Material Implication, Paradox of Material Implication and its Criticism

International Journal of Humanities and Social Science

© 2022 by SSRG - IJHSS Journal

Volume 9 Issue 5

Year of Publication : 2022

Authors : MD. Selim Reza

10.14445/23942703/IJHSS-V9I5P104

How to Cite?

MD. Selim Reza, "Material Implication, Paradox of Material Implication and its Criticism," SSRG International Journal of Humanities and Social Science, vol. 9,  no. 5, pp. 25-29, 2022. Crossref, https://doi.org/10.14445/23942703/IJHSS-V9I5P104

Abstract:

At first, George Boole introduced conditional propositions as the basis for the better development of propositional logic. A compound statement composed of two atomic statements (antecedent and consequent) by the connective 'if—then' is called propositional logic. For example: "If it is raining, then the roads are wet". Here the first statement of this conditional proposition, 'It is raining,' is called the antecedent, and the second, 'the roads are wet,' is called the consequent. The material conditional in which conditional is false only when the antecedent is true and the consequent is false, but it is always true in all other cases. So, a definition of a material implication is – a conditional proposition is true when either the antecedent is false, or the consequent is true. The conditional is false when the antecedent is true and the consequent is false. Whereas, if there is no relation between the antecedent and the consequent, then the truth-functional definition of material implication leads to a paradox called the paradox of material implication. Basically, the twin paradox arises here. For example, the conditionals 'if the earth is a star, then Socrates is a philosopher and 'if the earth is a star, then Socrates is not a philosopher are both true because the antecedent is false. Secondly, the conditionals 'if Islamabad is the capital of Pakistan, then New Delhi is the capital of India' and 'if Islamabad is not the capital of Pakistan, then New Delhi is the capital of India' are both true because the consequent is true. C.I. Lewis clearly establishes these paradoxes in 1912 '(I) a false proposition implies any proposition; and (II) a true proposition is implied by any proposition'.

Keywords:

Conditional statement, Truth value, Truth function, Material implication, Implier, Implicans, Paradox of material implication.

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