Factores de influencia en el clima social escolar:

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undetermined. But if the Subalternant false, then the Subalternante is also false. ―Some diseases are curable‖ – ‗All diseases are curable‖. If it is true that some diseases are curable, then it may or may nor be true that all diseases are curable; but if it is false that some disease are curable, then it is necessarily also false that all disease are curable.

Schematically:

If p is true, q is undetermined If p is false, q is false

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true. This means that the truth of one in no wise contradicts the truth of the other; on the other hand, the falsehood of one implies the truth of the other.

Propositions at the ends of the vertical sides differ in quantity only – universals at the top, particulars at the bottom. The propositions here have the same quality but differ in quantity, that is, A and I or E and O propositions. Generally, the relationship is said to be that of subalternation. If, however, the truth or falsity of the particular is dependent upon the truth or falsity of a corresponding universal, then the relation is said to be that of superalternation. If the universal proposition A and E is true, then the particular I or O must also be true; but if the universal A and E is false, the particular, I or O, may not be true; its truth value is undetermined. On the other hand, if the truth of the universal is considered as dependent upon the truth or falsity of the particular, the relation is called subalternation. If the particular proposition, that is I and O is true, then the universal may or may not be true; it is undetermined. But if the particular, I or O, is false, the universal is also false.

In summary, what the square expresses is that,

(a) If SaP is True, SeP is False, SiP is True and SoP is False

(b) If SaP is False, SeP is Undertermined, SiP Undertermined and SoP True (c) If SeP is True, SaP is False, SiP False and SoP True

(d) If SeP is False, SaP is Undetermined, SiP True and SoP Undetermined (e) If SiP is True, SaP is Undetermined, SeP False and SoP Undetermined (f) If SiP is False, SaP is False, SeP True and SoP True

(g) If SoP is True, SaP is False, SeP Undetermined and SiP Undetermined (h) If SoP is False, SaP is True, SeP False and SiP True

On the basis of this logical relations SaP is True is equivalent to SoP is False; that is A is equivalent to Not – O. Similarly, SeP is true is equivalent to SiP is False; that is E is equivalent to Not – I. This is understandable because SoP is False (that is Not – O) is the contradictory of the SaP is True (that is A), while SiP is False (Not I) is contradictory of the contradictory of SeP is True (E).

4.0 Conclusion

The traditional square of opposition provides a basis for the kind of immediate inference whereby given one of the four basic categorical propositions and a truth value, and using the described relations as rules of inference, a given person can infer the truth value of the remaining three propositions.

5.0 Summary

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The term ―opposition‖ was used by classical logicians to apply to the differences in quality (affirmative or negative) and quantity (universal or particular) between standard-form categorical propositions having the same subject and predicate terms. This process is visualized in the square of opposition that shows the logical relationships between categorical propositions with the same subject and predicate.

6.0 Tutor Marked Assignment

For each of the following propositions, assume that the given proposition is true, perform the required inference, and state the resultant proposition and its truth value..

1. What is the contrary of "All joggers are escapists"?

2. What is the contradictory of "Some tillers are not Snappers"?

3. What is the subaltern of "No logic teachers are exciting persons"?

4. What is the subaltern of "No disco music is acid rock"?

5. What is the superaltern of "Some tokunbo cars are expensive"?

6. What is the subcontrary of "Some soft drinks are not nutritional goods"?

7. What is the contrary of "No joggers are depressed persons"?

8. What is the subaltern of "All clowns are beggars"?

9. What is the superaltern of "Some balloons are not high-fliers"?

10. What is the subcontrary of "Some fruits are not foods

If it is true that ―Some of our leaders imagine they can fight for empire and credibility at the same time,‖ what can you say about the truth or falsity of each of the following propositions?

i. All of our leaders imagine they can fight for empire and credibility at the same time.

ii. Some of our leaders do not imagine they can fight for empire and credibility at the same time.

iii. None of our leaders imagine they can fight for empire and credibility at the same time.

If it is true that ―All men are equal under the moral law,‖ what can you say about the truth or falsity of each of the following propositions?

i Some men are equal under the moral law.

ii Some men are not equal under the moral law.

iii No men are equal under the moral law.

If it is true that ―No psychologist has ever fully understood the depths of human personality,‖ what can you say about the truth or falsity of each of the following propositions?

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i Some psychologists have fully understood the depths of human personality.

ii All psychologists have fully understood the depths of human personality.

iii Some psychologists have not fully understood the depths of human personality.

If it is true that ―Some problems cannot be solved mathematically," what can you say about the truth or falsity of each of the following propositions?

i . Some problems can be solved mathematically ii All problems can be solved mathematically.

Iii No problems can be solved mathematically.

If it is false that ―No men are pugnacious,‖ what can you say about each of the following propositions?

i Some men are not pugnacious.

ii All men are pugnacious iii Some men are pugnacious

If it is false that ―Some advocates of democracy are in favour of a dictatorship,‖ what can you say about the truth or falsity of each of the following propositions?

i Some advocates of democracy are not in favour of a dictatorship.

ii No advocates of democracy are in favour of a dictatorship.

iii All advocates of democracy are in favour of a dictatorship.

If it is false that ―Some theories do not explain what they were meant to explain,‖ what can you say about the truth or falsity of each of the following propositions?

i No theories explain what they were meant to explain.

ii. All theories explain what they were meant to explain.

iii. Some theories explain what they were meant to explain.

7.0 References/Further Reading

Bernhard, Peter. (2008) "Visualizations of the Square of Opposition." Logica Universalis 2.1: 31-41. Web.

Cohen & Nagel (1993) Introduction to Logic Second Edition Hackett Publishing,

DiMartino, Marc R. (2015), The Square of Opposition: Innovations in Teaching Logic

Senior Honors Projects. Paper 408.

http://digitalcommons.uri.edu/srhonorsprog/408

http://digitalcommons.uri.edu/srhonorsprog/408

Kelley, David (2014). The Art of Reasoning: An Introduction to Logic and Critical Thinking (4 ed.). New York, NY: W.W. Norton & Company, Inc.

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Parry & Hacker, (1990) Aristotelian Logic SUNY Press.

Uduma, U.O. (2000) The Fundamentals of Philosophy Abakaliki: Willyrose &

Appleseed

pub. Coy.

_______ (2015) Introduction to Logic and the Fundamentals of Formal Reasoning 2^nd ed . Accra: African Analytica Publishers