Modus Tollens
Modus Tollens is a fundamental rule of inference in logic. It states that if a conditional statement is true, and its consequent is false, then its antecedent must also be…
Modus Ponens
Modus Ponens is a fundamental rule of inference in logic. It states that if a conditional statement ('if P then Q') is true, and its antecedent (P) is also true,…
Model Theory
Model theory is a branch of mathematical logic exploring the connections between formal languages and their meanings in mathematical structures. It uses tools from set theory and algebra to understand…
Model-Theoretic Validity
Model-theoretic validity refers to the truth of a statement within all possible interpretations or models. It's a cornerstone of formal logic, ensuring statements hold universally across different structures.
Model-Theoretic Consequence
Model-theoretic consequence is a fundamental concept in logic, defining logical implication through the interpretation of formulas in models. It ensures truth preservation across all possible interpretations.
Model in Logic and Mathematics
A model in logic and mathematics interprets the symbols of a formal language, satisfying the axioms and theorems of a theory. It provides a concrete realization or interpretation of abstract…
Modality in Logic and Linguistics
Modality refers to the quality of propositions that express necessity, possibility, and other related concepts. It's crucial for understanding how we reason about what could be, must be, or might…
Modal Realism Explained
Modal realism posits that all possible worlds are as real as our own. This philosophical stance suggests that individuals and objects can exist in these other, equally real, worlds.
Modal Possibilism Explained
Modal possibilism posits that entities that are possible but not actual exist, often conceptualized within possible worlds. This contrasts with actualism, asserting a distinct mode of being for possibilities.
Modal Operators in Logic
Modal operators like necessity (◻) and possibility (◊) alter a statement's truth value, indicating whether it must be true or could be true, respectively. They are fundamental in modal logic.