By Pierre Wagner (auth.)
The ebook comprises a sequence of chapters on Carnap's excellent of explication instead to the naturalistic conceptions of technology, atmosphere it in its old context, discussing particular circumstances of explications, and enriching the on-going debate on conceptual engineering and naturalism in analytic philosophy.
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Extra info for Carnap’s Ideal of Explication and Naturalism
His pluralism extended to the means of reasoning, to logic itself, by way of an insistence on the plurality of languages. Explication or rigorization in the relevant sense is, generally speaking, theory-relative for Carnap, and hence it is dependent upon one’s choice of logic and language. It is thus natural for him to stress the importance of convention and arbitrariness in the erection of appropriately precise principles for a given part of science, as well as the role of ‘pragmatic’ and normative discussions of these choices.
The answer is that Turing clarified the idea of a formal system by picturing or modeling its use. A Turing Machine is the model, inspired by an image of a human computer. Turing fastens on how a human computer uses a formal system and what a human computer uses a formal system for. 16 It functions instead as a persuasive crystallization – that is, explication – of the characteristic marks of proof captured by formalization of the Hilbertian type. Turing is giving us a highly simplified, accessible and uncontroversial rendering of the very idea of a formal system, embedded in an image or snapshot of how things appear when a human being follows or applies a determine rule that is specified in advance, syntactically.
The difference between my view and the view I have ascribed to Ricketts is subtle. It is mainly a matter of the placement of Carnap’s ultimate philosophical sensibility. Ricketts’s Carnap is a bit more traditional than is mine – he wishes to distinguish mathematics from empirical science, he does so on the ground of the emptiness of mathematics, and then exploits this emptiness to explain how various mathematical systems can be applied in obtaining knowledge of nature (precisely because their emptiness precludes their inducing contradictions within the system of knowledge or between the theoretical language and the language of experience).