[Link] Eleven dogmas of analytic philosophy

crazy88

Closely related to some of Luke's recent discussions about philosophy, philosopher Paul Thagard has recently called for changes to the way we do philosophy:

I prefer an alternative approach to philosophy that is much more closely tied to scientific investigations. This approach is sometimes called “naturalistic philosophy” or “philosophy naturalized”, but I like the more concise term natural philosophy. Before the words “science” and “scientist” became common in the nineteenth century, researchers such as Newton described what they did as natural philosophy. I propose to revive this term to cover a method that ties epistemology and ethics closely to the cognitive sciences, and ties metaphysics closely to physics and other sciences.

In the same article, Thagard also lists eleven areas where modern philosophy goes awry. For example:

3. People’s intuitions are evidence for philosophical conclusions. Natural alternative: evaluate intuitions critically to determine their psychological causes, which are often more tied to prejudices and errors than truth. Don't trust your intuitions.

Source: Philosopher, Paul Thagard

Closely related to some of Luke's recent discussions about philosophy, philosopher Paul Thagard has recently called for changes to the way we do philosophy:

I prefer an alternative approach to philosophy that is much more closely tied to scientific investigations. This approach is sometimes called “naturalistic philosophy” or “philosophy naturalized”, but I like the more concise term natural philosophy. Before the words “science” and “scientist” became common in the nineteenth century, researchers such as Newton described what they did as natural philosophy. I propose to revive this term to cover a method that ties epistemology and ethics closely to the cognitive sciences, and ties metaphysics closely to physics and other sciences.

In the same article, Thagard also lists eleven areas where modern philosophy goes awry. For example:

3. People’s intuitions are evidence for philosophical conclusions. Natural alternative: evaluate intuitions critically to determine their psychological causes, which are often more tied to prejudices and errors than truth. Don't trust your intuitions.

Source: Philosopher, Paul Thagard

Actually, 3-SAT exhibits an interesting behavior where there's a 'phase transition' between likely satisfiable and unlikely to be satisfiable:

In the early 1990s, it was observed that the probability that a random 3-SAT instance is satisfiable exhibits sharp threshold behavior when the control parameter α = c/v passes a critical value (Cheeseman, Kanefsky, and Taylor 1991; Mitchell, Selman, and Levesque 1992). The width of the window in which this solubility phase transition takes place becomes narrower as the instance size grows. Most interestingly, a wide range of state-of-the-art SAT solvers exhibit dramatically longer runtimes for instances in this critical region. Intuitively, note that instances are underconstrained when α is small (there are few constraints, and therefore many solutions), and overconstrained when α is large (thereare many constraints, making it relatively easy to derive a contradiction). The so-called phase transition point occurs between these extremes, when the probability of generating a satisfiable instance is 0.5.

Crawford and Auton (1996) confirmed these findings in an extensive empirical study and proposed a more accurate formula for identifying the phase transition point: c = 4.258 · v + 58.26 · v −2/3 . Kirkpatrick and Selman (1994) used finite-size scaling, a method from statistical physics, to characterize size-dependent effects near the transition point, with the width of this transition narrowing as the number of variables increases. Yokoo (1997) studied the behavior of simple local search algorithms on uniform random 3-SAT instances, observing a peak in the hardness for solving satisfiable instances at the phase transition point. He attributed thishardness peak to a relatively larger number of local minima present in critically constrained instances, as compared to overconstrained satisfiable instances. Hoos and Stutzle (1999) further investigated the behavior of stochastic local search algorithms on random 3-SAT instances at the phase transition, demonstrating substantial runtime variability across sets of instances with the same number of variables and clauses, and showing that the runtime over independent runs on the same instance tends to be exponentially distributed (for near-optimal parameter settings of the algorithm).

So for a random 3-SAT with a googol clauses we could make a very accurate prediction about whether it is satisfiable.

(I was reading about this because even with tinier 3-SATs there's now polynomial-time algorithms with 70% classification accuracy, and I thought this might be useful in a successor to Bitcoin.)

Interesting, although I'm not sure what you say follows:

As the number of clauses increases, so should the number of variables (randomly chosen). That is, the alpha that your result mentions can well fluctuate between over-and-underconstrained values even with a googol clauses. Alpha, being the clauses-to-variables ratio does not increase solely because the clauses increase, since the variables are randomly filled in as well.
Even for overconstrained values of alpha, the problem is still in NP, i.e. exponential in the worst case. Being able to make an accurate prediction for overconstrained values is certainly possible, but would we call that heuristic an "intuition"?