# Publications

But life is short, and truth works far and lives long: let us speak the truth.

--- Schopenhauer

### Articles:

In press. "Transcending the theory of types", with Simone Picenni, in: M. Petrolo and G. Venturi (eds.), Paradoxes between truth and proof, Synthese Library

Based on the Gödel-Russell idea of ranges of significance, we present a natural type-free generalisation of the theory of types. Although the theory is based on Weak Kleene logic, we show that it relatively interprets classical simple type theory. This is made possible by the addition of novel quantifiers that restrict the range of a variable to the range of significance of a given concept.

2022. "Higher-order quantification and disquotational truth", with Lavinia Picollo, Journal of Philosophical Logic 51: 879-918 PDF (published version)

We provide some formal results in support of our thesis, defended in our 2018 paper, that the truth predicate is best understood as a device to emulate higher-order quantification in a first-order framework. More specifically, we show that any theory formulated in a higher-order language can be naturally and conservatively interpreted in a first-order theory with a disquotational truth or satisfaction predicate.

2022. "Unrestricted quantification and ranges of significance", Philosophical Studies PDF (published version)

Is it possible to provide a semantic theory for first-order languages in which the quantifiers are absolutely unrestricted? It has been argued that such a semantics can and indeed must be given in a plural or higher-order metalanguage. I argue that it is possible to provide such a semantic theory in a first-order metalanguage as well.

2022. "Deflationary Theories of Properties and their Ontology", Australasian Journal of Philosophy 100: 443-458 PDF (published version)

I raise a problem for Hofweber's nominalist theory of properties. In its stead, I formulate a theory of properties in analogy to Horwich's minimalist theory of truth. Although this theory relies on the existence of abstract objects, I argue that nevertheless it is appropriate to call the theory deflationary.

2022. "Steps Towards a Minimalist Account of Numbers", Mind 131: 865-893 PDF (published version)

I try to develop a minimalist view of (natural) numbers in strong analogy to the minimalist view of truth. The idea is that number terms serve a mere quasi-logical function, comparable to the role of the truth predicate. This allows us to explain the applicability and objectivity of arithmetic.

NOTE. In the originally published version of this manuscript, all occurrences of the character ‘#’ were omitted from the pdf version of the article, by an error of the publisher. These errors are not present in the html version of the article. The publisher has since published a correction which, unfortunately, still contains this error. I strongly recommend to read the html version only!

2021. "The Proper Formulation of the Minimalist Theory of Truth", with Julian Schlöder, Philosophical Quarterly PDF (published version)

We take up a challenge raised by Donald Davidson, Sten Lindström, and Tim Button according to which Horwich's minimalist theory of truth cannot be stated (or cannot be stated without collapsing it into the redundancy theory of truth). We show how it can be done!

2021. "Is Deflationism Compatible with Compositional and Tarskian Truth Theories?", with Lavinia Picollo, in: C. Nicolai and J. Stern (eds.), Modes of truth. The unified approach to truth, modality, and paradox, Routledge, pp. 41-68 PDF (published version)

We argue that, contrary to received wisdom, deflationary theories of truth are compatible with compositional or Tarski-style axioms for truth.

2021. "Does Semantic Deflationism Entail Meta-Ontological Deflationism?", with Benjamin Marschall, Philosophical Quarterly 71: 99-119 PDF (published version)

In a recent paper, Amie Thomasson has argued that deflationism about truth and reference entails deflationism about existence which in turn entails meta-ontological deflationism, which is defined as the view that the neo-Quinean approach to metaphysics is misguided. We argue that Thomasson's arguments fail.

2020. “A Note on Horwich’s Notion of Grounding”, Synthese 197: 2029-2038 PDF (published version)

I argue that Horwich's solution of the liar paradox doesn't work, and look at some alternatives.

