A reflection on modeling and the nature of knowledge
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This document discusses modeling as a method for generating scientific knowledge. It defines key criteria for knowledge to be considered scientific, including being falsifiable, generalizable, and the method being replicable and rationally linked to the claim. Modeling is proposed as an explicit method that meets these criteria when assumptions are clearly defined. While not all domains are scientifically knowable, modeling can be applied to study objects across various fields. The framework is presented as pragmatic rather than ideological and open to challenges from different perspectives like feminism.
![Bibliography
Gary King, J. P. (2013). How Censorship in China Allows Government Criticism but Silences
Collective Expression. American Political Science Review.
Guilliam, T., & Jones, T. (Directors). (1975). Monty Python and the Holy Grail [Motion Picture].
Juola, P. (2015). The Rowling Case: A Proposed Standard Analytic Protocol for Authorship
Questions. Digital Scholarship in the Humanities.
McCain, K. (2015). Explanation and the Nature of Scientific Knowledge. Science & Education,
827–854.
McCain, K. (2016). The Nature of Scientific Knowledge. An Explanatory Approach. Switzerland:
Springer.
Meagher, M. (2020). Contemporary Feminist Theory. In G. Ritzer, & W. Wiedenhoft Murphy, The
Wiley Blackwell Companion to Sociology (pp. 398-416). Hoboken: John Wiley & Sons .
Popper, K. (1978). Three Worlds. The Tanner Lecture on Human Values. Delivered at the
University of Michigan.](https://image.slidesharecdn.com/areflectiononmodelingandthenatureofknowledge-200613225520/85/A-reflection-on-modeling-and-the-nature-of-knowledge-34-320.jpg)
A reflection on modeling and the nature of knowledge
- 1. A Reflection on Modeling and the Nature of Knowledge
- 2. Social vs. Natural Science Do methodologies for the social and natural sciences need to be intrinsically different?
- 4. Knowledge Falsifiable, General, Fruitful and Cumulative
- 5. Falsifiable Competing ideas contribute to the accumulation of knowledge because they are falsifiable, if there were not, a mounting body of contradictory factoids will clutter our understanding and impede progress altogether. This is not a philosophical position, but a pragmatic one. • One afternoon in the seventeenth century, Galileo allegedly dropped three balls of steel from the Tower of Pisa. • The balls had different sizes and weights and, contrary to common knowledge at the time • They all landed simultaneously
- 6. General, Fruitful and Cumulative “My coffee mug is blue” • Falsifiable • Likely be validated by countless independent methods • Of Little relevance beyond my immediate reality • One of the most influential theories of all times. • Key to modern evolutionary biology • Inspiration to theories outside biology such as game theory, linguistics and economics Darwin´s Theory of Evolution We sustain than it does, and that failing to apply it when constructing social theory can have dire consequences, the least of them being stagnation. • Why then, should we still hold to an exuberant variety of schools of thought in the social sciences? • Is it because the principle of accumulation and self-updating in the natural sciences simply does not apply?
- 7. Object of Study Measurable, Universal and Ubiquitous
- 8. Object of Study (Reality) • Does an objective world exist independently from the observer? • If so, can it be comprehended? • To quote Erwin Schrödinger, we assume that “the display of Nature can be understood” • Because if not, the pursuit of scientific knowledge is simply futile, and the conversation is over.
- 10. Our Modified Ontology The subset of elements within this ontology that are knowable is our object of study and what we call science is not a product but a process that generates claims, assembles theories and most importantly revises itself as claims are falsified.
- 11. The Process of Science As the network of claims grows exponentially from these inputs. The “most current edition” is the most relevant, because not only holds the claims that we consider true, but because it has discarded those that are not.
- 12. To Measure or not to Measure • The purpose of studying objects in any of these universes is to make falsifiable claims about their properties, which implies assigning an objective and intersubjective value to such claims. • Theory of Measurement provides a theoretical framework that, at a very basic level, consists on defining a homomorphism between an empirical relational system and a formal one, such that the relationships between the empirical objects are represented congruently by the measurement system defined by the morphism. • For our purposes, the general notion of measure as the assignment of a formal value to a property of the system under measurement will suffice.
- 13. To Measure or not to Measure • Without a measurement, claims cannot be falsified and hence do not belong to our framework. However, that does not mean that measurements must be infinitely precise. • The level of aggregation at which we study reality, together with the claim we want to make, determine the required accuracy and precision of our measure. • Investigating whether a certain breed of dog can distinguish the colors displayed by a stoplight. We only need a measure that distinguishes red, yellow, green, and “other”. • On the other hand, if our prospective claim is about the human limits to detect different colors, we might want to measure frequencies in the light spectrum.
