Related papers: Yablo's paradox and forcing
We note that some form of the condition "$p_1, p_2$ have a $\leq_{\mathbb{Q}}$-lub in $\mathbb{Q}$" is necessary in some forcing axiom for $\lambda$-complete $\mu^+$-c.c. forcing notions. We also show some versions are really stronger than…
This paper presents a plausible reasoning system to illustrate some broad issues in knowledge representation: dualities between different reasoning forms, the difficulty of unifying complementary reasoning styles, and the approximate nature…
There has been an upsurge of interest in the consequences for quantum physics of the so-called Wigner's Friend Paradox. In its original formulation, the paradox has been turned inside out, and virtually every aspect of it has been looked…
This thesis presents the strong and weak forms of the Banach-Tarski paradox based on the Hausdorff paradox. It provides modernized proofs of the paradoxes and necessary properties of equidecomposable and paradoxical sets. The historical…
We introduce a new method in the attempt to prove the Jacobian conjecture. In the complex dimension 2 case, we apply this method to prove some new results related the Jacobian conjecture.
A forcing extension may create new isomorphisms between two models of a first order theory. Certain model theoretic constraints on the theory and other constraints on the forcing can prevent this pathology. A countable first order theory is…
Logical paradoxes and inconsistent information pose deep challenges in epistemology and the philosophy of logic. Classical systems typically handle contradictions only through external checks or by altering the logical framework, as in…
Various theorems for the preservation of set-theoretic axioms under forcing are proved, regarding both forcing axioms and axioms true in the Levy-Collapse. These show in particular that certain applications of forcing axioms require to add…
I discuss some general information-theoretic properties of quantum mechanical probes in semiclassical gravity: their purview, i.e. what they can see and act on (in terms of a generalised entanglement wedge), their spontaneous evaporation…
We propose a solution to the quantum measurement paradox by first identifying its classical counterpart.
The search for a scientific theory of consciousness should result in theories that are falsifiable. However, here we show that falsification is especially problematic for theories of consciousness. We formally describe the standard…
In a sigma-closed forcing extension, the bounded forcing axiom for Namba forcing fails. This answers a question of Justin Tatch Moore.
We present a sufficient condition for irreducibility of forcing algebras and study the (non)-reducedness phenomenon. Furthermore, we prove a criterion for normality for forcing algebras over a polynomial base ring with coefficients in a…
We discuss the problem of defining a logic for analogical reasoning, and sketch a solution in the style of the semantics for Counterfactual Conditionals, Preferential Structures, etc.
These notes present a compact and self-contained approach to iterated forcing with a particular emphasis on semiproper forcing. We tried to make our presentation accessible to any scholar who has some familiarity with forcing and boolean…
It appears paradoxical that science is producing outstanding new results and theories at a rapid rate at the same time that researchers are identifying serious problems in the practice of science that cause many reports to be irreproducible…
We study the problem of generating referring expressions modulo different notions of expressive power. We define the notion of $\+L$-referring expression, for a formal language $\+L$ equipped with a semantics in terms of relational models.…
A demandance is a psychological "pull" exerted by a stimulus. It is closely related to the theory of "affordance". I introduce the theory of demandance, offer some motivating examples, briefly explore its psychological basis, and examine…
In this paper we investigate the existence and uniqueness of bounded, periodic and almost periodic solutions for second order differential equations involving reflection of the argument.The relationship between frequency modules of forced…
Here, by introducing a version of Unexpected hanging paradox first we try to open a new way and a new explanation for paradoxes, similar to liar paradox. Also, we will show that we have a semantic situation which no syntactical logical…