern relationship and so do the universal negative and particular negative terms.

Contradictory Terms are the terms that differ both in Quality & Quantity. Thisx means, in a pair of two contradictory terms, if one is universal affirmative, the other will be particular negative and if one is particular affirmative, the other will be universal negative.

Table to explain opposition of terms at a glance

Type of term	Quality	Quantity
Contradictory	X	X
Contrary	X	same
Sub Contrary	X	same
Subaltern	same	X

b) Distinctions between –

Proposition and Sentence,

Proposition and Judgment,

Proposition and Fact,

Constituent and Component.

To classify the propositions and compare them further with sentence, judgment, fact and so on, we must first note the basics of an expression.

Every time when we try to express some meaningful thing, we use a language. A language is made up of alphabets and connecting punctuation symbols. The first thing we get in any language is a basic meaningful combination of alphabets. A Word is a meaningful combination of Alphabets. Then we combine these meaningful combinations of alphabets to make more sense. This time we get a sentence. Sentence is a meaningful Combination of Words. In a sentence, as per the requirement of its meaning, we also use different punctuation marks. We have many different types of sentences, but all do not have the capacity to be used in logical arguments. Only the statements that state the presence of something or absence of something, that means, only the assertive sentences, are the ones that can be used in logical arguments. These are also called statements or propositions.

Statement or Proposition is any subject less or subject predicate, relational or class membership. universal, particular or singular, simple or compound, Affirmative or negative; assertive sentence.

i) Proposition and Sentence

As we have seen above, Sentence is a meaningful Combination of Words where as, Statement or Proposition is any subject less or subject predicate, relational or class membership. universal, particular or singular, simple or compound, Affirmative or negative; assertive sentence.

So, any sentence has a power to make a meaning, but it does not have a power to be a part of an argument. On the other hand, the sentences that can be used in an inference, are called statements or propositions.

Proposition is a sentence that asserts some thing in positive or negative manner. Propositions are of two types, simple and compound. Simple statements are either subject-less or with a subject and predicate. In either case, the verb seen in simple statements is only one. On the other hand, when two or more simple statements are combined together & form a statement we get compound statement.

ii) Proposition and Judgment

Proposition is a statement that states a matter of fact. It does not carry any opinion or view of the person making the statement. It just states what is. This means, a proposition or statement states only pure undiluted non-tampered facts without and smell of right and wrong, good or bad, proper or improper, desirable or undesirable, nice or not nice etc. etc.

Judgment is a statement Expressing the Opinion or View of Someone about some event or situation. This view may or may not indicate the fact or truth. Those who give a judgment, state if something is good or bad, right or wrong, and desirable or undesirable. This means, what they say, is not what is, but what they feel. In logic, we value what is, and not what we feel. So, proposition is something that is used in logic and not judgement.

Iii) Proposition and Fact.

Fact is the Actual Event or Things that can be objectively verified by any one. This means, fact is never true or false, right or wrong. Fact is just fact. Just as we do not need any one's opinion to check what is the time right now, watch in hand tells it to anyone, we need not check whether fact is true or not. It is always true.

Proposition is statement that states something as a matter of fact. This means, though the proposition is stating something, it may or may not be agreeing with actual fact. Sometimes, a statement says something as a matter of fact, but is actually not so, like, in a statement, “Chintu met a man who had a tail and two horns on his head.” here, the proposition is stating something as a fact, but actually, it is an imagination that is contrary to fact. The argument based on such statement may be logically correct, but still may not be stating facts.

iv) Constituent and Component

This is like any other thing or class, every proposition has two main parts.

One is the part without which a statement cannot stand. This is the constituent.

The other is a part that enhances the statement, but the statement can still stand without this part. Such part is called a component.

In short, constituent is like the vital parts of a person without which one cannot be alive, while, components are like the body parts, without which, one may be disabled, incomplete or handicapped, but still will be alive.

Exactly like that, a proposition can become a proposition just because a constituent, and that proposition gets enhanced in the presence of its components.

So, a Constituent is the integral part of any proposition and gives meaning to the proposition, without which the proposition cannot exist.

