Chiara Ambrosio (UCL)
Diagrammatic Practices and the Moral Economy of Science
“I do not think I ever reflect in words,” Charles S. Peirce reminisced in 1909, “I employ visual diagrams firstly because this way of thinking is my natural language of self- communion, and secondly because I am convinced that it is the best system for the purpose” (R619:8). Regularly featuring in the literature on Peirce’s approach to diagrams, this passage has offered precious evidence in support of a characterization of Peirce as a uniquely diagrammatic thinker, lending further validation to the broader role that diagrammatic reasoning played in his pragmatist philosophy. But it has also raised epistemological concerns about its twofold nature, with Peirce scholars agonising over how to reconcile the descriptive and normative considerations it seems to conflate. In this presentation, I want to suggest that a bigger story lurks in the background of Peirce’s twofold statement, a story that brings his logical and mathematical – and distinctively pragmatist – approach to diagrams in dialogue with the history as well as the epistemology of science. In particular, I will locate Peirce’s work on diagrams within what historians and philosophers of science have described as the “moral economy” of nineteenth- century science: the system of epistemic virtues that enabled scientists to approach and use diagrams as “working objects,” around which they negotiated their identities and commitments (Daston 1995; Daston and Galison 2007). The questions I will ask, therefore will be: how did diagrams come to be Peirce’s language of self-communion? And what allowed them to become naturalized, and elevated to “the best system for the purpose” of discovering and experimenting upon logical and mathematical relations? At a very basic level, this tells us something new and interesting about Peirce’s own approach to diagrams, but my goal is methodologically more ambitious. Diagrams are only one example of a much broader array of practices that pragmatist philosophy capitalises upon in its focus on epistemic activities, processes, and the values and epistemic virtues that inform scientific inquiry. These practices demand joining forces with the history and historiographies of science, mathematics, and logic for their contextualisation. The pay-off of this approach, I will argue, will be a richer understanding of the very genealogy of pragmatism, as well as new integrations between the history and philosophy of science, mathematics and logic.
Diagrammatic Practices and the Moral Economy of Science
“I do not think I ever reflect in words,” Charles S. Peirce reminisced in 1909, “I employ visual diagrams firstly because this way of thinking is my natural language of self- communion, and secondly because I am convinced that it is the best system for the purpose” (R619:8). Regularly featuring in the literature on Peirce’s approach to diagrams, this passage has offered precious evidence in support of a characterization of Peirce as a uniquely diagrammatic thinker, lending further validation to the broader role that diagrammatic reasoning played in his pragmatist philosophy. But it has also raised epistemological concerns about its twofold nature, with Peirce scholars agonising over how to reconcile the descriptive and normative considerations it seems to conflate. In this presentation, I want to suggest that a bigger story lurks in the background of Peirce’s twofold statement, a story that brings his logical and mathematical – and distinctively pragmatist – approach to diagrams in dialogue with the history as well as the epistemology of science. In particular, I will locate Peirce’s work on diagrams within what historians and philosophers of science have described as the “moral economy” of nineteenth- century science: the system of epistemic virtues that enabled scientists to approach and use diagrams as “working objects,” around which they negotiated their identities and commitments (Daston 1995; Daston and Galison 2007). The questions I will ask, therefore will be: how did diagrams come to be Peirce’s language of self-communion? And what allowed them to become naturalized, and elevated to “the best system for the purpose” of discovering and experimenting upon logical and mathematical relations? At a very basic level, this tells us something new and interesting about Peirce’s own approach to diagrams, but my goal is methodologically more ambitious. Diagrams are only one example of a much broader array of practices that pragmatist philosophy capitalises upon in its focus on epistemic activities, processes, and the values and epistemic virtues that inform scientific inquiry. These practices demand joining forces with the history and historiographies of science, mathematics, and logic for their contextualisation. The pay-off of this approach, I will argue, will be a richer understanding of the very genealogy of pragmatism, as well as new integrations between the history and philosophy of science, mathematics and logic.
Jessica Carter (Aarhus)
Mathematics as dealing with 'Hypothetical States of Things'
C.S. Peirce’s writings, which are based on an extensive knowledge of the mathematics of his time, provide an invaluable source of inspiration for a philosopher of mathematical practice.
