Philosophy for Everyone

The lack of diversity in academic philosophy has been well documented. This paper examines the reasons for this issue, identifying two intertwining norms within philosophy which contribute to it: the assertion that the Adversary Method is the primary mode of argumentation and the excessive boundary policing surrounding what constitutes “real” philosophy. These norms reinforce each other, creating a space where diverse practitioners must defend their work as philosophy before it can be engaged with philosophically. Therefore, if we are to address the diversity issue, these norms must change. I advocate for the community of philosophical inquiry to serve as a new standard of practice, as it requires a simultaneous reimagining of both norms, thereby addressing the issues that arise from the two elements working in tandem. With its emphasis on epistemic openness and constructive collaboration, and a broader definition of philosophy which conceptualizes it as a method of questioning/analyzing rather than a particular subject matter, I posit that its implementation would facilitate a more welcoming climate for diverse practitioners. While these changes are unlikely to solve the diversity problem “once and for all,” I argue that they would significantly help to improve it.

Adversary lower bounds for the collision and the set equality problems

We prove tight \Omega(n^{1/3}) lower bounds on the quantum query complexity of the Collision and the Set Equality problems, provided that the size of the alphabet is large enough. We do this using the negative-weight adversary method. Thus, we reprove the result by Aaronson and Shi, as well as a more recent development by Zhandry.

Explicit relation between all lower bound techniques for quantum query complexity

The polynomial method and the adversary method are the two main techniques to prove lower bounds on quantum query complexity, and they have so far been considered as unrelated approaches. Here, we show an explicit reduction from the polynomial method to the multiplicative adversary method. The proof goes by extending the polynomial method from Boolean functions to quantum state generation problems. In the process, the bound is even strengthened. We then show that this extended polynomial method is a special case of the multiplicative adversary method with an adversary matrix that is independent of the function. This new result therefore provides insight on the reason why in some cases the adversary method is stronger than the polynomial method. It also reveals a clear picture of the relation between the different lower bound techniques, as it implies that all known techniques reduce to the multiplicative adversary method.

The Authority of the Fallacies Approach to Argument Evaluation

Popular textbook treatments of the fallacies approach to argument evaluation employ the Adversary Method identified by Janice Moulton (1983) that takes the goal of argumentation to be the defeat of other arguments and that narrows the terms of discourse in order to facilitate such defeat. My analysis of the textbooks shows that the Adversary Method operates as a Kuhnian paradigm in philosophy, and demonstrates that the popular fallacies pedagogy is authoritarian in being unresponsive to the scholarly developments in informal logic and argumentation theory. A progressive evolution for the fallacies approach is offered as an authoritative alternative.

The quantum query complexity of certification

We study the quantum query complexity of finding a certificate for a d-regular, k-level balanced \nand formula. We show that the query complexity is $\tilde\Theta(d^{(k+1)/2})$ for 0-certificates, and $\tilde\Theta(d^{k/2})$ for 1-certificates. In particular, this shows that the zero-error quantum query complexity of evaluating such formulas is $\tilde O(d^{(k+1)/2})$. Our lower bound relies on the fact that the quantum adversary method obeys a direct sum theorem.

Quantum lower bound for recursive Fourier sampling

We revisit the oft-neglected `recursive Fourier sampling' (RFS) problem, introduced by Bernstein and Vazirani to prove an oracle separation between BPP and BQP. We show that the known quantum algorithm for RFS is essentially optimal, despite its seemingly wasteful need to uncompute information. This implies that, to place \mathsf{BQP} outside of PH[\log] relative to an oracle, one would need to go outside the RFS framework. Our proof argues that, given any variant of RFS, either the adversary method of Ambainis yields a good quantum lower bound, or else there is an efficient classical algorithm. This technique may be of independent interest.