Arezoo Islami | San Francisco State University (original) (raw)
At the intersection of philosophy of mathematics and philosophy of science (physics in particular) lies the applicability problem (AP) -- why is it that mathematics is applicable to natural sciences?. This question raised by mathematicians, physicists and philosophers, sits at the heart of my current research. In doing philosophy, and in thinking about the relationship between mathematics and physics, I am very attracted to historically-informed and detailed case studies.
Address: Department of Philosophy, Humanities 359, San Francisco State University, San Francisco
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Papers by Arezoo Islami
Phenomenological Approaches to Physics, 2020
Anyone interested in understanding the nature of modern physics will at some point encounter a pr... more Anyone interested in understanding the nature of modern physics will at some point encounter a problem that was popularized in the 1960s by the physicist Eugene Wigner: Why is it that mathematics is so effective and useful for describing, explaining and predicting the kinds of phenomena we are concerned with in the sciences? In this chapter, we will propose a phenomenological solution for this "problem" of the seemingly unreasonable effectiveness of mathematics in the physical sciences. In our view, the "problem" can only be solved-or made to evaporate-if we shift our attention away from the why-question-Why can mathematics play the role it does in physics?-, and focus on the how-question instead. Our question, then, is this: How is mathematics actually used in the practice of modern physics?
Synethese Library , 2019
Anyone interested in understanding the nature of modern physics will at some point encounter a pr... more Anyone interested in understanding the nature of modern physics will at some point encounter a problem that was popularized in the 1960s by the physicist Eugene Wigner: Why is it that mathematics is so effective and useful for describing, explaining and predicting the kinds of phenomena we are concerned with in the sciences? In this chapter, we will propose a phenomenological solution for this "problem" of the seemingly unreasonable effectiveness of mathematics in the physical sciences. In our view, the "problem" can only be solved-or made to evaporate-if we shift our attention away from the why-question-Why can mathematics play the role it does in physics?-, and focus on the how-question instead. Our question, then, is this: How is mathematics actually used in the practice of modern physics?
Keywords: Geometric vs algebraic constructions Ontological and historical differences Synthesis a... more Keywords: Geometric vs algebraic constructions Ontological and historical differences Synthesis and applications Eastern and western traditions Measurement Space Biological evolution and mathematics a b s t r a c t The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of " geometric judgments " from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and reexamine the interactions with natural sciences. In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as a cross-disciplinary and cross-cultural issue and will be examined in Mathematical Physics and Biology. We finally discuss how the current notions of mathematical (phase) " space " should be revisited for the purposes of life sciences.
Review of the book: Mathematics as a Tool
In his seminal 1960 paper, the physicist Eugene Wigner formulated the question of the applicabili... more In his seminal 1960 paper, the physicist Eugene Wigner formulated the question of the applicability of mathematics in physics in a way nobody had before. This formulation has been (almost) entirely overlooked due to an exclusive concern with (dis)solving Wigner's problem and explaining the effectiveness of mathematics in the natural sciences, in one way or another. Many have attempted to attribute Wigner's unjustified conclusion– that mathematics is unreasonably effective in the natural sciences– to his (dogmatic) formalist views on mathematics. My goal is to show that this reading misses out on Wigner's highly original formulation of the problem which is presented throughout his body of work in physics as well as in philosophy. This formulation, as I will show, leads us in a new direction in solving the applicability problem.
This paper is published in Synthese 2016, pp. 1-23: http://link.springer.com/article/10.1007/s11229-016-1171-4?wt_mc=Internal.Event.1.SEM.ArticleAuthorOnlineFirst
Phenomenological Approaches to Physics, 2020
Anyone interested in understanding the nature of modern physics will at some point encounter a pr... more Anyone interested in understanding the nature of modern physics will at some point encounter a problem that was popularized in the 1960s by the physicist Eugene Wigner: Why is it that mathematics is so effective and useful for describing, explaining and predicting the kinds of phenomena we are concerned with in the sciences? In this chapter, we will propose a phenomenological solution for this "problem" of the seemingly unreasonable effectiveness of mathematics in the physical sciences. In our view, the "problem" can only be solved-or made to evaporate-if we shift our attention away from the why-question-Why can mathematics play the role it does in physics?-, and focus on the how-question instead. Our question, then, is this: How is mathematics actually used in the practice of modern physics?
Synethese Library , 2019
Anyone interested in understanding the nature of modern physics will at some point encounter a pr... more Anyone interested in understanding the nature of modern physics will at some point encounter a problem that was popularized in the 1960s by the physicist Eugene Wigner: Why is it that mathematics is so effective and useful for describing, explaining and predicting the kinds of phenomena we are concerned with in the sciences? In this chapter, we will propose a phenomenological solution for this "problem" of the seemingly unreasonable effectiveness of mathematics in the physical sciences. In our view, the "problem" can only be solved-or made to evaporate-if we shift our attention away from the why-question-Why can mathematics play the role it does in physics?-, and focus on the how-question instead. Our question, then, is this: How is mathematics actually used in the practice of modern physics?
Keywords: Geometric vs algebraic constructions Ontological and historical differences Synthesis a... more Keywords: Geometric vs algebraic constructions Ontological and historical differences Synthesis and applications Eastern and western traditions Measurement Space Biological evolution and mathematics a b s t r a c t The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of " geometric judgments " from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and reexamine the interactions with natural sciences. In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as a cross-disciplinary and cross-cultural issue and will be examined in Mathematical Physics and Biology. We finally discuss how the current notions of mathematical (phase) " space " should be revisited for the purposes of life sciences.
Review of the book: Mathematics as a Tool
In his seminal 1960 paper, the physicist Eugene Wigner formulated the question of the applicabili... more In his seminal 1960 paper, the physicist Eugene Wigner formulated the question of the applicability of mathematics in physics in a way nobody had before. This formulation has been (almost) entirely overlooked due to an exclusive concern with (dis)solving Wigner's problem and explaining the effectiveness of mathematics in the natural sciences, in one way or another. Many have attempted to attribute Wigner's unjustified conclusion– that mathematics is unreasonably effective in the natural sciences– to his (dogmatic) formalist views on mathematics. My goal is to show that this reading misses out on Wigner's highly original formulation of the problem which is presented throughout his body of work in physics as well as in philosophy. This formulation, as I will show, leads us in a new direction in solving the applicability problem.
This paper is published in Synthese 2016, pp. 1-23: http://link.springer.com/article/10.1007/s11229-016-1171-4?wt_mc=Internal.Event.1.SEM.ArticleAuthorOnlineFirst