LOGICCC

Inference 

is a type of reasoning whereby from known truths of premise(s) a logical conclusion is derived

Mediate inference

is a type of reasoning that draws a logical conclusion from two or more premises. 

Immediate inference

is a type of reasoning that draws a logical conclusion from one premise or proposition. 

  The First Principles or Laws of Thought

are attributed to Aristotle. These are principles whose truths are self-evident

The Principle of Identity

   The ____ states “A thing is what it is.” A statement is identical to itself. If a statement is true, then it is true. It cannot be otherwise.

The Principle of Non-Contradiction

  The _______states “Nothing can both be and not be at the same time and in the same sense.” A statement cannot both be true and false at the same time and in the same sense.

The Principle of the Excluded Middle

 The ______ states “Something either is or is not.” Nothing exists and does not exist at the same time. This means that there is no middle ground between two contradictories. A statement is either true or false.

The Square of Opposition

involves the oppositional relations involving A, E, I and O propositions. 

The Law of Contrariety

 This logical relationship exists between universal propositions that differ in quality (affirmative or negative). Statements A and E are contraries. 

1.If one of the contraries is true, the other is false.

2.If one of the contraries is false, the other is doubtful, i.e., either true or false.

 The Law of Subalternation

 This is a logical relationship that exists between universal and particular propositions having the same quality. Propositions A and I as well as statements E and O are subalterns.

1.If the universal is true, the particular is true.

2.If the universal is false, the particular is doubtful, i.e., either true or false.

3.If the particular is false, the universal is false.

4.If the particular is true, the universal is doubtful, i.e., either true or false.

         

The Law of Subcontrariety

   This is a logical relationship that exists between particular propositions that differ in quality (affirmative and negative). Statements I and O are subcontraries.

 The law of contrariety governs the relationship between propositions I and O.

1.If one of the subcontraries is true, the other is doubtful, i.e., either true or false.

2.If one of the subcontraries is false, the other is true.

The Law of Subalternation

 

governs the relationship between statements A and I as well as statements E and O.
1.If the universal is true, the particular is true.

2.If the universal is false, the particular is doubtful, i.e., either true or false.

3.If the particular is false, the universal is false.

4.If the particular is true, the universal is doubtful, i.e., either true or false.

The Law of Contradiction

governs the logical relationship between propositions A and O and propositions E and I.

1.Contradictories cannot both be true at the same time; if one is true, the other is false.

2.Contradictories cannot both be false at the same time; if one is false, the other is true.

Eduction 

is a form of immediate inference in which from a given proposition another proposition which differs in quality and quantity of the subject term and/or predicate term is arrived at

obversion, conversion, contraposition, and inversion. 

Types of Eduction

Obversion

 is a process of eduction whereby from a given proposition, called the obverse, another proposition called the obvertend is formed

Conversion

is a process in which from a given proposition called a convertend, a new proposition called a converse is derived. 

 

Contraposition

is a form of eduction which involves the process of obversion and conversion

Inversion

This is a form of eduction that involves the process of obversion and conversion whereby new statements are derived, namely, the simple inverse and the complete inverse

Apprehending 

an intellectual perception or grasp of reality without confirming or denying anything concerning it

Judging 

an act of the mind affirming or denying the agreement between two ideas (subject & predicate)

Reasoning 

an act of the mind in which a conclusion is inferred from a given premise or premises

singular

signifies one definite thing

       e.g.: Peter, Philippines, This river

universal

 applies to every, each, or all members of the 

       class being signified

       e.g.: Every man, each woman, all teacher

collective

refers to all members of the class taken as a            whole

       e.g.: family, flock, library, herd

particular

signifies indefinite or indeterminate            number of the members of a class

       e.g.: some planets; most fruits; not all beggars

univocal

used in exactly the same sense

       e.g.: The floor is wet. The floor is made of wood.

equivocal

used in entirely different senses:

       e.g.: This house is mine. This is a gold mine. 

analogous

used in partly similar and partly different            senses

       e.g.: Central bank. River bank

real

a term signifies an object in the realm of reality

       e.g.: stone, flower, sand

logical

signifies things that exist in the mind

       e.g.: Man is condemned to be free

imaginary

signifies something fictional or imagined

       e.g.: unicorn, Pegasus, Manggagaway, Ungo

metaphorical

signifies something true by virtue of 

       analogy

symbolic

signifies something that is true by virtue of            convention

       e.g.: Lakers, Devils, Golden State Warriors

material

signifies something as a verbal symbol

       e.g. Judas’ kiss sounds like hiss. Love rhymes with            dove

Judgment 

is an act of the mind which unites at least two ideas by affirmation or separates by negation

Proposition 

is any statement that is either true or false

Synthetic statements/propositions

 Truth or falsity based on    facts

Analytic statements/propositions

Truth or falsity based on    reason logic, or principle

Conditional

If the universe cannot exist by itself, then a creator 

       exists.

Disjunctive

Either Philippines is correct or China is wrong.

Categorical

God is the supreme being. 

       No man is an island. 

       Every Cebuano is a Filipino. 

       Some students are beautiful.

       Not all prisoners are guilty.

subject term

denotes something about which something is 

   affirmed or denied

predicate term

denotes something that is affirmed or denied 

   of the subject

copula 

is a linking verb (is, am, are), an indicative mood of the 

   verb “to be.” 

A standard categorical proposition

 follows the S-C-P 

   (subject-copula-predicate) form

 

Affirmo

(I affirm)

Nego

(I negate)

Circle

 represents class; subject and predicate

Shaded area of the circle

represents a void or  empty class

Letter X

signifies that at least some members of the    class exist

Scientia Scientiarum

 

●Logic is science of sciences

●Science as systematic body of knowledge

●Logic is a systematic body of knowledge of formal principles of inference

Ars Artium

Logic as art of arts

●Art as production (poesis) useful and representation (mimesis) of the beautiful

●human intellect as cause of all forms of art

Deductive Arguments 

●Necessary

●Conclusion necessarily follows from the premises

●Valid and sound

Inductive Arguments

●Probability

●Conclusion only probably follows from the premises

●Cogent, strong, weak

The Principle of Validity

•The conclusion necessarily follows from the premises 

•premises may be false

The Principle of Soundness

•The conclusion necessarily follows from the premises

•The premises must be true

Deductive Arguments

 Propositions

Conditional, Disjunctive and Categorical