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What Makes a Sentence True or False? Predicate Logic
What Makes a Sentence True or False? Predicate Logic
Published: 2015/10/07
Channel: The Ling Space
SEM121 - Propositions
SEM121 - Propositions
Published: 2013/05/08
Channel: The Virtual Linguistics Campus
What is TRUTH CONDITION? What does TRUTH CONDITION mean? TRUTH CONDITION meaning & explanation
What is TRUTH CONDITION? What does TRUTH CONDITION mean? TRUTH CONDITION meaning & explanation
Published: 2016/11/15
Channel: The Audiopedia
Truth Table Tutorial - Discrete Mathematics Logic
Truth Table Tutorial - Discrete Mathematics Logic
Published: 2014/03/26
Channel: Emily Jane
Value Semantics: It aint about the syntax!
Value Semantics: It aint about the syntax!
Published: 2014/09/24
Channel: BoostCon
How Do We Capture the Truth of Beliefs? Type Theory
How Do We Capture the Truth of Beliefs? Type Theory
Published: 2016/12/15
Channel: The Ling Space
Linguistic Micro-Lectures: Propositions
Linguistic Micro-Lectures: Propositions
Published: 2014/09/08
Channel: The Virtual Linguistics Campus
What Is Meant By A Theory Of Semantics?
What Is Meant By A Theory Of Semantics?
Published: 2017/09/09
Channel: Funny Question
Syntax vs Semantics (Philosophical Distinctions)
Syntax vs Semantics (Philosophical Distinctions)
Published: 2015/09/20
Channel: Carneades.org
Jacque Fresco - Looking Backward, Truth, Learning, Semantics
Jacque Fresco - Looking Backward, Truth, Learning, Semantics
Published: 2010/10/07
Channel: The Venus Project
What is SEMANTIC EXTERNALISM? What does SEMANTIC EXTERNALISM mean? SEMANTIC EXTERNALISM meaning
What is SEMANTIC EXTERNALISM? What does SEMANTIC EXTERNALISM mean? SEMANTIC EXTERNALISM meaning
Published: 2016/10/10
Channel: The Audiopedia
Truth condition
Truth condition
Published: 2016/09/19
Channel: Wikivoicemedia
Can We Define "Must"? The Semantics of Modality
Can We Define "Must"? The Semantics of Modality
Published: 2017/06/29
Channel: The Ling Space
Truth trees for propositional logic 1
Truth trees for propositional logic 1
Published: 2013/01/19
Channel: Kane B
Propositional Logic: Semantics, Part 2
Propositional Logic: Semantics, Part 2
Published: 2015/06/03
Channel: David Agler
Ernest Sosa on Epistemology - The Nature & Value of Knowledge
Ernest Sosa on Epistemology - The Nature & Value of Knowledge
Published: 2013/04/16
Channel: Philosophical Overdose
M2 Lec 2 - Propositional Logic: Syntax and Truth Values
M2 Lec 2 - Propositional Logic: Syntax and Truth Values
Published: 2016/01/12
Channel: NOC16 Jan-May CS02
What is PRINCIPLE OF BIVALENCE? What does PRINCIPLE OF BIVALENCE mean?
What is PRINCIPLE OF BIVALENCE? What does PRINCIPLE OF BIVALENCE mean?
Published: 2017/08/30
Channel: The Audiopedia
What Is The Definition Of Propositional?
What Is The Definition Of Propositional?
Published: 2017/07/21
Channel: top sparky
Truth Table
Truth Table
Published: 2011/05/31
Channel: easymathk12
6.2 Truth Functions Part 1
6.2 Truth Functions Part 1
Published: 2016/05/02
Channel: Melvin Sanchez
What is Vacuous Truth?
What is Vacuous Truth?
Published: 2015/10/25
Channel: Carneades.org
Hilary Putnam on Meaning & Externalism
Hilary Putnam on Meaning & Externalism
Published: 2016/03/25
Channel: Philosophical Overdose
1.3 Formal Definition of Truth Tables
1.3 Formal Definition of Truth Tables
Published: 2016/05/13
Channel: Lassonde Student
Part 2: Symbolic Logic (WFFs & calculating truth functional statements)
Part 2: Symbolic Logic (WFFs & calculating truth functional statements)
Published: 2013/04/07
Channel: teachphilosophy
Simple Example Involving Truth Values
Simple Example Involving Truth Values
Published: 2012/11/05
Channel: lbowen11235
