logic - workbook summary

Philosophy is an activity rather than a
subject, you do philosophy rather than learn
about it. Philosophy is thinking about
thinking.
Not a theory but a vision of life (darsan). Not
merely “love of wisdom” but it signifies a real
“possession” of it.
Came from Greek words, philos “love” and
Sophia “wisdom”

Man is gifted with his rational ability, has the
capacity to create his ideas and express it in
the manner he would understand and has a
capability to organize his thoughts.
The study of Logic is geared towards the
honing the reasoning and critical ability of
man as man would experience things in the
world and as man would interact with other
people. The study of Logic offers us the
following:

1. To understand the general rules or principles of
correct reasoning.
2. To enable man to become a critical and logical
thinker.
3. To develop the art and skill of expressing ideas
and improve our reasoning skills.
4. To improve judgment skills in evaluating the
validity of an argument or soundness of an
argument.
5. To identify and avoid the faulty and misleading
errors of formal and informal arguments of day
to day experience.

 Logic derived from logikewhich means
“thought”. Aristotle, the father of logic in his
book Analytics, he considered logic as an
“organon”. The science in gaining knowledge
and a tool of correct thinking. Thus, logic is
towards developing correct thinking or
reasoning.
 The science and art of correct inferential
thinking. Logic is an art of reasoning.

An argument is a set of statements of
which – the one being argued for – taken
to be established as true on the basis of
all the others.
Supporting statements arecalled
premises, while the statement taken to
support are conclusion.

 Deductive is the process whereby a
particular idea orpremise is established
as true based from a general law or
principle that is assumed to be true.
 Inductiveprocess on the other hand is a
reasoning process whereby the human
mind processes particular instances to a
universal/general truth.

 Logic gives emphasis on the validity of
reasoning be it deductive or inductive.
1. Formal Logic concerns the forms of thought
or the very structure or pattern of our
reasoning process.
2. Material Logicis focused on the truth of the
propositions.

1. Simple Apprehension the simple
understanding or grasping the meaning of an
idea. This mental activity brings about the use
of terms to express such idea.
2. Judgment the comparison of two ideas whether
there is agreement or disagreement. This
mental activity results with formulation of a
proposition.
3. Reasoning the derivation of a new truth from
previously established and known truth. This
mental activity arrives at the construction of an
argument.

The task of understanding, analyzing
and evaluating an argument is
considering the starting point. An
idea is an outcome of a process.
Known as an intellectual image or
representation of a thin. Serves as a
building block of the argumentative
process.

 Using our senses, we are able to perceive
external realities. Such sensory experience
creates an image in the mind. This image is
further identified as phantasm or a mental
picture of the external object we perceive.
The intellect now gives attention to this
sense-image in order to make its own
representation of the thing. Abstraction
which is getting the essential characteristics
or elements of the object perceived.

1. It is a representation
 But not a limited representation.
2. It is a representation of an essence
 Essence of a thing that makes it what it is.
3. It is a representation of an essence of
a thing in the mind
 Not in the senses or in the imagination.

1. Empirical. The kind of idea observable
in its nature with use of sensory
experience.
2. Theoretical. This idea entails the use of
extending devices to perceive such
concepts.
3. Metaphysical. This kind of idea exist
beyond the realm of space and time.

4. Fictitious. This kind of idea which is
believed as a creation of the mind.
5. Abstract. An idea understood by the
mind but not perceived by the senses.
6. Dispositional. An idea pertains to the
observable manifestation of a certain
operation
7. Evaluative. Used to signify our
evaluative judgment on certain matters.

 An idea is just an abstract
representation of a thing that we
create in our mind. A sensible,
artificial, material, arbitrary and
conventional sign, expressive of an
idea.

Sign is something which stands for
something other than itself.
Signified thing is made known.
Signifying thing makes it known.
Connection between the two is the
power to signifying thing to convey
knowledge.

Comprehension (designation/intention),
is the sum total of the characteristics
which make up an idea. Notes
(intelligible elements)
Extension (denotation), particular
things were the comprehension can be
applied to.

Greater the comprehension,
the more specific the term
becomes. But the greater the
extension, the more general
the term becomes.

1. Singular terms stands for one
individual/group and designates it
definitely.
2. Particular terms stands for more than
one but not all.
3. Universal terms stand for each of the
subjects to which is applied to.

1. Univocal terms signifies the same
essence in at least two occurrences
of the term.
2. Equivocal terms are used in two or
more different senses or meanings.
3. Analogous terms one that is
applied to unlike, but related things.