- 14. Local vs. Universal Our knowledge that people have two legs and two feet allows us to design pants and cars and shoes and create games like football. Generality spawns knowledge, enables technology and it has undeniably changed all three universes in our framework. “My coffee mug has a handle” • Falsifiable • Likely be validated by countless independent methods • Of Little relevance beyond my immediate reality (local) • Falsifiable • General (universal) • Explains my mug and all others “All mugs have a handle”
- 16. Method: Replicable and rationally linked to claim “The fact that the standards of scientific success shift with time does not only make the philosophy of science difficult; it also raises problems for the public understanding of science. We do not have a fixed scientific method to rally around and defend.” Steven Weinberg
- 17. Method: Replicable and rationally linked to claim We confine the term method to the mechanism that connects knowledge to the object known: • Measuring the value of a property, • Making an inference about an object from measurements of its effects, or • Arriving at a conclusion through logical reasoning from established facts. For a method to be considered scientific within our framework, it needs to be replicable and provide a rationale for how the results of its application are tied to the underlying claim.
- 18. Method: Replicable and rationally linked to claim Consider the witch scene from Monty Python’s and the Holy Grail where Sir Bedevere, quite socratically, helps the villagers conclude that an accused woman is a witch because she weighs the same as a duck, and since ducks are made out of wood, she must therefore be a witch! While the method proposed by Sir Bedevere is clearly replicable, the rationale by which he links its result to the nature of the accused is ludicrously flawed. The range of applicability of a method is supplementary to its validity and lends it hierarchical status.
- 20. Modeling as a Method In a sense, all methods are models. As we formulate or apply any method to generate knowledge about an object, we are running a model. “The choice, then, is not whether to build models; it is whether to build explicit ones. In explicit models, assumptions are laid out in detail, so we can study exactly what they entail. On these assumptions, this sort of thing happens. When you alter the assumptions that is what happens. By writing explicit models, you let others replicate your results.” Joshua Epstein
- 21. Applicability of Models • Explicit modeling affords clarity and replicability to the process • Is a medium of exploration that can yield results well beyond its initial purpose • The logistic function was introduced by Verhulst in the mid-19th century to model the population growth of France, Belgium, Essex and Russia • Since then, it has found applications in economics, chemistry, biology, and sociology to name just a few fields. • A Google Scholar search for “application of logistic function” returned 1,410,000 results.
- 22. Types of Models Conceptual Formal* Closed-form Qualitative Numerical *Classification is in terms of the solutions 𝐾(𝑡) = 𝐾0 𝑒 𝑎𝑡 𝑑𝐾(𝑡) 𝑑𝑡 = 𝑎𝐾(𝑡) ⇒ Specify the elements of the model and its interactions, without providing a detailed or operational description of such interactions. Usually the starting point for many formal models. Typically represented as mathematical formulas. Both specific—as it can give us a precise answer given the right set of parameters—and general—as it describes a broad range of cases. Provide information about the behavior of the system we are modeling, answering questions about existence, uniqueness, and general behavioral patterns such as fixed points or bifurcations. They can be quite general, but do not provide concrete answers. Numerical solutions on the other hand are specific, providing a concrete answer for given parameter values. They are realizations of the model. They are frequently approximations and often, the only ones we have.
- 24. Positivism and Critical Realism • Both have been criticized for assuming that social phenomena can be explained from simple premises and challenged by feminists of having a masculine orientation of sociological knowledge • Our framework doesn’t make any assumptions about the complexity of explanations nor assumes that everything can be explained, but instead it rescues falsifiability of claims and replicability of the method as the basic demarcation criteria between what we call scientific knowledge and other kinds of knowledge. • Without these features the process of science lacks a mechanism to purge itself and evolutionarily select the best available explanation and be prepared to revise itself as new evidence becomes available.
- 25. Positivism and Critical Realism • Our framework defines an ontology from which the objects of study are available, but it doesn’t impose a formal notion of reality in a deep philosophical sense, but instead, leverages that ontology along with the process of science as a framework for exploration, discovery and revision. • While we do propose a demarcation of science, we do not advance any value judgement and recognize that knowledge generated or acquired outside the scope of science, can and do influence scientific inquiry. • We also detach from any ideological background and focus only on the process.
- 26. Feminism • As women have been oppressed both physically and ideologically for the better part of modern civilization, suspicion of the establishment are natural reactions as we become more aware of the circumstances that they have been victims of through history, resulting on much of the discussion to naturally become political. • In the words of Michelle Meagher: “feminist theory in the late twentieth and early twenty‐first centuries is not limited to thinking about the lives of men and women and all those in between, but rather, offers explanations of how gender shapes the entire social world.” • In this light, we argue that progress can be made beyond dialectics.
