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! ====Deductive==== A deductively valid argument is one whose premises guarantee the truth of its conclusion.{{sfnm|1a1=McKeon|2a1=Craig|2y=1996|2loc=Formal and informal logic}} For instance, the argument "(1) all frogs are amphibians; (2) no cats are amphibians; (3) therefore no cats are frogs" is deductively valid. For deductive validity, it does not matter whether the premises or the conclusion are actually true. So the argument "(1) all frogs are mammals; (2) no cats are mammals; (3) therefore no cats are frogs" is also valid because the conclusion follows necessarily from the premises.{{sfn |Evans |2005 |loc=8. Deductive Reasoning, [https://books.google.com/books?id=znbkHaC8QeMC&pg=PA169 p. 169]}} According to an influential view by [[Alfred Tarski]], deductive arguments have three essential features: (1) they are formal, i.e. they depend only on the form of the premises and the conclusion; (2) they are a priori, i.e. no sense experience is needed to determine whether they obtain; (3) they are modal, i.e. that they hold by [[logical necessity]] for the given propositions, independent of any other circumstances.{{sfn |McKeon}} Because of the first feature, the focus on formality, deductive inference is usually identified with rules of inference.{{sfn|Hintikka|Sandu|2006|pp=13–4}} Rules of inference specify the form of the premises and the conclusion: how they have to be structured for the inference to be valid. Arguments that do not follow any rule of inference are deductively invalid.{{sfnm|1a1=Hintikka|1a2=Sandu|1y=2006|1pp=13-4|2a1=Blackburn|2y=2016|2loc=rule of inference}} The modus ponens is a prominent rule of inference. It has the form "''p''; if ''p'', then ''q''; therefore ''q''".{{sfn |Blackburn |2016 |loc=rule of inference}} Knowing that it has just rained (<math>p</math>) and that after rain the streets are wet (<math>p \to q</math>), one can use modus ponens to deduce that the streets are wet (<math>q</math>).{{sfn |Dick |Müller |2017 |p=157}} The third feature can be expressed by stating that deductively valid inferences are truth-preserving: it is impossible for the premises to be true and the conclusion to be false.{{sfnm|1a1=Hintikka|1a2=Sandu|1y=2006|1p=13|2a1=Backmann|2y=2019|2pp=235–255|3a1=Douven|3y=2021}} Because of this feature, it is often asserted that deductive inferences are uninformative since the conclusion cannot arrive at new information not already present in the premises.{{sfnm|1a1=Hintikka|1a2=Sandu|1y=2006|1p=14|2a1=D'Agostino|2a2=Floridi|2y=2009|2pp=271–315}} But this point is not always accepted since it would mean, for example, that most of mathematics is uninformative. A different characterization distinguishes between surface and depth information. The surface information of a sentence is the information it presents explicitly. Depth information is the totality of the information contained in the sentence, both explicitly and implicitly. According to this view, deductive inferences are uninformative on the depth level. But they can be highly informative on the surface level by making implicit information explicit. This happens, for example, in mathematical proofs.{{sfnm|1a1=Hintikka|1a2=Sandu|1y=2006|1p=14|2a1=Sagüillo|2y=2014|2pp=75–88|3a1=Hintikka|3y=1970|3pp=135–152}} 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