Logic Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.Anti-spam check. Do not fill this in! ====First-order logic==== [[File:BS-12-Begriffsschrift Quantifier1-svg.svg|thumb|alt=Symbol introduced by Gottlob Frege for the universal quantifier|[[Gottlob Frege]]'s ''[[Begriffschrift]]'' introduced the notion of quantifier in a graphical notation, which here represents the judgment that <math>\forall x. F(x)</math> is true.]] {{main|First-order logic}} First-order logic includes the same propositional connectives as propositional logic but differs from it because it articulates the internal structure of propositions. This happens through devices such as singular terms, which refer to particular objects, [[Predicate (mathematical logic)|predicates]], which refer to properties and relations, and quantifiers, which treat notions like "some" and "all".{{sfnm|1a1=Shapiro|1a2=Kouri Kissel|1y=2022|2a1=Honderich|2y=2005|2loc=philosophical logic|3a1=Michaelson|3a2=Reimer|3y=2019}} For example, to express the proposition "this raven is black", one may use the predicate <math>B</math> for the property "black" and the singular term <math>r</math> referring to the raven to form the expression <math>B(r)</math>. To express that some objects are black, the existential quantifier <math>\exists</math> is combined with the variable <math>x</math> to form the proposition <math>\exists x B(x)</math>. First-order logic contains various rules of inference that determine how expressions articulated this way can form valid arguments, for example, that one may infer <math>\exists x B(x)</math> from <math>B(r)</math>.{{sfnm|1a1=Nolt|1y=2021|2a1=Magnus|2y=2005|2loc=4 Quantified logic}} Summary: Please note that all contributions to Christianpedia may be edited, altered, or removed by other contributors. If you do not want your writing to be edited mercilessly, then do not submit it here. You are also promising us that you wrote this yourself, or copied it from a public domain or similar free resource (see Christianpedia:Copyrights for details). Do not submit copyrighted work without permission! Cancel Editing help (opens in new window) Discuss this page