- 27. Feminism • A recent paper by (Clifton, et al., 2019) introduces a mathematical model that explores the role of bias and homophily in the progression of women in various professional hierarchies, suggesting policies to achieve gender parity. • Another model by (Zazueta & Accinelli) explores the evolution of the gender gap in the labor market by explicitly modeling cross-bias by gender. • The authors’ conclusions are falsifiable and their (modeling) method replicable and their arguments are free from ideology and open to be challenged or supported, informing policy from a non-partisan point of view.
- 28. Language • Language is especially suited for scientific analysis and mathematical methods have been extensively applied to its study. • Applications include • Measuring political influence on Twitter (Barberá, Jost, Nagler, Tucker, & Bonneau, 2015), • Uncovering what the Chinese government is censoring online (Gary King, 2013), • Identifying authorship based on style (Juola, 2015) • Exploring the ideological structure of political parties (Zazueta & Aguilera).
- 29. Conclusions
- 30. Conclusions • We propose a pragmatic research framework that sets minimal requirements for knowledge to be considered scientific • Sketch an ontology to help us reflect on the potential objects of research that builds from Popper’s original proposal, but refrains for giving reality an objective meaning • Not all objects are knowable in a scientific sense, but those that are, can be studied through our framework. • The process of science is a feedback loop that accumulates new knowledge, but also purges its content through falsifiability.
- 31. Conclusions • By demarcating what we believe is scientific knowledge, we are not making any value judgments • The creative process by which researchers structure new claims, is to a large extent non-scientific. Is only when we want to label a new claim as scientific, that we need to abide by the minimal rigor defined in this paper.
- 32. Questions?
- 33. Bibliography Barberá, P., Jost, J. T., Nagler, J., Tucker, J. A., & Bonneau, R. (2015). Tweeting From Left to Right: Is Online Political Communication More Than an Echo Chamber? Psicological Science, 26(10), 1531-1542. Clifton, S. M., Hill, K., Karamchandani, A. J., Autry, E. A., McMahon, P., & Sun, G. (2019). Mathematical Model of Gender Bias and Homophily in Professional Hierarchies. Chaos: An Interdisciplinary Journal of Nonlinear Science, 29, 023135. Cramer, J. (2002). The Origins of Logistic Regression. Tinbergen Institute Working Paper, No. 2002-119/4. Currie, G. (1978). Popper's Evolutionary Epistemology: A Critique. Synthese, 37, 413–431. Darwin, C. (1859). The Origin of Species by Means of Natural Selection or the Preservation of Favoured Races in the Struggle for Life. London: John Murray. Epstein, J. M. (2008). Why Model? Journal of Artificial Societies and Social Simulation, 12. Frigeiro, A., Giordani, A., & Luca, M. (2010). Outline of a General Theory of Measurement. Synthese, Vol. 175, No. 2, pp. 123-149.
- 34. Bibliography Gary King, J. P. (2013). How Censorship in China Allows Government Criticism but Silences Collective Expression. American Political Science Review. Guilliam, T., & Jones, T. (Directors). (1975). Monty Python and the Holy Grail [Motion Picture]. Juola, P. (2015). The Rowling Case: A Proposed Standard Analytic Protocol for Authorship Questions. Digital Scholarship in the Humanities. McCain, K. (2015). Explanation and the Nature of Scientific Knowledge. Science & Education, 827–854. McCain, K. (2016). The Nature of Scientific Knowledge. An Explanatory Approach. Switzerland: Springer. Meagher, M. (2020). Contemporary Feminist Theory. In G. Ritzer, & W. Wiedenhoft Murphy, The Wiley Blackwell Companion to Sociology (pp. 398-416). Hoboken: John Wiley & Sons . Popper, K. (1978). Three Worlds. The Tanner Lecture on Human Values. Delivered at the University of Michigan.
- 35. Bibliography Popper, K. (1979). Objective Knowledge. An Evolutionary Approach. Oxford: Clarendon Press. Schrödinger, E. (2014). Nature and the Greeks and Science and Humanism. Cambridge University Press. Stevens, S. (1946). On the theory of scales of measurement. Science, 103, 677–680. Suck, R. (2015). Measurement, Representational Theory of. In J. D. Wright, International Encyclopedia of the Social & Behavioral Sciences (Second Edition) (Vol. 14, pp. 856-861). Elsevier. Tal, E. (2017). Measurement in Science. In E. N. (ed.), The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. Weinberg, S. (1995). The Methods of Science… and Those by Which we Live. Academic Questions, 8(2): 7–13. Zazueta, J., & Accinelli, E. (n.d.). Exploring the Dynamics of the Gender-Gap in the Labor Market: An Evolutionary Approach. Manuscript in preparation. Zazueta, J., & Aguilera, A. (n.d.). Exploring the Ideological Structure within a Local Legislation Process: An Application of the Structured Topic Model. Manuscript in preparation.