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2.1: Basic Ideas and Tools

  • Page ID
    1661
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    • 2.1.1: Logic As the Science of Argument
      More generally, studying deductive logic can be an aid in clear thinking. The point is that, in order to make the nature of deductive validity very precise, we must learn a way of making certain aspects of the content of sentences very precise. For this reason, learning deductive logic can pay big dividends in improving your clarity generally in arguing, speaking, writing, and thinking.
    • 2.1.2: Sentences and Connectives
      Sentence logic symbolizes its shortest unambiguous sentences with Atomic Sentences, also called Sentence Letters, which are written with capital letters: 'A', 'B', 'C' and so on. We can use Connectives to build Compound Sentences out of shorter sentences. In this section we have met the connectives '~' (the Negation Sign), '&' (the Sign of Conjunction), and 'v' (the Sign of Disjunction).
    • 2.1.3: Truth Tables and the Meaning of '~', 'and', and 'v'
      An Assignment of Truth Values to a collection of atomic sentence letters is a specification, for each of the sentence letters, whether the letter is (for this assignment) to be taken as true or as false. The word Case will also be used for 'assignment of truth values'. A Truth Table for a Sentence is a specification of all possible truth values assignments to the sentence letters which occur in the sentence, and a specification of the truth value of the sentence for each of these assignments.
    • 2.1.4: Truth Functions
      A Truth Function is a rule which, when you give it input truth values, gives you a definite output truth value. A Truth Functional Connective is a connective defined by a truth function. A Truth Functional Compound is a compound sentence forked with truth functional connectives.
    • 2.1.5: Compounding Compound Sentences
      The Main Connective in a compound sentence is the connective which was used last in building up the sentence from its component or components. When you need to evaluate the truth value of a complex sentence, given truth values for the atomic sentence letters ,analyze the complete sentence into its components by identifying main connectives. Write out the components, in order of increasing complexity, so that you can see plainly how the larger sentences are built up from the parts.
    • 2.1.6: Rules of Formation and Rules of Valuation
      The Rules of Formation are explicit rules which tell us what counts as a sentence of sentence logic and how to determine the truth values of compound sentences if we are given the truth values of the components. The Rules of Valuation can be used to always calculate the truth value of a compound sentence, no matter how complex if  we have been given truth values for the ultimate constituent atomic sentence letters.
    • 2.1.S: Basic Ideas and Tools (Summary)

    Contributors and Attributions

    • Paul Teller (UC Davis). The Primer was published in 1989 by Prentice Hall, since acquired by Pearson Education. Pearson Education has allowed the Primer to go out of print and returned the copyright to Professor Teller who is happy to make it available without charge for instructional and educational use.


    2.1: Basic Ideas and Tools is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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