8 citations · 16 across the 22 of their papers we have counts for
7 papers · 1 filter
Are there parts of our arithmetical competence that no sound formal system can duplicate?
Bhupinder Singh Anand
In 1995, David Chalmers opined as implausible that there may be parts of our arithmetical competence that no sound formal system could ever duplicate. We prove that the recursive n…
Some consequences of a recursive number-theoretic relation that is not the standard interpretation of any of its formal representations
Bhupinder Singh Anand
We give a precise definition of a formal mathematical object as any symbol for an individual constant, predicate letter, or a function letter that can be introduced through definit…
Goedel's Incompleteness Theorems hold vacuously
Bhupinder Singh Anand
In an earlier paper, "Omega-inconsistency in Goedel's formal system: a constructive proof of the Entscheidungsproblem" (math/0206302), I argued that a constructive interpretation o…
Omega-inconsistency in Goedel's formal system: a constructive proof of the Entscheidungsproblem
Bhupinder Singh Anand
If we apply an extension of the Deduction meta-Theorem to Goedel's meta-reasoning of "undecidability", we can conclude that Goedel's formal system of Arithmetic is not omega-consis…
Reviewing Goedel's and Rosser's meta-reasoning of undecidability
Bhupinder Singh Anand
I review the classical conclusions drawn from Goedel's meta-reasoning establishing an undecidable proposition GUS in standard PA. I argue that, for any given set of numerical value…
Beyond Goedel : Simply consistent constructive systems of first order Peano's Arithmetic that do not yield undecidable propositions by Goedel's reasoning
Bhupinder Singh Anand
In this paper, we argue that formal systems of first order Arithmetic that admit Goedelian undecidable propositions validly are abnormally non-constructive. We argue that, in such…