# Program

## Room Arrangement

Date | Address, Room |
---|---|

30.07.2017 | Geschwister-Scholl-Platz 1, room E106 (Senatssaal) (floor plan) |

31.07. - 04.08.2017 | Geschwister-Scholl-Platz 1, room numbers in program below (floor plan) |

05.08.2017 | Geschwister-Scholl-Platz 1, room E106 (Senatssaal) (floor plan) |

Sunday, 30 July

Time | Topic |
---|---|

16:45 - 17:45 | Registration. |

17:45 - 18:00 | Welcome. |

18:00 - 19:15 | Welcome Lecture: What is Mathematical Philosophy? (Stephan Hartmann & Hannes Leitgeb, MCMP). |

19:15 | Country Taste |

## Monday, 31 July

Time | Topic |
---|---|

08:00 - 09:00 | Registration. (Room B015) |

09:00 - 10:15 | Elements of Set Theory and Probability Theory (Marianna Antonutti and Lavinia Picollo, MCMP). (Room A022) |

10:15 - 10:45 | Coffee Break. (Room B011) |

10:45 - 12:00 | Tutorial for 'Elements of Set Theory and Probability Theory' (Marianna Antonutti and Lavinia Picollo, MCMP). (Room A022) |

12:00 - 13:30 | Lunch Break. |

13:30 - 14:45 | First-Order Logic: Language, Proofs and Models (Gil Sagi, University of Haifa/MCMP). (Room A022) |

14:45 - 15:15 | Coffee Break. (Room B011) |

15:15 - 16:30 | Tutorial for 'First-Order Logic: Language, Proofs and Models' (Gil Sagi, University of Haifa/ MCMP). (Room A022) |

16:30 - 16:45 | Break. |

16:45 - 18:00 | Parallel MCMP Fellows' Sessions:
1: Neil Dewar: Category Theory. (Room C005) |

## Tuesday, 1 August

Time | Topic |
---|---|

09:00 - 10:15 | Lecture Stream 1: Conditional Sentences and Causal Reasoning (Katrin Schulz, University of Amsterdam). (Room A022) |

10:15 - 10:45 | Coffee Break. (Room B011) |

10:45 - 12:00 | Tutorial: Conditional Sentences and Causal Reasoning (Katrin Schulz, University of Amsterdam). (Room A022) |

12:00 - 13:30 | Lunch Break. |

13:30 - 14:45 | Lecture Stream 2: Philosophy of Mathematics from Computability to Local Foundations: A Holistic Approach (Juliette Kennedy, University of Helsinki). (Room A022) |

14:45 - 15:15 | Coffee Break. (Room B011) |

15:15 - 16:30 | Tutorial: Philosophy of Mathematics from Computability to Local Foundations: A Holistic Approach (Juliette Kennedy, University of Helsinki). (Room A022) |

16:30 - 16:45 | Break. |

16:45 - 18:00 | Lecture Stream 3: Semantic Paradoxes and Self-Reference (Roy Cook, University of Minnesota, Twin Cities). (Room A022) |

## Wednesday, 2 August

Time | Topic |
---|---|

09:00 - 10:15 | Tutorial: Semantic Paradoxes and Self-Reference (Roy Cook, University of Minnesota, Twin Cities). (Room A022) |

10:15 - 10:45 | Coffee Break. (Room B011) |

10:45 - 12:00 | Lecture Stream 1: Conditional Sentences and Causal Reasoning (Katrin Schulz, University of Amsterdam). (Room A022) |

12:00 - 13:30 | Lunch Break. |

13:30 - 14:45 | Tutorial: Conditional Sentences and Causal Reasoning (Katrin Schulz, University of Amsterdam). (Room A022) |

14:45 - 15:15 | Coffee Break. (Room B011) |

15:15 - 16:30 | Lecture Stream 2: Philosophy of Mathematics from Computability to Local Foundations: A Holistic Approach (Juliette Kennedy, University of Helsinki). (Room A022) |

16:30 - 16:45 | Break. |

16:45 - 18:00 | Tutorial: Philosophy of Mathematics from Computability to Local Foundations: A Holistic Approach (Juliette Kennedy, University of Helsinki). (Room A022) |

19:00 - 20:30 | Evening Lecture: Intellectual Arrogance and Vanity in Debate and Testimony (Alessandra Tanesini, Cardiff University). (Room E106) |

## Thursday, 3 August

Time | Topic |
---|---|

09:00 - 10:15 | Lecture Stream 3: Semantic Paradoxes and Self-Reference (Roy Cook, University of Minnesota, Twin Cities). (Room A022) |

