Understanding Occam’s Razor

Introduction

The true objective of Science could be comprehended to be the exploration of various manner through which simpler explanations of complicated facts could be generated. The perception is considerably entrenched that simplicity is the speciality within theoretical constructs of Science. Preferences to simplistic theoretical constructs could be possible when things could be equal. This could be effectively propounded within the history of philosophy and science. This is termed as the Occham’s Razor. Nonetheless, simplicity is also defined in how theories work to explain nature. For instance, the theory might be simpler as compared to other if it consists of fewer adjustable parameters, invokes lesser extraneous assumptions, or gives highly unified data explanation. This paper is supporting the fact that preference for simplicity is justified with the support of Bayesian model of evidence in science. Several philosophers and scientists endorse a methodological principle of “Occham’s Razor”. Occam’s razor defines that if two models have been fitting equally well, then the simpler model is most probably to be an improved description of reality. Bayesian model of evidence in science justified the Occam’s razor as the simpler hypotheses hold higher posterior probabilities if they make a good fit (Baron & Tallant, 2018). It is because the simple model makes sharper predictions as compared to a more complex model. For instance, the consideration for fitting a linear model as well as a cubic model is good. Well, the cubic model is a lot more general and have better data fit. It is because the linear model is highly restrictive and is easier to falsify (Volpi, Schoups, Firmani & Vrugt, 2017). But, if both these models fit, Bayes’ theorem has been “rewarding” the linear model to present a bolder prediction. Occham’s razor quite away from being merely an ad hoc principle and can under several practical situations within scientific field becomes justifiable as the consequence of Bayesian inference (Baron & Tallant, 2018). The Bayesian analysis is able to shed new light over the notion of “simplest” hypothesis being consistent with the meaning of data in actual. It is Bayesian reformulation that means that it is basically the scientific heuristic. It has the intuitive reason stating that the unnecessary hypotheses only make the model more o mistakes and errors (Volpi et al., 2017).

Bayesian model of evidence did not give a mathematical proof for Occam’s Razor being true or other thing, but it has been a proof of defining that under some of the mild assumptions the principle occurs as the consequence (Matt, 2014). It is to decide if hypothesis A or B is the improved statistical model wherein A and B defined the observed data to be equally well, but B is having additional parameter. It is to figure out in probabilistic terms for and . There is a “probability that is the true provided data ” and the “probability of to b true provided the data (Matt, 2014).” (Baron & Tallant, 2018) It is to compare the two quantities as When the quotient is close to, they are approximately equally good models. When the quotient is large, it defines to be the improved hypothesis and in case quantity is near to , then is termed as improved hypothesis. It is not to assume that Occam’s Razor is always the best principle. It is to compare the assumption using Bayes’ theorem for converting the quantities towards things known as (Matt, 2014). Here, certain complexity is present with the hypothesis still as implicitly the assumption depends over certain extra parameter . For simplifying argument, it is assumed that lies in certain range: (Matt, 2014). Once this is specified, there is a uniform possibility of being anything within the range as for within range and otherwise (Volpi et al., 2017). Observable maximizes the function of likelihood for best fit. Select for having interval of providing reasonable certainty of the best . For, is present. This can be plugged into original comparison ratio and being factual that both are equally good to explain data as (Matt, 2014). This provides two main conclusions. First, if we assume the two models to be roughly equivalent predictions over the data that is , thus, is preferred as the plausible range for providing a factor within the numerator to be bit larger as compared to . It is exactly Occam’s Razor. This clearly defines that the extra parameter penalizes the theory (Matt, 2014).

