In Defence of the Material Conditional

TL;DR

This paper defends the material conditional by arguing that its paradoxes stem from misunderstandings and cognitive biases, and that it accurately captures indicative reasoning about correlation, not causation, which is essential in scientific logic.

Contribution

It clarifies the proper interpretation of the material conditional as indicative, resolving paradoxes and emphasizing its role in representing correlation without causation.

Findings

The paradoxes result from misreading and cognitive biases.

The material conditional correctly models indicative reasoning.

It is essential for scientific reasoning about correlation.

Abstract

The material conditional has long been charged with paradox. Defined truth-functionally, it renders true any conditional whose antecedent is false or consequent true -- hence, seemingly absurd statements such as `If unicorns exist, then $2+2=4$'. This has been taken as proof that the connective cannot capture the meaning of ordinary if-then sentences, which appear to imply a causal or evidential link. I argue, by contrast, that the paradoxes arise from a confusion of what it expresses caused by cognitive biases. The material conditional properly belongs to the class of indicative, not subjunctive, conditionals -- those that register patterns of co-variation rather than counterfactual dependence. When understood as a formal device marking entailment under a background theory, it faithfully represents a mode of reasoning essential to science itself: correlation without causation. The faults ascribed to it, therefore, are not flaws in meaning or standard use, but as misapplication and misreading.