New PDF release: Mathematics and Reality

By Mary Leng

ISBN-10: 0191576247

ISBN-13: 9780191576249

ISBN-10: 0199280797

ISBN-13: 9780199280797

Mary Leng bargains a safety of mathematical fictionalism, in response to which we haven't any cause to think that there are any mathematical items. might be the main urgent problem to mathematical fictionalism is the indispensability argument for the reality of our mathematical theories (and as a result for the lifestyles of the mathematical gadgets posited via these theories). based on this argument, if we've cause to think something, now we have cause to think that the claims of our greatest empirical theories are (at least nearly) real. yet on the grounds that claims whose fact will require the lifestyles of mathematical items are fundamental in formulating our greatest empirical theories, it follows that we've got sturdy cause to think within the mathematical items posited by means of these mathematical theories utilized in empirical technology, and hence to think that the mathematical theories used in empirical technological know-how are actual. past responses to the indispensability argument have focussed on arguing that mathematical assumptions could be disbursed with in formulating our empirical theories. Leng, in contrast, bargains an account of the function of arithmetic in empirical technological know-how based on which the winning use of arithmetic in formulating our empirical theories don't need to depend on the reality of the maths applied.

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209). Rather, the only external question that Carnap thinks can be asked about a given theoretical framework is the practical one, of whether adopting the framework is convenient for the purposes of theoretical investigation. Our adoption of the ‘linguistic forms which constitute the framework of numbers’, as opposed to the linguistic forms which constitute the framework of (for example) astrology in our empirical scientific theorizing should not be thought of as indicative that we have reason to believe in the reality of numbers, but rather, as indicative only that we have found that form of speaking convenient.

However, I suspect that in her more careful moments Maddy would continue to qualify her quietism, as she does here. naturalism and ontology 29 argument for philosophical quietism regarding the question of what we are (really) justified in believing, before considering Quine’s own conversion of Carnap’s negative motivation for the rejection of first philosophy into a positive motivation for the recasting of ontological questions as answerable by recourse to our ordinary scientific methods of inquiry.

Rejecting ‘First Philosophy’ The characteristic mark of Quinean naturalism is the rejection of the idea of a distinctively philosophical inquiry into the nature of reality. According to Quine, naturalism requires the ‘abandonment of the goal of a first philosophy. It sees natural science as an inquiry into reality, fallible and corrigible but not answerable to any supra-scientific tribunal, and not in need of any justification beyond observation and the hypothetico-deductive method’ (Quine 1975: 72).

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Mathematics and Reality by Mary Leng


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