Conference hydra::dejavu

    
    Re.0 Brian - I was wondering the same thing.
    
    Re.1 Perry - I think you were a bit *too* concise for me.  (;^)  
    I didn't get it.
    
    Cindy

RE: < Note 1012.2 by CLUE::PAINTER "Wage Peace" >
-< Try, try again please? >-

Hi, Cindy. Occam's Razor says that if you're presented with a number
of possible solutions to a problem, typically the simplest solution
will be the correct one.

I'm having trouble coming up with a clear illustration right
now...everything that I think of has to do with faith versus fact.
I'll try to come up with one this evening.

Perry

    In his book "Quodlibeta Septem" written about 1320, William of Occam
    (or, sometimes, Ockham) wrote "Entities should not be multiplied
    unnecessarily" (and yes, I did look this up).  This is the original
    statement of what has been come to be known as Occam's Razor.  Modern
    philosophers have broadened the concept a bit.

    It concerns itself with choosing between explanations for an event,
    and advises that all other things being equal, you should choose the
    "simpler."  Depending on the context, simpler can mean a great many
    things, and can be very subjective, but most often it used in a sense
    fairly close to the original statement: the simpler explanation is
    the one which makes fewer and/or smaller assumptions.

    Applying any explanation to any given circumstances requires making
    some assumptions.  If I find a penny on the sidewalk and explain it
    with "it was dropped here accidentally by someone", then I am assuming
    that someone with a penny walked by that spot some time in the past
    and was clumsy, a not very large set of assumptions.  I might consider
    that someone dropped the penny deliberately, but that would involve
    a much bigger assumption -- that the fairly unusual circumstance of
    someone having a motive for throwing away even small amounts of money
    existed.  So I would stick with the simpler explanation, unless there
    was some fact which was inadequately covered by that explanation, or
    which required me to make even more assumptions to account for.

    I could also attempt to explain my "mysterious" penny in terms of
    ghosts leaving the penny there as a specific sign to me.  Unless
    I have specific, independent reasons for believing that (1) there
    are ghosts (2) they wish to give me a message (3) they somehow
    can be assured that I and no one else would find the penny and (4)
    they have the material powers to materialize or transport the penny
    to that spot, then I will very strongly prefer the explanation that
    someone (human and corporeal) accidentally dropped the penny.  I have
    to make too many rather large assumptions for the "ghost theory" to
    be given much weight.

    This last example is important.  If I must assume something for a
    strongly preferred explanation (or for all of a group of preferred theories)
    then I can take the event requiring that assumption as evidence of
    the thing assumed.  This is one way of looking at what "evidence for
    something" really means.  So, for example, I can take the penny as
    evidence that someone with a penny passed that way, since my most
    strongly preferred explanation, accidentally dropped, assumed that (as
    did my runner-up explanation, deliberately dropped by human).

    Contriwise, I cannot say that some event is evidence for something
    because that thing has to be assumed for a more complex theory.  The
    penny simply is not evidence for the existence of ghosts as long as
    a corporeal source is plausible.  It does not matter that the penny
    is *consistent* with the ghost explanation (i.e., that it isn't
    evidence against ghosts having been there), so that we can say that
    ghosts *might* have left it -- it is not evidence of ghosts, their
    intentions or their abilities.

    On the other hand, the existence of a simpler explanation for the penny
    does not constitute evidence against the existence of ghosts, as many
    self proclaimed skeptics seem to assume (though they would vehemently
    deny such an assumption, they continue to act as though it were true).

    It is perhaps too strong a statement for some applications of Occam's
    Razor to describe it as "The simpler explanation is more likely to
    be true."  In some applications of it you might say instead, "use
    the simpler explanation as a working hypothesis since it is equally
    likely and easier to use."

    How's that, Cindy?  Does that help?

					Topher

    Question:  Didn't Occam's Razor run in the Preakness?  
    
    Answer:    No, that was a night mare.
        
    Question:  Who was that razor I saw you with last night?
    
