Just because is not axiomatically true (for all P) does not mean that is true (for some P); this would lead to the contradiction . In fact, the deduction is not valid in second-order .
Wikipedia foundation.
Intuitionistic logic — Intuitionistic logic, or constructive logic, is a symbolic logic system differing from classical logic in its definition of the meaning of a statement being true. In classical logic, all well formed statements are assumed to be either true or… … Wikipedia
intuitionistic logic — The logical system developed initially by A. Heyting (b. 1898) to formalize the reasonings allowed by mathematical intuitionism . It is designed so that p ∨ ¬ p is not a theorem, and the rule of inference from ¬¬ p to p is disallowed (the logic… … Philosophy dictionary
Intuitionistic type theory — Intuitionistic type theory, or constructive type theory, or Martin Löf type theory or just Type Theory is a logical system and a set theory based on the principles of mathematical constructivism. Intuitionistic type theory was introduced by Per… … Wikipedia
Logic (disambiguation) — Logic is the study of the principles and criteria of valid inference and demonstration.Logic may also refer to:In logic and mathematics*A branch of logic: **Inductive logic, also called induction or inductive reasoning **Informal logic, the study … Wikipedia
logic, history of — Introduction the history of the discipline from its origins among the ancient Greeks to the present time. Origins of logic in the West Precursors of ancient logic There was a medieval tradition according to which the Greek philosopher … Universalium
Logic — For other uses, see Logic (disambiguation). Philosophy … Wikipedia
logic, philosophy of — Philosophical study of the nature and scope of logic. Examples of questions raised in the philosophy of logic are: In virtue of what features of reality are the laws of logic true? ; How do we know the truths of logic? ; and Could the laws of… … Universalium
Logic programming — is, in its broadest sense, the use of mathematical logic for computer programming. In this view of logic programming, which can be traced at least as far back as John McCarthy s [1958] advice taker proposal, logic is used as a purely declarative… … Wikipedia
Category:Logic in computer science — Logic in computer science is that branch of mathematical logic which is approximately the intersection between mathematical logic and computer science. It contains: Those investigations into logic that are guided by applications in computer… … Wikipedia
Paraconsistent logic — A paraconsistent logic is a logical system that attempts to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that is concerned with studying and developing paraconsistent (or… … Wikipedia
