Dr. Bjørn Jespersen (Delft University of Technology)

Logical Foundations of Malfunction

The notion of malfunction is central both to philosophy of technology and philosopy of biology, since both artefacts and organisms may malfunction. This talk fills a lacuna in the existing literature by making available the logical means to reason about malfunction.

The concept of malfuntion emerges only at the end of a long story, preceded as it is by concepts like artefact, organism, function (functioning), proper function (properly functioning), and necessary property. The topic of malfunction is a case where logic and formal semantics are indispensable, since malfunctioning is a property modifier; no individual malfunctions simpliciter, but only relative to some property F, like being a corkscrew or being a liver. A property modifier is a mapping from property to property, such that the result of applying it to a property is another property. Modification requires the resources of intensional logic, because we need to manipulate intensional entities like properties directly. I put forward the necessary amount of logical machinery in the presentaiton.

This talk addresses two logico-semantic questions:
  • Does a malfunctioning F-object malfunction? [I]
  • Is a malfunctioning F-object an F? [II]
The obvious answer to [I] is Yes. But the logical derivation is not straightforward, for malfunctioning occurs as a modifier and malfunction as a property. So the derivation cannot be [Malf F]x∴ Malf x. The problem of shifting from property modifier to property crops up already in connection with intersective modification. In [GF]x∴ G*x Fx, G* cannot be detached from GF; but it can be pseudo-detached (as shown in detail in Duží, M., B. Jespersen, P. Materna (ms.), Transparent Intensional Logic (in submission as of April 30, 2007), §5.3.) The application of the rule of pseudo-detachment is this. If x is a malfunctioning F then there is a property p such that x is a malfunctioning p; define malfunctioning* as the property of being a malfunctioning p; then it follows that x malfunctions*.

But does the converse hold? Philosophically, it is far from obvious which way the answer to [II] should go. Logically, the question is whether the modifier malfunctioning is subsective or privative; [Malfs F] x∴ Fx vs. [Malfp F]x∴ ¬Fx. The choice is a philosophical one, and will not be made at this point. Instead my aim is to lay down the foundations necessary for raising this very question and answering it rigorously.

Born in Denmark.

Magister 1995, Århus Universitet.
Thesis on modality and reference in Kripke.

PhD 2000, Masaryková univerzita, Czech Republic.
Thesis on attitudes, sense and reference in Tichý's Transparent Intensional Logic.

Postdoc 2001-02, Leiden.
Project on procedural semantics and hyperintensionality in Tichý and Martin-Löf.

Docent 2003-04, Leiden.
Taught classes on epistemology, philosophy of language, philosophy of science, and German Idealism.

Postdoc 2005-09, TU Delft.
Project on infrastructure as socio-technical systems (NGI).

Since 2001 living in Leiden, previously in Budapest, Prague, and Florence.