Pub Date : 2020-03-25DOI: 10.1093/oso/9780198823667.003.0007
Justin Clarke‐Doane
This chapter discusses “realist pluralism” in mathematics and morality. It argues that, under the assumption of pluralism, factual questions get deflated while practical -- i.e., what-to-do -- questions do not. It then uses this contrast to formulate a radicalization of Moore’s Open Question Argument. Practical questions remain open even when the facts, including the evaluative facts, come cheaply. The chapter concludes that practical realism must be false, but practical questions are objective in a paradigmatic respect. Conversely, mathematical realism is true, but mathematical questions fail to be objective. An important upshot of the discussion is that the concepts of realism and objectivity, which are widely identified, are actually in tension.
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Pub Date : 2020-03-25DOI: 10.1093/oso/9780198823667.003.0004
Justin Clarke‐Doane
This chapter argues that mathematical beliefs have no better claim to being empirically – i.e., a posteriori -- justified than our moral beliefs. It shows that Harman’s influential argument to the contrary is fallacious. It then formulates a better argument for a lack of parity between the cases, in terms of indispensability. It argues that, while the necessity of mathematics is no bar to developing a mathematics-free alternative to empirical science, the contents of our arithmetic beliefs, realistically and even objectively construed, do seem to be indispensable to metalogic. But this at most shows that a subset of our mathematical beliefs have better claim to being empirically justified. Surprisingly, however, the range of moral beliefs that we actually have may be so justified, in a more direct way. The chapter concludes with the prospect that there is no principled distinction between intuition and perception, and, hence, between a priori and a posteriori justification.
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Pub Date : 2020-03-25DOI: 10.1093/oso/9780198823667.003.0008
Justin Clarke‐Doane
The Conclusion suggests a general partition of areas of philosophical interest into those which are more like mathematics and those which are more like morality. In the former category are questions of possibility, grounding, essence, logic, and mereology. In the latter are questions of epistemology, political philosophy, aesthetics, and prudential reasoning. The chapter argues that the former questions are like the question of whether the Parallel Postulate is true, qua a pure mathematical conjecture. By contrast, practical questions are immune to deflation in this way. The conclusion is that the objective questions in the neighborhood of questions of modal metaphysics, grounding, nature, and so forth are practical. Practical philosophy should, therefore, take center stage.
{"title":"Conclusion","authors":"Justin Clarke‐Doane","doi":"10.1093/oso/9780198823667.003.0008","DOIUrl":"https://doi.org/10.1093/oso/9780198823667.003.0008","url":null,"abstract":"The Conclusion suggests a general partition of areas of philosophical interest into those which are more like mathematics and those which are more like morality. In the former category are questions of possibility, grounding, essence, logic, and mereology. In the latter are questions of epistemology, political philosophy, aesthetics, and prudential reasoning. The chapter argues that the former questions are like the question of whether the Parallel Postulate is true, qua a pure mathematical conjecture. By contrast, practical questions are immune to deflation in this way. The conclusion is that the objective questions in the neighborhood of questions of modal metaphysics, grounding, nature, and so forth are practical. Practical philosophy should, therefore, take center stage.","PeriodicalId":254890,"journal":{"name":"Morality and Mathematics","volume":"272 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115902335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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