10:15 - 10:45 | Coffee Break. (Room B011) |

10:45 - 12:00 | Tutorial: Semantic Paradoxes and Self-Reference (Roy Cook, University of Minnesota, Twin Cities). (Room A022) |

12:00 - 13:30 | Lunch Break. |

13:30 - 14:45 | Parallel Sessions: Lecture Stream 1: Conditional Sentences and Causal Reasoning (Katrin Schulz, University of Amsterdam). (Room C022) Lecture Stream 2: Philosophy of Mathematics from Computability to Local Foundations: A Holistic Approach (Juliette Kennedy, University of Helsinki). (Room C016) Lecture Stream 3: Semantic Paradoxes and Self-Reference (Roy Cook, University of Minnesota, Twin Cities). (Room C005) |

15:00 - 16:15 | [Optional] Career Workshop (Christine Bratu, LMU Munich, and Alessandra Tanesini, Cardiff University). (Room A022) |

## Friday, 4 August

Time | Topic |
---|---|

09:00 - 10:15 | Parallel Sessions: Lecture Stream 1: Conditional Sentences and Causal Reasoning (Katrin Schulz, University of Amsterdam). (Room C022) Lecture Stream 2: Philosophy of Mathematics from Computability to Local Foundations: A Holistic Approach (Juliette Kennedy, University of Helsinki). (Room C016) Lecture Stream 3: Semantic Paradoxes and Self-Reference (Roy Cook, University of Minnesota, Twin Cities). (Room C005) |

10:15 - 10:45 | Coffee Break. (Room B011) |

10:45 - 12:00 | Parallel Sessions: Lecture Stream 1: Conditional Sentences and Causal Reasoning (Katrin Schulz, University of Amsterdam). (Room C022) Lecture Stream 2: Philosophy of Mathematics from Computability to Local Foundations: A Holistic Approach (Juliette Kennedy, University of Helsinki). (Room C016) Lecture Stream 3: Semantic Paradoxes and Self-Reference (Roy Cook, University of Minnesota, Twin Cities). (Room C005) |

12:00 - 13:30 | Lunch Break. |

13:30 - 14:45 | Parallel Sessions: Lecture Stream 1: Conditional Sentences and Causal Reasoning (Katrin Schulz, University of Amsterdam). (Room C022) Lecture Stream 2: Philosophy of Mathematics from Computability to Local Foundations: A Holistic Approach (Juliette Kennedy, University of Helsinki). (Room C016) Lecture Stream 3: Semantic Paradoxes and Self-Reference (Roy Cook, University of Minnesota, Twin Cities). (Room C005) |

14:45 - 15:15 | Coffee Break. (Room B011) |

15:15 - 16:30 | Parallel MCMP Fellows' Sessions: 1: Marianna Antonutti Marfori: What is Ordinary Mathematics? (Room C005) 2: Kristina Liefke: Logical Approaches to (Compositional) Natural Language Semantics. (Room C009) 2: Barbara Osimani: Exact Replication or Varied Evidence? Reliability, Robustness and the Reproducibility Problem. (Room C016) 4: Lavinia Picollo: Deflationism Broadened. (Room C022) |

16:30 - 17:45 | Student Poster Sessions. (Adalberthalle) |

19:30 | Summer School Dinner (Cafe Reitschule). |

## Saturday, 5 August

Time | Topic |
---|---|

09:15 - 09:45 | Student Presentation: Wittgensteinian Antirealism (Amber Sahara Donovan) |

09:45 - 10:15 | Student Presentation: Transfinite Ordinals from a Finitary Standpoint (Maria Hämeen-Anttila) |

10:15 - 10:45 | Coffee Break. |

10:45 - 11:15 | Student Presentation: Edgington's Counterfactual Conditionals (Alexandra B. Gustafson) |

11:15 - 11:45 | Student Presentation: An Experimental Study of Linguistic Intuitions (Ana Puljić) |

11:45 - 12:00 | Wrap up and closing. |

## Abstracts

## Main Lecture Streams

### Semantic Paradoxes and Self-Reference

Roy Cook (University of Minnesota, Twin Cities)

In this series of lectures we will examine what, exactly, a paradox is, and what options we have with respect to responding to these puzzles. We will then look at a number of well-known and lesser-known paradoxes involving semantic notions such as truth and falsity, including the Liar paradox, the Curry paradox, the Yablo paradox, the Open Pair, and others. Special attention will be paid to (i) the role that circularity plays in theorizing about and 'solving' semantic paradoxes, and (ii) the use of non-classical logics in accounts of or solutions to these paradoxes.

