a new appreciation for modal logic

As I venture deeper into my studies, I’m beginning to reaffirm my confidence in modal logic.  This is primarily a function of seeing how it can be used at an applied/industrial level.  I’m only beginning to understand, or in some cases, conjure, ways in which a logical model of a database, for instance, might be describable in modal propositional logic.  Since I haven’t been able to achieve this at a sufficient level, I’ll hold off on sharing my exact thoughts.  Needless to say, even this Stanford Encyclopedia of Philosophy entry on modal logic characterizes some of its commercial and/or industrial application.

The applications of modal logic to mathematics and computer science have become increasingly important. Provability logic is only one example of this trend. The term “advanced modal logic” refers to a tradition in modal logic research that is particularly well represented in departments of mathematics and computer science. This tradition has been woven into the history of modal logic right from its beginnings (Goldblatt, 2006). Research into relationships with topology and algebras represents some of the very first technical work on modal logic. However the term ‘advanced modal logic’ generally refers to a second wave of work done since the mid 1970s. Some example of the many interesting topics dealt with include results on decidability (whether it is possible to compute whether a formula of a given modal logic is a theorem) and complexity (the costs in time and memory needed to compute such facts about modal logics).

My recent attempt involved attempting to translate simple E-R logical data flows into modal propositions, though without quantification it was difficult and/or probably impossible.

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Old habits: maybe they don’t die hard

As an undergraduate, I certainly acted on that impulse to procrastinate. In my limited experience, philosophers or aspiring philosophers are not different in this regard, and in some ways, seem to procrastinate to an even greater degree.

Is this part of the philosopher in me slowly dying? If picture below is any indication, then either (p) I’m growing up or (q) I’m slowly divorcing myself from philosopher-type habits. As it turns out, if p or q, then r: D tracks his assignments.

The emergence of an old problem: if there’s a problem with a reductio, what do you call it?

I’ve been attempting to finish a midterm in one of my classes before July 4th rolls around.  I was delighted tonight to realize that my opinion of one of the arguments I was to assess was to argue against the effectiveness of what I took to be a reductio ad absurdum.

I remember first learning what a reductio was while reading one of Plato’s dialogues.  I can’t remember exactly which one, probably The Theaetetus.  In any event, I came to the familiar question of how exactly to name my opposition to this particualr reductio.  Since a reductio ad absurdum is deductively invalid by definition, I could say “and this is inconsistent because…” The function of the argument WAS to be invalid and thus not sound.

I can’t discuss the specifics, but needless to say, it was entertaining to see a familiar problem arise in a quite distinct context or discourse.

Here are a few legitimate sources of information on reductio ad absurdum’s:

• Standard Encyclopedia article on Democritus

A reductio ad absurdum argument reported by Aristotle suggests that the atomists argued from the assumption that, if a magnitude is infinitely divisible, nothing prevents it actually having been divided at every point. The atomist then asks what would remain: if the answer is some extended particles, such as dust, then the hypothesized division has not yet been completed. If the answer is nothing or points, then the question is how an extended magnitude could be composed from what does not have extension

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