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Hyperintensionality and Synonymy HYPERINTENSIONALITY AND SYNONYMY A logical, philosophical, and cognitive investigation MSc Thesis (Afstudeerscriptie) written by Levin Hornischer (born October 17th, 1991 in Filderstadt, Germany) under the supervision of Prof. Dr. Franz Berto and Prof. DDr. Hannes Leitgeb, and submitted to the Board of Examiners in partial fulfillment of the requirements for the degree of MSc in Logic at the Universiteit van Amsterdam. Date of the public defense: Members of the Thesis Committee: June 23rd, 2017 Dr. Maria Aloni Prof. Dr. Franz Berto Dr. Luca Incurvati Prof. DDr. Hannes Leitgeb Prof. Dr. Benedikt Löwe (chair) Prof. Dr. Frank Veltman ABSTRACT We investigate the related and important concepts of synonymy and hyperintension- ality (i.e. criteria for identity that are more fine-grained than necessary equivalence). We show how, for every language, validity uniquely determines a co-hyperinten- sionality relation (that ensures substitution salva veritate). The ordering of operators by their ability to discriminate sentences is not linear (e.g. truthmaking and necessity are incomparable). However, co-hyperintensionality is not a cognitively adequate individuation of content. Instead, we analyze cognitive synonymy (or likeness in cognitive role) concep- tually via defeasible rules, algorithmically via logic programming, and neurally by constructing an appropriate neural network. This explains the contextual stability of synonymy (given by the rules) and its flexibility (some contexts defeat the rules). We introduce the notion of a scenario that has a representational component (like Fregean senses) and an interpretational component (like a possible world). Scenarios can be grounded, e.g., in neural networks, and they have a constructive notion of distance. We use them to provide a hyperintensional semantics including a counter- factual and belief and conceivability operators. This scenario framework allows reconstructing many notions of synonymy. We provide a logic for content identity in scenario semantics. We observe that it is incon- sistent to hold both (i) if no scenario distinguishes two sentences, they are identical in content, and (ii) content identity entails identity in subject matter. Scenario se- mantics satisfies (i) and Fine’s logic of analytic containment satisfies (ii), though it is not the most coarse-grained one above scenario semantics. A semantics with a content-granularity like analytic containment requires moving from scenarios to sets of scenarios. We conclude our investigation with a pluralistic conception of synonymy: because of the sheer number of notions of synonymy, and because it is the only way to reconcile the many opposing features of synonymy. iii ACKNOWLEDGMENTS First of all, I would like to thank my supervisors Franz and Hannes: Franz, thank you for your many helpful comments, for the inspiring meetings discussing the thesis, for your honest interest in my ideas, for encouraging me to further pursue this research, for inviting me to give a talk at your LoC seminar, for your academic support— and for so much more. Hannes, thank you for your astute remarks, for suggesting very helpful literature, for your fruitful questions, for the great conversations, and – especially – for accepting to supervise the thesis from abroad—this means a lot to me. Moreover, I would like to thank Michiel van Lambalgen for introducing me to logic programming, its neural implementation, and its fruitfulness in modeling cognitive phenomena—as well as for many other stimulating insights ranging from Kant, over the philosophy of spacetime, to large cardinals in set theory. Also, I would like to thank Mark Jago and Greg Restall for their comments when I presented chapter2 in Franz’ seminar. And, in general, I would like to thank the audiences at that seminar and at the 2017 Logik zwischen Mathematik und Philosophie conference in Göttingen for their remarks and questions. Furthermore, I’m grateful to all those from whom I’ve learned during my studies. I’m glad I could spend two years at the ILLC. I enjoyed the open-minded and inspir- ing community of researchers and fellow students—and the fact that you can keep talking logic all night long without having to worry weird looks. Last but not least, I want to thank my family, my partner, and my friends for their great support during my studies—without you this thesis wouldn’t exist! v CONTENTS Abstract iii 1 Introduction1 1.1 General introduction.............................1 1.2 The background................................4 1.2.1 A very brief history of synonymy.............5 1.2.2 Intensionality and hyperintensionality...........6 1.2.3 Modern approaches to hyperintensionality.........8 1.2.4 A glance at synonymy in linguistics and cognitive science.... 