Philosophy Relationship Between Truth And Validity In An Argument

Running Head: PHILOSOPHY 1

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Philosophy – Relationship between Truth and Validity in an Argument

PHILOSOPHY 2

Philosophy – Relationship between Truth and Validity in an Argument

Introduction

Logic, is concerned with arguments and the standards and criteria which determine

their validity. It provides procedures for determining the questions of validity

. Many

scholars have provided various definition as to what logic is, however, for the purposes of

this paper, the most relevant definition will be selected. Logic, according to Peter Suber, is

the study of argument. In which sense, argument, can be said to be examples of reasoning

where one or more statement are offered as support, evidence or justification for something

through the conclusion and prior statements supporting the conclusion

When assessing the worth of an argument, the two major properties of arguments

must first be established and understood. They include; the truth of the premises and the

validity of the reasoning

. This connection between validity and the truth, and the relationship

between the validity (or otherwise) of an argument and the truth to its conclusion, within

logical reasoning is the focus of this essay. It will be explained using modern propositional

calculus and traditional syllogistic logic as examples of how truth and validity relate and how

one can help determine the other through the use of truth tables and the square of opposition.

Part 1: Validity – The Concern of Logic

Peter Suber states that there are various scenarios where an argument can be

considered to be valid. These scenarios include the following; where the truth of the

McDonell, Cyril, Traditional Syllogistic Logic, NUIM Lecture Notes.

<https://2017.moodle.maynoothuniversity.ie/pluginfile.php/592177/mod_resource/content/0/01_TRADITIONA

L_LOGIC_2016_edited.pdf>. [accessed 19 April 2017].

Suber, Peter, Propositional Logic Terms And Symbols, NUIM Lecture Notes.

<https://2017.moodle.maynoothuniversity.ie/pluginfile.php/581861/mod_resource/content/0/1f_Peter%20Suber

%2C%20_Propositional%20Logic%20Terms%20and%20Symbols_.pdf>. [accessed 19 April 2017

Suber, 2017.

PHILOSOPHY 3

conclusion is guaranteed by the truth of its premises, or, when it is impossible to prove the

conclusion false and hence all the premises are said to be true at the same time, or, where

certain valid rules can deduce the conclusion in accordance to how they are stipulated. All

these scenarios are equivalent and hence where an argument is not valid, then it is said to be

invalid

. The same, however, does not apply to statements.

According to the first fundamental principle of logic, truth and validity must be

independent of each other. Therefore, statements can either be true or false, but the same does

not apply to arguments. Arguments are pertinent to reasoning but truth is pertinent to

propositions. Propositions in this case is the truth or false nature of certain combinations of

sentences that are either valid or invalid

. When defining validity, it pertains to reasoning and

not to propositions. Hence, when the reasoning behind the argument is valid, then all of its

premises can be said to be true and sound. If there are any premises termed as untrue, then the

argument is termed as unsound. The conclusion derived from a sound argument is logical and

believable and anyone who goes against it is illogical

Understanding the truth to the premises in argument then defines an argument as

either deductive or inductive. When all the premises in the argument are conclusive and

provide grounds aiding to the truth of the conclusion or supporting it with necessity, then they

are deductive. However, when the premises provide a milder claim as to be supporting, but

not guaranteeing the conclusion, they are said to be inductive. Hence, deductive arguments

Suber, 2017

Mcauley, Harry, Logic, Propositions, Arguments, Validity & Truth, NUIM Lecture Notes. <

https://2017.moodle.maynoothuniversity.ie/pluginfile.php/581853/mod_resource/content/0/1b_Logic_1_HMcC

auley.pdf>. [accessed, 19 April 2017].

Mcauley 2017.

PHILOSOPHY 4

are the only ones which can be valid or invalid as they strongly support the truth in their

conclusions

Part 2: Truth – And its Relationship to Validity

When discerning the truth of premises in an argument, the possibility that the

conclusion is false is impossible. Trying to make a link between truth and validity is

complex. The main concern of logic is discerning the validity of arguments and not the truth

behind propositions. However statements are present in an argument and must be discerned

as either true or false in order for the argument to be termed as valid or invalid

When learning of the relationship between truth and validity, one must identify that a

valid argument cannot have true premises and a false conclusion. the tests conducted to prove

the premises in an argument determine the truth behind the conclusions. If they all support it

and are true, then the conclusion is also true and the argument termed to be valid, however,

there cannot be an argument with true premises and a false conclusion, this in essence brings

forth an invalid argument

Part 3: Truth and Validity in Logic – Propositional Calculus and Syllogistic Logic

For an argument to be defined as logical, the distinction between truth and validity is

fundamental, this means that propositions are true and reasoning’s are valid. However, this

relationship is not always straightforward as a situation where all premises are true and the

conclusion false renders the argument invalid. In this case. Invalidity is defined as the

presence of true premises with a false conclusion

Suber 2017.

