Questions tagged [formal-system]
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Does Gödel’s incompleteness theorems imply the necessity of an infinite recursive hierarchy of “proofs”, and that any “proof” is relative?
My understanding is that Gödel’s incompleteness theorems state that the consistency of any axiomatic system cannot be proven within that axiomatic system, and requires a stronger axiomatic system in ...
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What is the proof of that self-application in the λ-calculus is not inconsistent?
The SEP entry on lambda calculus discusses its consistency, surmising:
Early formulations of the idea of λ-calculus by A. Church were indeed inconsistent. The Church-Rosser theorem gives us, among ...
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An erratum in Allan Gibbard's "Manipulation of Voting Schemes: A General Result"
This question is in the philosophy site but it could have been in the one about mathematics, more ideally in a "voting theory" site. It's here because Gibbard was most of all a philosoph.
I'...
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Why is completeness (as in Gödel completeness theorem) a desirable feature?
When justifying the dominance of first-order theory, an argument that is often made is that it is complete (as shown by Gödel).
This means that a theory formulated in first-order logic has a model if ...
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Can set elements be predicated of objects?
If we define a set as a cartesian product of properties, do you think that the cartesian product can be predicated of an object?
For example if we define:
Set of names of Captials N = { The name ...
user50018
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Axiomatic and formal establishment of Plato's dialectics
After years of studying Plato I have seen some attempts to formalize somehow Plato's dialectics. To be more precise, I have found writers who present Plato's dialectics (especially as it is presented ...
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What is the name of the internal relationship system of human experience?
In the course of his life, the subject receive an experience with which he differentiated and perceive the world. Therefore, we can say that there are categories inside its "term name". Here ...
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The relationship between logical systems and natural language semantics
Every student of philosophy knows that there are systems of logic and that those systems are analyzed in terms of logical properties like soundness, consistency, decidability, completeness, etc. These ...
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General sentence operators
There are lots of operators that act on sentences. Here are a few examples:
P and Q
not P
forall x.P
necessarily P
eventually P
x believes that that P
it is obligatory that P
etc. The first two ...
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What happens when you deny an axiom? [closed]
There is no proof that the axiom is true.
There is no proof by “Proof by contradiction”.
That means that even if you deny the axiom, there will be no contradiction.
And if a contradiction is created ...
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