Premises: the premises that has the major term is callled major premises and the premises that has the minor term is called minor premise.
Term:the predcate of major premises is called major term ans is denoted by S and the terms which are common in both the premises are called middle term which is denoted by M. for example:
All men are mortal (Major Premises)
Ram is man (Minor premise)
Ram is mortal (Conclusion)
Here 'mortal is a major tern and its subject is ot minor term hence because it is in minor premise also so it is middle term. Minor term here is "ram".
Type of Syllogism:
1. Categorical: Here all the prepositions are categorical in positive or negative form and no doubtfullness is seen at all, e.g.,
All graduates are eligible (major)
All eligible are men (Minor)
Some Eligible are graduates (Con...)
2. Hypothetical: The syllogism of this type uses prmise of conditions "If he works had, he will succeed." Here the first part is called antecedent and the second part is called consequent. in this type of syllogism the major premise is hypothetical losing some thing and the minor premise will be categorical, e.g., If he comes, I shall meet Him. In this syllogism
If he come (Major)
I shall meet him (Minor)
3. Disjunctive: In this type of syllogism the major premise is disjunctive and the other two premises are categorical, e.g.,
Either he is an hionest man or a thief. (Major)
He is an honest man (Minor)
He is not a thief (concl....)
4. Relational: Here relations between various terms are shown orderl, e.g.,
A>B, B>C, C>D
so A>D (Concl....)
5. Deilmma: In such type of syllogism the major premise is double hypthetical and minor premise is a double hypthotical and minor premise is of disjunctive type and the conclusion will either disjunctive or categorical,.eg.
(i) If these books confirm to Quran they are reliable if they do noot they ary are superfluous.
(ii) Either they confirm to Quaran or they do not
(iii) Either they are reliable or superfluous
In the above example the seconf and third premises are disjunctive.
6. Copula: The verb used in the premises in logic is called copula. for this purpose "is" and "are" generally used and logicians always talks in the term of the present
Types pf Prepositions;
1. From the quantative point of view:-from the quality of point of view it is of two types:
1. Universal Affirmative:- It is called "A" prepositions, ie,
All labourers are hard working
all children are true speaking
2. Universal negative:-they are callled "E" prepositions, ie,
No minister is dedicated
No human being is happy etc.
3. particular Affirmative: They are callef "I" prepositions, ie,
some men are hard-working
some people are lobourious
4. particular Negative:-they are called "O" prepositions,ie,
Some men are not hardworking
some ministers are not honest
Disturb of terms in propositions:
In case of A propositions only subject is disturbed
In case of E propositions both subject and predicate are disturbed
In case of I propositionsneither subject nor predicate is disturbed
In case of O propositions only predicate is disturbed
Types of Logical Inferences:
A. Immediate Inference
B. Mediate Inference
a) Predicate becomes the subject and the subject becomes the predicate.
b) Quality of proposition does not undergo and change, ie, Affirmative propositions will lead to affirmative conclusion and negative proposition well lead to negative conclusion.
c) A proposition is converted into I proposition. I proposition is converted into I and E into E itself.
d) Proposition O can not be converted at all. Examples will illustrates these point
* All ministers are politicians (A propositions). its converted from is
Some politicians are ministers (I pro-positions)
* Some men are har-working ((I pro-position) It converted from is:
Some hard working are men (I pro-Position)
* No man is immortal (E Proposition). is converted as
No Immortal is man (E proposition)
* Some students are not intelligent(O Proposition). it can be converted as
Some intelligent are not students.
2. Observations: Observed from of inference is based on the following rules:
b) Negative propostions are changed into affirmative and vice-versa, ie, A is observed into E and E is observted into A proposition.
c) The quality of the proposition will remain the same. If the proposition is universal it will remain universal and if it is particular it will remain particular in the observed from the conclusion.
Following example will illustrated these points clearly
1. all religious people are contended people (Proposition A)
No religious is not contended people (E)
2. No man is fully impartial (E)
All men are not fully impartial (A)
3. Some men are hard of hearing. (O)
Some men are not hard of Hearing (I)
4. Some doctors are not good (O)
Some doctors are good (I)
Validity table: In order to test the validity of the conclusions we may also use the following table Here
T & t = Truth
F & f = False
d = Doubtful
The whale is a mammal (Minor)
The whale is a certebrate (Concl...)
2. Every categorical syllogism must containn only three premises-major, minor and the conclusion,eg,
Man is Mortal (1)
Cow is mortal (2)
Ram is a man (3)
There are three major premises excluding conclusion so no conclusion can be drawn from them.
4. the term is not distributed in the premises cannot be distributed in the conclusion. an example will illustrate the point:
All rational beings are responsible for their action (1)
Brutes are not rational being (2)
Brutes are not responsible for their action (3)
5&6: Two negative premises yeild no conclusion and if one of the premises is negative, the conclusion muse be negative,ie,
No student dislikes games (1)
No game is fully satisfactory (2)
No conclusion can be drawn from these two premises.
No human being dislikes justice (1)
Students are human being (2)
Students do not dislike justice (concl...)
This man is not throughtly upright
This man is not to be trusted.
7. No conclusion can be drawn from two particular premises
8. If one of the premises is particular the conclusion must be partcular.
Four Possible arguments in a LOGIC;
S= Subject or Minor Term
P= Predicate of Major Term
M= Middle Term
Figure 1 Figure II Fugure III Figure IV
1. AAA 5. EAE 09. AAI 15. AAI
2. EAE 6. AEE 10. IAI 16. AEE
3. AII 7. AIO 11. AII 17. IAI
4. EIO 8. AOO 12. EAO 18. EAO
13. OAO 19. EIO
14. EIO
Some examples will illustrate these points
1. All spirituals love humanity (A)
All indians are spirituals (A)
All indians love spirituality (A)
AAA sylogism is here. thus conclusion is correct according to Figure no 1
2. All students are hardworking (A)
Anil is a students (I)
Anil is hard working (I)
Syllogism no 3 (ALL) is Here according to Figure no 1
3. No human being is animal (E)
All animals have four legs(A)
No man has four legs (E)
this conclusion is not valid becasue EAE is not in Figure 4
4. Some studetns are faithful (I)
All students are Indian (A)
Some Indians are faithful (I)
Syllogism no 10 (IAI) is here. Thus it is valid according to figure no 3
5. All animals like grass (A)
Lion does not like grass (O)
Lion is not an animal (O)
This conclusion is valid because AOO is their in the figure no 2 so this conclusion is correct.
Rules of Hyoithetical Syllogism: It si based on the conclusion between a supposition or condition and its consequences. It starts by the word, if, supposing, granted that, as etc. This part of the syllogism which expresses the condition is called antecedent ans the clause stating the result is called comsequent. In such type of syllogism the hypothetical premise is the major premise and the categorical proposition is the major premise. Following rules must be kept in view whole arriving at valid conclusions in such cases.
Either affirm the antecedent or deny the consequent, eg,
1. If he were well, he would leave the place
2. he has not left the place
3. Conclusion (He is not well)
Here the consequent is denied. in the following example antecedent is affirmed
1. If it rains toady, he shall not go to school
2. It is raining
3. Conclusion (He shall not go to school)
So always affirm the antecedent or deny the consequent as the case may be for valid conclusions. If by mistake, consequent is affirmed the following invalid conclusion will be drawn
1. If prefect justice prevailed, the rich would not be permitted to exploit the poor.
2. The rich are not premitted to explot the poor
3. Conclusion 9Perfect justice is prevailing)
The above rules is also followed in disjunctive syllogism.