Component is the part of a proposition that enhances the proposition by adding itself to the constituent, but which can be detached from the proposition without extinguishing the existence of the proposition.

100. Distribution of terms - universal, particular, affirmative, negative terms.

Distribution of Terms : When we state something about the entire group indicated by the Terms, the Term is distributed. In a universal proposition Subject is Distributed and in a negative proposition Predicate is Distributed.

Quantity of Proposition : It is the quantity of the group of the subject of a proposition. This is of two types. Universal & Particular. The Universal quantity distributes the subject not the particular.

Quality of Proposition : - It is the quality of the Predicate of the proposition. This is affirmative or negative. Affirmative says that subject or its group belongs to the group of predicate. Here the predicate terms is not distributed. Negative quality says that the subject or its group does not belongs to the group of predicate. Here the predicate is distributed.

TABLE explaining the DISTRIBUTION of terms

Type	S	P
A	Universal	Affirmative
E	Universal	Negative
I	Particular	Affirmative
O	Particular	Negative

 For the proposition types:

A   S X

E   S P

I    X X

O  X P

CHAPTER 1: NATURE OF LOGIC

1. NATURE OF LOGIC

A) Traditional and Modern definitions of Logic
B) Basic features of Inductive and Deductive reasoning. Their uses in Law Courts
C) Some basic logical concepts –Form, Content, Truth , Validity, Inference, Implication.

Logic is a science of valid reasoning.

Logic is a word that comes from the Greek word λογική pronounced as logikē that means, the study of reasoning.

All the places where reasoning is needed, logic is needed. The more accurately we use our reasoning, the more effective is our work in that area. So all those who think, use logic knowingly or unknowingly.

Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, and computer science. Logic examines general forms which arguments may take, which forms are valid, and which are fallacies. It is one kind of critical thinking. In philosophy, the study of logic falls in the area of epistemology, which asks: "How do we know what we know?" In mathematics, it is the study of valid inferences within some formal language.

Logic has origins in several ancient civilizations, including ancient India, China and Greece. In west, Logic was established as a discipline by Aristotle, who established its fundamental place in philosophy.

The study of logic was part of the classical trivium. Averroes defined logic as "the tool for distinguishing between the true and the false." Richard Whately, defined logic as "the Science, as well as the Art, of reasoning." Frege, defined logic as "the science of the most general laws of truth."

The concept of logical form is central to logic, it being held that the validity of an argument is determined by its logical form, not by its content. Traditional Aristotelian syllogistic logic and modern symbolic logic are examples of formal logic.

Informal logic is the study of natural language arguments. The study of fallacies is an especially important branch of informal logic. The dialogues of Plato are good examples of informal logic.

Formal logic is the study of inference with purely formal content. An inference possesses a purely formal content if it can be expressed as a particular application of a wholly abstract rule, that is, a rule that is not about any particular thing or property. The works of Aristotle contain the earliest known formal study of logic. Modern formal logic follows and expands on Aristotle. In many definitions of logic, logical inference and inference with purely formal content are the same. This does not render the notion of informal logic vacuous, because no formal logic captures all of the nuances of natural language.

Symbolic logic is the study of symbolic abstractions that capture the formal features of logical inference. Symbolic logic is often divided into two branches: propositional logic and predicate logic.

Mathematical logic is an extension of symbolic logic into other areas, in particular to the study of model theory, proof theory, set theory, and recursion theory.

A) Traditional and Modern definitions of Logic

Traditional Logic is the type of logic propagated by Aristotle. This is popularly known as traditional formal logic. This is because here, the form of statements used in arguments is given total importance. The traditional formal logic is general designation for the systems of deductive logic that do not involve the use of formal languages, or the apparatus of mathematical logic. The basis of traditional logic is syllogistic reasoning.

Traditional logic is defined as “a system of formal logic mainly concerned with the syllogistic forms of deduction that is based on Aristotle and includes some of the changes by contemporary logicians.”

Modern Logic on the other hand contains more form based relationships in the logical thinking. So, the modern logic is not limited to syllogism based arguments, but it goes much beyond them. It becomes mathematical and symbolic. This is the reason why after the modern logic was developed, it started being used practically in every science where thinking in the right way is needed.

