Prime Causation

Yablo, Stephen

doi:10.1111/j.1933-1592.2005.tb00541.x

Cited by 10 publications

(8 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The notion of proportionality in causation was introduced by Yablo () and features heavily in his subsequent work (, , ). It has also gained recent prominence in the work of Menzies and List (), Sartorio () and Weslake () .…”

Section: Proportionalitymentioning

confidence: 99%

The Deviance in Deviant Causal Chains

McDonnell¹

2015

Thought: A Journal of Philosophy

View full text Add to dashboard Cite

Abstract:Causal theories of action, perception and knowledge are each beset by problems of so-called 'deviant' causal chains. For each such theory, counterexamples are formed using odd or co-incidental causal chains to establish that the theory is committed to unpalatable claims about some intentional action, about a case of veridical perception or about the acquisition of genuine knowledge. In this paper I will argue that three well-known examples of a deviant causal chain have something in common: they each violate Yablos proportionality constraint on causation. I will argue that this constraint provides the key to saving causal theories from deviant chains.

show abstract

Section: Proportionalitymentioning

confidence: 99%

The Deviance in Deviant Causal Chains

McDonnell¹

2015

Thought: A Journal of Philosophy

View full text Add to dashboard Cite

show abstract

“… Yablo's paradox suggests a wide mathematical and philosophical context relevant to the present paper and elaborated by Yablo himself along with many other researchers. He discusses proper philosophical ideas in many papers (e.g Yablo 1982;1985;1992a;1992b;1997a;1997b;2000a;2000b;2005a;2005b;2016)…”

mentioning

confidence: 99%

Fermat’s Last Theorem Proved in Hilbert Arithmetic. I. From the Proof by Induction to the Viewpoint of Hilbert Arithmetic

Пенчев¹

2022

Preprint

View full text Add to dashboard Cite

In a previous paper (https://dx.doi.org/10.2139/ssrn.3648127 ), an elementary and thoroughly arithmetical proof of Fermat’s last theorem by induction has been demonstrated if the case for “n = 3” is granted as proved only arithmetically (which is a fact a long time ago), furthermore in a way accessible to Fermat himself though without being absolutely and precisely correct. The present paper elucidates the contemporary mathematical background, from which an inductive proof of FLT can be inferred since its proof for the case for “n = 3” has been known for a long time. It needs “Hilbert mathematics”, which is inherently complete unlike the usual “Gödel mathematics”, and based on “Hilbert arithmetic” to generalize Peano arithmetic in a way to unify it with the qubit Hilbert space of quantum information. An “epoché to infinity” (similar to Husserl’s “epoché to reality”) is necessary to map Hilbert arithmetic into Peano arithmetic in order to be relevant to Fermat’s age. Furthermore, the two linked semigroups originating from addition and multiplication and from the Peano axioms in the final analysis can be postulated algebraically as independent of each other in a “Hamilton” modification of arithmetic supposedly equivalent to Peano arithmetic. The inductive proof of FLT can be deduced absolutely precisely in that Hamilton arithmetic and the pransfered as a corollary in the standard Peano arithmetic furthermore in a way accessible in Fermat’s epoch and thus, to himself in principle. A future, second part of the paper is outlined, getting directed to an eventual proof of the case “n=3” based on the qubit Hilbert space and the Kochen-Specker theorem inferable from it.

show abstract

mentioning

confidence: 99%

Fermat’s last theorem proved in Hilbert arithmetic. I. From the proof by induction to the viewpoint of Hilbert arithmetic

Пенчев¹

2022

Preprint

View full text Add to dashboard Cite

The present paper elucidates the contemporary mathematical background, from which an inductive proof of FLT can be inferred since its proof for the case for “n = 3” has been known for a long time. It needs “Hilbert mathematics”, which is inherently complete unlike the usual “Gödel mathematics”, and based on “Hilbert arithmetic” to generalize Peano arithmetic in a way to unify it with the qubit Hilbert space of quantum information. An “epoché to infinity” (similar to Husserl’s “epoché to reality”) is necessary to map Hilbert arithmetic into Peano arithmetic in order to be relevant to Fermat’s age. Furthermore, the two linked semigroups originating from addition and multiplication and from the Peano axioms in the final analysis can be postulated algebraically as independent of each other in a “Hamilton” modification of arithmetic supposedly equivalent to Peano arithmetic.

show abstract

Prime Causation

Cited by 10 publications

References 1 publication

The Deviance in Deviant Causal Chains

The Deviance in Deviant Causal Chains

Fermat’s Last Theorem Proved in Hilbert Arithmetic. I. From the Proof by Induction to the Viewpoint of Hilbert Arithmetic

Fermat’s last theorem proved in Hilbert arithmetic. I. From the proof by induction to the viewpoint of Hilbert arithmetic

Contact Info

Product

Resources

About