    Answer:    That was no razor, that was my knife.
    
    Just to up the ante on pennies, I would personally include how I
    felt about the penny and its location in my ruminations.  If I got
    strong "vibes" about it, I might be more inclined to consider odd-ball
    explanations.  That is to say, I trust my feelings enough to include
    them amongst the data to be considered.

    DR
        
    

RE: .6 (DR)
    
    Your feelings are included among those observations (weighted by your
    judgement of their reliability) which the competing explanations must
    explain.  Some may disagree with you on the inadequacy of the corporeal
    theories in explaining your feelings, but for anybody who agrees with
    your assesment Occam's Razor applies.  Note that application of the
    Razor brought to the surface the source of the disagreement -- the
    existence/reliability of your gut reaction to the penny.
    
    				Topher 

    Re.4             
    
    Thanks Topher - yes, it makes sense now.
    
    Cindy

Occam's Razor is a type of heuristic that someone might apply when evaluating
different possible explanations.  It is certainly no "law" and is guaranteed
to yield false conclusions when the person framing the question inserts the
wrong set of assumptions as to what's "simple" and what's not.

Of more practical use to practical people than of any theoretical use to
philosophers.
								paul

    
    
    <<ENTER SARCASM MODE>>
    
    Yes and
    
    	IF all X is Y, and
    	   all Z is X, then
    	   all Z is Y
    
    is clearly not a "law" either, but simply a heuristic of no interest
    to philosophers (smart people) though of practical use to practical
    people (grunts -- who are incapable of understanding the beauty of
    of thought untrammeled by the restrictions of mere logic) since it
    is "guaranteed to yield false conclusions when the person framing the
    question inserts the wrong set of assumptions as to" whether or not
    all X *is* Y and all Z *is* X (actually, of course it is not guaranteed
    by any means, but that is no concern to a *philosopher*, only to
    practical grunts).
    
    <<LEAVE SARCASM MODE>>
    
    At root Occam's Razor is a statement about the relative justifications
    for different inductions (generalizations), and, by extension about
    when induction is justified at all.  Other than induction-deduction
    duality it is the only foundation upon which that necessary step in
    reasoning is built.
    
    <<ENTER SARCASM MODE>>
    
    I guess you consider Descartes (first example to come to mine) a
    "practical person" rather than a philosopher, because of his silly
    insistence that he work from the known ("I think") and extend that
    only to that minimum necessary to assume in order to explain that
    which is known ("...therefore I am").  You must feel, for example,
    that he wimped out as a philosopher when he only postulated *two*
    monads rather than an infinite number, since he only had justification
    for the two.  As if *that* mattered to a *real* philosopher.
    
    <<LEAVE SARCASM MODE>>
    
    A philosopher who neglects the Principle of Parsimony is as useless
    as a philosopher who neglects consistency.  A "game" without rules is
    no game at all.
    
    					Topher
    
    (Please excuse the sarcasm -- no insult was intended.  It's just that
    however I tried to say what I wanted it came out somewhat sarcastic
    so I decided to "go with the flow" and let it all hang out.)

    re: .10 (Topher)
    
          A game without rules is no game at all?  I'm surprised you'd
    make that generalization.  Rather, if I were to use those words
    at all, I'd say, "A game without rules is not a game I would play"
    OR "Life is but a game, it has no rules, you can play this game
    anyway you want."
    
    Frederick
    

    	As I was sitting in my chair
    	I knew the arms were not there
    	Nor legs, nor seat nor back
    	But I just sat,
    	Ignoring little things like that.
    
    A game without rules is no game at all, just as a chair without arms,
    legs, seat or back (or reasonable facsimiles thereof) is not a chair.
    
    Most games, however, have broader rules than we choose to play by, and
    many games the rules are actually meta-rules of some number of levels
    which describe how the players are allowed to change the rules as they
    are instantiated at any moment of play.
    
    The secret is to get beyond the rules of the moment and to understand
    the real or meta- rules.
    
