• TheMadFool
    13.8k
    Occam's Razor is an abductive heuristic used in scientific hypothesis construction and in other situations where we're looking for an explanation for something. The bottomline of Occam's razor consists of the following rule:

    Entia non-sunt multiplicanda praeter necessitatem (Entities must not be multiplied beyond necessity) — Wikipedia

    The wikipedia article, if you wish to pursue the topic further, is detailed enough and provides a variety of views on the logic behind Occam's Razor, its impact on science, its limitations and so forth.

    That said, in this post, my aim is to provide a simple proof of Occam's Razor and I would like you all to give your views on whether my proof is any good or not.

    My proof will require an imaginary scenario but it will, in all likelihood, be familiar enough to you all. Mutatis mutandis, the scenario is applicable to science and all other occasions where an explanation is being sought.

    Imagine a doctor who's called to a house where young girl has fallen ill. He picks up the necessary medical equipment and arrives at the house.

    Upon arriving he notices that the family has also consulted the local shaman and he's also at the house, looking into the matter of the girl's illness.

    The doctor greets the family and ask to be taken to the patient. After inquiring into the illness and its circumstances the doctor comes to the conclusion that the likely cause is food the girl ate at a neighbor's house the other day.

    The shaman too carries out his own investigation and comes to the same conclusion - it's the food the girl ate at her neighbor's - but then the shaman doesn't stop there; he claims that the neighbor is a witch and that there's an evil spirit that possessed the girl through the food and is making her sick.

    Let's now compare the explanatory hypotheses of the doctor and the shaman, assigning made up probabilities to each component of the hypotheses:

    Doctor's hypothesis:

    1. The food the sick girl ate at her neighbor's is the cause. Probability of this being true is, say, 2/3 = 67%

    The probability the doctor's hypothesis is true = 67%

    Shaman's hypothesis:

    1. The food the sick girl ate at her neighbor's is the cause. Probability of this being true is, say, 2/3 = 67%

    AND

    2. The neighbor's a witch. The probability of this being true is, say, 3/4 = 75%

    AND

    3. There are evil spirits. The probability of this being true is, say, 9/10 = 90%

    The probability that the shaman's hypothesis is true = (67%)*(75%)*(90%) = 45%

    As you can see, even when I assigned high probabilities to components 2 (neighbor's a witch) and 3 (there are evil spirits) for the shaman, the shaman's hypothesis is less probable than the doctor's hypothesis: shaman's hypothesis has a 45% chance of being true and doctor's hypothesis has a 67% chance of being true.

    The only relevant difference between the doctor and the shaman is the number of components ("entities") required to explain the girl's sickness: the shaman's hypothesis has more components ("entities") than the doctor's. And we observe, very clearly, that multiplying entities reduces the overall probability of a hypothesis being true.

    Ergo, since multiplying entities in a hypothesis reduces the probability of the hypothesis being true, Occam's Razor is a well-justified rule.

    :chin:

    N.B: An important part of Occam's Razor is what exactly do "entities" mean? Since Occam's Razor is about explanatory hypotheses, we need to review what they (explanatory hypotheses) are?

    An explanatory hypothesis, for me, attempts to provide some reasons why some possibilities are observed as facts of this universe and some possibilities don't actualize. The way an explanatory hypothesis is built resembles the familiar axiomatic systems of math: some initial propositions are assumed as true and then the explanatory hypothesis is constructed around these initial propositions or "axioms". Given this is true about explanatory hypothesis, the only viable candidate I see as a referent for "entities" are the initial propositions of an explanatory hypothesis for there is no sense in which any other component of an explanatory hypothesis can multiply i.e. increase numerically.
  • Wayfarer
    22.4k
    So what do you reckon old Bill would make of the multiverse? I reckon he’s be turning in his grave.
  • TheMadFool
    13.8k
    So what do you reckon old Bill would make of the multiverse? I reckon he’s be turning in his grave.Wayfarer

    Entities must not be multiplied beyond necessity is all I can say. :chin:
  • Wayfarer
    22.4k
    doesn’t apply to the Universe?

    Actually on a more serious note, there’s something your OP doesn’t say, which is what the types of ‘entities’ were that Ockham had in mind. It was something of high philosophical significance. Any guesses as to what?
  • TheMadFool
    13.8k
    doesn’t apply to the Universe?

    Actually on a more serious note, there’s something your OP doesn’t say, which is what the types of ‘entities’ were that Ockham had in mind. It was something of high philosophical significance. Any guesses as to what?
    Wayfarer

    Yes, what do "entities" refer to? In my humble opinion, "entities" are the components of an explanatory hypothesis that together enable a given hypothesis to give an account of observation(s) in question. I've interpreted "entities" as those propositions that must be assumed as true for a hypothesis or explanation to do its thing - explain!