10 1.3 The problem(s)................................ 11 1.3.1 The problem of co-hyperintensionality........... 12 1.3.2 Related problems................... 13 1.3.3 The Lewis-Stalnaker objection to hyperintensionality...... 13 1.4 Importance of hyperintensionality and synonymy............ 14 1.5 Outlook..................................... 15 1.5.1 The main contributions of this work............ 17 2 The structure of hyperintensionality 19 2.1 The problem of co-hyperintensionality................... 19 2.2 There is exactly one co-hyperintensionality relation........... 20 2.2.1 The notion of a language underlying the problem....... 21 2.2.2 Co-hyperintensionality for an operator........... 22 2.2.3 Co-hyperintensionality for a language........... 25 2.2.4 Putting the results into perspective............ 27 2.3 The structure of hyperintensional operators: The granularity order.. 28 2.4 Further philosophical consequences and open questions........ 32 2.4.1 Co-hyperintensionality is not cognitively adequate...... 32 2.4.2 A universal co-hyperintensionality relation?......... 34 2.4.3 Logical pluralism?.................. 35 2.4.4 Further ideas and open questions............. 36 2.5 Conclusion................................... 38 3 Cognitive synonymy 39 3.1 Cognitive synonymy: Conceptually.................... 40 3.1.1 A first approximation of cognitive synonymy........ 40 3.1.2 What kind of content does cognitive synonymy individuate?... 41 vii 3.1.3 The agent-based and generic knowledge base........ 42 3.1.4 An informal criterion for cognitive synonymy........ 44 3.2 Cognitive synonymy: Algorithmically................... 45 3.2.1 Logic programming.................. 46 3.2.2 A logico-algorithmic individuation of cognitive role...... 49 3.3 Cognitive synonymy: Neurally....................... 51 3.3.1 Neural implementation of logic programming........ 51 3.3.2 Some further comments................ 59 3.3.3 Neural individuation of cognitive role........... 59 4 Scenarios 61 4.1 Describing scenarios............................. 61 4.1.1 Defining scenarios.................. 61 4.1.2 The structure of the class of scenarios: Accessibility relations... 63 4.1.3 The structure of the class of scenarios: Pseudometric...... 64 4.1.4 The structure of the class of scenarios: Negligible sets..... 66 4.1.5 Grounding scenarios................. 66 4.1.6 Comparing scenarios................. 67 4.2 Semantics with scenarios........................... 68 4.2.1 Defining the semantics................. 68 4.2.2 Describing the notions of validity............. 73 4.2.3 The counterfactual in the semantics............ 78 5 Notions of synonymy 81 5.1 A zoo of notions of synonymy........................ 81 5.2 Characterizing content identity....................... 85 5.2.1 A sound and complete logic for strict synonymy....... 86 5.2.2 Related systems................... 89 5.3 Something paradoxical about synonymy.................. 90 5.3.1 Characterizing Fine’s analytic containment (AC)....... 91 5.3.2 Move on up: From strict synonymy to analytic synonymy.... 93 5.3.3 Resolving the paradox................. 95 5.4 Pluralism about synonymy......................... 95 Appendix 99 A More on knowledge bases.......................... 99 B Outsourced proofs.............................. 100 B.1 Proof of the replacement rule.............. 100 B.2 Proof of the theorem characterizing AC........... 100 B.3 Proof of the theorem characterizing super strict synonymy.... 102 B.4 Proof of the “semantics with sets of scenarios” theorem..... 104 Bibliography 107 viii 1st Chapter INTRODUCTION We start with a broad and informal introduction to the topic of the thesis, including a description of the perplexing phenomenon of synonymy. Then we provide the background for our investigation of synonymy and hyper- intensionality. This includes a brief history of synonymy and a characterization of the concept of hyperintensionality, also indicating why it is tightly linked to synonymy. Moreover, we sketch existing approaches to provide a hyperinten- sional notion of meaning—that is, a notion of meaning according to which some necessarily equivalent sentences still can differ in meaning. Next, we outline the main open problems of hyperintensionality and mention why they are important. Finally, we summarize what we will do in this thesis including a list of its main contributions. 1.1 General introduction We give a broad and informal introduction to the topic of the thesis. The focus is not on precision and completeness but on “giving a feel” for the topic. One of the big questions in philosophy is: What is meaning? More specific sub- questions include: What is the meaning of words and sentences? Is “the meaning” of a sentence an entity? And if so, is it something like a mind-independent abstract
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