Logical Consequence

Definition

Logical consequence refers to a relationship between statements where one statement necessarily follows from another. If a set of premises logically entails a conclusion, that conclusion is considered a logical consequence of the premises. This relationship is fundamental in the study of logical systems and plays a crucial role in establishing the validity of arguments.

5 Must Know Facts For Your Next Test

1. Logical consequence can be represented symbolically in formal systems, allowing for rigorous proof and analysis of arguments.
2. The concept is central to both classical logic and alternative logical systems, providing a foundation for understanding argument structure.
3. In modal logic, logical consequence can also include possible worlds, expanding the idea of what it means for one statement to follow from another.
4. Logical consequence relies on established rules of inference that dictate how new truths can be derived from existing ones.
5. Understanding logical consequence helps in evaluating arguments critically, ensuring that conclusions drawn are sound based on the premises provided.

Review Questions

• How does logical consequence relate to entailment and validity in the context of formal logical systems?
  • Logical consequence, entailment, and validity are closely related concepts within formal logic. Logical consequence describes when a conclusion necessarily follows from premises, making it an essential part of entailment. Validity then assesses whether an argument maintains this relationship: if the premises are true, must the conclusion also be true? Thus, understanding these concepts helps in evaluating whether arguments are correctly formed and logically sound.
• Discuss the importance of understanding logical consequence when constructing and evaluating arguments in philosophical discourse.
  • Understanding logical consequence is crucial in philosophical discourse as it allows individuals to construct coherent arguments and assess their validity. By recognizing which conclusions logically follow from specific premises, one can ensure that discussions are grounded in sound reasoning. This awareness helps avoid fallacies and strengthens persuasive arguments by demonstrating clear relationships between ideas.
• Evaluate the implications of logical consequence on different types of logic systems, such as classical and modal logic.
  • The implications of logical consequence vary significantly across different logical systems. In classical logic, it provides a clear framework for determining truth values and relationships between propositions. However, in modal logic, logical consequence extends to consider possible worlds, where statements may not only be true or false but may also have different truth values depending on varying conditions. This evaluation reveals how foundational concepts like logical consequence adapt to accommodate more complex interpretations of truth and necessity.

Related terms

Entailment: Entailment is the relation between statements where one statement must be true if another statement is true, often associated with logical consequence.

Validity: Validity is a property of an argument that indicates if the premises logically lead to the conclusion, ensuring that if the premises are true, the conclusion must also be true.

Inference: Inference is the process of deriving logical conclusions from premises known or assumed to be true, which often involves recognizing logical consequences.