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In logic, the logical form of a statement is a precisely-specified semantic version of that statement in a formal system.Informally, the logical form attempts to formalize a possibly ambiguous statement into a statement with a precise, unambiguous logical interpretation with respect to a formal system.
The fifth and sixth examples are meaningful declarative sentences, but are not statements but rather matters of opinion or taste. Whether or not the sentence "Pegasus exists." is a statement is a subject of debate among philosophers. Bertrand Russell held that it is a (false) statement. [citation needed] Strawson held it is not a statement at all.
Equivocation – using a term with more than one meaning in a statement without specifying which meaning is intended. [21] Ambiguous middle term – using a middle term with multiple meanings. [22] Definitional retreat – changing the meaning of a word when an objection is raised. [23]
In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements.For example, in the conditional statement: "If P then Q", Q is necessary for P, because the truth of Q is guaranteed by the truth of P.
The sequent calculus is a formal system that represents logical deductions as sequences or "sequents" of formulas. [100] Developed by Gerhard Gentzen, this approach focuses on the structural properties of logical deductions and provides a powerful framework for proving statements within propositional logic. [100] [101]
A false statement, also known as a falsehood, falsity, misstatement or untruth, is a statement that is false or does not align with reality. This concept spans various fields, including communication, law, linguistics, and philosophy. It is considered a fundamental issue in human discourse.
The Pythagorean theorem has at least 370 known proofs. [1]In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. [a] [2] [3] The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems.
A statement can be called valid, i.e. logical truth, in some systems of logic like in Modal logic if the statement is true in all interpretations. In Aristotelian logic statements are not valid per se. Validity refers to entire arguments. The same is true in propositional logic (statements can be true or false but not called valid or invalid).