classical logic, intuitionistic logic, and similar logical systems, the principle of explosion is the law according to which any statement can be proven from a...

"the house is not white" holds. One reason to have this law is the principle of explosion, which states that anything follows from a contradiction. The law...

of logic that is concerned with studying and developing "inconsistency-tolerant" systems of logic, purposefully excluding the principle of explosion....

contradictions because classical rules of inference lead to the principle of explosion, an admissible rule of inference that makes it possible to infer...

(proof by contradiction). However, the principle of explosion (ex falso quodlibet) has been accepted in some varieties of constructive mathematics, including...

double negation elimination while paraconsistent logics reject the principle of explosion. Deductive reasoning plays a central role in formal logic and mathematics...

They achieve this by avoiding the principle of explosion found in classical logic. According to the principle of explosion, anything follows from a contradiction...

intuitions include the law of excluded middle, the double negation elimination, the principle of explosion, and the bivalence of truth. It was originally...

rejects both the law of the excluded middle as well as the principle of explosion (ex falso quodlibet), and therefore holding neither of the following two...

multiple meanings Principle of explosion: One of the fundamental laws in logic Syntactic ambiguity, Amphiboly, Amphibology: Ambiguity of a sentence by its grammatical...

the Principle of Explosion was widely accepted as self-evident, e.g. by logicians like George Boole and Gottlob Frege, though the formalization of the...

elimination implies consequentia mirabilis, in minimal logic. The principle of explosion itself may be formulated as ⊥ → ( A ∧ ⊥ ) {\displaystyle \bot \to...

flawed. Unexpected hanging paradox List of paradoxes When a white horse is not a horse Principle of explosion Łukowski, Piotr (2011). Paradoxes. Springer...

A dust explosion is the rapid combustion of fine particles suspended in the air within an enclosed location. Dust explosions can occur where any dispersed...

conservative extension of a consistent theory is consistent. If it were not, then by the principle of explosion, every formula in the language of T 2 {\displaystyle...

properties: Law of excluded middle and double negation elimination Law of noncontradiction, and the principle of explosion Monotonicity of entailment and...

would lead to the principle of explosion and thus trivialism. Popper concluded the essay with these words: "The whole development of dialectic should be...

(1937) Key Idea: Like intuitionistic logic but without assuming the principle of explosion (ex falso quodlibet, “from falsehood, anything follows”). Features:...

raining Therefore George Washington is made of rakes. This arises from the principle of explosion, a law of classical logic stating that inconsistent premises...

List of paradoxes Self-reference List of self–referential paradoxes Double bind Principle of explosion Russell, Bertrand (1919). "The Philosophy of Logical...

sound argument through the principle of explosion and it being considered an absurdity (reductio ad absurdum). Aristotle's law of noncontradiction and other...

well; Paraconsistent logic (e.g., relevance logic) rejects the principle of explosion, and has a close relation to dialetheism; Quantum logic Relevance...

an unrestricted comprehension principle leads to contradictions. According to the unrestricted comprehension principle, for any sufficiently well-defined...

systems may or may not contain the principle of explosion (ex falso quodlibet in Latin), ⊥ ⊢ φ for all φ. By that principle, contradictions and false are equivalent...

contradiction, as being true, it must discard the long-recognized principle of explosion, which asserts that any proposition can be deduced from a contradiction...

Empty function Paradoxes of material implication, especially the principle of explosion Presupposition, double question State of affairs (philosophy) Tautology...

Consequentia mirabilis) = IPC + p ∨ (p → q) (following from PEM via principle of explosion) Smetanich's logic (SmL): = IPC + (¬q → p) → (((p → q) → p) → p)...

deductive system (such as first-order logic) that satisfies the principle of explosion, this is equivalent to requiring that there is no sentence φ such...

then of course P holds. if ¬P holds, then we derive falsehood by applying the law of noncontradiction to ¬P and ¬¬P, after which the principle of explosion...

axiomatic systems, as the presence of contradiction would allow any statement to be proven (principle of explosion). Relative consistency comes into play...