2019. “Classes, Why and How”, Philosophical Studies 176: 407-435 PDF (published version)

I introduce a type-free theory of classes that admits a universal class, i.e. a class containing absolutely everything, including itself. I show that the theory allows us to reconstruct second-order arithmetic. Moreover, I argue that the theory provides a positive solution to the problem of absolutely unrestricted quantification.

2018. “Deflationism and the Function of Truth”, with Lavinia Picollo, Philosophical Perspectives 32: 326-351 PDF (published version)

We argue that the truth predicate is best understood as a means to simulate higher-order quantification in a first-order framework. Indeed, truth allows us to simulate full impredicative higher-order comprehension. We conclude from this that deflationary theories of truth do not have to be conservative.

2018. “Disquotation and Infinite Conjunctions”, with Lavinia Picollo, Erkenntnis 83: 899-928 PDF (published version)

Deflationists claim that the truth predicate exists solely for a certain logical function. However, what that function is has never been spelled out properly. We look at two accounts of spelling out that function and argue that they are unsatisfactory. We also argue that, if you're a deflationist, then considerations of natural language are largely irrelevant when it comes to the regimentation of our truth talk.

2018. “Some Notes on Truth and Comprehension”, Journal of Philosophical Logic 47: 449-479 PDF (published version)

This paper contains a systematic study of translations between the language of truth and languages that allow for second-order quantification. There are also some fun theorems to the effect that truth and satisfaction are not ontologically innocent as many have claimed.

2017. “A Graph-Theoretic Analysis of the Semantic Paradoxes”, with Timo Beringer, Bulletin of Symbolic Logic 23: 442-492 PDF (published version)

In this 50-page whopper, we investigate what reference patterns lead to semantic paradox by assigning reference graphs to sentences containing the truth predicate. We show that there two patterns underlying all paradoxes: the loop and the double path.

2016. “Reference Graphs and Semantic Paradox”, with Timo Beringer, in P. Arazim and M. Dancak (eds.), Logica Yearbook 2015, College Publications: London, pp. 1-15 PDF (preprint)

This paper provides a birds-eye view of our 2017 paper.

2016. “Arithmetic with Fusions”, with Jeff Ketland, Logique et Analyse 234: 207-226 PDF (preprint)

This paper investigates the proof-theoretic strength of classical mereology / fusion theory.

2015. “A Disquotational Theory of Truth as Strong as Z2-“, Journal of Philosophical Logic 44: 395-410 PDF (preprint)

This paper introduces a disquotational truth theory as strong as Z2-. (The acronym stands for second-order arithmetic without parameters. But it actually follows from a theorem of Harvey Friedman that this is arithmetically equivalent to full second-order arithmetic.)

2014. “La Paradoja de Cantor (Cantor’s Paradox)”, in E. Barrio (ed.), Paradojas, Paradojas y más Paradojas, College Publications: London, pp. 199-212 [in Spanish] PDF (English version)

A survey article on Cantor's paradox of the class of all classes.

2014. “Axioms for Grounded Truth”, The Review of Symbolic Logic 7: 73-83 PDF (revised and expanded version)

This paper introduces an axiomatic formulation of Leitgeb's theory of truth and alternative formulations of the Kripke-Feferman theory and Cantini's supervaluational theory.

### Teaching material:

2018. “Set Theory ”, Lecture Notes, University of Cambridge, 40 pp.

2014. “Tarski Hierarchies, Grounded Truth, and Ramified Analysis”, Lecture Notes, University of Buenos Aires, 15 pp. PDF

2013. “Set Theory ”, with Catrin Campbell-Moore, Lecture Notes, LMU Munich, 53 pp. PDF

### Reports:

2013. “Putnam's Model-theoretic Arguments”, The Reasoner 7: 84 PDF

2013. “Paradox and Truth”, with Catrin Campbell-Moore, The Reasoner 7: 84-85 PDF

### Dissertation:

2015. Type-free truth. LMU Munich. 161 pp. PDF

Me and frequent collaborateur, Lavinia Picollo

Mendoza, Argentina, 2014