## Invited Speakers

- Elke Brendel (University of Bonn)
- Andrea Cantini (University of Florence)
- Michał Godziszewski (University of Warsaw)
- Volker Halbach (University of Oxford)
- Joel David Hamkins (City University of New York)
- Deborah Kant (Humboldt University of Berlin)
- Peter Koepke (University of Bonn)
- Lavinia Picollo (MCMP, Munich)
- Graham Priest (City University of New York)
- Lorenzo Rossi (University of Salzburg)
- Thomas Schindler (University of Cambridge/MCMP, Munich)
- Peter Schuster (University of Verona)
- Albert Visser (University of Utrecht)
- Philip Welch (University of Bristol)

## Titles and abstracts (not complete)

**Tbc.**

*(Elke Brendel).*

Truthmaker maximalism (TMM) is the view that every true sentence has a truthmaker, where a truthmaker of a sentence σ is conceived as an entity whose mere existence necessitates the truth of σ. Peter Milne has attempted to refute TMM via a self-referential sentence M “saying” of itself that it doesn’t have a truthmaker. Milne argues that M turns out to be a true sentence without a truthmaker and thus provides a counterexample to TMM.

In contrast to Milne’s argument, it will be shown that M leads to a provable contradiction no matter how one assesses TMM. M turns out to be a liar-like sentence that gives rise to a Truthmaker-Paradox (TP). TP is an interesting paradox in its own right, but has no significance for the still virulent question of whether TMM is a philosophically plausible account.

**From self-reference to unboundedness**

*(Andrea Cantini)*.

As a starting point, we reconsider the paradoxes of Russell-Zermelo vs. Burali-Forti and

Mirimanoff. We then deal with Yablo's paradox by projecting it into different

formal frameworks.

In particular we discuss:

(i) a recent attempt to understand structural aspects underlying Yablo's paradox;

(ii) the same paradox in a classical theory of Frege structures and in a theory of stratified truth.

On some metalogical properties of Visser - Yablo sequences and potential infinity

*(Michal Tomasz Godziszewski).*

You can find the abstract here.

**Self-reference in arithmetic**

*(Volker Halbach).*

Many sentences in arithmetic that are of metamathematical interest are described as self-referential. In particular, the Gödel sentence is described as a sentence that claims its own unprovability, while the Henkin sentence is described as a sentence claiming its own provability. More recently philosophers have discussed whether Visser-Yablo sentences are self-referential. The notion of self-reference, however, seems blurry in these discussion; in other cases the analysis of self-reference seems just inadequate. The emphasis of the talk will be on the consequences of the analysis of self-reference for formal results in metamathematics.

**Self-reference in the universal algorithm**

*(Joel David Hamkins).*

I shall give an elementary account of the universal algorithm, due to Woodin, showing how the capacity for self-reference in arithmetic gives rise to a Turing machine program e, which provably enumerates a finite set of numbers, but which can in principle enumerate any finite set of numbers, when it is run in a suitable model of arithmetic. Furthermore, the algorithm can successively enumerate any desired extension of the sequence, when run in a suitable top-extension of the universe. Thus, the algorithm sheds some light on the debate between free will and determinism, if one should imagine extending the universe into a nonstandard time scale. An analogous result holds in set theory, where Woodin and I have provided a universal locally definable finite set, which can in principle be any finite set, in the right universe, and which can furthermore be successively extended to become any desired finite superset of that set in a suitable top-extension of that universe.

Comments and inquires can be made on the speaker's blog at http://jdh.hamkins.org/self-reference-in-the-universal-algorithm.

**This sentence is not provable**

*(Graham Priest).*

Gödel’s first Incompleteness Theorem is often phrased as: any (sufficiently strong) axiomatic

arithmetic is incomplete. This is inaccurate: what Gödel’s proof shows is that it is either

incomplete or inconsistent. Of course, if classical logic is used, then inconsistency implies

triviality; so it is natural enough to ignore the inconsistency alternative. However, this is not so if

a paraconsistent logic is used. Indeed, it is now known that there are axiomatic arithmetics that

are complete, inconsistent, and non-trivial. In this talk, I will explain what these theories a like,

and then turn to the question of what one should make of their existence philosophically.

A theory of paradoxes, with an application to some variants of Yablo’s and Visser’s paradoxes

*(Lorenzo Rossi).*

Tbc.

A graph-theoretic analysis of the semantic paradoxes

**(Thomas Schindler).**Tbc.