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The connection present between Bayesian statistics and Occham’s razor is quite implicit within the work of Harold Jeffreys (University of Cambridge) who published his book “Theory of Probability” in 1993 (Bickel, 2018). This has been the imperative landmark into modern revival of Bayesian methods. Several others works have proven this connection. Jeffreys discussed an illuminating introduction to the issues that could occur if Occham’s razor is placed towards testing as the implementation of scientific methodology (Velasco, 2017). If some data is being collected on the motion of falling bodies as supposed by Galileo at the Tower of Pisa, the weight is dropped and recorded for its position (s) at various moments (t) during the fall. Challenge is devising the mathematical law to describe the motion (Bickel, 2018). They develops a quadratic equation of s= a + ut + 1/2gt2. The a, u and g are adjustable parameters that remains constant being assignable to arbitrary values for fitting into empirical data. There are available straightforward simple methods for findings these values to reduce certain measure of error. Thus, simple methods are surely more acceptable than complex ones (Velasco, 2017). The problems of justification of the preference of more simple theories could be highlighted as the key aspects regarding philosophical estimates of Science as the consideration of simplicity are apparently central to the methods of Science as well as the actual association between Science and other philosophical problems which are imperative in nature (Blanchard, Lombrozo & Nichols, 2018). Currently, there lacks any agreement between the philosophers about what is termed as the most promising path. Even skepticism is present in several circles regarding if there is an adequate justification plausible (Sober, 2015). The broader perspectives could attest to the fact that simplicity representative accounts generally indicate the nature of truth. More simple theories could be confirmed better through utilisation of empirical information in comparison to complicated ones (Blanchard et al., 2018); other accounts testify of simplicity not being indicative of truth and these outline various methodological alternatives regarding justification of preferences of more simple theories (Sober, 2015); apart from these, various approaches, which are deflationary in nature, reject the perception of the justification of more simple theories. These attempt to analyse various concepts of simplicity concerning the theoretical and other problematic elements of Science (Blanchard et al., 2018).

The historical view, which has been dominant in the “simplicity as an indicator of truth,” has been related to the preference of the theories which are more simplified compared to the ones which are more complicated ones(Green & Armstrong, 2015).. These theories are necessitated to be more grounded over a more generalised thesis of metaphysical nature concerning the simplicity of the nature. A large number of great scientific personnel such as Aristotle, Galileo, Copernicus, Kepler, Einstein, Maxwell and Newton have endorsed this view in an explicit manner. The popularity of the justification related to theology in the early phases of the modern period was of a considerable extent amongst the scientists (Rouder & Morey, 2018). The justification of the meta-inductive nature which was put forward by Einstein, propounded the perception that history of physics could justify the belief that nature is primarily the realisation of the mathematical ideas and opinions which have been simplest in nature. As an instance, the work of the physicists on the atomic nucleus could be mentioned which had taken place during the early phase of the 20th Century and this exemplified the perception that matter is generally comprised of electrons and protons and no other element such as neutrinos or neutrons as well as any other weak or strong nuclear force could be present within the atomic structure could be present and only electromagnetism exists (Green & Armstrong, 2015). An extensive number of various scientific revelations have put forward the argument that the complicated structure of the nature could be responsible for the development of infinitely greater complicated theoretical constructs. This further put forward the claim that in spite of the fact that nature could be complicated when it is viewed in terms of various respects which are superficial in their nature, however, a simplicity could be found to be present deep under the fundamental structural aspects of the nature (Rouder & Morey, 2018).