    What else could "entities" mean?

    P.S I've made some changes to the OP, if you'd like to have a look.
  • Wayfarer
    22.4k
    What else could "entities" mean?TheMadFool

    There is an answer to that, which is highly specific to William of Ockham and his place in intellectual history. Hint: it is mentioned precisely once in the Wikipedia article on his Razor.
  • TheMadFool
    13.8k
    There is an answer to that, which is highly specific to William of Ockham and his place in intellectual history. Hint: it is mentioned precisely once in the Wikipedia article on his Razor.Wayfarer

    Thank you very much. I don't know if the wikipedia article was edited in the past couple of hours because I didn't see it there when I read it last. I wonder what Occam would've thought about that? :chin:

    Occam's razor says that when presented with competing hypotheses that make the same predictions, one should select the solution with the fewest assumptions, and it is not meant to be a way of choosing between hypotheses that make different predictions. — wikipedia
  • Frank Apisa
    2.1k
    Occam's Razor should be outlawed in philosophical discussion everywhere.
  • TheMadFool
    13.8k
    This is a profound statement indeed. Speaking for myself, more often than not, philosophical matters tend to be just that bit more complex than first perceived that it prevents a full understanding of a philosophical issue.

    Is it a matter of inherent complexity in philosophy or is it that we're so confused that we fail to see the simplicity?

    "There is more to Occam's Razor than meets the eye" is a perfectly meaningful statement. :chin:
  • Frank Apisa
    2.1k
    "There is more to Occam's Razor than meets the eye" is a perfectly meaningful statement. :chin:TheMadFool

    I agree, TMF.

    And that is the reason I suggest it should be outlawed in philosophical discussions.

    Used incorrectly, which it is 98.7% of the time...it does more to cloud the issues and misinform...than any good.

    I have NEVER seen it used to good advantage on the Internet...where most philosophical discssions seem to occur...and I have been participating in Internet discussions since the late 1990's.
  • deletedusercb
    1.7k
    Occam's Razor is not an ontological hypothesis. It is not suggesting that simplicty is more likely to be true (because things are more likely to be simple, say). It is a methodoligical suggestion that we NOT add entities if it does not add anything. That is, given the choice between two explanations that both work, take the one with the least entities.
  • TheMadFool
    13.8k
    Occam's Razor is not an ontological hypothesis. It is not suggesting that simplicty is more likely to be true (because things are more likely to be simple, say). It is a methodoligical suggestion that we NOT add entities if it does not add anything. That is, given the choice between two explanations that both work, take the one with the least entities.Coben

    It is sometimes paraphrased by a statement like "the simplest solution is most likely the right one" — wikipedia

    "We may assume the superiority ceteris paribus [other things being equal] of the demonstration which derives from fewer postulates or hypotheses." — wikipedia

    :chin:
  • deletedusercb
    1.7k
    It is sometimes paraphrased by a statement like "the simplest solution is most likely the right one" — wikipedia
    That is decidely wrong. At least it was not Occam's intention or meaning. Further it is not the scientific use of parsimony either. Yes, it is commonly misunderstood as being an ontological hypothesis.
    "We may assume the superiority ceteris paribus [other things being equal] of the demonstration which derives from fewer postulates or hypotheses." — wikipedia
    And this one, presumably quoting Occam or someone who understand or agrees with him is NOT an ontological assertion. 'Other things being equal' eliminates any ontological claim (that simpler things are more likely to be true).
    Here are two explanations not only that the first quote is a misinterpretation of Occam, but really problematic. It's a category error and actually bad science, for example...
    https://towardsdatascience.com/stop-using-the-occams-razor-principle-7281d143f9e6
    https://www.theatlantic.com/science/archive/2016/08/occams-razor/495332/
  • TheMadFool
    13.8k
    https://towardsdatascience.com/stop-using-the-occams-razor-principle-7281d143f9e6
    https://www.theatlantic.com/science/archive/2016/08/occams-razor/495332/

    The author of the first article disregards

    1. The fact that a hypothesis is considered adequate only when all observations have been explained - the hypothesis has to be complete.

    2 The clause "beyond necessity" in Occam's Razor is there to ensure that the above requirement isn't sacrificed for simplicity.
  • tim wood
    9.3k
    Actually on a more serious note, there’s something your OP doesn’t say, which is what the types of ‘entities’ were that Ockham had in mind. It was something of high philosophical significance. Any guesses as to what?Wayfarer

    Universals. He was a nominalist opposing scholastic realism.
  • Wayfarer
    22.4k
    Right! That is the missing context from the OP. As the linked Wikipedia article notes, many others, right back to Aristotle, were all for parsimony when it comes to postulates. But the 'entities' which Ockham wished to eliminate were indeed universals.

