The argument from irreducible complexity is a descendant of the teleological argument for God (the argument from design or argument from complexity). This states that because certain things in nature are very complicated, they must have been designed, just as the existence of a watch implies the existence of a watchmaker (in William Paley's famous argument of 1802). This argument has a long history and can be traced back at least as far as Cicero's De natura deorum, ii. ...

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Irreducible complexity, Irreducible complexity - Definitions, Irreducible complexity - Stated examples, Irreducible complexity - Flagella, Irreducible complexity - Blood clotting cascade, Irreducible complexity - Forerunners, Irreducible complexity - Criticisms of irreducible complexity, Irreducible complexity - Gradual replacement, Irreducible complexity - Handicaps and sexual selection, Irreducible complexity - Falsifiability and experimental evidence, Irreducible complexity - Behe's own Criticisms, Irreducible complexity - God and Irreducible Complexity, Irreducible complexity - Claimed significance

Read more here: » Irreducible complexity: Encyclopedia II - Irreducible complexity - Forerunners

Behe argues that organs and biological features which are irreducibly complex cannot be wholly explained by current models of evolution. He argues that: An irreducibly complex system cannot be produced directly (that is, by continuously improving the initial function, which continues to work by the same mechanism) by slight, successive modifications of a precursor system, because any precursor to an irreducibly complex system th ...

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Irreducible complexity, Irreducible complexity - Definitions, Irreducible complexity - Stated examples, Irreducible complexity - Flagella, Irreducible complexity - Blood clotting cascade, Irreducible complexity - Forerunners, Irreducible complexity - Criticisms of irreducible complexity, Irreducible complexity - Gradual replacement, Irreducible complexity - Handicaps and sexual selection, Irreducible complexity - Falsifiability and experimental evidence, Irreducible complexity - Behe's own Criticisms, Irreducible complexity - God and Irreducible Complexity, Irreducible complexity - Claimed significance

Read more here: » Irreducible complexity: Encyclopedia II - Irreducible complexity - Claimed significance

Zeno's paradoxes - Achilles and the tortoise. "You can never catch up." "In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead." (Aristotle Physics VI:9, 239b15) In the paradox of Achilles and the tortoise, we imagine the Greek hero Achilles in a footrace with the plodding reptile. Because he is so fast a runner, Achilles graciously allows the tortoi ...

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Zeno's paradoxes, Zeno's paradoxes - The Paradoxes of motion, Zeno's paradoxes - Achilles and the tortoise, Zeno's paradoxes - The dichotomy paradox, Zeno's paradoxes - The arrow paradox, Zeno's paradoxes - Proposed solutions, Zeno's paradoxes - Proposed solutions to the arrow paradox, Zeno's paradoxes - Proposed solutions both to Achilles & the tortoise and to the Dichotomy, Zeno's paradoxes - Problem with the calculus-based solution, Zeno's paradoxes - Are space and time infinitely divisible?, Zeno's paradoxes - Does motion involve a sequence of points?, Zeno's paradoxes - Conceptual approaches, Zeno's paradoxes - Status of the paradoxes today, Zeno's paradoxes - Two other paradoxes as given by Aristotle, Zeno's paradoxes - The quantum Zeno effect

Read more here: » Zeno's paradoxes: Encyclopedia II - Zeno's paradoxes - The Paradoxes of motion

Behe and others have suggested a number of biological features that they believe may be irreducibly complex. Irreducible complexity - Flagella. The flagella of certain bacteria constitute a molecular motor requiring the interaction of about 40 complex protein parts, and the absence of any one of these proteins causes the flagella to fail to function. Behe holds that the flagellum "engine" is irreducibly complex because if we try to reduce its complexity by positing an earlier and simpler stage of its evolu ...

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Irreducible complexity, Irreducible complexity - Definitions, Irreducible complexity - Stated examples, Irreducible complexity - Flagella, Irreducible complexity - Blood clotting cascade, Irreducible complexity - Forerunners, Irreducible complexity - Criticisms of irreducible complexity, Irreducible complexity - Gradual replacement, Irreducible complexity - Handicaps and sexual selection, Irreducible complexity - Falsifiability and experimental evidence, Irreducible complexity - Behe's own Criticisms, Irreducible complexity - God and Irreducible Complexity, Irreducible complexity - Claimed significance

Read more here: » Irreducible complexity: Encyclopedia II - Irreducible complexity - Stated examples

The term "irreducible complexity" was originally defined by Behe as: A single system which is composed of several interacting parts that contribute to the basic function, and where the removal of any one of the parts causes the system to effectively cease functioning". (Darwin's Black Box p9) Supporters of the intelligent design use this term to refer to biological systems and organs that they believe could not have come about by an incremental series of small changes. They argue that anything less th ...

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Irreducible complexity, Irreducible complexity - Definitions, Irreducible complexity - Stated examples, Irreducible complexity - Flagella, Irreducible complexity - Blood clotting cascade, Irreducible complexity - Forerunners, Irreducible complexity - Criticisms of irreducible complexity, Irreducible complexity - Gradual replacement, Irreducible complexity - Handicaps and sexual selection, Irreducible complexity - Falsifiability and experimental evidence, Irreducible complexity - Behe's own Criticisms, Irreducible complexity - God and Irreducible Complexity, Irreducible complexity - Claimed significance

Read more here: » Irreducible complexity: Encyclopedia II - Irreducible complexity - Definitions

Many scholars have debated over what Gödel's incompleteness theorem implies about human intelligence. Much of the debate centers on whether the human mind is equivalent to a Turing machine, or by the Church-Turing thesis, any finite machine at all. If it is, and if the machine is consistent, then Gödel's incompleteness theorems would apply to it. One of the earliest attempts to use incompleteness to reason about human intelligence was by Gödel himself in his 1951 Gibbs lecture entitled "Some basic theorems on the foundations of mat ...

