Reply to Powers

The powers of noise-fitting: reply to Barth and Paladino.

Barth and Paladino (2011) argue that changes in numerical representations are better modeled by a power function whose exponent gradually rises to 1 than as a shift from a logarithmic to a linear representation of numerical magnitude. However, the fit of the power function to number line estimation data may simply stem from fitting noise generated by averaging over changing proportions of logar...

Kant’s Model of Causality: Causal Powers, Laws, and Kant’s Reply to Hume

KANT’S VIEWS ON CAUSALITY have received an extraordinary amount of scholarly attention, especially in comparison with Hume’s position. For Hume presents powerful skeptical arguments concerning causality, yet Kant claims to have an adequate response to them. Since it turns out to be far from obvious what even the main lines of Kant’s response are, scholars have felt the need to clarify his posit...

The Authors’ Reply

Raising to powers revisited

We consider the theory of algebraically closed fields of characteristic zero with raising to powers operations. In an earlier paper we have described complete first-order theories of such a structures, provided that a diophantine conjecture CIT does hold. Here we get rid of this assumption. The theory of complex numbers with raising to real powers satisfies the description if Schanuel’s conject...

The Authors’ Reply