By joining a hypothetical proposition with an ordinary proposition we create a Hypothetical Proposition. For instance: "_If_ York contains a cathedral it is a city; York _does_ contain a cathedral; therefore, York is a city." Or: "If _dogs_ have four feet, they are quadrupeds; dogs _do_ have four feet; therefore dogs _are_ quadrupeds." The Hypothetical Syllogism may be either affirmative or negative; that is, its hypothetical proposition may either hypothetically _affirm_ or hypothetically _deny_. The part of the premise of a Hypothetical Syllogism which conditions or questions (and which usually contains the little word "if") is called the Antecedent. The major premise is the one usually thus conditioned. The other part of the conditioned proposition, and which part states what will happen or is true under the conditional circumstances, is called the Consequent. Thus, in one of the above examples: "If dogs have four feet" is the Antecedent; and the remainder of the proposition: "they are quadrupeds" is the Consequent. The Antecedent is indicated by the presence of some conditional term as: _if_, _supposing_, _granted that_, _provided that_, _although_, _had_, _were_, etc., the general sense and meaning of such terms being that of the little word "_if_." The Consequent has no special indicating term. Jevons gives the following clear and simple _Rules regarding the Hypothetical Syllogism_: I. "If the Antecedent be affirmed, the consequent may be affirmed. If the Consequent be denied, the Antecedent may be denied." II. "Avoid the fallacy of affirming the consequent, or denying the antecedent. This is a fallacy because of the fact that the conditional statement made in the major premise _may not be the only one_ determining the consequent." The following is an example of "Affirming the Consequent:" "_If_ it is raining, the sky is overclouded; the sky _is_ overclouded; therefore, it _is raining_." In truth, the sky may be overclouded, and still it may _not_ be raining. The fallacy is still more apparent when expressed in symbols, as follows: "_If_ A is B, C is D; C _is_ D; therefore, A is B." The fallacy of denying the Antecedent is shown by the following example: "_If_ Radium were cheap it would be useful; Radium is _not_ cheap; therefore Radium _is not_ useful." Or, expressed in symbols: "_If_ A is B, C is D; A is _not_ B; therefore C _is not_ D." In truth Radium may be useful although not cheap. Jevons gives the following examples of these fallacies: "If a man is a good teacher, he thoroughly understands his subject; but John Jones thoroughly understands his subject; therefore, he is a good teacher." Also, "If snow is mixed with salt it melts; the snow on the ground is _not_ mixed with salt; therefore it does _not_ melt."