This document discusses reasoning and inference. It defines reasoning as a mental process of inferring the agreement or disagreement of two ideas based on their relation to a common third idea. There are two methods of reasoning: induction and deduction. Inference refers to drawing conclusions from given propositions. There are two types of inference - immediate and mediate. Immediate inference draws directly from one proposition to another. Mediate inference involves reasoning through multiple steps. The document also discusses various logical rules and relationships between categorical propositions like conversion, obversion, and opposition.

1. Reasoning: Immediate
Inference
This chapter takes , as its focus, the third mental operation called
Reasoning and the processes it involves.

2.  Reasoning is a mental operation through which the
agreement or disagreement of two(2) ideas is inferred from
their known relation to a common third idea.
A. Definition of Reasoning

3.  There are two methods involved in reasoning :
1. Induction, and
2. Deduction
Induction or inductive reasoning is one which
proceeds from universal data to particular and
individual conclusion, e.g. :
Juan is a man.
Juan is mortal.
All men are mortal.
B. Methods of Reasoning

4. On the other hand, deduction or deductive reasoning is one
which proceeds from universal data to particular and individual
conclusion, e.g. :
All animals are mortal.
All humans are animals
All humans are mortal.
We will, however, explain in detail the logical
principles governing deduction and induction in the
succeeding pages. As of the moment, we will
concentrate on inference.

5. In the preceding pages, we made sample
explanations that reasoning is expressed
through inference. By this we mean that when
we speak of reasoning we mean inference or
vice-versa.
True enough, inference has its distinct meaning
(compared to reasoning), but then since inference is the
manner through which reasoning , as a mental operation
, is expressed, so it would be good to take these two
terms as having correlative existence and likewise having
synonymous meaning.

6. Definition of Inference
Inference refers to any process through which the mind proceeds
from one or more propositions to other propositions whose
meanings are already implied in the former.
Examples:
All men are mortal.
Julius is a man.
Julius is mortal.
John is man.
John is mortal.

7. In the first example, the first proposition: “All men are mortal”
enunciates that all creature who are human beings bound to be
mortal.
In the second and thirds propositions, respectively: ”Julius is a
man,” therefore,” Julius is mortal” the sweeping idea that any
human being is bound to be mortal permeates. Thus in as much
Julius is a human being therefore, he is bound to be mortal.
Simply put in inference the mind proceeds to draw one or more
propositions (the first proposition :”All men are mortal”, to other
propositions (Julius is a man” therefore, “Julius is mortal”).
Evidently, the meaning of both the second and the third
propositions are already contained by the first proposition.
The same contention can be pursed with regard to the second
example: “John is a man. Therefore, john is a mortal”. This is
because the idea “mortal” is impliedly contained in the idea of
“man” so that if one is a man it follows that he must necessarily
be mortal.

8. D. Kinds of inference
Basically, there are two (2) kinds of inference, namely : (1)
Immediate: and (2) Mediate. Under the immediate
inference, we will discuss the following : eduction and
logical proposition (or oppositional inference). In our
advertent discussion of eduction, we will consider the
following conversion, obversion, contraposition, and
invension. And in our treatment of logical opposition, we
will discuss contradictory, contrary, subcontrary, and
subaltern oppositions and the rules governing their
oppositions. Under mediate inference, we will discuss only
simple categorial syllogism.

9. E. Immediate Inference
Immediate inference is a process of
reasoning, through which the mind passes
directly from one proposition to a new
proposition which is nothing else but a
reformulation (partial or complete) of the
very exact meaning or truth as expressed in
the original proposition.

10. It contains only two terms :
1. Subject term
2. Predicate term
Example :
No metals are stones.
(S) (P)
No stones are metals.
(P) (S)

11. E.1 Eduction
This is a kind of immediate inference where a new proposition is
being formulated either by interchanging the subjectand predicate terms of
the original proposition or by the use or removal of negatives.
4 kinds of Eduction
1. Conversion
2. Obversion
3. Contraposition
4. Inversion

12. E.1.1 CONVERSION
This refers to a formulation of a new proposition by way of
interchanging the subject and the predicate terms of an original
propositions, however, the quality of the original proposition is
retained.

