Agnosticism / Atheism: What's Hot Now: inference rules

Agnosticism / Atheism: What's Hot Now These articles that had the largest increase in popularity over the last week // via fulltextrssfeed.com

inference rules Sep 13th 2011, 10:01 inference rules Back to Last Page >     Glossary Index>  Related Terms • categorical proposition • axiom   Definition: Complex deductive arguments can be judged valid or invalid based on whether or not the steps in that argument follow the nine basic rules of inference. These rules of inference are all relatively simple, although when presented in formal terms they can look overly complex. Conjunction: 1. P 2. Q 3. Therefore, P and Q. 1. It is raining in New York. 2. It is raining in Boston 3. Therefore, it is raining in both New York and Boston Simplification: 1. P and Q. 2. Therefore, P. 1. It is raining in both New York and Boston. 2. Therefore, it is raining in New York. Addition: 1. P 2. Therefore, P or Q. 1. It is raining 2. Therefore, either either it is raining or the sun is shining. Absorption: 1. If P, then Q. 2. Therfore, If P then P and Q. 1. If it is raining, then I will get wet. 2. Therefore, if it is raining, then it is raining and I will get wet. Modus Ponens: 1. If P then Q. 2. P. 3. Therefore, Q. 1. If it is raining, then I will get wet. 2. It is raining. 3. Therefore, I will get wet. Modus Tollens: 1. If P then Q. 2. Not Q. (~Q). 3. Therefore, not P (~P). 1. If it had rained this morning, I would have gotten wet. 2. I did not get wet. 3. Therefore, it did not rain this morning. Hypothetical Syllogism: 1. If P then Q. 2. If Q then R. 3. Therefore, if P then R. 1. If it rains, then I will get wet. 2. If I get wet, then my shirt will be ruined. 3. If it rains, then my shirt will be ruined. Disjunctive Syllogism: 1. Either P or Q. 2. Not P (~P). 3. Therefore, Q. 1. Either it rained or I took a cab to the movies. 2. It did not rain. 3. Therefore, I took a cab to the movies. Constructive Dilemma: 1. (If P then Q) and (If R then S). 2. P or R. 3. Therefore, Q or S. 1. If it rains, then I will get wet and if it is sunny, then I will be dry. 2. Either it will rain or it will be sunny. 3. Therefore, either I will get wet or I will be dry. The above rules of inference, when combined with the rules of replacement, mean that propositional calculus is "complete." Propositional calculus is simply another name for formal logic. To say that it is "complete" means that, in this system, the axioms used are sufficient to demonstrate any true proposition or to justify any valid argument. Also Known As: none Alternate Spellings: none Common Misspellings: none Related Resources: What is the Logic and the Philosophy of Language? The two fields Logic and the Philosophy of Language are often treated separately, but they are nevertheless close enough that they are presented together here. Logic is the study of methods of reasoning and argumentation, both proper and improper. The Philosophy of Language, on the other hand, involves the study of how our language interacts with our thinking. What is Philosophy? What is philosophy? Is there any point in studying philosophy, or is it a useless subject? What are the different branches of philosophy - what's the difference between aestheitcs and ethics? What's the difference between metaphysics and epistemology? Back to Last Page >     Glossary Index>

You are receiving this email because you subscribed to this feed at blogtrottr.com. If you no longer wish to receive these emails, you can unsubscribe from this feed, or manage all your subscriptions