Dear All,
our next speaker in the Philosophy of Science Colloquium organized by
the Institute Vienna Circle is IVC fellow Valérie Lynn Therrien (McGill
University), who will give a talk on February 22, 3.00-4.30pm (CEST).
Title: Towards a History of Model Theory
Abstract: My current research centers on the question of how to
adjudicate an appropriate background logic for axiomatizations of
mathematics. Currently, first-order logics are the default background
logic. They have the advantage of being simple yet expressive,
deductively complete, but has two main disadvantages. The first is that
it is not categorical, which means that there are infinitely many
non-isomorphic models for e.g., the natural number sequence 0, 1, 2, 3,
4, . . . — most including strange entities like “non-standard” numbers
capable of being greater than all natural numbers, and in which addition
and multiplication aren’t computable! The second disadvantage is that
making first-order logics expressive enough to axiomatize the natural
numbers renders it incomplete! In many ways, first-order logics simply
are not up to the task. Second-order logics are deductively incomplete,
but have the advantage of being categorical, which makes them far more
suitable to talk with precision about a mathematical structure. As such,
I intend to use the history of model theory as of scientific progress
and decision-making with respect to our background theories when the
advantages and disadvantages aren’t themselves decisive. But first, this
history must be generated, and the early history of model theory is what
I will focus on for this talk.
Venue: HS 3D, NIG, Universitätsstraße 7, 1090 Wien
All are welcome!
Georg Schiemer
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