In one such fallacy, "affirming the consequent," the categorical proposition affirms the consequent of the conditional, and the conclusion affirms the antecedent, as in the example: If John is a bachelor, then he is male.
A syllogistic consequence is a formal consequence whose antecedent is a conjunction of two quantified propositions and whose consequent is a third quantified proposition.
In the form known as modus tollens, the categorical proposition denies the consequent of the conditional, and the conclusion denies the antecedent.
The consequent pattern derives the new proposition the unicorn might not exist.
The consequent pattern derives the new proposition the unicorn exists (no negation in the sem slot of the verb).
As a direct consequent of part (c) of Proposition 2.4, for any uniformly r-prox-regular subset K r of ℋ, we have N K r C ( x ) = N K r P ( x ).
Philo regarded all conditionals as true except those which with a correct antecedent had an incorrect consequent, and this meant a proposition such as "if it is day, then I am talking," is true unless it is day and I fall silent.
Conditionals were understood to be non-simple propositions containing one proposition as antecedent and one as consequent.
An if — then proposition is a hypothetical necessity provided the consequent logically follows from the antecedent.
Consequence is defined as the impossibility of the antecedent's being true without the consequent's also being true — truth itself being such that howsoever the proposition signifies things to be, so they are.
Brouwer then gives a method to transform any such demonstration, when analyzed into that canonical form, into a mathematical construction that makes the proposition "T contains a well-ordered bar", true, thereby establishing the consequent.
