People criticized many versions of "Occam's razor," the idea that simple theories should be preferred in science over complex ones.

Think about how these issues might look from the point of view of a subjectivist Bayesian model of evidence in science. Does that view of evidence help us understand why a preference for simplicity might be justified, or might not be justified?

- define terms: occam's razor, simplicity, bayesian model etc.

- go straight to answer the question: how might bayesian model of evidence in science impact simplicity?

- 3 files attached: essay guide (structure) and 2 references to be used

## The Philosophy of Occam’s Razor

In this paper, I will argue that the simple theories should be preferred in science over the complex ones from a subjective point of view using the Bayesian model of evidence in science. In this paper, I will explore the various standpoints of people criticising the several versions of the “Occam’s razor” that inherently talks about the preference of the simple theories over the complex theories that are used in the field of science. As a notion of conclusion, this assignment strives to reflect that the fact that simplicity in science is not always justified and the complexity of the scientific theories are required to be considered as well for deriving the best results.

The advancement of science and technologies has reached a certain height of standards for over the years. Although the scientific theories have been provided with several substantial evidences, there have been criticism as well about the level of complexity of these theories. According to the theory stated by William of Ockham, the theories of science should be of a level that is not beyond the understanding level of common human beings (Engström et al.). The Bayesian model however categorises these uncertainties according to the evidences that supports the level of simplicity in stating the scientific theories. The new radical views of the confirmation and the evidences of the scientific theories forms a viewpoint termed as Bayesianism.

The Occam’s razor is based upon the philosophy that was formulated by the William of Ockham. According to the philosophy, simple theories in the field of science should be preferred than the theories which are devoted in stating complex explanations as these explanations require a lot of speculations to be made than the simple theories of science (Van Den Berg). According to Ockham the abstractions and generalisations were mental concepts that were basically derived from the perceiving of the particulars and categorising them among the similarities, derivations, affinities and the kinds of such type (Vapnik). Conception can be defined as the role of perception of the level of understanding of an individual object in some ways that are corresponding on of the particular concept. However, the abstractions on the other hand were to be regarded as the objects according to their own state. These entities termed as universals were one problem among many that was confined towards making the syllogistic logic more complex, unpretendingly huge and way less powerful than the much more rationalised system that are used today (Van Den Berg). Ockham’s razor principally was devised to provide with faith from the rational enquiries but the modern elaborations of the Occam’s razor states that it is unwise to make a lot of speculations keeping in mind the name of God (Valkenburg et al.).

There may be various ways in which the simplicity can be regarded as the most demanding feature in the field of scientific theories. The simpler theories are often regarded as the easily perceived ones or very much elegant than the theories that are complex in comparison to these theories (Nola, Robert, and Sankey). The simpler theories of science are much easier to understand and is more flexible to work with. However, many of the scientists and the philosophers believe that simplicity is something that cannot be associated with the relevance of the theories that described in the field of science (Rothe and Peter). Additionally they believe that simplicity in the genre of science should not be taken into account every time especially when the researches are taking place absolutely fine and are moving on the right track of discovery. Instead of this, simplicity should be regarded as one of the main criteria to evaluate and select from the theories that are in contradiction to the theory that is being worked upon (Bhaskar and Roy). Simplicity considerations are also considered as the integral to several methods of standardization that the scientists use to interfere with the hypotheses from the empirical data that is the most common explanation of this being the most fitted one.

## The Bayesian Model of Evidence in Science

The Bayesian model or Bayesianism is devoted upon the understanding of the evidence using the theory of probability that is quite a popular ideology. There is a dedicated formula for the justification of the Bayes’s theorem (Efron and Bradley. This theorem is very much simple in the field of mathematics and this idea is very simple. Bayesianism is one of the very best set of ideas that can be used for the explanation of the complexity level of the scientific theories (Godfrey-Smith). There is one simplest form of the Bayes’s theorem and the other formula is useful in depicting the benefits in the application of the scientific theories (Morey et al). These two formulas is based upon the different types of hypotheses and thee evidences. These two formulas are very much effective in explaining the complexity of the theories using the theory of probability. The Bayesian model is entirely based upon the concept about what the audience is about to be experienced with (Salmon and Wesley). The probabilities for the probabilities of hypotheses are far more controversial since the computation of these probabilities are based on the priorities of occurrence. Therefore, although the it is wise to discuss the probabilities of evidence using the theory of probability it would be unwise to use the same to discuss the probability of the hypotheses.