### Philosophy of Mathematics from Computability to Local Foundations: A Holistic Approach

Juliette Kennedy (University of Helsinki)

With these lectures we hope to give students a flavour of the tightly interconnected web of ideas, that philosophy of mathematics is about. The ideology here is that one cannot think about the debates in one area, without an understanding of the debates taking place in the others.

I. The emergence of computability and the *complexity hierarchy*. The first “simple” proof of the First Incompleteness Theorem, due to Gödel, specifically the distinction between the concepts “true in the standard model of arithmetic” and “provable from the axioms of Peano Arithmetic.” The identification of finitism with *PRA* (primitive recursive arithmetic).

II, III. Categoricity and the first order/second order debate. The completeness of first order logic, the impossibility of a completeness theorem in the second order case (for standard models), the Henkin completeness theorem for second order logic relative to the Henkin semantics, the theorem that validity in second order logic is Pi2-complete in the Levy hierarchy. Categoricity today; other issues in the philosophy of model theory.

IV. Logical consequence. Debates surrounding the model-theoretic notion of consequence; Tarski and others on *logicality*; the question whether one can extract the logical constants from a given notion of consequence, and vice versa. (Papers of Westerstahl and Bonnay.)

V. Critiques of semantic methods often turn on the status of set theory. Is axiomatic set theory an adequate foundation for mathematics? Does the naturalist’s deference to the practice mean she can dispense with talk of truth in set theory? Does decidability in set theory necessarily involve commitment to a particular ontology, or can one be committed to decidability without any such commitment?

VI. Contemporary developments (model-theoretic and set theoretic) built around the idea of “local” vs global foundations.

### Conditional Sentences and Causal Reasoning

Katrin Schulz (University of Amsterdam)

That the meaning of conditional sentences and causal reasoning are closely related seems generally accepted. However, it is still highly debated what the nature of this relation is. Following David Lewis (Lewis 1973) we should define causal dependence based on the meaning of conditionals. Lewis’ proposal came accompanied by an approach to the semantics of conditional sentences, which still dominates the field. Others have argued that the dependency is exactly the other way around (Hiddleston, 2005): conditionals are interpreted based on information about causal dependencies. Such approaches often make use of the Causal Network Approach to causation (Pearl 2000, Spirtes et al. 2000). Goal of this lecture series is to get a good understanding of both positions and the formal models involved. We will see how the research done on both approaches can benefit from insights and results from the other side. We will also have a look at the cognitive evidence for both positions. And, hopefully, we will end up with some answers on what exactly the relation is between conditionals and causal reasoning.

## Public Evening Lecture

### Intellectual Arrogance and Vanity in Debate and Testimony

Alessandra Tanesini (Cardiff University)

Recently political debate has become increasingly ill tempered; displays of arrogance and vanity are widespread, whilst intellectual humility is in short supply. These vices are harmful: morally and epistemically. In this lecture, I develop my view that they flow from one's own evaluations of the intellectual worth of one's character and that these evaluations are guided by the desires to fit within social groups or to defend one's ego. I argue that these vices are often gendered because of their connections to structures of domination and subordination. I show that they are morally harmful because their display is instrumental in the promotion of opposing vices in other individuals. I explore the negative effects that these psychological features have on public debate and on testimony to highlight the epistemic harms that flow from them. Finally, I propose some interventions to reduce the prevalence of arrogance and vanity.

## Parallel MCMP Fellows' Sessions' Abstracts

### What is Ordinary Mathematics?

Marianna Antonutti Marfori

Both mathematicians and philosophers of mathematics often distinguish between set-theoretic mathematics (that part of mathematics that essentially employs set-theoretic methods and concepts) and ordinary, non-set-theoretic mathematics [see notably Simpson 2009]. For example, mathematicians often talk about paradoxes arising from self-referential sentences as not being genuinely mathematical problems, and philosophers talk about a certain foundational framework being able to recover ordinary mathematics. In this talk, I will sketch two ways in which this notion can be characterised more precisely: one according to which ordinary mathematics consists of all that mathematics which is directly or indirectly faithfully representable in second order arithmetic, one according to which ordinary mathematical knowledge is the knowledge attainable without using set-theoretic resources (i.e. on the basis of our grasp of second order arithmetic). I will argue that both views run into counterexamples, and I will assess the prospects for formulating an adequate account of the notion of ordinary mathematics.top

### Category Theory

Neil Dewar

Various areas of philosophy have started to become interested in the use of category-theoretic tools: roughly speaking, in analysing mathematical structures in terms of the structure-preserving mappings between them. (Thus, the category of groups consists of all groups, together with the group homorphisms between them; the category of vector spaces consists of all vector spaces, together with linear transformations between them; the category of topological spaces consists of all topological spaces, together with continuous transformations between them; and the category of sets consists of all sets, together with functions between them.)