McDonnell 2017.

Mcauley 2017.

Suber 2017.

PHILOSOPHY 5

Logicians test validity through invalidity. In a weak sense, an argument can be said to

be valid only when it is not invalid, and hence, logicians test for invalidity. Logicians do not

pay attention to whether a statement is true or false, rather, they test the falsity of the

conclusion and derive how far they can get away with it. If all premises is true and the

conclusion false, then I all possible universes where the test was conducted, the argument is

invalid in all universes tested

. In this way, the logician does not necessarily have to know

whether the actual premises are true or not, rather they examine all possible combinations of

truth and false In order to reveal whether there are any invalid combinations that will appear.

In propositional logic, there is the “truth-Table Method” that provides a list of all possible

truths for a statement

Truth-Table Method

In the truth Table, all statements are marked with Truths (derived as “T”) and Falses

as “F”). Combinations derived from these form the three types of propositions. Various

statements will have combinations of T’s and F’s they are known as Contingencies, those that

are purely T’s are termed as Tautologies, those with purely F’s are termed as Contradictions.

In the conditional, “p” is the first statement and is termed as the “if Clause”. It is the

antecedent. “q” is the second statement, also known as the “then clause” and termed as the

consequent, however, there are more complicated conditionals that render the antecedents

and consequents as compounds rather than simple statements

. An argument can be

expressed as a compound statement when all the premises are conjoined and made a

conjunction of the antecedent of a conditional, the conclusion is made to be the consequent.

The statement that is derived from this is called a Corresponding conditional.

Suber 2017

Mcauley, 2017

Suber 2017.

PHILOSOPHY 6

For every argument, there is a corresponding conditional and the implication statements

have a corresponding argument. With this, an argument can only be valid if the corresponding

conditional is a tautology; as the corresponding conditional of an argument is a statement. In

this way, the statements can either be a contradiction, contingency or a tautology. Truth tables

are adequate to test validity, tautology, contradiction, contingency, consistency, and

equivalence. This is important because truth tables require no ingenuity or insight, just patience

and the mechanical application of rules. Truth tables correctly constructed will always give us

the right answer

Syllogistic Logic

Traditional Syllogistic Arguments are all comprised of Categorical propositions and

address arguments that modern propositional logic cannot test their validity

. It mainly

concentrates on internal features of categorical propositions in order to determine the validity

of an argument. The validity of arguments placed in categorical propositions is valued through

the assessment of the “categories” and how they linked together logically or deductively

Logicians make a determination of the validity after discerning the proper structure of the

argument, and analysing the arguments to discern which are valid and which are invalid. A

Logician does this through determination of what the conclusion is and what the premises are

and that all the propositions present in both the premises and conclusion are in a strict logical

form

To test for validity in syllogistic logic a tool called The Square of Opposition is used.

It is a diagram which embodies groups of theses. The diagram keeps the theses straight and is

Suber 2017

McDonnell 2017

McDonell 2017

Daly, Donal, Some Notes On Logic, St Patrick’s College Maynooth.

<https://2017.moodle.maynoothuniversity.ie/pluginfile.php/591445/mod_resource/content/0/Daly%20Logic_No

tes%20%282010%29%2C%20SCF_pp.18-21.pdf>. [accessed 19April].

PHILOSOPHY 7

not necessarily essential. These theses provide four logical forms that are concerned in logical

relations. They are the Universal Affirmative, Negative, particular Affirmative and

negative

In the same way that truth tables were used, the square of opposition is employed to

test for validity by investigating the relationship between truth and validity and how the truth

of an argument’s premises, if true, guarantee the truth of its conclusion and this then can be

used to determine the overall validity of the argument.

Conclusion

Truth and Validity are independent but the relationship is clearly derived when

accessing the validity of an argument. The relationship is complex but is to be understood in

order to derive whether an argument is logical or illogical. Validity pertains to reasoning and

truth pertains to propositions. Arguments are valid or invalid and statements are true or false

and hence all statements within the argument must be true in order for the argument to be

valid, otherwise it is invalid. This essay has investigated the connection between validity and

truth focusing on arguments and their validity (or otherwise) and the truth (or otherwise) of

their conclusion, within logical reasoning. Through the use of modern propositional calculus

and traditional syllogistic logic examples, the connection of how truth and validity relate and

how one can help determine the other through the use of truth tables and the square of

opposition has been explained.

Parsons, Terrance, ‘The traditional Square of Opposition’, Stanford Encyclopedia of Philosophy.

<https://plato.stanford.edu/entries/square/>. [accessed[19 April 2017].

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Philosophy Relationship between Truth and Validity in an Argument

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