LECTURA SELECCIONADA: HUELLAS DE AMOR

72 Unit 3 Logical Form and Formal Validity Contents

1.0 Introduction

2.0 Intended Learning Outcomes (ILO’s)

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of the propositions that are embodied in the premises and the conclusion. It thus focuses on the feature of an argument that recommends its validity; that is, the feature of an argument that makes it valid or otherwise invalid. It also exposes the learner to the fundamental nature of logic

2.0 Intended Learning Outcomes

It is expected that at the end of this unit, you will be able to:

1. Clearly understand that the validity of an argument is not dependent on the truthfulness and falsity of the propositions that are embodied in its premises and the conclusion.

2. Clearly understand what actually makes an argument valid or invalid

3. represent the logical form of an argument by replacing the specific content words with letters used as place-holders

4. Identify valid and invalid arguments by examining their logical form 5. Understand that the fundamental nature of logic

6.

3.0 Main Content

Our discourse on validity and invalidity on one hand, and soundness and unsoundness on the other makes it clear that a valid or logically correct argument is not necessarily one with true premises and a true conclusion. We have valid arguments, otherwise called unsound arguments, that have false or a mixture of false and true premises and conclusion. The point on relief, therefore, is that the validity of an argument is not dependent on the truthfulness and falsity of the propositions that are embodied in the premises and the conclusion. The apposite question then is: what feature of an argument recommends its validity? that is, what is it that makes an argument valid or otherwise invalid?

Simply, an argument by virtue of the form of the argument, the logical relationship between the premises of an argument and its conclusion is a relationship of form or structure, not of truth and falsity. The import here is that validity depends not on the subject matter or material content of an argument, but on the form or structure.

3.1 Logical Form

Whether or not the premises of an argument are true depends on their specific content, but the validity or invalidity of an argument is determined entirely by its logical form. The logical form of an argument is that which remains of it when one abstracts away from the specific content of the premises and the conclusion, i.e., words naming things, their properties and relations, leaving only those elements that are common to

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discourse and reasoning about any subject matter, i.e., words such as "all", "and", "not",

"some", etc. One can represent the logical form of an argument by replacing the specific content words with letters used as place-holders or variables.

For example, consider these two arguments:

All humans are mammals.

No mammals are invertebrates.

Therefore, no humans are invertebrates All mosquitoes are spiders.

No spiders are animals.

Therefore, no mosquitoes are animals.

These arguments share the same form:

All p is q;

No p is q ;

Therefore, No p is r.

All arguments with this form are valid. Because they have this form, the examples above are valid. However, the first example is sound while the second is unsound, because its premises are false. The schematic representation of the arguments points out that any argument, which has the form, will be valid irrespective of what is substituted for p, q and r. In this connection, the schema in is called inference form and the arguments are then instances of the inference form. The letters, p, q, r mark the places into which expressions of a certain type may be inserted. The feature of the schema that guarantees that every instance of it will be valid is its construction in such a manner that every uniform way of replacing its variable to make the premises true automatically makes the conclusion true, too; or in other words, that no instance of it can have true premises but a false conclusion. Now consider:

All humans are mortal Elephants are mortal.

Therefore, elephants are humans.

All Presidents of Nigeria reside at Aso Rock.

General Buhari resides at Aso Rock.

Therefore, General Buhari is a President.

These arguments also have the same form:

All p is q;

r is q;

Therefore, r is p.

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Arguments with this form are invalid. This is easy to see with the first example.

The second example may seem like a good argument because the premises and the conclusion are all true (at least in 2019), but note that the conclusion's truth isn't guaranteed by the premises' truth. It could have been possible for the premises to be true and the conclusion false. This argument is invalid, and all invalid arguments are unsound.

The import here is that validity depends not on the subject matter or material content of an argument, but on the form or structure. Accordingly, logic as a study of the conditions of validity is a formal discipline. In other words, because the formal structure of an argument determines the validity of an argument, logic is a formal science and its subject matter is formal validity. Logic studies the forms of arguments in order to classify argument forms into two mutually exclusive exhaustive divisions; one division being reserved for formally valid argument forms, the other for formally invalid forms.

The object of logic, as a formal science, is thus obtained when logical techniques and methods are available by means of which it is possible, in principle, to identify all formally valid arguments as formally valid, and formally invalid arguments as formally invalid.

That the validity of an argument is a matter of it‘s logically form as opposed to its content makes it evident that the test for validity and invalidity does not depend on the truthfulness and falsity of the propositions that make up the argument. “The attributes of validity and invalidity belong to arguments not to propositions…., the attributes of truthfulness and falsity belong to propositions, not to arguments” (Copi 1973:3) This point is further buttressed by the following examples of valid arguments with (i) False premises and False conclusion (ii) False premises and True conclusion, and (iii) True premises and True conclusion:

(i) All black-complexioned individuals are hardworking All girls are black-complexioned

Therefore, all girls are hard working

A valid argument with false premises and false conclusion (ii) All Christians are Africans

Nigerians are all Christians Therefore, Nigerians are Africans

A valid argument with false premises and a true conclusion

(iii) Nigeria is a member of the Economic Community of West African Countries.

Member-nations of Economic Community of West African Countries are categorized as black nations

Therefore, Nigeria is categorized as a black-nation

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A valid argument with true premises and true conclusion

But, it is not possible to have as valid, an argument with all true premises and a false conclusion. The result thus is that any argument that has an all true premises and a false conclusion is sure to be invalid; this is because the conclusion of such an argument could not have been derived (deduced) from the premises, the point is that the information in the conclusion cannot be found in the premises, and in all valid arguments the conclusion cannot give any information not already contained in the premises.

The point on relief here is that the test for validity and invalidity does not depend on truthfulness and falsity. In this connection, questions revolving around truth and validity make it necessary that we do not talk of the material truth of propositions in talking about validity and invalidity; indeed, the actual truth of the premises and its conclusion is irrelevant to logic. In talking about the validity of an argument, we are not concerned with whether the premises of an argument and the conclusion are actually true or not but only in their logical form.