Archive for the ‘teaching’ Category

More Precisely

Wednesday, March 11th, 2009



Math for philosophers.

I like when people I like write books I like (what’s not to like?). Case in point: More Precisely: The Math You Need to Do Philosophy by Eric Steinhart, my good buddy and colleague at the Department of Philosophy of William Paterson University. [Link to publisher’s website.] (Have you Brain Hammer-heads seen the ad on Leiter’s blog?) I am geekily excited to own a single reference work where I can look up philosopher-friendly explanations of, for example, Bayes’s theorem, transfinite cardinalities, counterpart-theoretic modal semantics, and finite state automata. Damn! That’s cool. Dig this table of contents: [link].

I look forward to seeing what the general uptake of this book is going to be. I wonder, for instance, about the viability of an undergraduate philosophy course designed around such a text. Imagine a philosophy curriculum that, say, de-emphasized the cranking out of proofs in the sentential and predicate calculi and created room for a broad survey of the math needed to keep up with advances in contemporary analytic philosophy. Imagine increasing numbers in the profession who assuage their math envy with fewer fake formalisms (”S knows that P…”) and more real math.

The Shadow Problem as a Metaphilosophical Test Case

Wednesday, November 14th, 2007

The shadow problem is a cute little puzzle about the metaphysics of shadows.

Consider four objects, L, A, B, and C arranged like this

*L*_____[A]_____[B]_____(C)

where L is a lamp providing the only light, A and B are opaque objects, and no light is falling on C.

Consider also some non-controversial propositions concerning shadows, their casters, and shaded objects.

1. An object can cast a shadow only if it is opaque and light is falling on it.
2. Shadows cannot be cast through opaque objects
3. An object is in the shade only if some other object is casting a shadow upon it.

Here’s the problem: Is C in the shade? If it is, then by principle 3 either A or B must be casting a shadow on it. However, principle 1 rules out B as the shadow caster, since no light falls on B and principle 2 rules out A, since A’s shadow can’t be cast through B. We are led to the absurd conclusion, then, that C is not in the shade.

Further reflection may lead us to reject one or more of the three principles. Or increase their number to four or more. (Personally, I’m a shade and shadow eliminativist.)

While the shadow problem is fun to regard as a first-order philosophical problem, I like how it reflects on various higher-order problems, like: what are philosophical subject matters and methods? Or: when, if at all, do philosophers ever arrive at solutions to problems?

One thing I especially like these days about the shadow problem is how it illustrates to students what a philosophical problem is. It’s pretty clear, I think, that this isn’t going to be solved by simply opening the dictionary, or asking the scientists in the department of shadow studies.

Some other meta-philosophical issues I’ve been thinking about in connection with the shadow problem are:

What, if anything, is added by describing anything here as intuitive or as deliverances of intuition?

Would the methods of experimental philosophy do a damn bit of good here? Suppose that there were survey results demonstrating a small yet statistically significant difference in people’s willingness to abandon one of the propositions? Would that thereby make one solution to the problem better than another?

(My presentation of the shadow problem is adapted from the way Peter Suber formulates it [link]. (For other formulations and a brief history of the problem, see pp39-40 of Roy Sorensen’s 1999 J. Phil article “Seeing Intersecting Eclipses”.))

Wanted: Philosophy Examples for Sentence Logic

Thursday, September 20th, 2007

I’d appreciate any suggestions of cool philosophical arguments or puzzles that exemplify (or lend themselves to the exemplification of) key concepts of the sentential calculus.

I find it’s much easier to come up with this sort of thing for the predicate calculus. For example, discussions of Anselm’s ontological argument for the existence of God or Descartes’s argument for substance dualism (or the Heideggarian suggestion that nothing noths) are fun to discuss with students who can handle symbolizations with quantifiers and predicates. But I’m sniffing around for fun things of philosophical applicability to do with students who are just learning to toss around the dots, vels, tildes, and horseshoes.

Thanks in advance!

Monsters of Logic

Monday, September 17th, 2007
Monsters of Logic

Monsters of Logic,
originally uploaded by Pete Mandik.

It’s that time of the semester again: time to tell logic students the bad news that material conditionals are false only when they have true antecedents and false consequents.

I’m always looking for new ways to take the sting out of the false antecedent cases. Poking around the internet yielded some nice resources.

I especially liked this survey of methods of teaching material conditionals: A Comparison of Techniques for Introducing Material Implication

See also:
Conditional Statements and Material Implication
and
Material Implication Revisited