Why is symbolic logic important

The logical operator "and," as we will see, will be symbolized as " ". In addition to propositions, propositional logic contains another element: operators on propositions. Propositions can be thought of like the sticks of a tinker-toy set. Operators are like the connecting blocks.

By adding more and more operators, we get more complex structures. For evaluation of statements, there is only one condition to be learned: " In order to know the truth value of the proposition which results from applying an operator to propositions, all that need be known is the definition of the operator and the truth value of the propositions used. Philosophy Introduction to Logic The Language of Symbolic Logic Abstract: Conventions for translating ordinary language statements into symbolic notation are outlined.

Students with a year course in calculus are more than prepared for the material contained here, and for the majority of exercises no more background than college algebra is required. The exercises form a particularly important part of the project, and were designed to simultaneously provide students with practice applying the ideas discussed and to extend the discussion to new material.

Several exercises introduce concepts from logic, number theory, the theory of relations, and other topics that are not normally covered until later in a discrete mathematics course.

All such exercises are elementary, and may be taken as a stand-alone opportunity to study the primary material, or as an invitation to explore more advanced concepts. Because it is customary to cover logic at the beginning of a discrete mathematics course, the instructor may wish to begin with the material here, and use these exercises as a way of connecting logic to the material covered later in the course.

Several exercises e. In our opinion, this stimulates independent thinking, as well as provides an opportunity for further in-class discussion. Developing the logical skills necessary to read and write mathematical proofs is emphasized throughout. The instructor may wish to discuss the material covered here and proceed to introduce basic proofs using number theory or naive set theory. The instructor may even use exercises that discuss concepts from number theory or the theory of relations as a jumping off point to assign outside exercises on reading or writing proofs before the material here is completed.

This provides an extremely quick way of exposing students to proofs. Download the project An Introduction to Symbolic Logic as a pdf file ready for classroom use.

Download the modifiable Latex source file for this project. The development of curricular materials for discrete mathematics has been partially supported by the National Science Foundation's Course, Curriculum and Laboratory Improvement Program under grants DUE and DUE for which the authors are most appreciative. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Skip to main content. Search form Search. On the contrary, this trend toward believing everything you hear is why the need for logical thinking is more crucial than ever. Actively scan device characteristics for identification. Use precise geolocation data. Select personalised content.

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List of Partners vendors. Share Flipboard Email. Emrys Westacott. Professor of Philosophy. Emrys Westacott is a professor of philosophy at Alfred University. He is the author or co-author of several books, including "Thinking Through Philosophy: An Introduction. Updated September 03, Featured Video. Cite this Article Format. Westacott, Emrys. Fallacies of Relevance: Appeal to Authority.