For a couple of years now, I’ve been working on my second book that focuses on topics like abstract objects, god, and the philosophy of science

Current table of contents:

0 Introduction 

1 Platonist Accounts and General Realist Accounts 

1.1 Classical Platonism 

1.1.1 Temporal Ontology 

1.1.2 Diachronic Identity 

1.1.2.1 No to Presentism 

1.1.3 Synchronic Identity 

1.1.3.1 Dialectic is Important 

1.1.4 Katz’s Mistakes 

1.1.4.1 Existential Dependency 

1.1.4.2 Identity Dependency 

1.1.4.3 Into Tallant’s Transtemporal Accounts 

1.1.4.3.1 Transitivity? Who Needs It? 

1.1.4.3.1 Tallant’s False Explanans  

1.1.4.4 Identity of Indiscernibles and Edward Feser 

1.2 Mathematical Platonism 

1.2.1 Fregeanism 

1.2.2 Neo-Fregeanism 

1.2.3 Plebani’s Combinations 

1.2.3.1 Mathematical Platonism and Ontological Pluralism 

1.2.3.2 Plural Platonism 

1.2.4 Heavy Duty Platonism: How Do We Know? 

1.3 Mathematical Pluralism 

1.3.1 Balaguer’s Odd Position 

1.3.2 FBP Is Inconsistent 

1.3.2.1 FBP Is Directly Compatible with Possibilism 

1.3.2.2.1 From Possibilism to Possibilist Psychologism 

1.4 Mathematical Fictionalism 

1.4.1 Quine-Putnam Indispensability Argument 

1.4.1.1 Non-Quinean Indispensability Argument 

1.4.2 Barbosa’s Reply to Objections to Platonism 

1.4.3 Natural Science and Its Ontological Commitment to Mathematical Objects 1.4.4 Enhanced Indispensability Argument 

1.5 Semi-Platonism 

1.5.1 Aristotelian Realism 

1.5.1.1 Franklin’s View 

1.5.1.1.1 Uninstantiated Properties 

1.5.1.1.1.1 Still Realism? 

1.5.1.1.2 Principle of Irrelevance  

1.5.1.3 Thomistic Foundations 

1.5.1.3.1 Maurer’s Formalization

1.5.1.3.2 Miller’s Formalization 

1.5.1.3.3 Quantity Cannot Work 

1.5.1.3.3.4 Quantity Explained Mathematically 

1.5.1.3.3.4.1 Quantity as A Lewisian Tool 

1.6 Mathematical Causalism 

1.6.1 Mathematical Objects are Causally Capable? 

1.6.2 Callard’s Inconsistencies 

1.6.2.1 Empirical Laws Defy 

1.6.2.1 Metaphysical Actualia and Metaphysical Possibilia 

1.6.3 Park’s Failures and Successes  

1.6.3.1 The Tricle Is Reductio 

1.6.3.2 Computational Neuroscientism 

1.6.3.2.1 Spatiotemporal Dynamical Complexities 

1.6.4 Juvshik’s Expositions 

1.6.4.1 Causal Exclusion and Its Success 

1.6.4.2 General Relativity and Special Relativity 

1.7 Conclusion 

2 Proofs of Abstract Objects  

2.1 Neo-Pythagoreanism 

2.1.1 Ineligibility of Using Monadism 

2.2 Feser’s Augustinian Proof 

2.2.1 Falsity of Related Relata 

2.2.2 Aristotelian and Neo-Aristotelian Powerism 

2.2.2.1 Powers of the Intellect 

2.2.2.2 Can the Intellect Create Abstract Objects?  

2.2.2.3 Sudden Bootstrapping of an Augustinian God 

2.3 Vallicella’s Onto-Cosmological Proof 

2.3.1 Vicious Circularity 

2.3.2 Armstrong’s Non-Reductionism 

2.3.2.1 Connectedness and Nexus 