13. Two parts of Conversion:
1. Convertend 2. Converse
Example:
No fish is a mouse. (Convertend)
(S) (P)
No mouse is a fish. (Converse)
(S) (P)

14. TWO KINDS OF CONVERSION
1. Simple Conversion
- a kind of conversion where the quantity of the converted is
retained in the converse.
Examples:
No men are mortals. (E)
No mortals are men. (E)
Some mortals are men. (I)
Some men are mortals. (I)

15. 2. Partial Conversion
- a kind of conversion where the quantity of the converted is
reduced from universal to particular. This implies that partial
conversion is applicable only to “A” and “E” propositions.
Examples:
All computers are gadgets. (A) to
(Su) (Pp)
Some gadgets are computers. (I)
(Sp) (Pp)

16. E.1.2 OBVERSION
is kind of education where a new
proposition is formulated by retaining
the subject term and the quantity of the
original proposition; however, the
quality of the original proposition is
change and the predicate term replaced
by its contradictory. simply put in
obversion a new propositon (obverse)
is being formulated through the
following:

17. Obversion is, however, applicable to all kinds of categorical
propositions (A, E, I and O) Examples:
Obvertend Obverse
(1) All men are mortal. (A)
Su Pp
(1) No men are non-mortal. (E)
Su Pp
(2) No men are mortal. (E)
Su Pu
(2) All men are non-mortal. (A)
Su Pp
(3) Some men are mortal. (I)
Sp Pp
(3) Some men are not non-mortal. (O)
Sp Pu
(4) Some men are not mortal. (O)
Sp Pu
(4) Some men are non-mortal. (I)
Sp Pp

18. This is a kind of education which results from
a formulation of a new proposition whose subject
term is the contradictory of the predicate term in the
original proposition.
In principle, contraposition is a product of
both conversion and obversion . Thus like conversion
, contraposition involves an interchange of the
subject and predicate terms, and like obversion , it
involves either the use or removal of negatives which
affects the copula and the terms.

19. We can immediately see that there are two types of
Contraposition. They are Partial or Simple and
Complete.
Partial Contraposition consists the formulation of a
new proposition (contraposit) through the following:
a. Its (contraposit) subject is the contradictory of the
predicate term of the original proposition
(contraponend),
Ex. (Contraponend) All whales are mammals. (A) to
Su Pp
(Contraposit) No non-mammals are whales. (E)
Su Pu

20. b. The quality of the contraponend is changed in the
contraposit; and
Ex. (Contraponend) No fishes are dogs. (E) to
Su Pu
(Contraposit) Some non-dogs are fishes. (I)
Sp Pp
c. The predicate term in the “A” proposition is changed
to “E”, while “E” proposition to “I”, and an “O”
proposition to “I”.
Ex.(Contraponend) Some students are not studios.(O) to
Sp Pu
(Contraposit) Some non-studious are not non-students.(E)
Sp Pp

21. Complete Contraposition. a new proposition
(contraposit) is formulated through the following steps:
1 .The subject term in the contraposit is the contradictory of the predicate
term in the contraponend ,
(Contraponend) All whales are mammals. (A) to
Su Pp
(Contraposit) All non-mammals are non-whales.(A)
Su Pp
2.The quality of the contraponend is not changed in the contraposit ; and
2. (Contraponend) No fish is a dog. (E) to
Su Pu
(Contraposit) Some non-dog is not a non-fish. (O)
Sp Pu

22. 3.The predicate term in the contraposit is the
contradictory of the subject term in the contraponend.
(Contraponend) Some students are not studious.(O) to
Sp Pu
(Contraposit) Some non-studious are not students.(O)
Sp Pu

23. E.1.4 INVERSION
 This is a method of eduction in which the
mind, through obversion and conversion,
finally arrives at a judgment whose subject
and predicate terms are contradictories of the
subject and predicate terms in the original
proposition.

24. Ii
Steps involve in inversion:
 (Invertend) All birds are animals. (A) to
(Obverse) No birds are non-animals. (E)
 (Obverse) No birds are non-animals. (E) to
(Converse:Simple) No non-animals are birds. (E)
 (Converse:Simple) No non-animals are birds. (E) to
(Obverse) All non-animals are non-birds. (A)

25. Ii
Steps involve in inversion:
 (Obverse) All non-animals are non-birds. (A) to
(Converse:Partial) Some non-birds are non-animals. (I)
 (Invertend) All birds are animals. (A) to
(Inverse) Some non-birds are non-animals. (O)

26. Ii
Steps involve in inversion:
(Invertend) All birds are animals. (A) to
(Obverse) No birds are non-animals. (E) to
(Converse:Simple) No non-animals are birds. (E) to
(Obverse) All non-animals are non-birds. (A) to
(Converse:Partial) Some non-birds are non-animals. (I)
(Inverse) Some non-birds are non-animals. (O)

27. E.1.3 Logical Opposition
Opposition exists between two propositions when these
propositions have the same subject and predicate terms but they
differ from each other either in quantity or quality or both in
quantity or quality.

