Valuation in Formal Languages
A valuation assigns semantic values, like truth values, to formulas in a formal language. It's essentially an interpretation, crucial for understanding the meaning and logic of these languages.
Understanding Logical Validity
Explore the concept of validity in logic, focusing on deductive arguments where true premises guarantee a true conclusion. Understand its formal definitions in semantics and proof theory.
Understanding Vagueness: Precision, Ambiguity, and Indeterminacy
Vagueness describes terms lacking clear boundaries, leading to indeterminate cases. It's distinct from ambiguity, focusing on the fuzzy edges of meaning rather than multiple distinct interpretations.
Vacuous Quantifier
A vacuous quantifier is a logical operator that does not bind any variables within its scope. An example is the second quantifier in ∀x∀y Rxx, where 'y' is not referenced…
Understanding ‘Use’ in Philosophy and Language Analysis
In philosophy, 'use' signifies the actual application of words in sentences to convey meaning. It contrasts with 'mention,' focusing on referring to real-world concepts and objects.
Unsound Deductive Argument
An argument that fails to guarantee its conclusion due to either an invalid logical structure or at least one false premise. It does not establish the truth of its conclusion.
Upward Löwenheim–Skolem Theorem
The upward Löwenheim–Skolem theorem states that if a first-order theory has an infinite model, it has models of arbitrarily large infinite cardinalities. This has profound implications for the expressiveness of…
Universe of Discourse
The universe of discourse defines the scope of elements relevant to a logical or mathematical discussion. It acts as the domain for quantifiers, specifying where statements apply.
Universal Variable in Predicate Logic
A universal variable, bound by a universal quantifier (∀), represents any and all individuals within the domain of discourse in predicate logic. It asserts a property holds for every element.
Universal Quantifier (∀)
The universal quantifier (∀) in predicate logic signifies that a statement is true for every individual within a specified domain. It's fundamental for expressing general truths and universal claims in…