Philosophical Concepts And Theories Codexery

Logical consequence

A fundamental concept in logic describing valid inference.

Last updated

Logical consequence is the relation where a conclusion follows from premises in a valid argument.[1][2] It is considered necessary and formal, often explained through proofs or models.[2] The concept is central to logic and addresses what it means for a conclusion to be a consequence of premises.[3][1]

Quick Facts

Field
Logic
Key features
  • Necessary and formal
  • relies on logical form
  • a priori
  • has a modal component

Facts from the source article.

Key facts and history

Alfred Tarski identified three features of an adequate characterization of logical consequence: it is formal, a priori, and has a modal component.[4][3] Tarski distinguished between logical and non-logical terms, stating that X is a logical consequence of K only if no interpretation of non-logical terms makes K true and X false.[3] Syntactic consequence is defined by the existence of a formal proof within a formal system.[5] Semantic consequence holds if there is no model in which all premises are true and the conclusion is false.[6]

Formal consequence depends on the form of sentences, not their substance.[2][3] Material consequence, unlike formal consequence, requires understanding the content of the claims involved.[2][7] Accounts of logical consequence are currently developed using two main methods: one based on proofs and another based on models.[8][2] Frege first used the ⊢ symbol in 1879, but its modern application began with Rosser and Kleene's work in 1934–1935.[9]

One can know that a deductively valid argument is valid without needing any empirical experience, meaning such knowledge is a priori.[2][10]

What the cited sources add

Beall and Restall note that contemporary analyses take logical consequence to be both necessary and formal, explicated via proofs or models.[2] They state that metaphysical necessity is too coarse to determine logical consequence, as it may render too many arguments valid.[2] McKeon explains that Tarski’s 1936 paper used observations of the common concept of logical consequence to guide theoretical development.[3] McKeon adds that Tarski’s basic move was to distinguish logical from non-logical terms.[3]

Beall and Restall observe that the model-centered approach takes validity as absence of counterexample.[2] According to McKeon, Tarski held that the logical consequence relation is necessary, formal, and unaffected by empirical knowledge.[3]

References

  1. Wikipedia, "Logical consequence" (CC BY-SA 4.0), which cites: Beall, JC and Restall, Greg, Logical Consequence The Stanford Encyclopedia of Philosophy (Fall 2009 Edition), Edward N. Zalta (ed.).; Quine, Willard Van Orman, Philosophy of Logic. (we also read that source) en.wikipedia.org
  2. Beall, JC and Restall, Greg, Logical Consequence The Stanford Encyclopedia of Philosophy (Fall 2009 Edition), Edward N. Zalta (ed.).. facts only, no text reused. plato.stanford.edu
  3. McKeon, Matthew, Logical Consequence Internet Encyclopedia of Philosophy.. facts only, no text reused. iep.utm.edu
  4. Wikipedia, "Logical consequence" (CC BY-SA 4.0), which cites: McKeon, Matthew, Logical Consequence Internet Encyclopedia of Philosophy. (we also read that source) en.wikipedia.org
  5. Wikipedia, "Logical consequence" (CC BY-SA 4.0), which cites: Dummett, Michael (1993) philosophy of language Harvard University Press, p.82ff; Lear, Jonathan (1986) and Logical Theory Cambridge University Press, 136p.; Creath, Richard, and Friedman, Michael (2007) Cambridge companion to Carnap Cambridge University Press, 371p.; FOLDOC: "syntactic consequence"; S. C. Kleene, Introduction to Metamathematics (1952), Van Nostrand Publishing. p.88. (original not read by us) en.wikipedia.org
  6. Wikipedia, "Logical consequence" (CC BY-SA 4.0), which cites: Etchemendy, John, Logical consequence, The Cambridge Dictionary of Philosophy (original not read by us) en.wikipedia.org
  7. Wikipedia, "Logical consequence" (CC BY-SA 4.0), which cites: Beall, JC and Restall, Greg, Logical Consequence The Stanford Encyclopedia of Philosophy (Fall 2009 Edition), Edward N. Zalta (ed.). (we also read that source) en.wikipedia.org
  8. Wikipedia, "Logical consequence" (CC BY-SA 4.0), which cites: Kosta Dosen, "Logic and Scientific Methods: Volume One of the Tenth International Congress of Logic, Methodology and Philosophy of Science, Florence, August 1995", Springer, 1996, p. 292 (we also read that source) en.wikipedia.org
  9. Wikipedia, "Logical consequence" (CC BY-SA 4.0), which cites: S. C. Kleene, Introduction to Metamathematics (1952), Van Nostrand Publishing. p.88. (original not read by us) en.wikipedia.org
  10. Wikipedia, "Logical consequence" (CC BY-SA 4.0), which cites: Beall, JC and Restall, Greg, Logical Consequence The Stanford Encyclopedia of Philosophy (Fall 2009 Edition), Edward N. Zalta (ed.).; Beall, JC and Restall, Greg, Logical Consequence The Stanford Encyclopedia of Philosophy (Fall 2009 Edition), Edward N. Zalta (ed.). (we also read that source) en.wikipedia.org

Each numbered sentence above was checked against the source it cites before publication. Sentences citing Wikipedia adapt text from the English Wikipedia article Logical consequence (contributors), used under CC BY-SA 4.0; this entry is available under the same licence. Other sources were used for facts only; no text or images are copied from them.

More in Philosophical Concepts And Theories

Logical positivismMaterialismMeaning (philosophy)Meaning of lifeMental representationMetaethicsMetaphilosophyMetaphysical naturalismMetaphysicsMimesisMind–body dualismMind–body problem

Sources

Compiled from Wikipedia and the sources listed below. Text from Wikipedia is available under CC BY-SA 4.0; this entry is adapted from it.

Spotted an error? Know more?

Reader corrections go straight into our review queue. Suggest an edit · How this site is sourced

Comments

Loading…
Open in the interactive codex →