Deductive System Soundness

A Deductive System Soundness is a Formal System Soundness that produces a Sound Deductive Argument.

• AKA: Soundness.
  • …
• Counter-Example(s):
  • Logical System Soundness,
  • Deductive System Completeness.
• See: Deductive System, Truth, Mathematical Logic, Logical System, Formula (Mathematical Logic), Formal Semantics (Logic), Informal Fallacy.

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References

2020a

• (Wikipedia, 2020) ⇒ https://en.wikipedia.org/wiki/Soundness#Soundness Retrieved:2020-1-9.
  • Soundness of a deductive system is the property that any sentence that is provable in that deductive system is also true on all interpretations or structures of the semantic theory for the language upon which that theory is based. In symbols, where S is the deductive system, L the language together with its semantic theory, and P a sentence of L: if ⊢_S P, then also ⊨_L P.

2020b

• (Wikipedia, 2020) ⇒ https://en.wikipedia.org/wiki/Formal_system#Deductive_inference Retrieved:2020-1-9.
  • A deductive system, also called a deductive apparatus, consists of the axioms (or axiom schemata) and rules of inference that can be used to derive theorems of the system.

    Such deductive systems preserve deductive qualities in the formulas that are expressed in the system. Usually the quality we are concerned with is truth as opposed to falsehood. However, other modalities, such as justification or belief may be preserved instead.

    In order to sustain its deductive integrity, a deductive apparatus must be definable without reference to any intended interpretation of the language. The aim is to ensure that each line of a derivation is merely a syntactic consequence of the lines that precede it. There should be no element of any interpretation of the language that gets involved with the deductive nature of the system.

2020c

• (IEP, 2020) ⇒ (2020). "Validity and Soundness". The Internet Encyclopedia of Philosophy, ISSN 2161-0002. Retrieved:2020-1-9.
  • A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid.

    A deductive argument is sound if and only if it is both valid, and all of its premises are actually true. Otherwise, a deductive argument is unsound.

2020b

• (Rational Wiki, 2020) ⇒ https://rationalwiki.org/wiki/Soundness Retrieved:2020-1-9.
  • QUOTE: In deductive logic, soundness is a property of arguments importantly related to validity. An argument is valid if and only if it is impossible for the conclusion to be false while the premises are true (i.e. the conclusion must follow from the premises), but an argument is sound if and only if it is valid and its premises are actually true.

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