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Of the many and varied argument forms that can possibly be constructed, only very few are valid argument forms. In order to evaluate these forms, statements are put into logical form . Logical form replaces any sentences or ideas with letters to remove any bias from content and allow one to evaluate the argument without any bias due to its ...
The form shows that inference from P implies Q to the negation of Q implies the negation of P is a valid argument. The history of the inference rule modus tollens goes back to antiquity. [4] The first to explicitly describe the argument form modus tollens was Theophrastus. [5] Modus tollens is closely related to modus ponens.
The sentence can be given as a grammatical puzzle [7] [8] [9] or an item on a test, [1] [2] for which one must find the proper punctuation to give it meaning. Hans Reichenbach used a similar sentence ("John where Jack had...") in his 1947 book Elements of Symbolic Logic as an exercise for the reader, to illustrate the different levels of language, namely object language and metalanguage.
The second premise "affirms" the antecedent. The conclusion, that the consequent must be true, is deductively valid. A mixed hypothetical syllogism has four possible forms, two of which are valid, while the other two are invalid. A valid mixed hypothetical syllogism either affirms the antecedent (modus ponens) or denies the consequent (modus ...
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 ...
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:
Attention is given to argument and sentence form, because form is what makes an argument valid or cogent. All logical form arguments are either inductive or deductive. Inductive logical forms include inductive generalization, statistical arguments, causal argument, and arguments from analogy.
List of linguistic example sentences; Polyptoton; Semantic satiation; Other linguistically complex sentences: James while John had had had had had had had had had had had a better effect on the teacher; Lion-Eating Poet in the Stone Den (a Classical Chinese poem in which every syllable is pronounced as shi, though with varying tones).