Study guide Philosophy 09
Popular in Philosophy 09: Intro to Logic
Popular in PHIL-Philosophy
This 2 page Study Guide was uploaded by Tamina Sabnani on Wednesday December 9, 2015. The Study Guide belongs to Philosophy 09 at University of California - Santa Cruz taught by Kyle Robertson in Fall 2015. Since its upload, it has received 19 views. For similar materials see Philosophy 09: Intro to Logic in PHIL-Philosophy at University of California - Santa Cruz.
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Date Created: 12/09/15
Substitution instance a sentence obtained from a sentence form by replacing all the sentence variables in the sentence form by sentences making sure that every occurrence of a given sentence variable is replaced by the same sentence Ex A B is a substitution instance of p q Contingent sentence a sentence whose oneone form has at least one T and at least one F in the truth table Contradiction when the truth values of the main connective are all false Tautology theorem when the truth values of the main connective guarantee that it s true Wellformed formula a statement constructed according to the formation rules of a language Deductive argument an argument which you can prove the validity with all premises and a conclusion Validity valid if and only if it is not possible for all of its premises to be true and its conclusion false Consistent a set of statements is consistent if and only if it is possible for all the statements to be true Inconsistent a set of statements is inconsistent if and only if it is impossible for the statements to be true Direct proof infer a conclusion from premises given Indirect proof assume the opposite of what you want to show and prove a contradiction Sound any argument that is valid and has all true premises Unsound any argument that is either invalid or does not have all true premises Interpretation assigning a domain an assignment for each constant and the extension of each predicate to an argument making your own scenario to prove invalid Logically equivalent two predicate logic sentences are logically equivalent if and only if there is no interpretation in which they have different truth values truth value of their connectives must be equal Quasivariable a letter introduced by UI or EI that stands for any arbitrarily selected individual or some individual or other respectively Ex Tx x is quasivariable Quasivariables are not free variables otherwise UI and EI would lead us from true premises to conclusions that have no truth value SL connectives and or ifthen if and only if not Scope a sentence is truthfunctional if and only if the truth of a compound sentence containing that connective is completely determined by the truth of the atomic sentencs in the scope of that connective Explosion describes the phenomenon in our system that if you have a contradiction you can prove anything Some philosophers believe explosion is a bad thing and we should design a logic without it and should therefore allow some contradictions to be true Predicate is a grammar term used to describe the part of the sentence which talks about the subject and which has a verb Soundness of deductions you can prove all the premises and conclusion true Existential import
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