In this talk, I’ll do three things. The first is to provide a basic bluffer’s guide to category theory, outlining the notions needed to engage with a lot of the philosophical applications of category theory (namely categories, functors, natural transformations and categorical equivalence). The second is to articulate some of the mathematical benefits of category-theoretic analysis, especially unification and non-arbitrariness. Finally, I’ll give a sketch of some of the uses to which category theory is being put in contemporary philosophy of science.top

### Where Philosophy of Language and Psychology of Reasoning Meet: The Case of Indicative Conditionals

Karolina Krzyżanowska

Indicative conditionals, that is, sentences of the form “If p, (then) q,” belong to the most puzzling phenomena of language: even the most fundamental questions about their semantics and pragmatics are the subject of a contentious debate. In this lecture, I will explore how philosophy, linguistics, and psychology of reasoning can join their forces towards a better understanding of how people interpret indicative conditionals and how they reason with them. Finally, I will discuss limitations and challenges that such an interdisciplinary research has to face.top

### Logical Approaches to (Compositional) Natural Language Semantics

Kristina Liefke

Many of the summer school's lecture and tutorials will presuppose the possibility of translating natural language sentences into interpretable logical formulas. This session introduces an explicit procedure for such a translation, along the lines of Montague-style formal semantics. The use of this semantics will enable us to explain the productivity and systematicity of linguistic understanding, to evaluate the truth (or falsity) of natural language sentences (via the truth/falsity of the sentences’ translating formulas), to predict the relation of entailment between sentences, and to explain speakers’ judgements about consistency, presupposition, anaphoric relations, etc. The session will start by observing a mismatch between the grammatical form of disambiguated natural language sentences and the logical form of their predicate-logical translations, and will introduce a typed lambda logic which resolves this mismatch. We will then use this logic for the systematic translation and interpretation of natural language. Finally, we will discuss extensions of Montague-style semantics (esp. hyperintensional semantics and situation semantics), which extend/improve upon the modeling scope of Montague semantics.top

### Exact Replication or Varied Evidence? Reliability, Robustness and the Reproducibility Problem

Barbara Osimani

The “Reproducibility Project: Psychology” by the Open Science Collaboration caused some stir among psychologists, methodologists as well as scientists, since less than half of the replicated studies succeeded in reproducing the results of the original ones. The APA has attributed this result to hidden moderators that rendered the replications ineffective. Also publication bias and low power have been identified as possible sources for such mismatch. While some analysts have provided formal confirmation for the plausibility of such explanations (Etz and Vandekerkhove, 2016), others have further insisted on the problem of noisy data and suggested that “to resolve the replication crisis in science we may need to consider each individual study in the context of an implicit meta-analysis” (Andrew Gelman).

I investigate these positions through the lenses of Bayesian epistemology, and in particular of recent results on the Variety of Evidence Thesis, and its diverse versions, by delving in particular on the analysis presented by Bovens and Hartmann (2003), where the interaction of reliability and replication has an essential role in defining the epistemic value of varied evidence vs. replication.

I then present Claveau’s variation of this model (2013), which models unreliability as systematic error (bias), and go on to propose a model, where a distinction is made between random and systematic error (Osimani, Landes, 2017). This delivers results which are in contrast with both Bovens and Hartmann (2003), and Claveau (2013). Although the VET fails in all models, it does so under different conditions in each of them, which are especially linked to how reliability, dependence of observations, and consistency are modeled. This approach turns out to be fruitful in investigating the interaction of reliability, independence of evidence, and replication in scientific inference and, more broadly, casts a new light on the debate between advocates of a pluralist methodology in medical research, who insist on supporting hypotheses through various sources of evidence, and the contending view, represented by the Evidence Based Medicine paradigm, which relies on an “elitist” approach, where “best evidence” is searched for and exact replication is highly welcome.top