Modern logic is defined as “logic where the subject developed into a rigorous and formalistic discipline whose exemplar was the exact method of proof used in mathematics.” The development of the modern "symbolic" or "mathematical" logic is the most significant in the history of logic, and in human intellectual history.

B) Basic features of Deductive and Inductive reasoning.

Logic is divided into two types, these are inductive and deductive reasoning.

The Deductive Reasoning is a reasoning where the conclusion stays within the scope of its supporting statements. It is said that deductive reasoning involves in drawing logical conclusions from definitions and axioms. We can also say that deductive Reasoning involves in deriving known conclusions from known facts. As a result, the conclusions of deductive reasoning are certain.

The Inductive reasoning is a reasoning where conclusion goes beyond the scope of its supporting statements. Many say that inductive reasoning involves in drawing general conclusions from specific examples. We also say that Inductive Reasoning involves in deriving unknown conclusion from known facts. This is the reason why conclusions of Inductive reasoning are probable and not certain.

Though induction and deduction are the two types of logical reasoning, they are not watertight compartments. The general statements that we use as supporting statements in deductive arguments, actually are result of inductive inferences.

So, we find that Induction is of two types, perfect and imperfect.

In perfect induction, we get conclusion from supporting statements, i.e. premises, this conclusion goes beyond the scope of premises, and then we verify and test this conclusion by using some methods that are similar to deduction.

In imperfect induction, we get conclusion from the supporting statements, i.e. premises, this conclusion says something beyond the scope of premises, but then we do not verify and test this conclusion. We just leave it as it is. So, the conclusion of imperfect induction is always probable.

Deduction versus Induction

Aristotle used to classify the type of arguments using syllogism. But all arguments cannot be fitted in the type of syllogism. We can use a simple test for inductive and deductive arguments. The premises in a deductive argument guarantee the truth of the conclusion, so, 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 false conclusion.

Aristotle views inductive syllogism as scientific induction and therefore as a more rigorous form of inductive argument. 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.

Uses of logical reasoning in Law Courts:

In the field of law, we need reasoning in order to present the matter of any litigant effectively, so that we can help him get justice in the existing frames of law. But even the opposite side litigant who has a contrary view also wants justice, so the aim of a good lawyer is always to disclose the truth and just situation. Logical reasoning is absolutely necessary for this as without logical reasoning we cannot find out the truth behind the stories told by the litigants.

C) Some basic logical concepts – Form, Content, Truth , Validity, Inference, Implication.

Logic as we saw, is a science of valid reasoning. In order to know what is valid reasoning, we must first have some concepts clarified. Also, Logic can be best best understood if we understand the basic concepts of logic. So, let us see the definitions of some basic concepts in logic:

Word, is a meaningful group of alphabets used in any language.

Syncatagormatic word, are the words that are used to enhance the meaning of words that can stand on their own. So, the Syncatagormatic words do not make any meaning on their own. They depend on other words for their meaningfulness.

Catagormatic word, is a word that has its own meaning, so it can stand on its own in the process of expressing a meaningful concept.

Sentence, is a meaningful group of words used to convey any meaning.
Statement, is a sentence that asserts some affirmative or negative fact.
Proposition, is a statement used in logical arguments. This means, in logic, a statement is called a proposition.
Form, stands for the relationship of various parts of a statement within itself and in a set of statements called argument.
Content, is the matter of facts mentioned in the statement or argument.
Truth, is the agreement of facts mentioned in an argument with reality.
Validity, is the appropriateness of relationship between various parts of argument.
Inference, is a set of propositions or statements where, on the basis of one or more statements one statement is obtained as a conclusion.