1. Contradictory terms if one is the
simple negation of the other.
2. Contrary terms belong to the same
genus but differ from one another.
3. Relative terms one cannot bet
understood without the other.

A definition is a statement which
explains what a thing is.
Definiendum the term to be
defined.
Definiens a cluster of words that
defines that term.

1. To increase vocabulary
2. To eliminate ambiguity
3. To reduce vagueness
4. To explain theoretically
5. To influence attitude

Stipulative Definitions “self-definition”.
Lexical Definitions gives
characteristics that can be true or
false.
Denotative/Extensional Definitions
giving examples of the subject.

Ostensive/Demonstrative Definitions
points the definition instead of
naming.
Connotative/Intentional Definitions
giving the use of the subject.
Synonymous Definitions using
another word with the same meaning.
Operational Definitions, states that
the term is to be applied.

1. Must be complete.
2. Must not be circular.
3. Must neither be too broad now too
narrow.
4. Must not be expressed in ambiguous,
obscure or figurative language.
5. Must not be negative where it could be
affirmative.

A genus: an existing definition that
serves as a portion of the new
definition. Genera (more than one
genus)
The differentia: the portion of the
new definition that is not provided
by the genera.

 A proposition is defined as a
statement in which anything is
affirmed or denied. Expressed as
a declarative sentence. A
discourse that expresses either
truth or falsity.

1. Subject is that about which
something is affirmed or denied.
2. Predicate is what is affirmed or
denied of the subject.
3. Copula is either “is” or “is not”. It
connects the subject and the
predicate.

1. Singular standing for one definitely
designated individual or group.
2. Particular for an indeterminately
designated portion of its absolute
extension.
3. Universal standing for each of the
subject of the subjects to w/c it can be
applied to.

Affirmative is expresses a
positive mood like the use
“is”
Negative it expresses a
negative mood like the use
“is not”

Universal-Affirmative(A)
Universal-Negative (E)
Particular-Affirmative (I)
Particular-Negative (O)

 Logical form defined as the basic
structure of the part of a complex
logical unit.
 Complex logical units include
proposition and inferences, or
arguments but not terms.

Devised by John Venn. It
gives us a map of the
logical relations between
classes.

 A proposition “all S are P”
 Diagrammed by shading the area
of S which is not P.
 E proposition “no S is P”
 Diagrammed by shading the area
which is both S and P.

 I proposition “some S are P”
 Diagrammed by putting an X in the
area which is both S and P.
 O proposition “some S is not P”
 Diagrammed by putting an X in the
area of S which is not P.

 Originated with Aristotle.
Opposition is recognized when two
proposition are the same in terms of
their subject and predicate but
different or the same in their
quantity or quality.

 every S is P” and “some S is not P” are
contradictories.
 “no S is P” and “some S is P” are
contradictories.
 “every S is P” and “no S is P” are contraries.
 “some S is P” and “some S is not P” are sub
contraries.
 “some S is P” is a subaltern of “every S is P”.
 “some S is not P” is a subaltern of “no S is P”

 Contradictory
 difference inquantity and quality.
 Contrary
 difference in the quantity.
 Sub-contrary
 difference in the quality.
 Sub-alternation
 difference in the quantity but the qualityisthe
same.

 Law of Contradictions:
 1st rule: Contradictories cannot be true
together
 2nd rule: Contradictories cannot be false
together
 Law of Contrariety:
 1st rule: contraries cannot be true together
 2nd rule: contraries can be false together.

 Law of Sub-contrariety:
 1st rule: both sub contraries cannot be false together
 2nd rule: both sub contraries may be true together
 Law of Sub-alternation:
 1st rule: the truth of the universal involves the truth of
the particular but the truth of the particular does not
involve the truth of the universal.
 2nd rule: the falsity of the universal involves the falsity
of the particular but the falsity of the particular does
not involve the falsity of the universal.

 Eduction is the process of
immediate inference whereby,
from any proposition taken as
true, we derive other implied in
it, though differing from the first
in subject or predicate or both.

