Correction to: Self-referential propositions

Transformations between Self-Referential Sets

Self-Referential Definition of Orthogonality

There has for longer been an interest in finding equivalent conditions which define inner product spaces, and the respective literature is considerable, see for instance Amir, which lists 350 such results. Here, in this tradition, an alternative definition of orthogonality is presented which does not make use of any inner product. This definition, in the spirit of the recently developed non-wel...

How to Express Self-Referential Probability. A Kripkean Proposal

We present a semantics for a language that includes sentences that can talk about their own probabilities. This semantics applies a fixed point construction to possible world style structures. One feature of the construction is that some sentences only have their probability given as a range of values. We develop a corresponding axiomatic theory and show by a canonical model construction that i...

Differential electrophysiological response during rest, self-referential, and non-self-referential tasks in human posteromedial cortex.

The electrophysiological basis for higher brain activity during rest and internally directed cognition within the human default mode network (DMN) remains largely unknown. Here we use intracranial recordings in the human posteromedial cortex (PMC), a core node within the DMN, during conditions of cued rest, autobiographical judgments, and arithmetic processing. We found a heterogeneous profile ...

Operational Pointer Semantics: Solution to Self-Referential Puzzles I

In the t rad i t iona l approach to semant ics t r u t h values are assigned to sentence types. Moreover, the mean i ng of l inguistic expressions is given th rough a m a p which associates with t h e m extra l inguis t ic enti t ies, in such a way tha t the mean ing of a complex expression is derivable f rom tha t of its components . By t rea t ing equal ly all tokens of the same expression su...