Implication, is a type of statement where the truth of one component is indicated or suggested by the truth of another. Here, the component on which the truth of another component depends is the first component called antecedent and the component that follows from the first component is the consequent.

converting a statement into logical from

There are four standard forms of categorical propositions such as A, E, I and O-propositions having the structure of the form, 'All S is P' 'No S is P’, 'Some S is P' and 'Some S is not P' respectively. Thus, we know that the logical structure of any categorical proposition exhibits the following four items in the order as given below.
Quantifier (Subject term) copula (predicate term)
Here the first item is the 'quantifier' (or more precisely the words expressing the quantity of the proposition). It is attached to the subject term only. The second item in any logical proposition is the subject term. The predicate term, that expresses something about the subject, comes after the copula. The copula is placed in between the subject and predicate term.
Further, the quality of the proposition is expressed in and through the copula. The copula and the predicate term are respectively the third and fourth logical elements of a categorical proposition. Thus, a categorical proposition which is in standard form must exhibit explicitly the subject, the predicate, the copula, its quality and quantity. Let us call a categorical proposition regular if it is in its standard form, otherwise it is called irregular.
In our ordinary language most of the categorical propositions are irregular in nature. Even though there are irregular categorical propositions they can be put in their regular form. It should be noted that while reducing an irregular categorical proposition into its standard form, we should pay enough attention to the meaning of the proposition so that the reduced proposition is equivalent in meaning to its irregular counterpart.
Before describing the method of reduction of irregular propositions into their regular forms, it is profitable to understand the reasons for irregularity of a categorical proposition: The irregularity of any categorical proposition may be due to one or more of these following factors.
(i) The copula is not explicitly stated; rather it is mixed with the main verb which forms the part of the predicate
(ii) Though the logical ingredients of a categorical proposition are present in the sentence yet are not arranged in their proper logical order.
(iii) The quantity of a categorical proposition is not expressed by a proper word like 'all', 'no' (or none), 'some' or it does not contain any word to indicate the quantity of the proposition.
(iv) All exclusive, exceptive and interrogative propositions are clearly irregular.
(v) The quality of the proposition is not specified by attaching the sign of negation to the copula.
Keeping these factors in mind, let us describe systematically the method of reduction of an irregular categorical proposition into its standard form (or into a regular proposition). Below we describe the method of reduction.
I. Reduction of categorical propositions whose copula is not stated explicitly
In our ordinary use of language, very often the copula is not explicitly or separately expressed but is mixed with the main verb. The main verb in such a case forms the part of the predicate. The moment copula is identified; the other items of a logical proposition are brought out in a usual manner. We know that the copula of any logical proposition must be in present tense of the verb "to be" with or without the sign of negation.
Now let us consider an example of an irregular proposition, where the copula is not explicitly stated. "All sincere students deserve success". This is an irregular proposition, as the copula is clearly mixed with the main verb of the proposition. The method of reducing such irregular sentences into regular ones is as follows. The subject and the quantifier of the irregular proposition should remain as they are, while the rest of the proposition may be converted to a class forming property (i.e. term) which would be our logical predicate.
In our above example 'All' is the quantifier attached to the subject 'sincere students'. We should not touch the quantifier nor the subject term of the proposition, they should remain where they are. On the other hand, the rest of the proposition 'deserve success' should be converted into a class forming property 'success deserving'. This should be our logical predicate. Then we link the subject term with the predicate term with a standard copula. Thus,
"All sincere students deserve success." Irregular proposition.
"All sincere students are success deserving." A - Proposition.
"All people seek power." Irregular proposition.
"All people are power seekers." A - Proposition.
"Some people drink Coca Cola." Irregular proposition.
"Some people are Coca Cola drinkers." I - proposition
II. Irregular propositions where the usual logical ingredients are all present but are not arranged in their logical order.
Consider the following examples of irregular propositions. "All is well that ends well" and "Ladies are all affectionate." In these cases, first we have to locate the subject term and then rearrange the words occurring in the proposition to obtain the regular categorical proposition. Such reductions are usually quite straight forward. Thus we reduce the above two examples as given below.
"All is well that ends well." Irregular proposition
"All things that end well are things that are well." A - Proposition
"Ladies are all affectionate." Irregular proposition
"All ladies are affectionate." A - Proposition
III. Statements in which the quantity is not expressed by proper quantity words. Some propositions do not contain word like 'All', 'No', 'some' or contain no words to indicate the quantity. We reduce such a type of irregular proposition into its logical form as explained below.
Here we have to consider two sub-cases : sub-case (i) where there is indication of quantity but no proper quantity words like 'All', 'No', on 'Some' are used and Sub­ case (ii) where the irregular proposition contains no word to indicate its quantity.
Sub-case (i): Affirmative sentences that begin with words like 'every', 'any', 'each' are to be treated as A-propositions, where such words are to be replaced by the word "all" and rest of the proposition remains as it is or may be modified as necessary. The followings are some of the examples of this type.
"Every man is liable to commit mistakes." Irregular proposition.
"All men are persons who liable to commit mistakes." A - Proposition.
"Each student took part in the competition." Irregular proposition.
"All students are persons who took part in the competition." A - Proposition.
"Any one of my students is laborious." Irregular proposition.
"All my students are laborious." A - Proposition.
A negative sentence that begins with a word like 'every', 'any', 'each', or 'all' is to be treated as an O-proposition. Any such proposition may be reduced to its logical form as shown below.