 Conversion
 Obversion
 Contraposition

It is the re-expression of a proposition
by interchanging the places of the
subject and predicate while preserving
its quality.
 Rules for Conversion
▪ Interchange S an P
▪ Retain quality
▪ Do not extend any term (retain the
quantity except for A proposition)

It is the formulation of a new proposition by
retaining the subject and quantity of an
original proposition, changing its quality
and using as predicate contradictory.
 Rules for Obversion
▪ Retain the subject and the quantity of the
obvertend
▪ Change the quality. If the obvertend is negative,
the obverse must be affirmative
▪ As predicate, use the contradictory of the
predicate of the original proposition

Combination of conversion and
obversion.
 Rules for Contraposition
▪ Contradict the subject and the predicate
▪ Exchange the subject and the predicate
▪ Retain the quality
▪ Retain the quantity except for E
proposition (universal becomes particular)

Reasoning
 The derivation of a new truth from
previously established and know
truth.
Known as inference which is
externally manifested with the
construction of an argument.

 Argument
 A set of statements of which one – the one
being argued for – is taken to be
established as true on the basis of all the
others.
▪ The supporting statements are called
premises.
▪ The statement they are taken to support is
called the conclusion.

Deductive is the process whereby a
particular idea or a premise is established
as true based from a general law or
principle that is assumed to be true. (from
general to specific)
Inductive a reasoning process whereby
the human mind processes particular
instances to a universal/general truth.
(from specific to general)

oConclusion-indicators signals
what follows next is the
conclusion.
oPremise-indicators are words
or phrases serve to mark the
premises.

To understand
arguments and how the
conclusion is supported
by the premises.

A deductive argument in which a
conclusion is inferred from two
premises.
Two type of Syllogism:
Categorical Syllogism and
Hypothetical Syllogism.

1. Minor term = the subject term of
the conclusion.
2. Major term = the predicate term of
the conclusion.
3. Middle term = appears twice in the
premises but not in the conclusion.

 – arrangement of the middle
terms in the syllogism.
1.MP 2. PM 3.MP 4.PM
SM SM MS MS
SP SP SP SP

– order of propositions
according to their
quality and quantity.

 A valid standard-form categorical syllogism
must contain exactly three terms, each which
is used in the same sense throughout the
argument.
 Fallacy of Four Terms.
 In a valid standard-form categorical
syllogism, the middle term must be
distributed in at least one premise.
 Fallacy of Undistributed Middle.

 If either term is distributed in the
conclusion then it must be distributed in
the premises.
 Fallacy of Illicit Major Term.
 Fallacy of Illicit Minor Term.
 No standard-form categorical syllogism
having two negative premises is valid.
 Fallacy of Exclusive Premises/ Fallacy of
Two Negative Premises.

 If either premise of a valid standard-form
syllogism is negative, then the
conclusion must be negative.
 Fallacy of Drawing an Affirmative
Conclusion from a Negative Premise.
 No standard-form categorical syllogism
with a particular conclusion can have
two universal premises.

 An argument can be evaluated by using
the rule of categorical syllogism as
exemplified in the previous chapter. But
another approach is the use of Venn
diagram. The technique is simply to
draw in the premises. If we find that we
have drawn in the conclusion follows,
then the argument is valid.

 A deductive argument which uses
hypothetical propositions.They do not
contain direct, straightforward assertion
of agreement or disagreement between
the subject and predicate. They express
the disagreement of the truth or falsity
of one statement upon the truth or
falsity of another statement.

A syllogism which contains a conditional
proposition as the major premise. Conditional
propositions are “if statements.” There are
two parts to such a proposition.
The truth of the antecedent follows the truth
of the consequent;The falsity of the
antecedent follows the falsity of the
consequent.

 Antecedent (1st part) gives the ground, the
reason, the cause.
 Consequent (2nd part)gives the result, the
dependent, the effect.
 From the truth of the antecedent follows
the truth of the consequent; the falsity of
the consequent follows the falsity of the
antecedent.

Fallacy of Denying the
Antecedent.
Fallacy of Accepting the
Consequent.

 It is one whose major premise consists of a
disjunctive proposition. A disjunctive proposition
is an “either-or” statement.
 Strict Disjunction – Proper Disjunction
▪ Components are called disjunct, can neither be true nor false
together.
 Broad Disjunction – Improper Disjunction
▪ Is a hypothetical syllogism whose major premise is broad
disjunctive proposition.
▪ Is a complete disjunctive proposition in which one or both
disjuncts must be true. The disjunction must be complete.
Otherwise, truth may be found in the missing disjunct.

 The least difficulties among the hypothetical
syllogisms. In the major premise states that
two or more things are impossible at the
same time.
 Conjuncts can be true at the same time; but
they may all, be false together.
 From the truth of one member follows the
falsity of the others; but from the falsity of one
member, the truth of the other(s) does not
follow.

logic - workbook summary

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