2.3.3 Reductionism and Its Success  

2.3.3.1 Truthmaker Intuition 

2.3.3.2 Anti-Meinongian Intuition 

2.3.3.3 Infinite Regress of Truthmakers 

2.3.4 Intrinsic Reference or Locution 

2.3.4.1 Principle of Irrelevance  

2.3.4.2 Hyperintensionality 

2.3.4.3 Indexicality and Referents 

2.3.4.4 Existential Dependency 

2.3.4.5 Intensional Objects 

2.3.4.5.1 Causal Semantics 

2.3.4.5.2 If Conditions and Causation 

2.3.5 The Primitive Ontology of Metaphysical Complexities  

2.3.5.1 Explanatory Monism 

2.3.5.2 Explanatory Pluralism

2.3.5.3 Arguing for Pluralism Onto-Cosmologically 

2.3.5.3.1 The Vectors of 3D Space 

2.3.5.3.2 Linguistic Constituents of the Metaphysical Complexity 

2.3.5.3.3 Set-Theoretic Realism is False 

2.3.5.3.4 Quantum Mechanics Answers Priority Pluralism! 

2.3.5.4 Arguing for Monism Onto-Cosmologically 

 2.3.5.4.1 Macrophysical Emergence 

 2.3.5.4.2 A Conditioned Reality Must Be Monistic 

2.3.5.4.3 Set-Theoretic Realism is True 

2.3.5.4.4 Quantum Mechanics Answers Priority Monism! 

2.3.6 Facts Without a Truthmaker and the Nature of a Truthmaker 

2.3.6.1 Brute Facts 

2.3.6.2 The WPSR and SPSR 

2.3.6.3 Vallicella’s S5 argument 

2.3.6.4 God as a Truthmaker 

2.3.6.4.1 Necessary Conditions 

2.3.6.4.2 If Conditions as Necessary Conditions 

2.3.6.4.3 Tallant’s Necessary Condition: Its Incoherency 

2.3.6.4.4 Lowe’s Necessary Condition: Its Coherency 

2.3.6.5 Truthmakers are Committed to the Existence of Facts 

2.4 Ontological-Linguistic Commitments 

2.4.1 Fregean Inspired Argument  

2.4.2 Natural Language is not Indexical 

2.4.3 Core-Periphery Distinction 

2.5 Wave Function Realism 

2.5.1 Laws of nature 

2.5.1.1 Neo-Humean Implications 

2.6 Cosmic Hylomorphism 

2.6.1 Abstract Cosmic Force 

2.6.2 Bohmian Primitive Ontology 

2.6.2.1 Goldstein-Durr-Zhangi Formulation 

2.6 Conclusion 

3 God and Abstract Objects 

3.1 Absolute Creationism 

3.1.1 Theistic Activism 

3.1.2 Critics 

3.1.3 B&B 

3.1.4 BBBO 

3.1.4.1 Logical Framework For BBBO 

3.2 Modified Theistic Activism 

3.3 Necessary Conditions, Again 

3.4 Divine Conceptualism 

3.4.1 Critics 

3.4.2 Theistic Ideaism 

3.4.3 Possibilist Divine Psychologism: Its Incoherency

3.4.4 Actualist Divine Psychologism: Its Coherency 

3.5 DEP 

3.5.1 Eternal Causation 

3.5.2 Co-Eternality 

3.5.3 Timeless or Eternal Artifacts 

3.5.4 Pure Atemporalism: Simultaneity 

3.5.5 ET-Simultaneity 

3.5.6 E-Simultaneity 

3.5.7 T-Simultaneity 

3.5.8 Existential Dependence  

3.5.9 Mutual Existential Relations 

3.6 Asymmetrical Existential Relations 

3.6.1 The Ultimacy Problem 

3.6.2 Bootstrapping 

3.6.3 Possible Worlds 

3.6.4 Divine Conceptualism and Bootstrapping 

3.6.5 Theistic Activism and Bootstrapping 

3.6.6 Creating the Platonic Horde 

3.6.7 Ought to Accept M&M 

3.6.8 Ought to Accept Causalism 

