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! ===Classical=== {{main|Classical logic}} [[Classical logic]] is distinct from traditional or Aristotelian logic. It encompasses propositional logic and first-order logic. It is "classical" in the sense that it is based on basic logical intuitions shared by most logicians.{{sfnm|1a1=Hintikka|1y=2019|1loc=§Nature and varieties of logic, §Alternative logics|2a1=Hintikka|2a2=Sandu|2y=2006|2pp=27-8|3a1=Bäck|3y=2016|3p=317}} These intuitions include the [[law of excluded middle]], the [[double negation elimination]], the [[principle of explosion]], and the bivalence of truth.{{sfn |Shapiro |Kouri Kissel |2022}} It was originally developed to analyze mathematical arguments and was only later applied to other fields as well. Because of this focus on mathematics, it does not include logical vocabulary relevant to many other topics of philosophical importance. Examples of concepts it overlooks are the contrast between necessity and possibility and the problem of ethical obligation and permission. Similarly, it does not address the relations between past, present, and future.{{sfn |Burgess |2009 |loc=1. Classical logic}} Such issues are addressed by extended logics. They build on the basic intuitions of classical logic and expand it by introducing new logical vocabulary. This way, the exact logical approach is applied to fields like [[ethics]] or epistemology that lie beyond the scope of mathematics.{{sfnm|1a1=Jacquette|1y=2006|1loc=Introduction: Philosophy of logic today|1pp=1–12|2a1=Borchert|2y=2006c|2loc=Logic, Non-Classical|3a1=Goble|3y=2001|3loc=Introduction}} ====Propositional logic==== {{main|Propositional calculus}} Propositional logic comprises formal systems in which formulae are built from [[atomic propositions]] using [[logical connectives]]. For instance, propositional logic represents the [[conjunction (logic)|conjunction]] of two atomic propositions <math>P</math> and <math>Q</math> as the complex formula <math>P \land Q</math>. Unlike predicate logic where terms and predicates are the smallest units, propositional logic takes full propositions with truth values as its most basic component.{{sfn |Brody |2006 |pp=535–536}} Thus, propositional logics can only represent logical relationships that arise from the way complex propositions are built from simpler ones. But it cannot represent inferences that result from the inner structure of a proposition.{{sfn |Klement|1995b}} ====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