We consider a pragmatic view of mathematics that is inspired by a reading of Peirce. According to this picture it is possible to say that mathematics is introduced by human agents, but is nevertheless “pragmatically” real.
Peirce famously described mathematics as the science of necessary reasoning concerning ‘hypothetical states of things.’ Mathematics thus consists of two parts. One is reasoning; and when reasoning one does not care what the statements refer to, or whether they refer to something real: “For all modern mathematicians agree with Plato and Aristotle that mathematics deals exclusively with hypothetical states of things, and asserts no matter of fact whatever; and further, that it is thus alone that the necessity of its conclusions is to be explained” [CP 4.232]. In Peirce’s view, necessary reasoning is ‘diagrammatic reasoning’, which he describes as a process of constructing and observing rational relations from “a diagram, or visual array of characters or lines” [CP 3.560].
The other part consists of formulating the hypotheses from which to reason. When doing so the question is whether mathematicians introduce real substances or just fictional ones. I defend a position referred to as ‘Pragmatic realism’ where the claim is that mathematics – at least for the most part - studies hypotheses that are related to the world of sensory appearances. This claim is based on Peirce’s ‘pragmatistic maxim of reality’ which states that an abstract substance is real — and not fictitious — if propositions about it can be reduced to statements concerning substances at a lower level.
Mathematics as dealing with 'Hypothetical States of Things'
C.S. Peirce’s writings, which are based on an extensive knowledge of the mathematics of his time, provide an invaluable source of inspiration for a philosopher of mathematical practice.
We consider a pragmatic view of mathematics that is inspired by a reading of Peirce. According to this picture it is possible to say that mathematics is introduced by human agents, but is nevertheless “pragmatically” real.
Peirce famously described mathematics as the science of necessary reasoning concerning ‘hypothetical states of things.’ Mathematics thus consists of two parts. One is reasoning; and when reasoning one does not care what the statements refer to, or whether they refer to something real: “For all modern mathematicians agree with Plato and Aristotle that mathematics deals exclusively with hypothetical states of things, and asserts no matter of fact whatever; and further, that it is thus alone that the necessity of its conclusions is to be explained” [CP 4.232]. In Peirce’s view, necessary reasoning is ‘diagrammatic reasoning’, which he describes as a process of constructing and observing rational relations from “a diagram, or visual array of characters or lines” [CP 3.560].
The other part consists of formulating the hypotheses from which to reason. When doing so the question is whether mathematicians introduce real substances or just fictional ones. I defend a position referred to as ‘Pragmatic realism’ where the claim is that mathematics – at least for the most part - studies hypotheses that are related to the world of sensory appearances. This claim is based on Peirce’s ‘pragmatistic maxim of reality’ which states that an abstract substance is real — and not fictitious — if propositions about it can be reduced to statements concerning substances at a lower level.
Hasok Chang (Cambridge)
“What should pragmatists mean by ‘reality’ and ‘realism’?”
Pragmatism asks for the meanings and functions of ideas in actual practices. This orientation should encompass ontological notions, which are not to be shunned as meaningless but turned into useful tools of thought. Starting with the very notion of reality, I offer the following definition: an entity is real to the extent that there are operationally coherent activities that can be performed by relying significantly on its existence and its properties. Reality (in the sense of real-ness) conceived in this way is a matter of degrees, and it is domain-dependent. We may also think of realities (in the sense of real entities) as entities conceived by the mind that turn out to be real through our practices. When we take ontology in the context of practices, ontological pluralism no longer appears absurd: there are different sets of realities operative in different systems of practice. Based on these notions, I also propose a re-orientation of what realism should mean. Instead of taking scientific realism as a thesis that science states the truth about the world, I conceive realism in and about science as a commitment to maximize our learning about realities. Realism as I see it is an operational and realistic ideal, because we can learn empirical truths about pragmatist realities by devising operationally coherent activities involving them. This realism (akin to internal realism, and perspectival realism) promotes an iterative and pluralist mode of inquiry. It follows an imperative of progress: always seek to increase and improve knowledge maximally. For this reason I designate my position as “activist realism”. I illustrate these points with a range of examples, drawn especially from the history of the physical sciences.
