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Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as ...
Tautology (logic) In mathematical logic, a tautology (from Greek: ταυτολογία) is a formula or assertion that is true in every possible interpretation. An example is "x=y or x≠y". Similarly, "either the ball is green, or the ball is not green" is always true, regardless of the colour of the ball. The philosopher Ludwig Wittgenstein ...
In logic, an argument is a set of statements expressing the premises (whatever consists of empirical evidences and axiomatic truths) and an evidence-based conclusion. An argument is valid if and only if it would be contradictory for the conclusion to be false if all of the premises are true. [3] Validity does not require the truth of the ...
The precise meaning of universalizability is contentious, but the most common interpretation is that the categorical imperative asks whether the maxim of your action could become one that everyone could act upon in similar circumstances. An action is socially acceptable if it can be universalized (i.e., everyone could do it). [citation needed]
Propositional formula. In propositional logic, a propositional formula is a type of syntactic formula which is well formed. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional formula may also be called a propositional expression, a sentence, or a sentential formula .
Cronbach's alpha (Cronbach's ), also known as tau-equivalent reliability ( ) or coefficient alpha (coefficient ), is a reliability coefficient and a measure of the internal consistency of tests and measures. [1] [2] [3] Numerous studies warn against using Cronbach's alpha unconditionally. Statisticians regard reliability coefficients based on ...
The semantic conception of truth, which is related in different ways to both the correspondence and deflationary conceptions, is due to work by Polish logician Alfred Tarski. Tarski, in "On the Concept of Truth in Formal Languages" (1935), attempted to formulate a new theory of truth in order to resolve the liar paradox.
Logical truth is one of the most fundamental concepts in logic. [1] Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity of its constituent propositions. In other words, a logical truth is a statement which is not only true, but one which is true under all interpretations of its logical components ...