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In classical logic, disjunctive syllogism [1] [2] (historically known as modus tollendo ponens (MTP), [3] Latin for "mode that affirms by denying") [4] is a valid argument form which is a syllogism having a disjunctive statement for one of its premises. [5] [6] An example in English: I will choose soup or I will choose salad. I will not choose ...
It does not leave the user with one statement alone at the end of the argument, instead, it gives an option of two different statements. The first premise gives an option of two different statements. Then it states that if the first one happens, there will be a particular outcome and if the second happens, there will be a separate outcome.
Affirmative conclusion from a negative premise (illicit negative) is a formal fallacy that is committed when a categorical syllogism has a positive conclusion and one or two negative premises. For example: No fish are dogs, and no dogs can fly, therefore all fish can fly.
In other words, the conclusion must be true if the premises are true. An argument can be “valid” even if one or more of its premises are false. An argument is sound if it is valid and the premises are true. It is possible to have a deductive argument that is logically valid but is not sound. Fallacious arguments often take that form.
The corresponding conditional of a valid argument is a logical truth and the negation of its corresponding conditional is a contradiction. The conclusion is a necessary consequence of its premises. An argument that is not valid is said to be "invalid". An example of a valid (and sound) argument is given by the following well-known syllogism:
The rule states that a syllogism in which both premises are of form a or i (affirmative) cannot reach a conclusion of form e or o (negative). Exactly one of the premises must be negative to construct a valid syllogism with a negative conclusion. (A syllogism with two negative premises commits the related fallacy of exclusive premises.)
Destructive dilemma [1] [2] is the name of a valid rule of inference of propositional logic. It is the inference that, if P implies Q and R implies S and either Q is false or S is false, then either P or R must be false. In sum, if two conditionals are true, but one of their consequents is false, then one of their antecedents has to be false.
Two premises are not enough to connect four different terms, since in order to establish connection, there must be one term common to both premises. In everyday reasoning, the fallacy of four terms occurs most frequently by equivocation : using the same word or phrase but with a different meaning each time, creating a fourth term even though ...