Related papers: Higher-Order Platonism and Multiversism
Salient object detection is a problem that has been considered in detail and many solutions proposed. In this paper, we argue that work to date has addressed a problem that is relatively ill-posed. Specifically, there is not universal…
We generalize the Lagrangian-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for…
Motivated by team semantics and existential second-order logic, we develop a model-theoretic framework for studying second-order objects such as sets and relations. We introduce a notion of abstract elementary team categories that…
Given a real finite hyperplane arrangement A and a point p not on any of the hyperplanes, we define an arrangement vo(A,p), called the *valid order arrangement*, whose regions correspond to the different orders in which a line through p can…
We examine Paul Halmos' comments on category theory, Dedekind cuts, devil worship, logic, and Robinson's infinitesimals. Halmos' scepticism about category theory derives from his philosophical position of naive set-theoretic realism. In the…
A description of physical reality in which wholeness is the foundation is discussed along with the motivation for such an attempt. As a possible mathematical framework within which a physical theory based on wholeness may be expressed,…
Some aspects of the development of physics and the mathematics set one think about relation between complex numbers and reality around us. If number to spot as the relation of two quantities, from the fact of existence of complex numbers…
This paper develops a categorical framework to clarify the relationship between the completeness and compactness theorems in classical first-order logic. Rather than claiming that different model constructions yield naturally isomorphic…
We present a higher well-ordering principle which is equivalent (over Simpson's set theoretic version of $\text{ATR}_0$) to the existence of transitive models of Kripke-Platek set theory, and thus to $\Pi^1_1$-comprehension. This is a…
Compositionality proofs in higher-order languages are notoriously involved, and general semantic frameworks guaranteeing compositionality are hard to come by. In particular, Turi and Plotkin's bialgebraic abstract GSOS framework, which…
Finetuning and Naturalness are extra-empirical theory assessments that reflect our expectation how scientific theories should provide an intuitive understanding about the foundations underlying the observed phenomena. Recently, the absence…
S. Gudder and, later, S. Pulmanova and E. Vincekova, have studied in two recent papers a certain ordering of bounded self-adjoint operators on a Hilbert space. We present some further results on this ordering and show that some structure…
Eternalism is the view that the past, the present and the future exist simpliciter. A typical argument in favor of this view leans on the relativity of simultaneity. The 'equally real with' relation is assumed to be transitive between…
We investigate higher-dimensional $\Delta$-systems indexed by finite sets of ordinals, isolating a particular definition thereof and proving a higher-dimensional version of the classical $\Delta$-system lemma. We focus in particular on…
We are interested in aligning how people think about objects and what machines perceive, meaning by this the fact that object recognition, as performed by a machine, should follow a process which resembles that followed by humans when…
We analyze the precise modal commitments of several natural varieties of set-theoretic potentialism, using tools we develop for a general model-theoretic account of potentialism, building on those of Hamkins, Leibman and L\"owe, including…
We discuss a class of linear representations of the product poset of totally ordered sets $P= T_1 \times \cdots \times T_n$ which decompose into interval representations for block intervals. These can be characterised in terms of a…
The recently introduced model of representations has been defined and motivated somewhat ex-nihilo. In this document, I will show that representations are related to a more ''classical'' model through a 2-adjunction. The target model is…
An algebraization of the notion of topology has been proposed more than seventy years ago in a classical paper by McKinsey and Tarski. However, in McKinsey and Tarski's setting the model theoretical notion of homomorphism does not…
Set theory brought revolution to philosophy of mathematics and it can bring revolution to philosophy of physics too. All that stands in the way is the intuition that sets of physical objects cannot themselves be physical objects, which…