LOGICAL PROPOSITION

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LOGICAL PROPOSITION

Here starts the lesson !

KASIM, ABERON SYN C .

HECHANOVA, CYRA HUINDA, GENEVEIV

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In Lesson 3 of Chapter II, we discussed the A, E, I , and O propositions. These propositions are closely linked with and connected to the four kinds of logical opposition, namely: contradictory, contrary, sub-contrary, and sub-altern. In the latter, we will dissect in depth how one proposition may be logically and consequently related to another as truth or falsity. Knowledge of logical opposition and its rule is necessary for purposes if immediate inference.

Introduction

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After the lesson, students are expected to be able to:

1. Discuss the nature of logical opposition . 2. Enumerate and discuss the four kinds of logical opposition . 3. Comprehend and apply the rules under each type . 4. Illustrate the knowledge by way of examples .

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Logical Opposition of propositions is the relation of truth and falsity existing between propositions with the same subject and predicate but with different quantity and quality or both quantity and quality (Reyes, 1988).This is the disagreement or difference same subject and same predicate (Piñon, 1994).

What Is This Topic All About?

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The forgoing definitions are better understood by the illustration of the traditional square of opposition given.

Description: PDF] The traditional square of opposition and generalized quantifiers ∗ | Semantic Scholar

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In the illustration, there are 4 kinds of logical opposition. 1. Contradictory 2. Contrary 3. Sub-contrary 4. Sub-altern

Chapter 2: Logical Opposition

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E xists between two propositions that differ in both quality and quantity. Rules: 1. If one pair of the opposition is true, the other is false. 2. If one proposition is false, the other is true .

Ex: Every dog is an animal . Some dogs are not animals . No dog is an animal . Some dogs are animal.

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Contrary Opposition

E xists between two universal propositions that differ in quality. Rules: 1. If one of the opposed proposition is true, the other is false. 2. If one of them is false, the other is doubtful. The proposition can be both false at the same time, but can never be true at the same time. (doubtful).

Ex: All Muslims are Filipinos No Muslims are Filipinos All Filipinos are Muslims No Filipinos are Muslims

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Sub-contrary Opposition

E xists between two particular propositions that differ in quality. Rules: 1. If one of the opposed propositions i s false, the other is true. 2. If one of them is true, the other is false.

Ex: Some teachers are lazy. Some teachers are not lazy. Some teachers are not lazy. Some teachers are lazy.

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Sub-altern Opposition

E xists between two propositions that differ in quantity. Rules: 1. If the universal proposition is true, the particular one is also true. But if the universal is false, the particular is doubtful. Ex: All persons are human. Some persons are human. No person is human. Some persons are not human.

2. If the particular proposition is true, the universal one is doubtful. But if the particular is false, the universal is false. Ex: Some plants are flowers. All plants are flowers. Some roses are not flowers. All roses are not flowers.

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Review of Concepts

Under the forgoing rule, we can draw or infer the truth or falsity of one proposition from the truth or falsity of another proposition. This reasoning is known as immediate inference. To summarize: 1. If A is true, E is false If A is false, O is true. I is true E is doubtful O is true I is doubtful 2. If E is true, A is false. If E is false, I is true I is false A is true O is false O is doubtful

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Review of Concepts

Under the forgoing rule, we can draw or infer the truth or falsity of one proposition from the truth or falsity of another proposition. This reasoning is known as immediate inference. To summarize: 3. If I is true, A is false If I is false, A is false A is doubtful E is true O is doubtful O is true 4. If O is true, A is false If O is false, A is true E is doubtful E is false I is doubtful I is true

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Note: Further discussion and application of immediate inferences is held in abeyance until Chapter III on Reasoning, the third mental act is presented.