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Caesar problem A problem in the philosophy of language and logic regarding the applicability of mathematical concepts to non-mathematical objects, famously illustrated by Gottlob Frege's question of whether the concept of being a successor in number applies to Julius Caesar.
In computability theory, an undecidable problem is a decision problem for which an effective method (algorithm) to derive the correct answer does not exist. More formally, an undecidable problem is a problem whose language is not a recursive set ; see the article Decidable language .
As another example, a C function to implement the second example from the table, Σ, would have a function pointer argument (see box below). Lambda terms can be used to denote anonymous functions to be supplied as arguments to lim, Σ, ∫, etc. For example, the function square from the C program below can be written anonymously as a lambda ...
Physicalist and materialist approaches to the Gettier problem generally attempt to ground knowledge in causal or reliabilist terms, avoiding appeal to abstract justification. For instance, the causal theory of knowledge, proposed by Alvin Goldman, suggests that for a belief to count as knowledge, it must be caused by the fact that makes it true ...
In logic, a true/false decision problem is decidable if there exists an effective method for deriving the correct answer. Zeroth-order logic (propositional logic) is decidable, whereas first-order and higher-order logic are not. Logical systems are decidable if membership in their set of logically valid formulas (or theorems) can be effectively ...
Predicate logic. First-order logic. Infinitary logic; Many-sorted logic; Higher-order logic. Lindström quantifier; Second-order logic; Soundness theorem; Gödel's completeness theorem. Original proof of Gödel's completeness theorem; Compactness theorem; Löwenheim–Skolem theorem. Skolem's paradox; Gödel's incompleteness theorems; Structure ...
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
In syllogistic logic, there are 256 possible ways to construct categorical syllogisms using the A, E, I, and O statement forms in the square of opposition. Of the 256, only 24 are valid forms. Of the 24 valid forms, 15 are unconditionally valid, and 9 are conditionally valid.