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The logic is simple: if a claim has not been conclusively refuted, then that is a good reason to believe it.
According to the standard logical empiricist story (Schlick 1915, 1917, 1921, 1922), their theory conclusively refuted the Kantian conception of the synthetic a priori: Euclidean geometry was not only one geometry amongst many, it also was not the one that characterized empirical reality.
In particular, the report from the University Group Diabetes Program UGDPP) almost 40 years ago of increased cardiovascular mortality in DM patients receiving the first-generation sulfonylurea tolbutamide has not been conclusively refuted [ 11, 12].
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In a word, an exception, far from 'proving' a rule, conclusively refutes it".
There has been some dispute on the issue as to whether Gödel's theorems conclusively refute logicism (see the entry on logicism).
Our findings also suggest that both large-scale, well-designed association studies and functional studies are warranted to either reliably confirm or conclusively refute the initial hypothesis regarding the role of CAPN10 in T2D risk.
While these findings leave numerous questions open, they nevertheless conclusively refute the picture long dominant due to A.J. Ayer's popularisation of the Vienna Circle's doctrines in his Language, Truth and Logic.
This should conclusively refute any suggestion that Senator Obama is somehow out of the mainstream.
It seems impossible to conclusively refute that in the future elasticity is > 1, in the case of radically new technology that is a closer substitute for labor.
Our data are incompatible with this hypothesis and, although they do not conclusively refute it, tend to reduce its plausibility.
"In fact, the evidence from the other 11 jurors conclusively refutes DeMarco's highly implausible accusation that Fernandez threatened DeMarco with 'gang signs' and physical violence in the jury room," Joel J. Seidemann, an assistant district attorney, wrote in the brief.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com