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The second thesis is more surprising.
The reasoning behind the second thesis is murky.
The first thesis can easily be recast so as to be unacceptable unless the second thesis is accepted.
The second thesis is that the problem for the logicist would be to show how to 'logicize' this theorizing by (i) defining those mathematical concepts in purely logical terms, and then (ii) deriving as logical theorems the translations induced by those definitions of the erstwhile mathematical theorems.
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Sider (2001) argues that the third thesis is a standalone part of Lewis's theory.
The first thesis is that there is some clearly identifiable body of mathematical theorizing, employing mathematical concepts, whose eligibility for logicist reduction is in question.
The argument in defence of the first thesis is based on the assumption that human affairs are organized mechanistically, i.e. according to a concatenation of purely efficient causes that would make the being of each totally dependent on the external being of everything else.
Bhāvavevika's second thesis is that at the level of ultimate truth, all phenomena are intrinsically unreal (niḥsvabhāvataḥ), therefore Madhyamaka rejects ultimately intrinsic reality.
The question is made more pressing by Quine's dilemma: if Brentano's second thesis is correct, then one must choose between it and a physicalist ontology.
A second thesis is that CDS does not function in isolation, but rather that it operates in the context of some sort of application environment.
Ockham's second thesis was the principle of parsimony: also known as Ockham's razor.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com