Capstone: Form-Spotting Drill

This capstone runs short arguments in plain English at speed, deliberately interleaving the valid forms with their invalid twins, because the pair members are indistinguishable in conversation unless the form is named.

One: if the shipment cleared customs it arrived Tuesday; it cleared customs; so it arrived Tuesday. Symbolize, name it — affirming the antecedent. Valid. Two: if the shipment cleared customs it arrived Tuesday; it arrived Tuesday; so it cleared customs. The same two sentences in the other order. This affirms the consequent, and it is invalid — the shipment could have arrived Tuesday by some other route. Three: if the bill passes the tax rises; the tax did not rise; so the bill did not pass. Denying the consequent. Valid. Four: if the bill passes the tax rises; the bill did not pass; so the tax did not rise. Denying the antecedent, and invalid — something else could raise the tax. Five: either the server is down or the cable is cut; the server is not down; so the cable is cut. Disjunctive syllogism, valid. Six: either the server is down or the cable is cut; the server is down; so the cable is not cut. Invalid, because an inclusive disjunction permits both. Seven: if it rains the match is postponed, and if the match is postponed refunds issue; so if it rains refunds issue. A chain, valid. Eight: if it rains the match is postponed, and if it rains refunds issue; so if the match is postponed refunds issue. Not a chain at all — both conditionals share an antecedent rather than linking, and the argument is invalid.