Mathematical Anti-Realism and Modal Nothingism

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Cover Title page Copyright page Mathematical Anti-Realism and Modal Nothingism Contents 1 Introduction Mathematical Anti-Realism 2 What Is Mathematical Anti-Realism? 2.1 Opening Remarks 2.2 Mathematical Realism 2.2.1 Mathematical Realism Defined 2.2.2 The Argument for Mathematical Realism 2.2.3 Platonism as the Only Tenable Version of Mathematical Realism 2.2.4 Why You Might Be Unhappy with Platonism (and, Hence, Attracted to Anti-Realism) 2.3 Three Versions of Mathematical Anti-Realism 2.3.1 Paraphrase Nominalism and the Rejection of Premise [1] 2.3.2 Mathematical Error Theory and the Rejection of Premise [3] 2.3.3 Deflationary-Truth Nominalism and the Rejection of Premise [2] 2.4 Some Arguments against Paraphrase Nominalism and Deflationary-Truth Nominalism 2.4.1 An Argument against Paraphrase Nominalism 2.4.2 Two Arguments against Deflationary-Truth Nominalism 2.5 Error Theory Takes Center Stage 3 Mathematical Error Theory Defended 3.1 Opening Remarks 3.2 A FAPP-ist Account of Objective Mathematical Correctness 3.2.1 The Objective-Correctness Argument 3.2.2 FAPP-Truth 3.2.3 FAPP-ism 3.2.4 Proto-Mathematical Truths 3.2.5 The Argument for FAPP-ism 3.3 Objections and Responses 3.3.1 Intended Parts of the Mathematical Realm 3.3.2 Counterfactuals Involving Reference Failures 3.3.3 Counterpossibles 3.4 Other Arguments against Error Theory 3.4.1 The Quine-Putnam Argument 3.4.2 Mooreanism 3.4.3 Laughable Presumption 3.5 The Reliance-on-Modality Objection to Error Theory 3.6 Counterfactualism over Necessitarianism 4 Paraphrase Nominalism and Deflationary-Truth Nominalism Revisited 4.1 Opening Remarks 4.2 Problems for Paraphrase Nominalism 4.3 Problems for Deflationary-Truth Nominalism Modal Nothingism 5 Modal Semantics and Modal Truthmaking 5.1 Opening Remarks 5.2 The Semantic Question 5.2.1 The Possible-Worlds Analysis of Ordinary Modal Discourse 5.2.2 The Primitivist Analysis of Ordinary Modal Discourse 5.2.3 Hybrid-Mess-ism 5.3 The Truthmaking Question 5.4 The Mathematical Anti-Realist’s Predicament 6 Possible Worlds 6.1 Opening Remarks 6.2 Realism about Possible Worlds 6.3 Modal Error Theory 6.4 Deflationary Truth and Modality 6.5 Summing Up 7 Modal Primitivism 7.1 Opening Remarks 7.2 Possibility* as the Broadest Kind of Possibility 7.3 Why Analyticity Doesn’t Help 7.4 Sider-Style Conventionalism 7.5 Essentialism 7.6 Powers and Potentialities 7.7 Generalizing 8 Modal Nothingism to the Rescue 8.1 Opening Remarks 8.2 What Is Modal Nothingism? 8.2.1 Initial Statement of the Theory 8.2.2 The Scope of Modal Nothingism 8.2.3 Bruteness and Explanation 8.2.4 Epistemology 8.3 How Modal Nothingism Could Be True (and How TMR Could Be False) 8.4 The Literali’s Argument For 8.5 The Argument for Modal Nothingism 8.6 The Mathematical Anti-Realist’s Modal Sentences 8.7 Semantic Neutrality 8.8 A Slight Wrinkle: Applications of Mathematics 8.9 Why Modal Nothingism Isn’t a Deflationary-Truth View References