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Garrulo
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Why in first order logic theories are not possible a demonstration with infinite steps?
No infinite step, only finite steps but infinity pasesGarrulo said:Ok. But the problem I see is that demostration could have non standard steps, because for first order logic is impossible let she the non standard models out of a theory in first order language
Garrulo said:No infinite step, only finite steps but infinity pases
I recognize that English is not your native language, but frankly, what you have written is pretty much incomprehensible, especially "infinity pases" and "a number non standard natural numbers finite of steps". These make no sense.Garrulo said:infinite steps, sorry. But I refer to a demostration in a number non standard natural numbers finite of steps
I still don't get what you're asking. What do you mean by "non standard natural numbers steps"?Garrulo said:Other way: why not a formal demostration in a non standard natural numbers steps?
First order logic, also known as predicate logic, is a formal system used to represent and reason about relationships between objects. In this system, proofs are constructed by applying a finite set of inference rules to a set of axioms. Since infinite steps would require an infinite number of inference rules and axioms to be applied, it is not possible to demonstrate first order logic theories with infinite steps.
Even if we were to add an infinite number of axioms and inference rules, the resulting system would still not be able to demonstrate first order logic theories with infinite steps. This is because the process of applying rules and axioms is inherently finite, and cannot be extended infinitely.
While computers are capable of performing a large number of computations, they still operate within a finite system. This means that even with the help of a computer, it is not possible to demonstrate first order logic theories with infinite steps.
There are other formal systems, such as higher order logic or infinitary logic, that are designed to handle infinite steps. However, these systems are more complex and have their own limitations and drawbacks.
Limiting the number of steps in a proof is important because it ensures that the proof is sound and valid. Without this limitation, it would be possible to construct proofs that are not logically valid, which would undermine the entire purpose of using logic as a tool for reasoning and understanding the world.