Humanities Religion & Spirituality Hypothetical Proposition Share Flipboard Email Print Religion & Spirituality Atheism & Agnosticism Belief Systems Logic & Reasoning Ethics & Morality Key Figures Evolution Schools & Systems Misconceptions Christianity Catholicism Islam Judaism Hinduism Buddhism Latter-Day Saints Taoism Alternative Religion Angels & Miracles Sikhism Holistic Healing Paganism / Wicca Astrology View More by Austin Cline Austin Cline, a former regional director for the Council for Secular Humanism, writes and lectures extensively about atheism and agnosticism. Updated February 03, 2019 A hypothetical proposition is a conditional statement which takes the form: if P then Q. Examples would include: If he studied, then he received a good grade.If we had not eaten, then we would be hungry.If she wore her coat, then she will not be cold. In all three statements, the first part (If...) is labeled the antecedent and the second part (then...) is labeled the consequent. In such situations, there are two valid inferences which can be drawn and two invalid inferences which can be drawn - but only when we assume that the relationship expressed in the hypothetical proposition is true. If the relationship is not true, then no valid inferences can be drawn. A hypothetical statement can be defined by the following truth table: P Q if P then Q T T T T F F F T T F F T Assuming the truth of a hypothetical proposition, it is possible to draw two valid and two invalid inferences: Affirming the Antecedent The first valid inference is called affirming the antecedent, which involves making the valid argument that because the antecedent is true, then the consequent is also true. Thus: because it is true that she wore her coat, then it is also true that she will not be cold. The Latin term for this, modus ponens, is often used. Denying the Consequent The second valid inference is called denying the consequent, which involves making the valid argument that because the consequent is false, then the antecedent is also false. Thus: she is cold, therefore she did not wear her coat. The Latin term for this, modus tollens, is often used. Affirming the Consequent The first invalid inference is called affirming the consequent, which involves making the invalid argument that because the consequent is true, then the antecedent must also be true. Thus: she is not cold, therefore she must have worn her coat. This is sometimes referred to as a fallacy of the consequent. Denying the Antecedent The second invalid inference is called denying the antecedent, which involves making the invalid argument because the antecedent is false, then, therefore, the consequent must also be false. Thus: she did not wear her coat, therefore she must be cold. This is sometimes referred to as a fallacy of the antecedent and has the following form: If P, therefore Q.Not P.Therefore, Not Q. A practical example of this would be: If Roger is a Democrat, then he is liberal. Roger is not a Democrat, therefore he must not be liberal. Because this is a formal fallacy, anything written with this structure will be wrong, no matter what terms you use to replace P and Q with. Understanding how and why the above two invalid inferences occur can be aided by understanding the difference between necessary and sufficient conditions. You can also read the rules of inference to learn more. Continue Reading Logic: What is a Non-Argument? What Is a Logical Fallacy? Understanding Defective Arguments False Dilemma Fallacy Quoting Out of Context Fallacy (Changing Meaning) Refutation by Counterexample-A Simple Way to Refute Bad Arguments Argument and Rhetoric: Premises, Inferences, Conclusions How to Critique an Argument Logical Fallacies: Begging the Question What Are Oversimplification and Exaggeration Fallacies? 6 Good Reasons to Study Logic Appealing to Tradition Fallacy - Who Even Needs the New Stuff? Logical Fallacies: Appeal to Authority What is the Fallacy of Composition? What Is the Fallacy of Division? What Is Suppressed Evidence Fallacy? Tu Quoque - Ad Hominem Fallacy That You Did It Too!