What Is A Proposition Examples?
What Is A Proposition Examples?
Published: 2017/07/21
Channel: top sparky
Propositional Logic - Propositions, Assertions & Truth Values
Propositional Logic - Propositions, Assertions & Truth Values
Published: 2012/11/04
Channel: StudyYaar.com
NLP Values Elicitation: How To Discover Your Highest Values
NLP Values Elicitation: How To Discover Your Highest Values
Published: 2016/06/05
Channel: NLP Gym
What is PROOF-THEORETIC SEMANTICS? What does PROOF-THEORETIC SEMANTICS mean
What is PROOF-THEORETIC SEMANTICS? What does PROOF-THEORETIC SEMANTICS mean
Published: 2017/04/29
Channel: The Audiopedia
How Can One Greek Letter Help Us Understand Language? Lambda Calculus
How Can One Greek Letter Help Us Understand Language? Lambda Calculus
Published: 2016/05/04
Channel: The Ling Space
4.1 Truth Tables for Entailment, Equivalence, Etc.
4.1 Truth Tables for Entailment, Equivalence, Etc.
Published: 2012/11/10
Channel: jellologic
How Can Sentences Work Like Adjectives? The Syntax and Semantics of Relative Clauses
How Can Sentences Work Like Adjectives? The Syntax and Semantics of Relative Clauses
Published: 2017/06/01
Channel: The Ling Space
Presuppositions and two kinds of negation, Marie Duzi
Presuppositions and two kinds of negation, Marie Duzi
Published: 2017/08/07
Channel: Copernicus Center for Interdisciplinary Studies
What is TRUTH-VALUE LINK? What does TRUTH-VALUE LINK mean? TRUTH-VALUE LINK meaning
What is TRUTH-VALUE LINK? What does TRUTH-VALUE LINK mean? TRUTH-VALUE LINK meaning
Published: 2016/11/17
Channel: The Audiopedia
1.2 Many Valued Boolean Logic and Oppositional Semantics
1.2 Many Valued Boolean Logic and Oppositional Semantics
Published: 2014/11/24
Channel: Semantic Qube
Introduction to Logic
Introduction to Logic
Published: 2011/12/23
Channel: ProfessorSerna
What is PRINCIPLE OF COMPOSITIONALITY? What does PRINCIPLE OF COMPOSITIONALITY mean?
What is PRINCIPLE OF COMPOSITIONALITY? What does PRINCIPLE OF COMPOSITIONALITY mean?
Published: 2017/04/27
Channel: The Audiopedia
What Does Entailment Mean In Logic?
What Does Entailment Mean In Logic?
Published: 2017/07/03
Channel: sparky marketips
Primary Value Principle
Primary Value Principle
Published: 2015/12/10
Channel: Semantic Qube
Pragmatism, Beliefs & Propositions (Chris Hookway)
Pragmatism, Beliefs & Propositions (Chris Hookway)
Published: 2013/07/11
Channel: Philosophical Overdose
Semantics - The Rise and Fall of Muammar al Gaddafi
Semantics - The Rise and Fall of Muammar al Gaddafi
Published: 2013/10/21
Channel: Critical Productions
What Is The Referential Theory Of Meaning?
What Is The Referential Theory Of Meaning?
Published: 2017/09/09
Channel: Funny Question
FREGE RELOADED (1 to 5) Frege and truth-values as references
FREGE RELOADED (1 to 5) Frege and truth-values as references
Published: 2016/12/15
Channel: Claudio Costa
Linguistic Micro-Lectures: Conjunction (Logic)
Linguistic Micro-Lectures: Conjunction (Logic)
Published: 2014/09/08
Channel: The Virtual Linguistics Campus
What Is A Proposition In Philosophy?
What Is A Proposition In Philosophy?
Published: 2017/07/21
Channel: top sparky
THE HUGHES MATRIX-SEMANTICS
THE HUGHES MATRIX-SEMANTICS'S, KEY TO DECEPTION.
Published: 2017/05/25
Channel: Flat Earth Nation-Dei Aurea Praeterita
Valuation Meaning
Valuation Meaning
Published: 2015/04/18
Channel: SDictionary
A Pragmatist Perspective on Wittgenstein
A Pragmatist Perspective on Wittgenstein
Published: 2013/03/17
Channel: Philosophical Overdose
Linguistic Micro-Lectures: Implication (Logic)
Linguistic Micro-Lectures: Implication (Logic)
Published: 2014/09/10
Channel: The Virtual Linguistics Campus
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WIKIPEDIA ARTICLE

