Search results
Results From The WOW.Com Content Network
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 types of logical reasoning differ concerning the exact norms they use as well as the certainty of the conclusion they arrive at. [1] [15] Deductive reasoning offers the strongest support and implies its conclusion with certainty, like mathematical proofs. For non-deductive reasoning, the premises make the conclusion more likely but do not ...
As the study of argument is of clear importance to the reasons that we hold things to be true, logic is of essential importance to rationality. Arguments may be logical if they are "conducted or assessed according to strict principles of validity", [1] while they are rational according to the broader requirement that they are based on reason and knowledge.
For valid arguments, the logical structure of the premises and the conclusion follows a pattern called a rule of inference. [12] For example, modus ponens is a rule of inference according to which all arguments of the form "(1) p , (2) if p then q , (3) therefore q " are valid, independent of what the terms p and q stand for. [ 13 ]
That is, the word "valid" does not refer to the truth of the premises or the conclusion, but rather to the form of the inference. An inference can be valid even if the parts are false, and can be invalid even if some parts are true. But a valid form with true premises will always have a true conclusion.
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
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 following is an example of an argument that is “valid”, but not “sound”: Everyone who eats carrots is a quarterback. John eats carrots.
An argument for psychologism is based on the idea that logic is a sub-discipline of psychology: it studies not all laws of thought, but only the subset of laws corresponding to valid reasoning. [85] Another argument focuses on the thesis that we learn about logical truths through the feeling of self-evidence, which is in turn studied by ...