Kaplan (2017) had brought forward the argument that the perception regarding the more simple theoretical constructs having been better in comparison to the complicated ones regarding the various scientific disciplines and these could be regard in the form of fundamental regarding the prioritised principles. This could thus be obvious that the criteria regarding the evaluation of the theories which have been utilised by the scientists had resulted in a reliable manner, in the making of judgements which had been accurate concerning the accuracy of the theoretical constructs. Kaplan (2017) also opined that acceptability of the perception of simplicity being the effective indicator of probability of truth could be a definite fact. However, Kaplan (2017) has also propounded the belief that no empirical establishment of the connection in between the truth and simplicity could be in existence. This has been unconvincing for the various scientists and philosophers who do not regard more simple theories in any obvious manner. Moreover, one amongst the most popular scientific endorsements for Occham’s Razor is present in the work of Isaac Newton’s Mathematical Principles of Natural Philosophy (1687) also where he states 4 different ‘Rules of Reasoning’. Rule 1 is reflective of the perception that only those causalities of natural things could be admitted as sufficient and true which could provide acceptable explanations of the natural phenomena. This could be comprehended from the perspective that philosophers opined that nature always does things purposefully and greater number of causes remain present despite the fact that a lesser number could suffice the explanations (Rouder & Morey, 2018). Nature could be comprehended as simplified so as to not get embroiled within the process of redundancy of causes and issues. Rule 2 could thus indicate that the causalities of natural occurrences which could be similar, could as well be the same as far as could be possible. This perception clearly depicts that these examples are termed as the underlying causality of the process of respiration regarding both men and beasts and even regarding the displacement of stones within the continent of America as well as Europe or regarding the light of the Sun and light emanated from fires of any kitchen or concerning the light which planet Earth and other types of planets reflect (Rouder & Morey, 2018). Newton has not done much for justifying these defined rules, but within the unpublished commentary regarding the book of Revelations, Newton suggested that there could be one of the aspects regarding methodology formulation of Apocalypse (Baron & Tallant, 2018). The rule stated that “for selecting the constructions without straining decreases things towards higher simplicity. Its reason is that the truth needs to be outlined through simplicity as opposed to the factors of confusion or multiplicity based redundancies (Bickel, 2018). This is termed as the God’s work perfection to provide everything with simplistic considerations. When the worldly frame is understood, they need to endeavour to decrease their knowledge for every plausible simplicity (Baron & Tallant, 2018). This needs to seek consistently to acknowledge these defined visions. It is a thought process of Newton that simpler theories must be preferred as they make sense, irrelevant of the aspects of either making Biblical interpretations or outlining the physics based laws. In this respect, the Occham’s Razor could be considered to be correct concerning both the accounts since the creator of the Universe is expected to be God(Velasco, 2017).

Sober (2015) underlined that disputes related to taste do not exist regarding the values of complications and simplicities in various disciplines of art forms. However, the perspective of simplicity concerning Science, could never be related to the inclination of taste only. The existence of the parsimonious paradigms, three in number, which explain the relevance of simplicity aspect, could be considered to be relevant regarding this being acceptable universally (Green & Armstrong, 2015). Paradigm 1 highlights the occasional extensive probabilities of more simple theories. Paradigm 2 expounds the high support which could be received by more simple theories in terms of observations. Finally, Paradigm 3 highlights the relevance of simplicity in some of the cases regarding the actual predictive accuracy estimate formulation (Sober, 2015).

Conclusion

All the paradigms and points given to justify Occham razor perspective hold something important as a common place. Everything relies over the empirical assumptions regarding the problem. Though parsimony is quite relevant for the formulation of judgments regarding what the world is like, still there holds an end with no justification to be unconditional and presuppositionless for Occham’s Razor. The idea is truly supported that the simple theories must be preferred in science over complex ones. This becomes strong with the support of Bayesian model of evidence in science. It is evident to suggest that when extra parameters are added into the scientific concept, it becomes complex to understand and prove. It takes more time to analyze and make it complex for general people to accept the theory. kIn this respect, simplistic theories could be considered to be better in comparison to complicated theories.

References

Baron, S., & Tallant, J. (2018). Do not revise Ockham's razor without necessity. Philosophy and Phenomenological Research, 96(3), 596-619.

Bickel, D. R. (2018). Sharpen statistical significance: Evidence thresholds and Bayes factors sharpened into Occam's razors.

Blanchard, T., Lombrozo, T., & Nichols, S. (2018). Bayesian Occam's Razor Is a Razor of the People. Cognitive science, 42(4), 1345-1359.

Green, K. C., & Armstrong, J. S. (2015). Simple versus complex forecasting: The evidence. Journal of Business Research, 68(8), 1678-1685.

Rouder, J. N., & Morey, R. D. (2018). Teaching Bayes’ theorem: Strength of evidence as predictive accuracy. The American Statistician, 1-5.

Volpi, E., Schoups, G., Firmani, G., & Vrugt, J. A. (2017, April). Bayesian model selection: Evidence estimation based on DREAM simulation and bridge sampling. In EGU General Assembly Conference Abstracts (Vol. 19, p. 6549).