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In formal semantics, truth-value semantics is an alternative to Tarskian semantics. It has been primarily championed by Ruth Barcan Marcus,[1] H. Leblanc, and M. Dunn and N. Belnap.[2] It is also called the substitution interpretation (of the quantifiers) or substitutional quantification.

The idea of these semantics is that universal (existential) quantifier may be read as a conjunction (disjunction) of formulas in which constants replace the variables in the scope of the quantifier. E.g. ∀xPx may be read (Pa & Pb & Pc &...) where a,b,c are individual constants replacing all occurrences of x in Px.

The main difference between truth-value semantics and the standard semantics for predicate logic is that there are no domains for truth-value semantics. Only the truth clauses for atomic and for quantificational formulas differ from those of the standard semantics. Whereas in standard semantics atomic formulas like Pb or Rca are true if and only if (the referent of) b is a member of the extension of the predicate P, respectively, if and only if the pair (c,a) is a member of the extension of R, in truth-value semantics the truth-values of atomic formulas are basic. A universal (existential) formula is true if and only if all (some) substitution instances of it are true. Compare this with the standard semantics, which says that a universal (existential) formula is true if and only if for all (some) members of the domain, the formula holds for all (some) of them; e.g. ∀xA is true (under an interpretation) if and only if for all k in the domain D, A(k/x) is true (where A(k/x) is the result of substituting k for all occurrences of x in A). (Here we are assuming that constants are names for themselves—i.e. they are also members of the domain.)

Truth-value semantics is not without its problems. First, the strong completeness theorem and compactness fail. To see this consider the set {F(1), F(2),...}. Clearly the formula ∀xF(x) is a logical consequence of the set, but it is not a consequence of any finite subset of it (and hence it is not deducible from it). It follows immediately that both compactness and the strong completeness theorem fail for truth-value semantics. This is rectified by a modified definition of logical consequence as given in Dunn and Belnap 1968.[2]

Another problem occurs in free logic. Consider a language with one individual constant c that is nondesignating and a predicate F standing for 'does not exist'. Then ∃xFx is false even though a substitution instance (in fact every such instance under this interpretation) of it is true. To solve this problem we simply add the proviso that an existentially quantified statement is true under an interpretation for at least one substitution instance in which the constant designates something that exists.

See also[edit]

References[edit]

  1. ^ Marcus, Ruth Barcan (1962). "Interpreting quantification". Inquiry. 5 (1-4): 252–259. ISSN 0020-174X. doi:10.1080/00201746208601353. 
  2. ^ a b Dunn, J. Michael; Belnap, Nuel D. (1968). "The Substitution Interpretation of the Quantifiers". Noûs. 2 (2): 177. ISSN 0029-4624. doi:10.2307/2214704. 

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