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Gödel's incompleteness theorems is the name given to two theorems, proved by Kurt Gödel in 1931. They are theorems in mathematical logic.
In a formal system, there are axioms. Axioms are intrinsically true, self-evident statements. All axioms are assumed to be true, at any rate for the purpose of the logic. A theorem then comes up with other true statements from the axioms, using certain rules. A sequence of such statements is called a proof of a statement, because it shows that the statement is true, given the axioms.
Ideally, it should be possible to construct all true statements in the formal system in that manner. A system that has this property is called complete; one that does not is called incomplete. Another thing wanted of a theory is that there should be no contradictions. This means that it is not possible to prove that a statement is true and false at the same time. A system that does not include theories that allow this is called consistent.
Gödel said that every non-trivial formal system is either incomplete or inconsistent: [1]
For a given (non-trivial) formal system, there will be statements that are true in that system, but which cannot be proved to be true inside the system.
If a system can be proved to be complete using its own logic, then there will be a theorem in the system that is contradictory.
Most people think this shows that Hilbert's program to find a complete and consistent set of axioms for all of mathematics is impossible. This would give a negative answer to Hilbert's second problem.
A formal system or logical calculus is any well-defined system of abstract thought based on the model of mathematics. A formal system need not be mathematical as such; for example, Spinoza's Ethics imitates the form of Euclid's Elements.
originally posted by: visitedbythem
The truth is a who, not a what
Yeshua said " I am the way, the TRUTH, and the life.
No one cometh unto the Father,
But by me!
originally posted by: Astrocyte
16. Postmodernism is retarded nonsense. The only true philosophical orientation is pragmaticism/pragmatism. Things happen out of necessity; and so, if we do not do as we "should" do, it is because there is not yet enough of an impulse or motive-formation to compel some new attitudinal direction in functioning. New meanings must form, and sometimes ones affective life - social life - must be ripped apart for one to recognize just how dependent one was. If reincarnation is real (which I see as eminently plausible, in terms of an actuated realm and a potential realm which can be actuated again) one will have to be reborn to gain the "new eyes" necessary to see what could not be seen with the relational trauma that blocked perception in the earlier life.
One day two monks were in a garden arguing subjectivity versus objectivity. The Zen master hearing them arguing approached the two students. The Zen master asked, "that rock over there, does that exist inside your head or outside your head?". One of the monks looked up at the Zen master and replied, "Well, our religious bible tells us that all truth is subjective so that rock over there only exists inside my head." At which point the Zen master replies, "Then it must be pretty heavy all day walking around with that rock in your head!"
originally posted by: visitedbythem
The truth is a who, not a what
Yeshua said " I am the way, the TRUTH, and the life.
No one cometh unto the Father,
But by me!
originally posted by: TonyS
originally posted by: visitedbythem
The truth is a who, not a what
Yeshua said " I am the way, the TRUTH, and the life.
No one cometh unto the Father,
But by me!
Truly put. Unfortunately, many cant fathom that truth and if they do, they cnt handle it.
. You flaunt around pretty ideas like clothing yet you never have any real conversations about ideas