28. All Filipinos are Asians.
No Germans are Romans.
All Filipinos are Asians.
No Filipinos are Asians.

29. E.4 TYPES OF OPPOSITION
There are four types of opposition. They are as follows:
(1) Contradictory; (2) Contrariety; (3) Subcontrariety; and (4)
Subalternation or subalternity.

30. LOGICAL SQUARE

31. E.4.1 CONTRADICTORY OPPOSITION
This is an opposition existing between a pair of propositions
having the same subject and predicate terms. In the foregoing illustration
of the square of opposition, we see that the following propositions are
contradictories: A and O; and E and I. Examples: “All men are mortal” is
the contradictory of “Some men are not mortal,” and vice versa; and “No
man is mortal” is the contradictory of “Some men are mortal;” and vice
versa. In a contradictory opposition, therefore, one proposition simply
denies the other proposition. This means that contradictories cannot be
both type or true or false at the same time.

32. Rules of Contradictories. The following are the rules
governing contradictories:
(a) If one of the two contradictories is true the other is false
and vice versa.
(b) Contradictories cannot be simultaneously true or false at
the same time

33. E.4.2. Contrary Opposition (Contrariety)
This is an opposition existing between a pair of universal
propositions having the same subject and predicate terms but they differ in
quality since A is affirmative while E is negative. So one proposition "All
men are mortal", is the contrary of the proposition "No man is mortal" and
vice versa. Thus, we can make an immediate inference that if one is true, the
other must be false.
Rules of Contrariety. The following are the rules governing contrariety.
(a) If one of the contraries is true, the other is false.
(b) If one of the contraries is false, the other is doubtful.

34. Based on the foregoing rules, we can draw the following conclusions:
(a) If A is true, E is false.
A: All dogs are animals. (True)
E: No dogs are animals. (False)
(b) If E is true, A is false.
A: All cats are dogs. (False)
E: No cats are dogs. (True)

35. (c) If A is false, E is doubtful.
A: Every students are rich. (False)
E: No students are rich. (Doubtful)
(d) If E is false, A is doubtful.
A: Every man is white. (Doubtful)
E: No man is white. (False)

36. E.4.3. Subcontrary Opposition
This is an opposition existing between a pair of particular
propositions having the same subject and predicate terms but they differ in
quality. In this definition, we can clearly see that “I” and “O” propositions are
subcontraries. This is because both “I” and “O” propositions are particular
but they differ in quality since “I” is affirmative while “O” is negative.
Rules of Subcontraries. The following are the rules governing subcontraries.
(a)If one of the subcontraries is true, the other is doubtful.
(b)If one of the subcontraries is false, the other is true.

37. Based on the foregoing rules, we can draw the following conclusions:
(a)If I is true, O is doubtful.
I: Some students are girls. (True)
O: Some students are not girls. (Doubtful)
(b)If O is true, I is doubtful.
O: Some policemen are not honest people. (True)
I: Some policemen are honest people. (Doubtful)

38. (c) If I is false, O is true.
I: Some books are covered. (False)
O: Some books are not covered. (True)
(d) If O is false, I is true.
O: Some employees are not working. (False)
I: Some employees are working. (True)

39. E.4.4. Subaltern Opposition
This is an opposition existing between a pair of propositions having
the same subject and predicate terms and having the same quality, but
different quantity.
Rules of Subalternation: The following are the rules governing
Subalternation.
(a) if the universal is true, the particular is true.
(b) if the universal is false, the particular is doubtful.
(c) if the particular is true, the universal is doubtful.
(d) if the particular is false, the universal is false.

40. Based on the aforestated rules we can draw the following
conclusions:
(a) if A is true, I is true.
(b) if A is false, I is doubtful.
(c) if E is true, O is true.
(d) if E is false, O is doubtful.
(e) if I is true, A is doubtful.
(f) if I is false, A is false.
(g) if O is true, E is doubtful.
(h) if O is false, E is false.