3.6.9 Aristotelianism and Divine Conceptualism 

3.6.9.1 Substances Are Aristotelian 

3.6.9.2 God is Emergent 

3.7 IDP 

3.7.1 Abstract Objects Are Independent of God 

3.7.1.1 Propositionalism 

3.7.1.2 Theistic Propositionalism 

3.7.1.3 Necessitarian Theism 

3.7.1.4 Necessitarian Atheism 

3.7.1.5 Plain Theism 

3.7.1.6 Plain Atheism 

3.7.2 Divine Aseity 

3.7.3 Divine Sovereignty 

3.7.4 Ontological Relativity 

3.7.5 Positive Ontologies 

4 Vague Objects and Mereological Indeterminacy 

4.1 Metaphysical Identities 

4.2 Advanced to Abstract Objects? 

4.2.1 Abstract Objects are Mereologically Indeterminate 4.2.2 Natural Language Cannot be Necessarily Indexical 4.2.3 Discourse About Mathematics  

4.2.3.1 Linguistics of Mathematical Discourse 

5 Quantum Mechanics and Platonism 

5.1 Quantum Nonlocality as Platonic Abstract Objects 5.1.1 Ad Hoc for the Platonist

5.1.2 Platonic Information (PI) Vs Naturalist Information (NI) 

5.1.3 NI Yields Better Results 

5.1.3.1 Better for Quantum Information Theory 

5.1.4 PI Yields Better Results 

5.1.5 NI Is More “Natural” 

5.1.5.1 The Natural Sciences Accommodate Quantum Nonlocality 

5.1.5.2 The Natural Sciences Accommodate QM as a Whole 

5.1.6 Materialistic Metaphysics Vs Platonic Metaphysics 

5.1.7 Platonic Metaphysics aren’t In Line with Theoretical Virtues 

5.1.8 Materialistic Metaphysics are Simpler 

5.1.9 Materialistic Metaphysics are More Preferrable 

5.2 Explanatory Power 

5.2.1 The Necessary Conditions for an Account of Explanatory Power 5.2.1.1 Platonism Fails 

5.2.1.2 Materialism and Naturalism Succeed  

5.2.1.3 Platonism Rebirthed 

5.2.1.4 Aristotelian Realism does it Better 

6 Metaontology of Abstract Objects 

6.1 Bob Hale: The Metaontology of Abstraction 

6.2 Excluding Abstract Objects 

6.2.1 Abstract Objects are Spooky 

6.2.2 Ontological Pegboards 

6.2.3 Ontological Pluralism 

6.2.3.1 Pluralism is Useless 

6.2.4 Ontological Monism 

6.2.4.1 Fits with Our Intuition 

6.3 Is Causalism All that Great? 

6.3.1 Simply Ad Hoc 

6.4 Platonic Ersatizm 

6.4.1 Pruss 

6.4.2 Modal Realism  

6.4.2.1 Platonism Helps Modal Realism 

6.4.2.1 Extreme Modal Realism (EMR) 

6.5 Modal Instantiation 

6.5.1 Ingram 

6.5.1.1 The Principle of Positivity 

6.5.1.2 Negative Facts Cannot Exist 

6.5.2 “Implicit Commitments to Negative Facts” 

6.6 Several Objections to Modal Realism 

6.6.1 Metaontological Objections to Modal Realism 

6.6.2 Humphrey’s Objection to Modal Realism

6.6.3 Kripkean Characterization 

6.6.3.1 Principle of Irrelevance 

6.6.3 The Set Objection to Extreme Modal Realism 

6.4 Conclusion 

7 Concluding Remarks 

7.1 The Best Argument for Abstract Objects 

7.2 A New Primitive Ontology of Abstract Objects 

Appendix: Spatiotemporal dynamic complexities 

Bibliography and Further Readings 

Index