Conditional Propositions: Hypothetical and Disjunctive

In one line

A hypothetical proposition asserts that one proposition follows from another; a disjunctive proposition asserts that at least one of two propositions is true.

In the wording a student can write in an examination: a hypothetical proposition has the form "if p then q", where p is the antecedent and q the consequent, and it asserts neither p nor q but only the connection. A disjunctive proposition has the form "either p or q", whose parts are called alternatives, and it asserts that at least one alternative holds without saying which.

Hypothetical propositions

"If the notice was validly served, the tenancy stood terminated."

The part after "if" is the antecedent; the part after "then", stated or understood, is the consequent.

Neither part is asserted. This was established at sequence 40 and it is the point students forget. The sentence does not say the notice was served and does not say the tenancy ended. It says only that the second would follow from the first.

The order of the parts is not fixed by the sentence. "The tenancy stood terminated if the notice was validly served" is the same proposition with the consequent written first. What identifies the antecedent is the word "if", not the position.

Words that introduce an antecedent: if, provided that, in case, where, when used conditionally, on condition that, in the event that. Legislative drafting uses "where" and "provided that" far more often than "if", and a student reading a statute must recognise them.

Words that introduce a consequent: then, in that case, thereupon, shall. The word "shall" in a section is very often the marker of a consequent.

The two valid moves and the two fallacies

Given "if p then q", exactly two inferences are valid and exactly two look valid and are not. This is the most useful single table in Module II.

Why the two fallacies are fallacies. "If p then q" says that p is enough for q. It does not say that p is necessary for q. There may be other routes to q.

Denying the antecedent, demonstrated. "If the document was registered, it is admissible. It was not registered. Therefore it is inadmissible." The conditional never said registration was the only path to admissibility, so the conclusion does not follow.

Affirming the consequent, demonstrated. "If the accused was at the scene, his fingerprints would be on the door. His fingerprints are on the door. Therefore he was at the scene." He may have touched the door the previous week. This fallacy is the single commonest error in reasoning from circumstantial evidence, and it is exactly what condition four in Sarda, at sequence 230, is designed to prevent: the fingerprints are consistent with guilt and do not exclude every other hypothesis.