English

In Defence of the Material Conditional

Logic 2026-03-16 v1

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=42+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.

Keywords

Cite

@article{arxiv.2603.13066,
  title  = {In Defence of the Material Conditional},
  author = {Alexander V. Gheorghiu},
  journal= {arXiv preprint arXiv:2603.13066},
  year   = {2026}
}
R2 v1 2026-07-01T11:18:34.599Z