As always, Joseph, you write well. I have long had a problem with "Occam's Razor" because it does not define "simpler."  William of Ockham was a philosopher of the High Middle Ages. For him, God was real. "God did it" was the simplest explanation, and a very real one. You do not need to google deeply to find political conservatives who denounce the President as a "Marxist Muslim who wants to destroy America."  That explains everything for them.  Personally, I see him as an empty suit managed by VP Joseph Biden, the same way that VP Dick Cheney watched over George W. Bush for those who were centered on George H. W. Bush.  For me, the Grand Conspiracy involves wheels within wheels that we do not perceive. For the simple-minded, the simple explanation is easy to grasp.

Politics aside, consider the problem of the "shortest path" cited below. We all know what street repair is like.  I headed straight up the main street and miles from my destination, traffic crawled. I remembered the signs...  Ah, yes... So, I cut across and went a different way.  That was yesterday. Today, I took the "indirect" route; it was much faster.  So, too, with epistemology.  Right now, I happen to be working on a project in topology.  (It's tough; I'm not that smart.)  My point is that with algebra  in particular and mathematics in general, you can state explicitly what your premises and assumptions are.  So, you can go "three sides around the barn" if you want; but the simplest route is best.  

But politics - morality, ethics, aesthestics, human events and human action in general - the theorems and axioms are not so nicely laid out.  Did America drift away from the individual rights of the Declaration and to the collectivism of Woodrow Wilson because of a progressive conspiracy, or did most people in most times and places just want more government action to solve common problems? Which is the simpler explanation?  

This is summed up in the famous slogan known as “Ockham's Razor,” often expressed as “Don't multiply entities beyond necessity.”  Although the sentiment is certainly Ockham's, that particular formulation is nowhere to be found in his texts. Moreover, as usually stated, it is a sentiment that virtually all philosophers, medieval or otherwise, would accept; no one wants a needlessly bloated ontology. The question, of course, is which entities are needed and which are not.

Ockham's Razor, in the senses in which it can be found in Ockham himself, never allows us todeny putative entities; at best it allows us to refrain from positing them in the absence of known compelling reasons for doing so. In part, this is because human beings can never be sure they know what is and what is not “beyond necessity”; the necessities are not always clear to us. But even if we did know them, Ockham would still not allow that his Razor allows us to deny entities that are unnecessary. For Ockham, the only truly necessary entity is God; everything else, the whole of creation, is radically contingent through and through. In short, Ockham does not accept the Principle of Sufficient Reason. -- http://plato.stanford.edu/entries/ockham/index.html

 

Ockham’s Razor is a principle; that is, it does not tell us that the simplest explanation is true (or what there is); but instead that we ought to prefer it on methodological grounds. We are counselled to adopt theories which are minimally efficient, insofar as they can do the same with less. Note that there is apparently no reason why we should do so: a direct route to a destination is neither better nor worse than a diversion unless we include the criterion that we wish to get there by the most direct route (and even then it may not be, so we will return to this analogy later.) Nevertheless, it seems plain enough that we are inclined to favour the simpler explanation, other things being equal. It is this assumption that we shall now examine. -- http://www.galilean-library.org/site/index.php/page/index.html/_/essays/philosophyofscience/ockhams-razor-r55

We've discussed Wolfram's NKS here before, but I can't help but see the principle of Occam's Razor as being related.

Wolfram's NKS can be summarized as "complexity can arise from simple rules; complexity does not require complex rules."   That doesn't imply that complexity can't also result from complex rules; it simply asserts-- based on observational science and experiment -- that complexity does not depend on complex rules.   Other corollaries are "it isn't usually possible to predict the complexity that can result from simple rules," and another way that same thought is expressed is "the law of unintended consequences."     Wolfram's NKS makes a serious case for making that pithy observation an actual law.

A candidate example is the 'simple' rule of gravity; the 'rule' is understood even if the source of the rule is not.   Ponder for a while all that has emerged in this Universe as a consequence of that 'simple rule.'    One example is, in a Universe made up predominantly of Hydrogen, every element heavier than Hydrogen; all of that minorty consuituent in this Universe-- the heavy elements -- forged inside of stars long dead as a result of gravity.  

I suspect, life itself, as in, colloidal suspensions (muddy water) of species made up of those heavy elements in solution along the shores of ancient seas in shallow pools ordered themselves by density into layers, creating billions of mile-years of lab experiments, gradients of gradients of concentrations of species...ordered by gradient. The driver for that order from chaos was yet again....gravity; the source of gradient.   The result was the building blocks of life; complex molecules and proteins and whatnot until what can happen happened.   A higher abstraction of 'simple rules' -- the combinations of GATC --  resulting in, well, things just like Justin Bieber.  Complexity from a simple rule running loose in the Universe...

