# unprovability

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**Natural deduction**— In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the natural way of reasoning. This contrasts with the axiomatic systems which instead use… … Wikipedia**Gödel's incompleteness theorems**— In mathematical logic, Gödel s incompleteness theorems, proved by Kurt Gödel in 1931, are two theorems stating inherent limitations of all but the most trivial formal systems for arithmetic of mathematical interest. The theorems are of… … Wikipedia**Busy beaver**— In computability theory, a busy beaver (from the colloquial expression for an industrious person) is a Turing machine that attains the maximum operational busyness (such as measured by the number of steps performed, or the number of nonblank… … Wikipedia**George Boolos**— Infobox Person name = George Boolos birth date = birth date|1940|9|4|mf=y birth place = New York, New York, U.S. death date = death date and age|1996|5|27|1940|9|4|mf=y death place = Cambridge, Massachusetts, U.S.George Stephen Boolos (September… … Wikipedia**Proof of impossibility**— A proof of impossibility, sometimes called a negative proof or negative result , is a proof demonstrating that a particular problem cannot be solved, or cannot be solved in general. Often proofs of impossibility have put to rest decades or… … Wikipedia**Zermelo–Fraenkel set theory**— Zermelo–Fraenkel set theory, with the axiom of choice, commonly abbreviated ZFC, is the standard form of axiomatic set theory and as such is the most common foundation of mathematics.ZFC consists of a single primitive ontological notion, that of… … Wikipedia**Proof theory**— is a branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively defined data structures such as plain lists, boxed… … Wikipedia**The Art of Fugue**— A portrait which may show Bach in 1750 The Art of Fugue (or The Art of the Fugue, original German: Die Kunst der Fuge), BWV 1080, is an incomplete work[1] by Johann Sebastian Bach (1685–1750). It was most likely started at the beginning of the… … Wikipedia**Norwood Russell Hanson**— (1924 – 1967) was a philosopher of science. Hanson was a pioneer in advancing the argument that observation is theory laden – that observation language and theory language are deeply interwoven – and that historical and contemporary comprehension … Wikipedia**Proof procedure**— In logic, and in particular proof theory, a proof procedure for a given logic is a systematic method for producing proofs in some proof calculus of (provable) statements.There are several types of proof calculi. The most popular are natural… … Wikipedia