"Every man is not honest". Irregular proposition
"Some men are not honest." O - Proposition
"Any student cannot get first class." Irregular proposition.
"Some students are not persons who can get first class." O - Proposition.
"All is not gold that glitters." Irregular proposition.
"Some things that glitter are not gold." O - Proposition.
Sub- Case (ii):
"Sentences with singular term or definite singular term without the sign of negation are to be treated as A-proposition. For example, "Ram is mortal.", "The oldest university of Orissa is in Bhubaneswar." are A-propositions.
Here the predicate is affirmed of the whole of the subject term. On the other hand, sentences with singular term or definite singular term with the sign of negation are to be treated as E-propositions. For example, "Ram is not a student" and "The tallest student of the class is not a singer" are to be treated as E-propositions. These are cases where the predicate is denied of the whole of the subject term.
IV. “Sentences beginning with the words like 'no', 'never', 'none' are to be treated as E-propositions. The following sentence is an example of this type.
"Never men are perfect." Irregular proposition
"No man is perfect." E - Proposition
V. Affirmative sentences with words, like 'a few', 'certain', 'most', 'many' are to be treated as I-propositions, while negative sentences with these words are to be treated as
O-propositions. Since the word 'few' has a negative sense, an affirmative sentence beginning with the word 'few' is negative in quality. A negative sentence beginning with the word 'few' is affirmative in quality because it involves a double negation that amount to affirmation. The following are examples of above type.
"A few men are present." Irregular proposition.
"Some men are present." I - proposition.
"Certain books are good." Irregular proposition.
"Some books are good." I - proposition.
"Most of the students are laborious." Irregular proposition.
"Some students are laborious." I - proposition.
Here we may note that 'most' means less then 'all' and hence it is equivalent to 'some'.
"Many Indians are religious." Irregular proposition.
"Some Indians are religious." I - proposition.
"Certain books are not readable." Irregular proposition
"Some books are not readable." O - Proposition
"Most of the students are not rich." Irregular proposition.
"Some students are not rich." O - Proposition
"Few men are above temptation." Irregular proposition
"Some men are not above temptation." O - Proposition
"Few men are not selfish." Irregular proposition
"Some men are selfish.' I
VI. Any statement whose subject is qualified with words like 'only', 'alone', 'none but', or 'no one else but' is called an exclusive proposition. This is so called because the term qualified by any such word applies exclusively to the other term. In such cases the quantity of the proposition is not explicitly stated.
The propositions beginning with words like 'only', 'alone', 'none but' etc are to be reduced to their logical form by the following procedure. First interchange the subject and the predicate, and then replace the words like 'only', 'alone' etc with 'all'. For example,
"Only Oriyas are students of this college." Irregular proposition.
"All students of this college are oriyas." A - Proposition.
"The honest alone wins the confidence of people." Irregular Proposition.
"All persons who win the confidence of people are honest." A-proposition.
VII. Propositions in which the predicate is affirmed or denied of the whole subject with some exception is called an exceptive proposition. An exceptive proposition may be definite or indefinite. If the exception is definitely specified as in case of "All metals except mercury are solid" then the proposition is to be treated as universal and if the exception is indefinite, as in case of "All metals except one is solid", the proposition is to be treated as particular.
"All metals except mercury are solid." is a universal proposition which means
"All non-mercury metals are solid."
Now let us consider an example where the exception is indefinite. For example, "All students of my class except a few are well prepared", it is to be reduced to an I-proposition as given below.
"All students of my class except a few are well prepared." Irregular proposition.
"Some students of my class are well prepared." I - proposition.
VIII. There are impersonal propositions where the quantity is not specified. Consider for example, "It is cold", "It is ten O'clock". In such cases propositions in question are to be reduced to A-proposition because the subject in each of these cases is a definite description.
"It is cold". Irregular proposition
"The whether is cold." A - Proposition.
"It is ten O'clock." Irregular proposition.
"The time is ten O'clock." A - Proposition.
There are some propositions where the quantity is not specified. In such cases we have to examine the context of its use to decide the quantity. For example, consider following sentences (1) "Dogs are carnivorous", (2) "Men are mortal", (3) "Students are present." In first two examples, the quantity has to be universal but in the third case, it is particular. Thus, their reductions into logical form are as follows.
"Dogs are carnivorous." Irregular proposition.
"All dogs are carnivorous." A - Proposition.
This is so because we know that "being carnivorous' is true of all dogs.
"Men are mortal." Irregular proposition.
"All men are mortal." A - Proposition
Here 'being mortal' is generally true of men. But in the proposition "Students are present", we mean to assert that some students are present". So the proposition "Men are mortal" is reduced to "All men are mortal" But in the example "Students are present", 'being present' is not generally true of all students.
So the proposition "Students are present" is reduced to "Some dents are present" which is an I-proposition. Thus the context of use of a proposition determines the nature of the proposition.
IX. Problematic propositions are particular in meaning. For example "The poor may be happy" should be treated as a particular proposition, because what such a proposition asserts is that it is sometimes true and sometimes false.
Thus, "The poor may be happy" is reduced to "Some poor people are happy", which is an I-proposition
X. Similarly, there are propositions where the quantity is not specified but their predicates are qualified by the words like 'hardly', 'scarcely', 'seldom'. Such propositions should be treated as particular negative. For example, "Businessmen are seldom honest", is an irregular proposition. It is reduced to "Some businessmen are not honest". If such a proposition contains the sign of negation that these proposition is to be treated as an I-proposition.
For example, "Businessmen are not seldom honest." is to be reduced to "Some businessmen are honest", which is an I - proposition. This is so because it involves a double negation which is equivalent to affirmation.

