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# Logic

## on Mar 19, 2011

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## LogicPresentation Transcript

• Presentation of logic:
• Presented To:
• Madam Uzma Rehman
• Presented By:
• Syed Ali Kamran Abidi. 50 Mirza Ali Raza. 90
• M. Jaffar Tayar. 48
• Syed Hussain Zain-ul-Abideen. 85
• Topic to be described:
• 1.) The Theory of Deduction.
• 2.) Categorical Propositions and classes.
• 3.) Quality, Quantity and Distribution.
• 4.) The Traditional Square of Opposition.
• (Contradictories, Contraries, Subcontraries, Subalternation).
• 1. The Theory of Deduction:
• “A deductive argument is one whose premises are claimed to provide conclusive grounds for the truth of its conclusion.”
• Logic is divided into two parts. The first of it is the “classical” or “Aristotelian” Logic. The second is called “Modern” or “Symbolic” Logic.
• 2. (a) Categorical propositions:
• Categorical proposition is the base for the Classical Logic. They are called categorical propositions because they are about categories or classes.
• Such propositions affirm or deny that some class S is included in some other class p, completely or partially.
• There are four types of categorical propositions which are also called Four Fold Scheme:
• 1. A (Inclusion). Universal Affirmative proposition.
• All politicians are liars.
• 2. E (Exclusion) Universal Negative proposition.
• No politicians are liars.
• 3. I (Partially Inclusion) Particular Affirmative Proposition.
• Some politicians are liars.
• 4. O (Partially Exclusion). Particular Negative Proposition.
• Some politicians are not liars.
• (b) Classes:
• Classical categories (special kinds) are three:
• Class Inclusion.
• Class Exclusion.
• Class Partially Inclusion and Exclusion
• 3. (a) Quality:
• Quality wise any proposition may be called negative or affirmative.
• If the proposition affirms some class inclusion, whether complete or partial, its quality is affirmative.
• If the proposition denies some class inclusion, whether complete or partial, its quality is negative.
• (b) Quantity:
• Quantity wise any proposition is divided into Universal & Particular.
• If the proposition refers to all members of the class designated by its subject term, its quantity is Universal.
• Thus A and E are Universal.
• If the proposition refers only to some members of the class designated by its subject term, its quantity is Particular.
• Thus I and O are Particular.
• (c) Structure of standard form categorical proposition:
• The general skeleton of proposition is:
• Quantifier + Subject + Copula + Predicate.
• (d) Distribution:
• In distribution we check the class inclusion and exclusion in propositions.
• A:
• A distribute its subject only.
• E:
• E distributes its subject as well as predicate.
• I:
• In I Both terms are not distributed.
• O:
• O distributes its predicate only.
• The Traditional Square of Opposition: The categorical propositions having same subject and predicate terms may differ in quality & quantity or in both. This differing is called “Opposition”. A Contraries E Subalternation Contradictories Subalternation I Sub Contraries O
• Contraries:
• Two propositions in contraries both cannot be true or false or truth and falsity of one entails on the other.
• Relation b/w A and E is called contraries.
Example: A : All judges are lawyers. E : No judges are lawyers. A E
• Subcontraries:
• Both cannot be false both can be true.
• Relation b/w I and O is called Subcontraries.
I O Example: I : Some judges are lawyers. O : Some judges are not lawyers.
• Subalternation:
• If universal is true than particular must be true. If universal is false than particular may be undecided.
• Relation b/w A & I and E & O is called Subalternation.
A I E O Example: A: All teachers are idealistic persons. I: Some teachers are idealistic persons. E: No teachers are idealistic persons O: Some teachers are not idelisti