Give a set of inconsistent sentence with only one member?

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The discussion centers on the possibility of creating a set of inconsistent sentences with only one member. An inconsistent set is defined as one where not all members can be true simultaneously, exemplified by the set { false }. The conversation highlights the distinction between propositional logic, where all atomic sentences are contingent, and predicate logic, which allows for atomic tautologies. The concept of contradiction is also introduced, emphasizing its relevance in understanding logical structures.

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  • Understanding of propositional logic
  • Familiarity with predicate logic
  • Knowledge of atomic sentences and their properties
  • Concept of tautologies and contradictions
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  • Research the differences between propositional and predicate logic
  • Study the definitions and examples of tautologies and contradictions
  • Explore the implications of atomic sentences in various logical frameworks
  • Examine the role of contingency in logical statements
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Students of logic, philosophers, and anyone interested in the foundations of logical reasoning and the nuances of sentence consistency.

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Is it possible to give a set of inconsistent sentences with only one member?

An inconsistent set of senteces requires that it is not possible for all members of that set to be true.
 
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{ false }.
 
In case that isn't clear enough, can the negation of a tautology ever be true? (Such a sentence is called a contradiction, if you want to look up a definition.)

There is at least one complcation, depending on (i) whether sentences (by your definition) can be simple or complex and (ii) what logic you're working in. In propositional logic, all simple, or atomic, sentences are contingent, i.e., non-tautologous and non-contradictory. This isn't so in, e.g., predicate logic, where you do have atomic tautologies.
 
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