computable function
Quick Summary
A computable function is one that can be calculated by an algorithm, often referred to as a mechanical or effective calculation. This concept is central to the theory of recursive functions, a significant branch of contemporary logic and a foundational area of computer science.123
The idea of computability was formalized through abstract automata like the Turing machine, which operates on an infinite tape. Functions that can be computed by such machines are called recursive functions. The Church-Turing thesis posits that all effectively calculable functions are precisely those that are recursive. This theory raises philosophical questions about the limits of mechanical thought and its implications for free will.134
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metalogicDecidability and undecidability…truth: that all recursive or computable functions and relations are representable in the system (e.g., in N). Since truth in the language of a system is itself not representable (definable) in the system, it cannot, by the lemma, be recursive (i.e., decidable).
Read More…truth: that all recursive or computable functions and relations are representable in the system (e.g., in N). Since truth in the language of a system is itself not representable (definable) in the system, it cannot, by the lemma, be recursive (i.e., decidable).
Read More- philosophy of logicLogic and computability
, of being effectively—or mechanically—calculable. Functions that can be so calculated are called recursive. Several different and historically independent attempts have been made to define the class of all recursive functions, and these have turned out to coincide with each other. The claim that recursive functions exhaust the class…
Read More, of being effectively—or mechanically—calculable. Functions that can be so calculated are called recursive. Several different and historically independent attempts have been made to define the class of all recursive functions, and these have turned out to coincide with each other. The claim that recursive functions exhaust the class…
Read More