By going through all the above three definitions of the Occam’s razor, the simplicity and the Bayesian model, it is understandable that these definitions play a vital role in shaping up the justification about the interpretation of the complexity of theories in the field of science and research (Van Den Berg). In due course of the investigation of this subjective progress, this has been found out the that most of the attempts to analyse the probability have taken the probabilities to few real and the objective feature of the events. The probability value is considered as calibrating the opportunity for the happening of some particular event. It may be that these opportunities somehow happens to be one of the aspects of the event or its location the world (Popper and Karl). This has also been found out that according to the subjectivist interpretation of the probabilities are the different degrees of belief. A probability is confined towards the measurement of the person’s degree of confidence in the truth of some proposition.

The subjectivist interpretation of the probability is not only important in the field of philosophy but also is equally important in the field of science and economics since it is central to the decision theory. This has been found that the majority of the philosophers who are interested in the usage of the Bayes’s theorem to perceive the idea of an evidence, holds a subjectivist point of view for the various types of probabilities (Berger and James). If not then the point of view is configured towards the applications of the probability theory to these set of problems and sometimes more in a generalised approach. Some of these probabilities are considered as a subjectivist approach because the philosophers feel that the probabilities are required to be in the order of the Bayes’s theorem. People, who are destined upon countering these thoughts, think that the concept of subjectivism is the only interpretation of the probabilities that makes a point anyway (Godfrey-Smith). The debates relating to the philosophy about Bayesianism also links to the debates about the probability within thin the mathematical statistics itself.

## The Role of Simplicity in Scientific Theories

As mentioned earlier, the subjective interpretation of probability of a certain individual is based upon the degree of his belief in the propositions or the hypotheses about the world. The Bayesianism model sometimes treat the people as not the actual people but in a form of idealized people (Gelman et al). According to the Bayesian point of view, all the events occurring in the lives are somehow related with the various nodes of probability and as probability is related with the measurement of chances created for the events there may be several risks associated with these events. Even the scientific theories are based on the probability of occurrence. Therefore, the complexity for setting up of each of them must be considered according to the way they are being stated and not by the degree of complexity they are associated with (Vehtari et al.). A person’s system of belief within a particular state of time can be described as a collective mesh of the subjective probabilities. These subjective probabilities are focussed towards the concern of the respective person’s behaviour.

The people who strongly have a strong belief on the Bayesian’s model acclaims to state one of the theory that is entirely based on the fact the a person’s total network for the degrees of belief is confined to a certain standpoint and depicts the calculative implications of reflecting a point that is rational in nature (Godfrey-Smith). These people who are strongly agreeable to the Bayesian model argue that a coherent set of the degrees of belief is bound to follow the standard rules of the mathematics of probability (Rigoux et al.). The treatment of the probabilities are acted upon by the support of simple series axioms. These axioms say that all the probabilities are in the number of 0 and 1. According to the second axiom, it says that if a proposition is a tautology then it has the probability of 1. The third axiom say that if one hypotheses h and h* are exclusive alternatives then P(h-or-h*) = P(h) + P(h*). The fourth axiom say that P(h|j) = P(h&j)/P(j) if P(j) > 0. The Bayes’s theorem is the consequence of the fourth axiom that has been mentioned here. The Bayes’s theorem can be broken down as P(h|j)P(j) and as P(j|h)P(h). Therefore, these two equations are equal to one another and the Bayes’s theorem follows trivially.

The argument that has been inferred from these two axioms state that if the degrees of belief do not follow the principles of the probability of calculus then there are possible gambling situations in which the person is guaranteed to fail no matter if the outcome of the event is positive or negative. The notion of guarantee is there because these are the situations in which an individual entirely depends upon the randomness of the event and not even a slightest inclination is tilted towards the positive outcome of the event through which the individual is capable of favouring himself (Marin et al.). Thus in the context of science it can be said that the complexity of the scientific theories does not only depends on the interpretation of thoughts but also on the methods through which these thoughts are being arranged in a manner that will be suitable for the successful outcome of the scientific research.

