Fudan Logic Seminar 2026
May 8
Location: HGW2403
Speaker: Hanoch Ben-Yami
Time: 13:30 - 15:00
On "2nd-order" Logic and Quarc
The so-called second-order logic has made negligent incursions into the formalisation of natural language. Its conception as being about properties, by contrast to the so-called first-order logic, is wrong. The syntactic features of the so-called 2nd-order Predicate Calculus do not make it second- or higher-order in any acceptable sense either. Basically, it is an artefact of Frege’s conception of quantification, not reflecting any general feature of logic. It does have some distinctive semantic features, primarily in allowing several domains of quantification, yet the Quantified Argument Calculus (Quarc) allows for that by determining the ‘domain of quantification’ through the unary predicate which attaches to the quantifier, in this way making redundant different types of quantification. Its applications in mathematics can also be captured by Quarc, by utilising sets conceived as mere pluralities.
April 29
Location: HGW2403
Speaker: Andrew Arana
Time: 18:30 - 20:00
Finitism revisited: Takeuti's philosophy of mathematics
Many accounts of mathematical knowledge take intuition to be a source. Knowledge of the infinite, then, poses a problem, for it seems difficult to intuit the infinite. In this talk I will discuss Gaisi Takeuti's account of mathematical knowledge of the infinite. Takeuti was a mathematical logician whose philosophical context drew on the work of Kitaro Nishida, the founder of the Kyoto School of philosophy. I will discuss Nishida’s conception of intuition, show how Takeuti adopted this conception, and explain how Takeuti could use this conception of intuition to give a more expansive account of intuitive knowledge of the infinite than is standard in the philosophy of mathematics since Hilbert. Slides.
March 30
Location: HGW2401
Speaker: Isaac Goldbring
Time: 16:00 - 17:30
On a problem of Fritz, Netzer, and Thom
After being open for 50 years, the Connes Embedding Problem (CEP) in operator algebras was settled several years ago as a consequence of the quantum complexity result MIP*=RE. One equivalent formulation of the CEP is that the group $F_2\times F_2$ is residually finite-dimensional (RFD), where $F_2$ is the free group on 2 generators. In their 2012 paper, Fritz, Netzer, and Thom proved that any RFD group $G$ is such that the standard presentation of the universal group C*-algebra $C^*(G)$ is computable and thus raised the question as to whether or not the standard presentation of the universal group C*-algebra $C^*(F_2\times F_2)$ is computable, for a negative answer to this question would refute the CEP. While MIP*=RE settled the CEP, it failed to resolve the question of Fritz, Netzer, and Thom. In this talk, I will show that the standard presentation of the universal group C*-algebra $C^*(F_2\times F_2)$ is not computable, using an even more recent quantum complexity result known as $\mathrm{MIP}^{\mathrm{co}}=\mathrm{coRE}$. Time permitting, I will discuss related results. The work presented in this talk is joint with Thomas Sinclair. No prior knowledge of operator algebras or quantum complexity will be assumed. Blackboard notes.