enow.com Web Search

Search results

1. Results from the WOW.Com Content Network

2. Curry's paradox - Wikipedia

   en.wikipedia.org/wiki/Curry's_paradox

   Here A, "this sentence is true", refers to the overall sentence, while B is "Germany borders China". So, assuming A is the same as assuming "If A, then B". Therefore, in assuming A, we have assumed both A and "If A, then B". Therefore, B is true, by modus ponens, and we have proven "If this sentence is true, then 'Germany borders China' is true ...

3. False premise - Wikipedia

   en.wikipedia.org/wiki/False_premise

   Another feature of an argument based on false premises that can bedevil critics, is that its conclusion can in fact be true. Consider the above example again. It may well be that it has recently rained and that the streets are wet. This does nothing to prove the first premise, but can make its claims more difficult to refute.

4. Trakhtenbrot's theorem - Wikipedia

   en.wikipedia.org/wiki/Trakhtenbrot's_theorem

   This proof is taken from Chapter 10, section 4, 5 of Mathematical Logic by H.-D. Ebbinghaus. As in the most common proof of Gödel's First Incompleteness Theorem through using the undecidability of the halting problem, for each Turing machine there is a corresponding arithmetical sentence , effectively derivable from , such that it is true if and only if halts on the empty tape.

5. Validity (logic) - Wikipedia

   en.wikipedia.org/wiki/Validity_(logic)

   The corresponding conditional of a valid argument is a logical truth and the negation of its corresponding conditional is a contradiction. The conclusion is a necessary consequence of its premises. An argument that is not valid is said to be "invalid". An example of a valid (and sound) argument is given by the following well-known syllogism:

6. Tautology (logic) - Wikipedia

   en.wikipedia.org/wiki/Tautology_(logic)

   The method of truth tables illustrated above is provably correct – the truth table for a tautology will end in a column with only T, while the truth table for a sentence that is not a tautology will contain a row whose final column is F, and the valuation corresponding to that row is a valuation that does not satisfy the sentence being tested.

7. Principle of explosion - Wikipedia

   en.wikipedia.org/wiki/Principle_of_explosion

   The procedure may be repeated to prove that unicorns do not exist (hence proving an additional contradiction where unicorns do and do not exist), as well as any other well-formed formula. Thus, there is an explosion of true statements.

8. Axiomatic system - Wikipedia

   en.wikipedia.org/wiki/Axiomatic_system

   An axiomatic system is said to be consistent if it lacks contradiction.That is, it is impossible to derive both a statement and its negation from the system's axioms. Consistency is a key requirement for most axiomatic systems, as the presence of contradiction would allow any statement to be proven (principle of explo

9. Proof by contradiction - Wikipedia

   en.wikipedia.org/wiki/Proof_by_contradiction

   We assume ¬¬P and seek to prove P. By the law of excluded middle P either holds or it does not: if P holds, 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 allows us to conclude P. In either case, we established P. It turns out that ...