Knowledge, Number and Reality: Encounters with the Work of Keith Hossack

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Throughout his career, Keith Hossack has made outstanding contributions to the theory of knowledge, metaphysics and the philosophy of mathematics. This collection of previously unpublished papers begins with a focus on Hossack’s conception of the nature of knowledge, his metaphysics of facts and his account of the relations between knowledge, agents and facts. Attention moves to Hossack’s philosophy of mind and the nature of consciousness, before turning to the notion of necessity and its interaction with a priori knowledge. Hossack’s views on the nature of proof, logical truth, conditionals and generality are discussed in depth. In the final chapters, questions about the identity of mathematical objects and our knowledge of them take centre stage, together with questions about the necessity and generality of mathematical and logical truths. Knowledge, Number and Reality represents some of the most vibrant discussions taking place in analytic philosophy today. Cover Halftitle page Series page Title page Copyright page Contents Notes on Contributors Introduction Contributions Notes References 1 A Summary of My Current Views 1. Relation dualism 2. Awareness as the irreducible mental relation 3. Circumstances 4. Epistemological ramifications of relation dualism 5. Metaphysical ramifications Hossack’s bibliography 2 Confronting Facts: On Hossack’s The Metaphysics of Knowledge 1. The basicness of knowledge 2. Conceptions of basicness 3. Inference and immediacy in testimony and perception 4. The openness of perception 5. Hallucination Notes References 3 Who Knows? 1. Plato’s forms and the objects of knowledge 2. Epistemic pluralism? 3. The Meno question 4. Piecemeal and systematic: the question of addition 5. Priorities 6. The phenomenology of understanding 7. The development of understanding 8. Knowing and saying Notes References 4 Knowledge-first Epistemology and the Input Problem1 1. Introduction 2. The theory of epistemic rationality 3. Epistemic targets 4. Evidential information 5. Evidential support 6. Conversion theory 7. Connecting the elements 8. The epistemic role of knowledge-first epistemology 9. The Input Problem 10. Reactions to the Input Problem 11. Reflexive evidence? 12. Propositional and doxastic rationality 13. Contra naïve conversion 14. The Münchausen constraint Notes References 5 Perceiving X = Consciousness of Perceiving X. Hossack and Brentano on the Identity Thesis 1. Introduction1 2. An argument for the Identity Thesis 3. The Identity Thesis and the metaphysics of events 4. Brentano on Cantor: what is logical (conceptual) division? 5. One mental act, different conceptual parts 6. What’s wrong with conceptual parts? Notes References 6 Facts, Knowledge and Knowledge of Facts 1. Vectors and combination 2. Knowledge and facts 3. The a priori and necessity 4. Conclusions Notes References 7 Necessity, Conditionals and Apriority 1. Inferribility 2. Far-fetchedness 3. Relative correctness of the truth-conditions of Goodman and of Lewis 5. Modal holism 6. Absolute correctness of the truth-conditions of Goodman 7. Defining necessity in terms of the counterfactual 8. Defining the a priori 9. The truth-conditions of Goodman entail modal rationalism Appendix – Proofs of theorems Note References 8 A Commentary on ‘Necessity, Conditionals and Apriority’ 1. Introduction 2. Goodman 3. Lewis 4. Far-fetchedness 5. ‘Relevance’ 6. Relative and absolute correctness 7. The necessary and the a priori 8. The dénouement: the necessary and the a priori coincide References 9 The Mathematicians’ Use of Diagrams in Plato1 1. Introduction 2. What mathematics is Plato recommending? 3. What is the cognitive shift effected by mathematics in general? 4. How does the use of diagrams facilitate conversion and ascent? 5. Conclusion Notes References 10 Generality 1. Introduction 2. Resemblance between universals. I 3. Resemblance between universals. II 4. The logic of generality 5. Comparison with other metaphysicians’ views on generality 6. Conclusion Notes References 11 We Belong Together: A Plea for Modesty in Modal Plural Logic1 1. 2. 3. 4. 5. Notes References 12 Aristotelian Aspirations, Fregean Fears: Hossack on Numbers as Magnitudes 1. Introduction 2. Mereology based on an addition operation 3. Equality 4. Magnitudes 5. The bad company problem Notes References 13 Mathematical Structures, Universals and Singular Terms1 1. Structures and universals 2. Structures and abstraction 3. The permutation argument 4. Structures and singular terms 5. Ante-rem vs. abstract structures Notes References 14 Arithmetic in a Finite World1 1. Kinds of quantities 2. Two kinds of fiction 3. Cardinality 4. Abstraction, lite 5. The shortage of objects problem 6. Zero, one, many, manys, manyses 7. The axiom of two 8. Back to kindergarten 9. An infinite sequence from two 10. From Frege to Peano Notes References Index