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jcsd

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- Thread starter jcsd
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jcsd

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mathman

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jcsd

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My underlying assumption is that a theory that can describe everything would be a formal axiomatic system, in which case it would contain unprovable statements.

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HallsofIvy

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jcsd

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Integral

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Hurkyl

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I have a thread on this in the Logic forum.

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jcsd

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As for Maxwell's equations the interpretation at the time did not lead to a constant speed of light in all inertial reference frames, infact it was taken to mean that light must propgate through a medium (i.e. ether).

The effect of Goedel's theorum on physical theories was not something a plucked out of thin air, infact the thread was sparked by browsing through my maths dictionary which said that Goedel's theorum is seen as a blow to the idea of a physical theory with the fewest possible axioms.

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jcsd

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Originally posted by Hurkyl

Hurkyl, my maths is mostly maths for physics, but surely Goedel's incompleteness theorum shows that no system can be complete?

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thermonuclear

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HallsofIvy

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Then they are models for physical theories, not physical theories.posted by jcsd

Physical theories exist as abstract formal systems regardless of experimental evidence and therefore must contain senetnces, S such that neother S nor ~S can be proved using the formal system.

It also, as Hurkyl pointed out, not follow that every formal system must not be complete. That is only true for formal systems that include the positive integers.

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jcsd

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Originally posted by HallsofIvy

Then they are models for physical theories, not physical theories.

It also, as Hurkyl pointed out, not follow that every formal system must not be complete. That is only true for formal systems that include the positive integers.

You see, I'm not a mathematician my undergrad training was in physics (though I've just decided to start a part-time undergrad. maths degree at the beginning of next year). Is it true only for systems with postive integers? My knowledge of Goedel's proof only comes from how it is layed out in my maths dictionary and it doesn't mention this.

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jcsd

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I've been to mathworld and does seem to say that the theorum only applies to number theory, but in other parts it suggests it applies to mathematical systems in general[?]

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Hurkyl

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Sorry, I was having computer troubles, so I made the dot post just to make sure I didn't forget about this thread!

Basically, Godel's theorem states that if a formal system can ask about its own consistency, then the system is inconsistent or the system cannot prove it is consistent (and is thus incomplete).

Number theory can encode logic, so any system that can encode number theory can then ask about its own consistency, and thus must be inconsistent or incomplete.

Basically, Godel's theorem states that if a formal system can ask about its own consistency, then the system is inconsistent or the system cannot prove it is consistent (and is thus incomplete).

Number theory can encode logic, so any system that can encode number theory can then ask about its own consistency, and thus must be inconsistent or incomplete.

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The purpose of a TOE is to integrate the (assumed) four fundamental interaction types into one deductive system, and provide some experimentally-testable propositions that indicate a level of success in the endeavor. Deriving every conceivable complicated proposition from it isn't in the gameplan. Likewise, there is no hope of performing every conceivable variation of every conceivable experiment, so we shouldn't expect to get absolutely-complete and absolutely-certain knowledge.

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