"M-Logic"

M-logic is the associated logic (with an infinitary "M-rule") to the notion(s) of truth for a model M of PA, as discussed last week. Last week we sketched Lachlan's argument that for there to be a truth definition M needs to be recursively saturated. The Krajewski-Kotlarski-Lachlan theorem is a completeness theorem for M-logic: if M is countable and M-logic is consistent then there is a truth definition. (It will turn out that (for countable M) M-logic is consistent if and only if M is recursively saturated.)

"From Molecules to Mathematicians: How could evolution produce mathematicians from a cloud of cosmic dust?"

I shall raise some questions about evolution inspired by considering
what might have happened if Alan Turing had lived longer and thought of
combining his early ideas about discrete Turing machines with his later
ideas about chemical morphogenesis involving mixtures of discrete and
continuous changes. I'll offer some arguments and speculations about
how organisms currently on this planet could have evolved, starting
from lifeless chemicals, and identify a long term research programme
for filling in the details: the Meta-Morphogenesis project, inspired
partly by reading Turing's 1952 paper on chemical morphogenesis. At all
stages there are mathematical structures involved in the evolutionary
progress and evolution blindly discovers and uses them. In later stages
of evolution, individual organisms develop abilities to discover and use
mathematical structures and processes, though without realising what
they were doing. Later still, humans began to think explicitly about
these processes and to discuss their properties. I suggest that
sort of history may have led to the collaborative production of
Euclid's Elements. At present there's very little we know about the
actual history of evolutionary developments. I'll try to show how the
meta-morphogenesis project sets out a strategy for trying to fill the
gaps, with the hope of answering not only evolutionary questions, but
also philosophical questions about the nature of mathematics and how
mathematical reasoning and knowledge differs from other kinds. Perhaps
that will also help us come up with robots and AI systems that are far
more intelligent than the current models are. It may also help us
produce much better mathematical education systems based partly on
deeper insights into the nature of mathematics and into the nature of
biological processes of learning and discovery.

Background to the seminar:

http://www.cs.bham.ac.uk/research/projects/cogaff/misc/mathsem.html

including links to various aspects of the Meta-Morphogenesis project.

The Midlands Logic Seminar was founded in 2011 and aims to cover all areas of mathematical logic, as well as related areas of theoretical computer science, and philosophy of mathematics. We typically have a study group session from 4:00-5:00 (term 1 topic: satisfcation classes) and a research talk from 5:00-6:00.

To get to campus, take train from Birmingham New Street to the University stop (7 minutes).

School of Mathematics

University of Birmingham

http://web.mat.bham.ac.uk/R.W.Kaye/

Dr Walter Dean

Department of Philosophy

University of Warwick

http://go.warwick.ac.uk/whdean