    From the opening pages of Richard Weaver's 1948 book, Ideas have Consequences:

    Like Macbeth, Western man made an evil decision, which has become the efficient and final cause of other evil decisions. Have we forgotten our encounter with the witches on the heath? It occurred in the late fourteenth century, and what the witches said to the protagonist of this drama was that man could realize himself more fully if he would only abandon his belief in the existence of transcendentals. The powers of darkness were working subtly, as always, and they couched this proposition in the seemingly innocent form of an attack upon universals. The defeat of logical realism in the great medieval debate was the crucial event in the history of Western culture; from this flowed those acts which issue now in modern decadence.

    :up:
  • deletedusercb
    1.7k
    1. The fact that a hypothesis is considered adequate only when all observations have been explained - the hypothesis has to be complete.TheMadFool
    He doesn't disregard it, he does say that many people do. And again this has little to do with Occam no intending to make an ontological claim, but rather methodological suggestion.
  • TheMadFool
    13.8k
    He doesn't disregard it, he does say that many people do. And again this has little to do with Occam no intending to make an ontological claim, but rather methodological suggestionCoben

    Read the Occam's Razor carefully.
  • deletedusercb
    1.7k
    No, you do that :smile:
  • TheMadFool
    13.8k
    No, you do that :smile:Coben

    I did.
  • TheMadFool
    13.8k
    But the 'entities' which Ockham wished to eliminate were indeed universals.Wayfarer

    Indeed and these universals would qualify as postulates, no?
  • deletedusercb
    1.7k
    Me too. We disagree. We could all tell people we disagree with to study X harder, but it really doesn't move anything forward.
  • TheMadFool
    13.8k
    Me too.Coben

    Then why are you disagreeing with me? :chin:
  • deletedusercb
    1.7k
    That's exactly it, We disagree with each other. Every person in every thread could say to people they disagree with 'study X harder', but it's essentially an ad hom.
  • TheMadFool
    13.8k
    That's exactly it, We disagree with each other. Every person in every thread could say to people they disagree with 'study X harder', but it's essentially an ad hom.Coben

    :lol: Take care. Good day
  • deletedusercb
    1.7k


    It's an implicit claim about me, not my arguments. You haven't read the OR. You haven't read it well enough or you would agree with me.

    That's to the man.

    You claiming to know what I didn't do. You are focusing on me or your assumptions about me, rather than what I have written, my points and arguments, etc. Here implying I haven't read what I should have read.

    It's rude. A small rudeness, in this case, .

    Take care, good day.
  • TheMadFool
    13.8k
    It's an implicit claim about me, not my arguments. You haven't read the OR. You haven't read it well enough or you would agree with me.

    That's to the man.

    You claiming to know what I didn't do. You are focusing on me or your assumptions about me, rather than what I have written, my points and arguments, etc. Here implying I haven't read what I should have read.

    It's rude. A small rudeness, in this case, .

    Take care, good day.
    Coben

    You are right about all of the above. Sorry if I offended you. Not my intention. I have an illness - I get sudden adrenaline rushes and if there's anything that can turn a man into a moron, it's adrenaline. Too excited to think well. Will get back to the issues you raised if and when I understand them. :smile:
  • Wayfarer
    22.4k
    Indeed and these universals would qualify as postulates, no?TheMadFool

    It's not that simple, but I'm not going to try and explain the conflict between scholastic realism and nominalism, which is an enormous topic.

    What's happened is that Ockham's idea was appropriated by later generations in a completely different context. It is now reduced to a principle of explanatory parsimony but in its original context it was about a much larger issue.

    Actually there's a mistake in the second sentence of the Wikipedia article. William of Ockham was not 'a theologian' - he was throughout his career 'a teacher of the Arts' i.e. a philosopher.
  • TheMadFool
    13.8k
    It's not that simpleWayfarer

    These words make me not want to shave :smile:

    What's happened is that Ockham's idea was appropriated by later generations in a completely different context. It is now reduced to a principle of explanatory parsimony but in its original context it was about a much larger issue.Wayfarer

    Agreed.

    @Coben

    I just want to know how ontology is relevant to Occam's Razor. You claimed that Occam's Razor is not an ontological claim. Where do you want to go with that?
  • tim wood
    9.3k
    We don't always agree, but I appreciate clarity when I see it (we know it by our own difficulties in trying to achieve it).. Well said.
bold
italic
underline
strike
code
quote
ulist
image
url
mention
reveal
youtube
tweet
Add a Comment

Welcome to The Philosophy Forum!

Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.