I can't help but see these topics as related to the same observations of what goes on in the Universe; complexity from simple rules.

regards,

Fred

(Edited by Fred Bartlett on 7/14, 2:47pm)

"A celibate clergy is an especially good idea, because it tends to suppress any hereditary propensity toward fanaticism." Carl Sagan 

Perhaps a contrary to Occam's Razor is the challenge that "Extraordinary claims require extraordinary evidence."  That is balanced by the assurance of guru Wayne Dyer, "You'll see it when you believe it."  Empedocles of Akragas was not alone in finding seashells on hilltops and then positing that the land was once under the sea. Living close to the sea, experiencing volcanoes and earthquakes, it was easy to believe.  

"William Smith (1769 – 1839) drew the first geological maps of England. He was born into a culture that was certain that the world had been created at 9:00 AM on Monday, October 23, 4004 BC.  He died twenty years before The Origin of Species was published.  Yet, he invented the predictive science of geology by marking time with fossils." -- The Map that Changed the World by Simon Winchester, reviewed on my blog here.  Smith worked in two areas: coal mines and canal building.  Cutting through England, he saw the underlying strata revealed. Coal was money; but farmers wanted to know if they had coal on their land before they let it be dug up. Smith knew how to predict the presence of coal from the geology, from the fossils.  Moreover, he foreshadowed Darwin by asserting (from evidence) that simpler forms of the same species always come beneath more complex forms, never the other way around -- unless the land had been "folded".  That, too, presaged the theory of tectonic plates.  William Smith's mind was open to the facts. They spoke to him simply and frankly and he accepted them.

For Sagan and others, if aliens had visited Earth or if God exists, or if Jesus or Mohammed (among others) were what they claimed, then proof would not be lacking. It would be available to everyone.  But, following Dyer, you have to believe it to see it. That was not the method of William Smith. He did not "believe" anything: he only observed facts and (successfully) attempted to order them.  A similar - less dramatic - story comes from Mendele'ev and the periodic table.  He sought some regular order, but did not know what it would be.  So, he put the characteristics of each element on a card and played solitaire... over a long time...

You could argue that he "believed" that order must exist, but many people believe in "order" and find the cause in God.  William of Ockham himself surely did.  

FB:  There is a scene in one of my favorite movies "Contact" where Jodie Foster discusses Occam's Razor with Matt McConnoughy's religionist character.  The context is, a discussion over 'The Creator' and 'Ellie' requiring proof.  That part of the movie was always a little unsatisfying.  ... researchers looking for -- and finding -- a 'message in Pi' .     The 'message' that was found was graphical; when run out to some massive number of significant digits in some base other than 10, the digits, when placed into a frame of some dimension, displayed a (rasterized) 'perfect circle' ...  

 

Base 13, as I recall.  But several steps in the process of "making sense" of the data led to the final surprising solution.  (See Smith and Mendele'ev above.)  In fact, I think that they actually built the transporters first; and then later they found the circle and pi in base 13 because they expected more information within the message.

But, we have to separate the movie from the book. (Look at all the conservatives who think that Atlas Shrugged is about socialism.  They do not see themselves as others see them.)  For a comparison, the single most popular page on my blog is "What Did Dorothy Learn?"  No one seems to know.

"Well... I think that it ... That it wasn't enough just to want to see Uncle Henry and Auntie Em.  And it's that if  I ever go looking for my heart's desire again, I won't look any farther than my own back yard because if it isn't there, I never really lost it to begin with."

 

That statement is nonsense -- and is not in the original story.   So, credit Hollywood with knowing that no one really wants to be struck dumb in the last minute of a movie.  (I saw that once.  Colossus: the Forbin Project.  Tension builds and builds as Forbin argues with Colossus, with scenes of world capitals presumably falling under Colossus's control, and Forbin insists that people will resist.  And Colossus says, "They will learn to love me."  The End -- but without even the card THE END. End of movie... lights go on...  We sat there.  We thought the film broke...  Someone in back spoke up: "Colossus is Greek for 'leaves ya hanging, folks!'"  It took a few seconds to sink in...

(Edited by Michael E. Marotta on 7/17, 9:47am)

"What Did Dorothy Learn?"  No one seems to know.

Yes, that line always seemed a little vaguely sappy.

I'm still trying to figure out why menacing monkey guards would march around chanting about Oreos.... o RE o.....   O RE o....

But think of the times; 1939, 1940.  Barely out of the Great Depression.  War rumbling in Europe.   There was a lot of sappy being sold.   People were yearning for sappy.

1940.  The Grapes of Wrath.    The kindly old benevolent government Santa Clause character running the clean government camp where decent folks policed the hoedown and kept the criminal capitalist thugs at bay.

"Wherever you see the l'il guy taking it on the chin, I'll be there, Ma Joad."

All kinds of sappy slop being sold back then.   Still is.