Proposition Relationships in EDUCTION @ glance

Proposition Relationships in EDUCTION @ glance

Relationship	Changed	Type	Original
Original = S-P			All S is P	No S is P	Some S is P	Some S is not P
			A	E	I	O
Obverse =	All S is non P	A		All S is non P
S-P	No S is non P	E	No S is non P
	Some S is non P	I				Some S is non P
	Some S is not non P	O			Some S is not non P
Converse =	All P is S	A				X
P-S	No P is S	E		No P is S		X
	Some P is S	I	Some P is S		Some P is S	X
	Some P is not S	O				X
Obv Conv=	All S is non P	A		All S is non P		X
P-S	No S is non P	E				X
	Some S is non P	I				X
	Some S is not non P	O	Some S is not non P		Some S is not non P	X
Part Inv =	All non S is P	A			X	X
S-P	No non S is P	E			X	X
	Some non S is P	I		Some non S is P	X	X
	Some non S is not P	O	Some non S is not P		X	X
Full Inverse =	All non S is non P	A			X	X
S-P	No non S is non P	E			X	X
	Some non S is non P	I	Some non S is non P		X	X
	Some non S is not non P	O		Some non S is not non P	X	X
Part Con +ve	All non-P is S	A			X
P-S	No non P is S	E	No non P is S		X
	Some non P is S	I		Some non P is S	X	Some non P is S
	Some non P is not S	O			X
Full Con +ve	All non P is non S	A	All non P is non S		X
P-S	No non P is non S	E			X
	Some non P is non S	I			X
	Some non P is not non S	O		Some non P is not non S	X	Some non P is not non S