### Philosophical Problems Concerning Phase Transitions

Patricia Palacios

A topic that has recently attracted the attention of many philosophers of physics concerns the phenomena of phase transitions. Phase transitions are those sudden changes observed, for example, when water turns from liquid into solid. The main philosophical discussion around phase transitions has focused on the apparent need for an infinite idealization in the statistical mechanical treatment of these phenomena. In this lecture, we will discuss the consequences of this infinite idealization for our understanding of reduction, scientific realism and the role of idealizations in scientific theories. At the same time, we will discuss other problems associated with phase transitions such as the notion of universality and the legitimacy of importing models based on phase transitions to other sciences like economics and biology.top

### Comprehensive Deflationism

Lavinia Picollo

The core of deflationism about truth is that the truth predicate’s only purpose in natural language is to allow for certain generalisations. Roughly, it enables us to quantify into sentence position. Relying on a nominalisation process that generates a name for each sentence, the truth predicate allows us to replace sentences with talk about sentences, without altering the truth conditions of expressions. Moreover, if a nominalisation process for predicates is available as well, together with certain syntactic operations the truth predicate also enables us to define a satisfaction predicate and, thus, to quantify into predicate position.

Different but structurally similar nominalisation processes can be employed to introduce talk of properties, classes, and propositions into the language. Coupled with this, predicates like property-possession and class-membership, that are governed by principles structurally similar to those that govern the satisfaction predicate, can serve the same expressive purposes as satisfaction. Such structural similarities make deflationism about properties, classes, propositions, property-possession, and class-membership appealing to deflationists about truth.

In my talk I will present this broadened version of deflationism in detail, along with some objections and challenges it must overcome.

### Knowledge of Validity

Luis Rosa

In logic we make statements such as 'Excluded-middle is a logical truth' and '*Modus ponens* is logically valid'. These claims are (at least implicitly) *universal* claims: they are about all sentences or arguments with a certain logical form, where there are infinitely many sentences or arguments sharing that form. So how can we have knowledge of the fact that those claims are true? Certainly it is not any form of *a posteriori* inductive knowledge, grounded on our verifying that in a certain class of instances sentences with that form were true, much in the same way we come to learn that *All ravens are black*. It would appear, then, that our knowledge of logical truths is in some sense grounded on pure thought: deductive reasoning plus rational *intuitions* (if you're a rationalist) or maybe definitions (if you're an empiricist). But can we have knowledge of the fact that certain forms of sentences/arguments are valid *without* already presupposing that they are so, thus arguing in circles? In this talk we will investigate into the nature of logical knowledge, its purported *a priori* status and the problem of rule-circularity.top

## Student Presentation Abstracts

### Wittgensteinian Antirealism

Amber Sahara Donovan

There has been much debate within philosophy of mathematics as to the nature of mathematical entities – e.g. numbers. Various theories have been developed in an attempt to determine whether mathematical entities exist. I propose to examine two of the most prevalent positions in the philosophy of mathematics: platonism and fictionalism; the former is a realist position, and the latter is an antirealist position. I aim to examine the effects of applying a Wittgensteinian account of meaning to both positions, in order to demonstrate that understanding meaning as such, allows for an ensuing position which arguably combines the merits of both. To do this, I will outline both platonism and fictionalism and detail the merits and common criticisms of each. For Fictionalism, this will involve specific attention to the indispensability argument and the problem of the objectivity; and for Platonism this will include the advantage of truth-value realism and the drawback of positing abstract entities. I will present an interpretation of Wittgenstein’s private language argument, which I will then apply to fictionalism to demonstrate the way in which the argument can provide the fictionalist with the resources to overcome the two principle objections to the position. I will then propose a Wittgensteinian account of truth with respect to language-games, which, if we accept, allows us to reject a central claim to both positions, namely that for a statement to be true it must succeed in referring to or quantifying over the objects that it purports to refer to and quantify over. This leads to a further antirealist position that can be seen to combine the merits of both positions – in that in some sense it satisfies the motivations for truth-value realism, overcomes the indispensability argument and the problem of the objectivity of mathematics, yet does not commit us to an ontology of abstract mathematical entities.top

### Edgington's Counterfactual Conditionals

Alexandra B. Gustafson

Dorothy Edgington, while advocating for a “No Truth Value” view of counterfactual conditionals, describes the difference between “Does/Doesn’t-Will” (DW) and “Had/Hadn’t-Would” (HW) counterfactuals as being essentially one of tense. As such, she claims that we can come to determine our conditional probability for an HW counterfactual by determining the conditional probability we would have had for a corresponding DW counterfactual at a hypothetical previous time, given what we know now.As long as her description of the probability relation is understood in this way, it appears to have great depth -however, we might worry that it lacks breadth, for it seems that this explanation unsatisfactorily applies only to counterfactual conditionals which have a temporal dimension, while neglecting “timeless” counterfactuals. In this project I first describe briefly the tense and probability relations between Does/Doesn’t-Will and Had/Hadn’t-Would counterfactual conditionals, according to Edgington, before attempting to illustrate the potential problem of “timeless” counterfactual conditionals; I conclude by outlining potential avenues for future revision.top

