Telephone: (609) 258-4432
Fax: (609) 258-1113
e-mail: phil@princeton.edu
Fall 2000 - on Sabbatical
Photographs and brief
Biography.
2. Reasoning about necessary conclusions
3. A study of conditional reasoning
4. A study of truth and falsity
5. Reasoning about probabilistic conclusions
6. Modal reasoning
7. Temporal reasoning
8. In collaboration with Bruno Bara and Monica Bucciarelli (University
of Turin), the application of the mental model theory to the development
of reasoning ability in children, and the study of how reasoners try to
falsify conclusions.
9. In collaboration with Keith Oatley (OISE, University of Toronto),
the study of how emotions affect reasoning.
10. In collaboration with Dr. Antonio Rizzo (Siena) and Victoria
Bell (Princeton), a study of how diagrams can help people to reason.
Some recent publications
Some computer programs implementing the mental model theory
Updated 8/00
The main aim of this project is to develop a unified account of how
individuals reason. Its theoretical background is the theory of mental
models developed in collaboration with Dr.
Ruth Byrne (Dublin). According to this theory, logically-untrained
individuals reason by using the meaning of assertions to construct mental
models of the situations that they describe. A conclusion is logically
necessary if it holds in all the models of the premises. A phenomenon predicted
by this theory (and not by other current theories of reasoning) is that
certain inferences should be illusory, i.e. they should have conclusions
that are compelling, drawn by most people, but totally wrong. Dr.
Fabien Savary, who is now a Web maestro, and I have confirmed their
existence. Here is an example.
Subjects overwhelmingly infer that there is an ace in the hand. This
phenomenon is predicted by the model theory, which postulates that reasoners
normally represent only what is true, and not what is false, in their models
of the premises. Notice, however, that if the first assertion is false
then there is a king in the hand, but not an ace. And if the second assertion
is false then there isn't a king in the hand and there isn't an ace in
the hand. Hence, either way, there isn't an ace in the hand. Current theories
of reasoning based on formal rules of inference, because they contain only
valid rules of inference cannot explain such a systematic error. Dr. Yingrui
Yang (Princeton) and I have recently shown that similar errors occur with
quantified assertions, such as 'All the beads are red'.
This study is being carried out in collaboration with Professor Juan
Garcia Madruga (Madrid) and Profesor Carlos Santamaria (Tenerife). It shows
that the transitivity of conditional assertions is influenced by their
content.
Patricia Barres (Princeton) has investigated how individuals generate
true instances of assertions and false instances of them. The model theory
predicts that there is no direct route to false instances, but rather that
they are generated by first considering what would be true. Barres's data
corroborate this prediction.
Dr. Savary and I showed that illusory inferences occur in inferences
about which is more likely of two events (see our paper in Acta Psychologica,
1996). More recently, we have developed a theory of probabilistic reasoning
in collaboration with Professor Paolo Legrenzi (President of the University
of Vita-Salute San Raffaele, Milan), Maria Legrenzi (Padova), Vittorio
Girotto (CREPCO, University of Aix-en-Provence), and Jean-Paul Caverni
(Director, CREPCO, University of Aix-en-Provence). The theory is based
on the theory of mental models, and it postulates that in simple cases
individuals assume by default that each model is equally probable, and
that the probability of an event is accordingly proportional to the number
of models in which it occurs. Experimental evidence has corroborated this
prediction. Thus, given an assertion, such as:
people tend to estimate the probability that there is a red marble
alone in the box as a third. This task also readily gives rise to illusory
inferences.
The aim of this project is to test whether the model theory accounts
for reasoning that yields conclusions about what is possible. Each model
corresponds to a possibility, and so the theory predicts a key interaction:
it should be easier to infer that an event is possible (one model) than
that it is necessary (all models), whereas it should be easier to infer
that an event is not necessary (one model) than that it is not possible
(all models). Victoria Bell (Princeton) has confirmed this interaction
in several experiments. Likewise, Yevgeniya Goldvarg (Princeton)has shown
that illusory inferences occur in this domain. For example, consider the
following problem.
Nearly every participant in our experiment responded: 'yes'. But, it
is an illusion. If there was an ace in the hand, then two of the premises
would be true, contrary to the opening remark that only one of them is
true. Various other colleagues, including Patrizia Tabossi (Trieste), Vittorio
Girotto (Aix-en-Provence), Mary Newsome (Princeton), have examined experimentally
conditions that reduce the propensity of reasoners to make illusory inferences.
Walter Schaeken (Leuven, Belgium) and I have shown that the model theory
gives a good account of temporal reasoning: premises that call for multiple
models yield more difficult inferences than those that call only for a
single model. The difficulty is apparent in both the participants' errors
and latencies. And they take longer to read, and presumably to understand,
the particular premise that calls for the construction of multiple models.
Human and Machine Thinking. Hillsdale, NJ: Lawrence Erlbaum
Associates, 1992.
Mental models and probabilistic thinking. Cognition, 50, 1994.
PropAI
-- a program that uses fully explicit models for propositional reasoning
and that draws its own maximally parsimonious conclusions.
Syllog
-- a program that makes syllogistic inferences based on mental models.
The output shows both the predicted errors and the correct response.