    Without rules, our game-goals become accomplished instantly and we
    cannot change them.
    
    					Topher

re: .10

>    Yes and
>    
>    	IF all X is Y, and
>    	   all Z is X, then
>    	   all Z is Y
>    
>    is clearly not a "law" either, but simply a heuristic of no interest

Seems like a statement of transitivity, which holds for some relations but
not for others.  The heuristic is that most of the relations that we find
useful are transitive, which is nice to know.  But it could be i'm missing
the point of the sarcasm.

The types of questions that i see Occam's Razor being misapplied to are
arguments such as whether it's more parsimonious to say that the universe
arose spontaneously from nothing versus being created by a God, etc.  There
are a number of open-ended questions that can't be reduced to a simplest
solution because the terms are not well enough defined, and they are not
questions that are unimportant to philosophy or necessarily "wrong".

These questions are every bit as worthy of the exercise of our intelligences
as are some of the mundane or practical questions we deal with--because they
define our human identity in an important way.  We can't always come to
conclusions by the rote application of logical principles or heuristics--in
some cases a "leap of faith" is required.  You could say that one measure of
intelligence lies in understanding where that leap is truly required as
opposed to where it is just an excuse to avoid having to think.
    
>    (Please excuse the sarcasm -- no insult was intended.  It's just that
>    however I tried to say what I wanted it came out somewhat sarcastic
>    so I decided to "go with the flow" and let it all hang out.)

That's okay.  I like you and i enjoy reading your notes, Topher.  A
conversation where everyone agreed about everything would get pretty boring!

								paul

RE: .13 (paul)

>re: .10
>
>>    Yes and
>>    
>>    	IF all X is Y, and
>>    	   all Z is X, then
>>    	   all Z is Y
>>    
>>    is clearly not a "law" either, but simply a heuristic of no interest
>
>Seems like a statement of transitivity, which holds for some relations but
>not for others.  The heuristic is that most of the relations that we find
>useful are transitive, which is nice to know.  But it could be i'm missing
>the point of the sarcasm.

    'Fraid I was being a bit too obscure.  The above is certainly an
    example of a transitive relation not a general statement of
    transitivity:  "is" is not a placeholder, but a specific relation.

    In particular this is one of the classic "syllogisms", the set of
    templates which was the foundation of "classical logic" which in turn
    was the foundation of classical philosophy.  Until George Boole, this
    was what was meant when someone referred to Logic.

    In modern terms the "is" relation combines aspects of the membership
    and subset (of first-order sets) relation.  In reality the
    "all" and the "is" were considered one relation, the others dealt with
    in the system were "Some ... are ..." and "No ... are ...".  A
    typical instantiation of this syllogism might be:

	    All Greeks are people and
	    Aristotle was a Greek, therefore
	    Aristotle was a person.

    (notice that there was some grammatical transformation involved in
    using this syllogism in English with a singular set, i.e., the set
    of all Aristotle).

    The point is that this is *not* a heuristic, but a logical rule, a
    "law of reasoning" so to speak.  If you violate this rule then your
    reasoning is flawed, and you have stated an unjustified belief *not*
    done philosophy.

>The types of questions that i see Occam's Razor being misapplied to are
>arguments such as whether it's more parsimonious to say ...
arose spontaneously from nothing versus being created by a God, etc.  There
>These questions are every bit as worthy of the exercise of our intelligences
>as are some of the mundane or practical questions we deal with--because they
>define our human identity in an important way.  We can't always come to
>conclusions by the rote application of logical principles or heuristics--in
>some cases a "leap of faith" is required.  You could say that one measure of
>intelligence lies in understanding where that leap is truly required as
>opposed to where it is just an excuse to avoid having to think.

    There is a big jump from "there are specific philosophical questions
    which I believe Occam's Razor has been misapplied to" to "Occam's
    Razor is simply a heuristic of some use in practical problems but
    of no use in solving philosophical problems."