### Transfinite Ordinals from a Finitary Standpoint

Maria Hämeen-Anttila

The development of late finitism in the 1930s is punctuated by two discoveries: Gödel’s incompleteness results in 1930, and Gentzen’s proof of the consistency of Peano Arithmetic, published in 1936. Many contemporaries, most notably Bernays, saw the latter as a direction for the way out of the “temporary failure” brought upon the finitistic programme by Gödel. The key feature, which extended methods used by the finitist in the 1920s, was the use of transfinite induction up to ε_{0}. But how could transfinite induction to that extent be constructive?

In my paper, I will investigate the method used by Gentzen to build hierarchical systems of constructive ordinals, and the possible reasons for its being considered finitistic in character. Moreover, I will consider the possibility envisioned by both Bernays and Gentzen of further extending the method to stronger systems. I will show that the n-fold sequence of well-orderings built by Gentzen can be stretched beyond type ε_{0} by adding one more argument place to the construction function in analogue to extended Veblen functions. The crucial question is, if this is an acceptable move, then when will such a method transcend the limits of finitistic reasoning? For finitism, there exists a danger of relaxing the earlier methodical restrictions enough to dilute the original character of the Programme, rendering it indistinguishable from a more general constructive viewpoint of, e.g., intuitionism. I will argue, however, that the danger was present even in the 1920s finitism, which already transcended primitive recursive methods at least in practice. If there is little logical ground for distinguishing finitism as essentially separate from other constructive views, then the distinctive characteristic of finitism has to be delineated in philosophical and epistemological terms, a task never quite completed by Hilbert and Bernays.top

### An Experimental Study of Linguistic Intuitions

Ana Puljić

Our study in progress aims to experimentally contribute to the debate in the philosophy of language about how the name refers to its referent. While for descriptivists, the description constitutes the meaning of a name and thus picks out the referent, for causal history theorists a description is only used to fix the name in the initial baptism after which the name is passed on link to link via a causal chain of communication.

Kripke’s (1977) widely accepted refutation of descriptivism rests upon thought experiments which demonstrate descriptivism reaches wrong reference judgements in certain cases. Machery et al. (2004) first suggested the public does not share these intuitions, reporting a cross-cultural difference in reference judgements. Lombrozo and Genone’s (2012) study confirmed this and also found a within-participants difference. However, both have been criticized for potentially testing the speaker’s reference (what the speaker intended to refer to)instead of the semantic reference (what the name itself semantically refers to) (e.g. Devitt, 2011; Martí, 2009). Martí (2009) further suggested to focus on linguistic intuitions about how a term should be used instead of meta-linguistic intuitions about what the term refers to. Our aim is, thus, to build upon these studies, but instead of the 3rd person reference judgements, to test the linguistic intuitions of the participants directly.

Participants will undergo a series of repeated experimental and control trials where a vignette and a prompt constitute one trial. In a basic vignette, the participants will be shown a picture of an item (A) paired with its name and its specific descriptive property (P) which will either be a uniquely identifying property or not. Afterward, it will be revealed that the property P actually belongs to a second item (B), alongside being shown B’s picture and name. Lastly, a picture of what looks like A will be shown, together with the suggestion that this item has the property P. They will then be asked to determine whether the item from the last picture is A or B.The assumption is that choosing B privileges the associated property as an identifier, which suggests descriptivist intuitions. Choosing A focuses on the causal history of the name first associated with the item, which suggests causal intuitions. The said items will belong to one of the following kinds: people, aliens, geographical places, natural kinds and artefacts.

A between-participants difference would suggest the public has intuitions different to philosophers, bringing some of Kripke’s arguments into question. A within-participants difference would suggest, as Lombrozo and Genone (2012) have noted, that plausibly people in real life use a combination of the two theories, suggesting a hybrid theory of reference. Both results would suggest future studies should focus on identifying factors that influence the intuitions for choosing one theory over the other in different contexts (e.g. uniqueness of the property).We plan to be finish the project by the end of June and do a future follow up study that will focus on testing such factors.