@barwiseLiarEssayTruth1989

Barwise and Etchemendy’s formal language

In order to have a way to systematically present statements complex enough to explore the Liar paradox and other issues of semantics, Barwise and Etchemendy develop a simple Formal language . has the following resources

• Constant symbols. The situation to be described involves a card game played between Claire and Max. As such, the constant symbols are the names Claire and Max, and the symbols for cards.
• Propositional demonstratives this, that₁, that₂, &c.
• Logical connectives ¬, ∨, ∧.
• Scope indicator ↓
• Binary relations Has and Believes, written in infix notation
• Unary relation True, written as a function.

we have atomic formulae

• (a Has c) where a is name and c is a card
• (a Believes th) where a is a name and th is a propositional demonstrative
• True(th) where th is a propositional demonstrative

and the class of all -formulae is the closure of atomic formulae such that if φ and ψ are formulae, so too are the following

• (φ ∧ ψ)
• (φ ∨ ψ)
• ¬φ
• (True φ)
• (a Believes φ) where a is a name
• ↓φ

this always refers to the sentence enclosed in a scope indicator ↓.

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