Re: Mathematical Philosophy

On 28 September 2013 21:55, Henry Story <henry.story@bblfish.net> wrote:

> Hi all,
>
>    this is a very interesting course on Mathematical Philosophy,
> that will really help I think in understanding the semantic web.
>
>    https://www.coursera.org/course/mathphil
>

Anything in particular that you find related to the semantic web?

Having studied maths at college, I found graph and network theory quite
related to web principles.  A graph being a topology of related nodes.  In
a network each edge can carry a weight, and you allow these weighting to
flow around the graph much like water through a set of pipes.  I think this
is a key element of the web that has not yet become ubiquitous and amounts
to a system of value creation and flow, creating incentives for people to
do things.

The other thing I have found interesting is the HR14 in terms of data being
invariant from the documents they live in, being a killer feature of the
semantic web, but still not hugely exploited.


>
> The course is in its final week, but you can follow the lectures
> from the beginning. It's free, but I think probably worth subscribing
> now, if I go from my experience following Oderski's Scala course
> where one has to wait to do the course for the next season to come
> along.
>
>   Apart from it being on the web, it does talk about possible worlds,
> Tarski and a number of other topics that came up here recently.
>
>
> About the Course
>
> Since antiquity, philosophers have questioned the foundations--the
> foundations of the physical world, of our everyday experience, of our
> scientific knowledge, and of culture and society. In recent years, more and
> more young philosophers have become convinced that, in order to understand
> these foundations, and thus to make progress in philosophy, the use of
> mathematical methods is of crucial importance. This is what our course will
> be concerned with: mathematical philosophy, that is, philosophy done with
> the help of mathematical methods.
>
> As we will try to show, one can analyze philosophical concepts much more
> clearly in mathematical terms, one can derive philosophical conclusions
> from philosophical assumptions by mathematical proof, and one can build
> mathematical models in which we can study philosophical problems.
>
> So, as Leibniz would have said: even in philosophy, *calculemus*. Let's
> calculate.
>
>
> Course Syllabus
> Week One: Infinity (Zeno's Paradox, Galileo's Paradox, very basic set
> theory, infinite sets).
>
> Week Two: Truth (Tarski's theory of truth, recursive definitions, complete
> induction over sentences, Liar Paradox).
>
> Week Three: Rational Belief (propositions as sets of possible worlds,
> rational all-or-nothing belief, rational degrees of belief, bets, Lottery
> Paradox).
>
> Week Four: If-then (indicative vs subjunctive conditionals, conditionals
> in mathematics, conditional rational degrees of belief, beliefs in
> conditionals vs conditional beliefs).
>
> Week Five: Confirmation (the underdetermination thesis, the Monty Hall
> Problem, Bayesian confirmation theory).
>
> Week Six: Decision (decision making under risk, maximizing xpected
> utility, von Neumann Morgenstern axioms and representation theorem, Allais
> Paradox, Ellsberg Paradox).
>
> Week Seven: Voting (Condorcet Paradox, Arrows Theorem, Condorcet Jury
> Theorem, Judgment Aggregation).
>
> Week Eight: Quantum Logic and Probability (statistical correlations, the
> CHSH inequality, Boolean and non-Boolean algebras, violation of
> distributivity)
> Recommended Background
> We will not presuppose more than bits of high school mathematics.
> Suggested Readings
> We will give you lists of additional references later in the course.
> Course Format
> The class will consist of lecture videos, which are between 8 and 15
> minutes in length. These contain 1-2 integrated quiz questions per video.
> FAQ
> *Will I get a Statement of Accomplishment after completing this class?*
>
> Yes. Students who successfully complete the class will receive a Statement
> of Accomplishment signed by the instructors.
> About the Instructors
> <https://www.coursera.org/instructor/hannesleitgeb>
> Hannes Leitgeb <https://www.coursera.org/instructor/hannesleitgeb>Ludwig-Maximilians-Universität
> München (… <https://www.coursera.org/lmu>
> <https://www.coursera.org/instructor/~342>
> Stephan Hartmann <https://www.coursera.org/instructor/~342>Ludwig-Maximilians-Universität
> München (… <https://www.coursera.org/lmu>
>
>