Is there a logic of information?

Abstract

Information-based epistemology maintains that ‘being informed’ is an independent cognitive state that cannot be reduced to knowledge or to belief, and the modal logic KTB has been proposed as a model. But what distinguishes the KTB analysis of ‘being informed’, the Brouwersche schema (B), is precisely its downfall, for no logic of information should include (B) and, more generally, no epistemic logic should include (B), either.

Keywords::

• modal logic
• epistemic logic
• B schema

Acknowledgements

I am indebted to Clark Glymour and Kevin Kelly for their comments on an earlier draft. I also benefited from discussions with Luciano Floridi, Franck Lihoreau, Paul Pedersen and Sonja Smets.

Notes

^1. Rule RR states that if (p & q) → r is a theorem, then (▪p & ▪q) → ▪r is also a theorem.

^2. Specifically, BAM 1 here is ▪(◊∼p → q) → (∼p → ▪q) and p codes ‘the circumference of a circle is a rational number’.

^3. Compare to Allo (2011), who proposes a weakening of the KTB analysis that nevertheless succumbs to BAM.

^4. Schema (5) is ◊p → ▪◊p.

^5. Schema (4) is ▪p → ▪▪p.

Additional information

Funding

This research is supported in part by an award from the European Science Foundation [grant number LogICCC/0001/2007] and an award from Portuguese Science Foundation [grant number PTDC/MHC-FIL/5363/2012].