Re: Mathematical Philosophy

On 28 Sep 2013, at 22:06, Melvin Carvalho <melvincarvalho@gmail.com> wrote:

> 
> 
> 
> 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?

All  the first 4 weeks are relevant. If you read the RDF Semantics  document
  http://www.w3.org/TR/rdf-mt/
you'll find 
 - week 1: set theory, ordered pairs, extensionality, deduction being used there 
     notions of infinity are looked at, and always useful 
 - week 2: truth and tarski make their appearance in the RDF semantics doc too 
 - week 3: propositions as sets of possible worlds ( and a bit of week1 )
 - week 4: ...

I have only looked at week 1, and it is really great to go over all this again. It's
a long time I read about this, so I am happy to get a refresher.

For those who are new to this, seeing the paralles between mathematical philosophy
( and not philosophy of mathematics btw ) and the semantic web, will help you
move along much faster, as it will help you tie intutions from differnt spaces together.


> 
> 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
> 
> Hannes Leitgeb
> Ludwig-Maximilians-Universität München (…
> Stephan Hartmann
> Ludwig-Maximilians-Universität München (…
> 
> 

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