Philosophy

Philosophy

The Concept of Negation in Logic

© 2012 byJensen dG. Mañebog
 
THE CONCEPT OF NEGATION introduces another operator which is so functional in logical operations, especially in determining the truth of falsity of compound statements with negated components. By operator, we mean a symbol, term, or other entity that performs or describes an operation, like the compound-statements symbols.
            Considered by some logicians as a special kind of compound statement, negation is a statement of denial or contradiction. It can also be interpreted as an assertion that a particular statement is false. The symbol used for negation is the tilde (~) or simply the negative sign (-). “It is not the case that”, “it isn’t true that”, and “it is false that” are the phrases that usually express the idea of negation. Sometimes, the single word ‘not’ embedded in a sentence is enough to indicate negation.
 
Examples:
It is not the case that Trillanes is Chinese. (-T)
It isn’t true that Azkals is a basketball team. (-A)
It is false that Obama is from Olongapo. (-O)
Mayweather is not gay. (-M)

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Notes on Natural Deduction

WE HAVE TO USE the appropriate rules of inference in constructing formal proofs of arguments’ validity depending on the kind of propositions they use. The following are some basic techniques in properly constructing proof of validity of arguments.

1.Always begin by identifying the conclusion and attempting to look for it in the premises.
2. If the conclusion is a letter that appears in the consequent of a conditional statement in the premises, consider obtaining it through modus ponens.
3.If the conclusion is a negative statement (negated letter) that appears in the antecedent of a conditional statement in the premises, consider getting it using modus tollens:
4. If the conclusion is a conditional statement, consider obtaining it via hypothetical syllogism:
5.If the conclusion is a letter that appears in a disjunctive statement in the premises, consider getting hold of it via disjunctive syllogism.
6. If the conclusion contains a letter that appears in a conjunction in the premises, consider obtaining that letter via simplification...

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Rules of Inference: Sample Exam

by @jensenismo
 
Determine whether the argument is valid or invalid. If the argument is valid, state the rule of inference used. If it is invalid, name the fallacy committed.

1. If millions of children die yearly from starvation, then something is wrong with the government. Millions of children die yearly from starvation.
Therefore, something is wrong with the government.

2. If world population continues to grow, then Manila will become hopelessly overcrowded.
If Manila become hopelessly overcrowded, then Manila will become polluted.
Therefore, if world population continues to grow, then Manila will become polluted.

3. Either the breach is a safety violation, or it is not subject to fines.
The breach is a not safety violation.
Therefore, it is not subject to fines.

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TYPES OF INFERENCE

TYPES OF INFERENCE
© 2012 by Jensen DG. Mañebog
 
AN INFERENCE is a mental process by which we pass from one or more statements to another
that is logically related to the former. Based on the number of their premise, inferences are basically classified into two:
 

1.Immediate Inference – consists in passing directly from a single premise to a conclusion. It is reasoning, without the intermediacy of a middle term or second proposition, from one proposition to another which necessarily follows from it.
Ex: No Dalmatians are cats. Therefore, no cats are Dalmatians.
     All squares are polygons. Therefore, some polygons are squares.

 
2.Mediate Inference- consists in deriving a conclusion from two or more logically interrelated premises. Involving an advance in knowledge, it is reasoning that involves the intermediacy of a middle term or second proposition which warrants the drawing of a new truth.
Ex: All true Christians are theists.
     Paul is a true Christian.
    Therefore, Paul is a theist.

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The Importance of Critical Thinking and Logic

 
 
The importance of Critical Thinking is emphasized by the fact that it calls for the ability to:
1. Recognize problems, to find workable means for meeting those problems
2. Understand the importance of prioritization and order of precedence in problem solving
3. Gather and marshal pertinent (relevant) information
4. Recognize unstated assumptions and values
5. Comprehend and use language with accuracy, clarity, and discernment
6. Interpret data, to appraise evidence and evaluate arguments ...

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Division and Classification: A Lecture in Logic

“EVERYTHING IS IN PLACE and a place for everything”
          Our mind is a repository of wealth of information that needs methodical and and easy-to-use tool in accessing what we need to use in our everyday conversation, decision making, and for just simple mental recall. As rational beings, we most of the times need to organize our thoughts. Besides definition, we have another method of making our ideas clear in order to arrive at a better understanding of their meaning: the method of division and classification ...
 

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Some Epistemological Distinctions

Epistemology is a branch of knowledge which deals with the study of scope, limits, and validity of knowledge. This terminology originated from two Greek words episteme which means to know and logos which means study. Practically speaking, almost all of  epistemological claims in whatever line of inquiry – whether be it social or behavioral sciences or pure or applied mathematics, three fundamental questions must be satisfied: the first is What can I know? The second question is How can I know? And the third question is Why do I have to know?

 
The first question deals with the scope and possible limitation of what man can know as far as knowledge of the external world is concerned; the second question deals with the methodology or manner of acquiring knowledge ...
 

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LOGIC: A Syllabus

Note to users (teachers & students): To become members of “OurHappySchool community” and enjoy its services, just click our FB LIKE button above (if you haven't done yet) and leave a simple message in the comment section below.
 

WEEK 1

I. SPECIFIC OBJECTIVES:
To state the importance of Logic in communication and in man’s being social

II. TOPICS/SUBJECT MATTER:
‘LOGIC IN COMMUNICATION’; ‘Language is Logic’; Logic in good usage; The 2 kinds of reasoning; Validity & probability (brief orientation)

III. READING/S:
Internet articles: “‘Logically’ Social (I)” & “‘Logically’ social (II)
site: www.OurHappySchool.com (*the articles can also be found by typing their title in the site’s own search engine
 

Subjects:

The Categorical Proposition in Logic

IN LOGIC, the statement that relates two classes or “categories” is called a categorical proposition. The classes in question are denoted respectively by the subject term and the predicate term. In effect, this type of proposition gives a direct assertion of agreement or disagreement between the two terms. The proposition asserts that either all or part of the class denoted by the subject term is included in or excluded from the classes denoted by the predicate term. Here are some examples of categorical statement.
 
1. All dogs are mammals.
2. No acids are bases.                                                                                 
3. Some philosophers are mathematicians.
4. Some Americans are not cheaters.
                                               
         The first example asserts that the whole class of dogs are included in the class of mammals; the second declares that the entire class of acids are excluded from the class of bases; the third states that a part of philosophers are included in the class of mathematicians; and the last one claims that a part of the class of Americans are excluded from the class of cheaters ...
 

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On Judgment, Proposition, and Sentence: A Lecture in Logic

On Judgment, Proposition, and Sentence: A Lecture in Logic
 

IN LOGIC, term represents idea or concept. Ideas are the raw materials of knowledge but they cannot be said to be true or false in themselves. Only after we compare or contrast two or more ideas, or express relations, or an agreement or disagreement between them that we can speak of truth or falsity. The mental operation involved here is called judgment.
          Judgment is an act in which the mind pronounces the agreement or disagreement of ideas among themselves. It is an act in which the intellect affirms or denies one idea of another. For instance, our intellect may relate the ideas this dog and Dalmatian and affirm, This dog is a Dalmatian. This is an example of a judgment expressed in a proposition. The proposition therefore is the oral or written expression of the judgment. Often used interchangeably with statement, it as a verbal expression proclaiming a truth or falsity ...
 

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