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Gödel's incompleteness theorem, Gödel's incompleteness theorem - First incompleteness theorem, Gödel's incompleteness theorem - Second incompleteness theorem, Gödel's incompleteness theorem - Gentzen's theorem, Gödel's incompleteness theorem - Meaning of Gödel's theorems, Gödel's incompleteness theorem - Examples of undecidable statements, Gödel's incompleteness theorem - Misconceptions about Gödel's theorems, Gödel's incompleteness theorem - Discussion and implications, Gödel's incompleteness theorem - Minds and machines, Gödel's incompleteness theorem - Proof sketch for the first theorem, Gödel's incompleteness theorem - Proof sketch for the second theorem, Gödel's incompleteness theorem - Footnotes

Read more here: » Gödel's incompleteness theorem: Encyclopedia II - Gödel's incompleteness theorem - Minds and machines

Mathematicians thought they had done away with Zeno's paradoxes with the invention of the calculus and methods of handling infinite sequences by Isaac Newton and Gottfried Wilhelm Leibniz in the 17th century, and then again when certain problems with their methods were resolved by the reformulation of the calculus and infinite series methods in the 19th century. Many philosophers, and certainly engineers, generally went along with the mathematical results. Nevertheless, Zeno's paradoxes are still hotly debated by philosophers in acade ...

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Zeno's paradoxes, Zeno's paradoxes - The Paradoxes of motion, Zeno's paradoxes - Achilles and the tortoise, Zeno's paradoxes - The dichotomy paradox, Zeno's paradoxes - The arrow paradox, Zeno's paradoxes - Proposed solutions, Zeno's paradoxes - Proposed solutions to the arrow paradox, Zeno's paradoxes - Proposed solutions both to Achilles & the tortoise and to the Dichotomy, Zeno's paradoxes - Problem with the calculus-based solution, Zeno's paradoxes - Are space and time infinitely divisible?, Zeno's paradoxes - Does motion involve a sequence of points?, Zeno's paradoxes - Conceptual approaches, Zeno's paradoxes - Status of the paradoxes today, Zeno's paradoxes - Two other paradoxes as given by Aristotle, Zeno's paradoxes - The quantum Zeno effect

Read more here: » Zeno's paradoxes: Encyclopedia II - Zeno's paradoxes - Status of the paradoxes today

The main problem in fleshing out the above mentioned proof idea is the following: in order to construct a statement p that is equivalent to "p cannot be proved", p would have to somehow contain a reference to p, which could easily give rise to an infinite regress. Gödel's ingenious trick, which was later used by Alan Turing to solve the Entscheidungsproblem, will be described below. To begin with, every formula or statement that can be formulated in our system gets a unique number, called its Gödel num ...

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Gödel's incompleteness theorem, Gödel's incompleteness theorem - First incompleteness theorem, Gödel's incompleteness theorem - Second incompleteness theorem, Gödel's incompleteness theorem - Gentzen's theorem, Gödel's incompleteness theorem - Meaning of Gödel's theorems, Gödel's incompleteness theorem - Examples of undecidable statements, Gödel's incompleteness theorem - Misconceptions about Gödel's theorems, Gödel's incompleteness theorem - Discussion and implications, Gödel's incompleteness theorem - Minds and machines, Gödel's incompleteness theorem - Proof sketch for the first theorem, Gödel's incompleteness theorem - Proof sketch for the second theorem, Gödel's incompleteness theorem - Footnotes

Read more here: » Gödel's incompleteness theorem: Encyclopedia II - Gödel's incompleteness theorem - Proof sketch for the first theorem

Let p stand for the undecidable sentence constructed above, and let's assume that the consistency of the system can be proven from within the system itself. We have seen above that if the system is consistent, then p is not provable. The proof of this implication can be formalized in the system itself, and therefore the statement "p is not provable", or "not P(p)" can be proven in the system. But this last statement is equivalent to p itself (and this equivalence can be proven in the system), so p can ...

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Gödel's incompleteness theorem, Gödel's incompleteness theorem - First incompleteness theorem, Gödel's incompleteness theorem - Second incompleteness theorem, Gödel's incompleteness theorem - Gentzen's theorem, Gödel's incompleteness theorem - Meaning of Gödel's theorems, Gödel's incompleteness theorem - Examples of undecidable statements, Gödel's incompleteness theorem - Misconceptions about Gödel's theorems, Gödel's incompleteness theorem - Discussion and implications, Gödel's incompleteness theorem - Minds and machines, Gödel's incompleteness theorem - Proof sketch for the first theorem, Gödel's incompleteness theorem - Proof sketch for the second theorem, Gödel's incompleteness theorem - Footnotes

Read more here: » Gödel's incompleteness theorem: Encyclopedia II - Gödel's incompleteness theorem - Proof sketch for the second theorem

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