## Subjectivist Interpretation of Probability

Thus in the summing up of this section in the most holistic approach, it can be said that according to the subjective interpretation of probability, there is not a single way out. These are the outlets that only a single set of degrees of belief can be considered as the belief and has the capability of moving towards the ideal facts of probability of an event (Godfrey-Smith). Therefore it is necessary to consider both of the degrees of probability. Relating with the context of science, it can be said that the Occam’s razor is partially true where certain simpler ideas of the theories can be preferred. In addition to all these, the wider concept demands the consideration of the complex theories of science as well so as to go in par with the development of new ideas and innovations in the field of scientific researches (Friston et al.). These are ways by which the issues arising with the complexity of the theories can be judged with a series of justification. Though some of the Bayesian people considers both the objective and the subjective agreements of interpretation of the probability of the scientific theories.

From the sections mentioned in the above parts of this essay, it can be said that the Bayesian model is helpful in determining the randomness of the complexity level of the several scientific theories. Accordingly, it also states that while working with the deductions drawn by the Occam’s model are true but the model is not suitable for every cases in the field of scientific research. The complexity level depends upon the level of perception of an individual but along with that an extra effort should be made towards simplifying the scientific theories to the possible maximum level.

The definitions of the Occam’s razor, the simplicity in the context of science along with the Bayesian model has been discussed in the first section of this assignment. The second section of the model is focussed towards the justification of the fact how the Bayesian model of evidence impacts the level of simplicity in science. An approach has been taken to show how the view of evidence is beneficial towards justifying the preference of simplicity in the field of science. Thus, the assignment strives to reflect that the fact that simplicity in science is not always justified.

References

Berger, James O. Statistical decision theory and Bayesian analysis. Springer Science & Business Media, 2013.

Bhaskar, Roy. A realist theory of science. Routledge, 2013.

Efron, Bradley. "Bayes' theorem in the 21st century." Science340.6137 (2013): 1177-1178.

Engström, Kerstin, et al. "Applying Occam's razor to global agricultural land use change." Environmental Modelling & Software 75 (2016): 212-229.

Friston, Karl J., et al. "Bayesian model reduction and empirical Bayes for group (DCM) studies." Neuroimage 128 (2016): 413-431.

Gelman, Andrew, et al. Bayesian data analysis. Chapman and Hall/CRC, 2013.

Godfrey-Smith, Peter. "Bayesianism and modern theories of evidence." Theory and reality. An introduction to the philosophy of science. The University of Chicago Press Chicago/London, 2003. 202-218.

Marin, Jean?Michel, et al. "Relevant statistics for Bayesian model choice." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 76.5 (2014): 833-859.

Morey, Richard D., et al. "Why hypothesis tests are essential for psychological science: A comment on Cumming." Psychological science 25.6 (2014): 1289-90.

Nola, Robert, and Howard Sankey. Theories of scientific method: an introduction. Routledge, 2014.

Popper, Karl. Realism and the aim of science: From the postscript to the logic of scientific discovery. Routledge, 2013.

Rigoux, Lionel, et al. "Bayesian model selection for group studies—revisited." Neuroimage 84 (2014): 971-985.

Rothe, J. Peter. The scientific analysis of personality. Routledge, 2017.

Salmon, Wesley C. The foundations of scientific inference. University of Pittsburgh Press, 2017.

Valkenburg, Wessel, Valerio Marra, and Chris Clarkson. "Testing the Copernican principle by constraining spatial homogeneity." Monthly Notices of the Royal Astronomical Society: Letters 438.1 (2013): L6-L10.

Van Den Berg, Hugo A. "Occam's razor: from Ockham's via moderna to modern data science." Science Progress 101.3 (2018): 261-272.

Vapnik, Vladimir. The nature of statistical learning theory. Springer science & business media, 2013.

Vehtari, Aki, Andrew Gelman, and Jonah Gabry. "Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC." Statistics and Computing 27.5 (2017): 1413-1432.

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