    I never said that Occam's Razor was applicable to all issues nor that
    it was the only principle which was important when it is applicable.

    In doing philosophy one makes certain assumptions, examines the
    consequences of those assumptions and demonstrates that those
    consequences have some bearing on perceived reality.  It isn't
    philosophy if you stop at the assumptions ("leaps of faith") and
    never justify those leaps of faith as being in some sense plausible
    or fruitful.  You are not doing philosophy if you just say "this is
    the way I want the universe to be."

    Occam's Razor applies unambiguously when there is a clear or at least
    undisputed metric of simplicity (e.g., when the second hypothesis makes
    exactly the same assumptions as the first, but makes additional ones
    as well) and when all other factors (e.g., explanatory power) are
    equal.  If you present me with a hypothesis about the origin of the
    universe and claim that it is better than another, apparently simpler
    hypothesis, you must either demonstrate either that an alternate,
    plausible simplicity metric exists under which your hypothesis is
    simpler or that there are other valid factors which outweigh
    simplicity.

    One of the strengths of Occam's Razor is that to apply it *properly*
    you must make explicit your assumptions and the metric you use under
    which you claim greater simplicity for that set of assumptions.

				    Topher

    Ockham's Razor is named after William of Ockham, a mediaeval monk
    as a previous reply stated.  His monastery was in the Surrey village
    of Ockham, near the M25/M3 junction and, although its name may have
    been spelt differently then, that is why I prefer the spelling
    "Ockham".  Incidentally there isn't even a shop in the village,
    which disappointed me because I had hoped to buy a razor there.
    
    Ockham wrote, in the original Latin, "Essentia non sunt multiplicanda
    praeter necessitatem", which translated loosely but in spirit means
    "entities should not proliferate beyond necessity".  The entities
    he refers to are those involved in explaining occurrences; thus
    the basic idea is "select the simplest theory which fits the facts
    well".  That last word "well" is crucial, as will be shown.
    
    Ockham's Razor principle has for centuries been part of philosophy;
    but just as deductive logic was invented by the ancient Greeks, and
    was finally translated into mathematics by George Boole in the last
    century (and anybody who works for a computer company and hasn't
    heard of Boolean Logic should be shot), Ockham's Razor now has a
    precise mathematical framework.  Mathematics is ultimately just
    a shorthand and is not essential to deployment; but it is such an
    effective tool that not to use it handicaps one.  (This will not
    become mathematical, by the way; I just want to make that point.)
     The mathematics underlying Ockham's Razor is in fact probability
    theory; to explain some experimental data one can consider two (for
    simplicity) theories, one with many adjustable constants which can
    be chosen to fit the data closely, the other with fewer constants.
     Intuitively, the fewer-constant theory is more attractive; on the
    other hand it may not be able to fit the data as closely as the
    other theory.  The many-parameter theory is  less attractive
    intuitively because it distributes some of the probability of the
    parameters where the data indicate they are very unlikely to be.
     There is a trade-off between number of parameters and goodness
    of fit, which probability theory makes precise and enables one to
    decide which theory is more probable.
    
    Of course, in many examples of human thought, translating this into
    mathematics is far beyond presentday techniques. But this is
    nevertheless the basic idea.

    re .15:
    
    I'm afraid I don't understand. Precisely *how* is Occam's razor put
    into mathematics? I'm a philosopher and a mathematician and rather
    confused.
    
    	Jon

Any solid evidence on why Ockham's Razor is called a "razor", before I go off
propounding theories, analyzing probabilities, and shooting down hypotheses?
									-Kevin

    If used as a practice it cuts away needless entities.
    
    I'd like to see your stuff.

Of course, that's exactly what seems reasonable.  But I've never actually seen
proof of where the "razor" comes from, or why it was called "razor" exactly.
Why not "knife" or "blade" or "sledgehammer"?  How did Ockham, himself, refer to
this principle?  Who coined the term "Ockham's Razor"?  When?  How do you go
about tracking down the origin of a phrase?  Any phrase.
							-Kevin