“What should pragmatists mean by ‘reality’ and ‘realism’?”
Pragmatism asks for the meanings and functions of ideas in actual practices. This orientation should encompass ontological notions, which are not to be shunned as meaningless but turned into useful tools of thought. Starting with the very notion of reality, I offer the following definition: an entity is real to the extent that there are operationally coherent activities that can be performed by relying significantly on its existence and its properties. Reality (in the sense of real-ness) conceived in this way is a matter of degrees, and it is domain-dependent. We may also think of realities (in the sense of real entities) as entities conceived by the mind that turn out to be real through our practices. When we take ontology in the context of practices, ontological pluralism no longer appears absurd: there are different sets of realities operative in different systems of practice. Based on these notions, I also propose a re-orientation of what realism should mean. Instead of taking scientific realism as a thesis that science states the truth about the world, I conceive realism in and about science as a commitment to maximize our learning about realities. Realism as I see it is an operational and realistic ideal, because we can learn empirical truths about pragmatist realities by devising operationally coherent activities involving them. This realism (akin to internal realism, and perspectival realism) promotes an iterative and pluralist mode of inquiry. It follows an imperative of progress: always seek to increase and improve knowledge maximally. For this reason I designate my position as “activist realism”. I illustrate these points with a range of examples, drawn especially from the history of the physical sciences.
Maria Serban (UEA)
Psychological measurement through a pragmatist lens
Measurement is commonly perceived as a fundamental process by which we can obtain reliable information about objects and events in the real world. This widely spread conception of measurement assumes: (1) that measurement delivers a mapping or correspondence between the empirical domain and the symbolic domain, wherever applied, and (2) that standards for validity of measurement should or can be universal across measurement practices.
This talk defends a pragmatist perspective on psychological measurement, treating it as a two-step process involving modelling and application, through which specific characteristics of objects or events in the empirical world are assigned symbolic descriptions that must satisfy certain objectivity and intersubjectivity criteria. The proposed analysis emphasises the normative value of the correspondence assumption in psychological measurement practices and challenges the necessity of validity-first framework in the social sciences like psychology.
Psychological measurement through a pragmatist lens
Measurement is commonly perceived as a fundamental process by which we can obtain reliable information about objects and events in the real world. This widely spread conception of measurement assumes: (1) that measurement delivers a mapping or correspondence between the empirical domain and the symbolic domain, wherever applied, and (2) that standards for validity of measurement should or can be universal across measurement practices.
This talk defends a pragmatist perspective on psychological measurement, treating it as a two-step process involving modelling and application, through which specific characteristics of objects or events in the empirical world are assigned symbolic descriptions that must satisfy certain objectivity and intersubjectivity criteria. The proposed analysis emphasises the normative value of the correspondence assumption in psychological measurement practices and challenges the necessity of validity-first framework in the social sciences like psychology.
Sandra Visokolskis (Cordoba, AR)
Metaphorical-Pragmatic Aspects of Knowledge in Peircean Writings: Creative Pre-sequences
The talk refers to the Peircean pragmatic maxim in its later versions dealing with conceivable consequences of acts, but instead we will concentrate on the formative pre-sequences of ideas or objects that could eventually arise when comparing a feasible situation with an infinite number of similar ones, given the relevance of an analysis of everything that is conceivable. This leads to the treatment of associative ties that link different domains in creative processes, where, according to Peirce, a productive imagination in the search for uberty operates (MS 682, EP 2:463-474). Contrary to William James, as well as against the Cartesian foundationalist tradition of knowledge, Peirce will employ metaphors in such associative processes that do not fall into the dichotomy between chains or trains of thought (Descartes) versus fluidity of thought (James) but rather two differentiated levels of them, applied in different contexts. Our proposal interprets the Peircean pragmaticist approach by relating it to metaphorical fluidity, presenting an associationist model of creativity based on metaphors inspired on Peirce's writings. Download extended abstract.
Metaphorical-Pragmatic Aspects of Knowledge in Peircean Writings: Creative Pre-sequences
The talk refers to the Peircean pragmatic maxim in its later versions dealing with conceivable consequences of acts, but instead we will concentrate on the formative pre-sequences of ideas or objects that could eventually arise when comparing a feasible situation with an infinite number of similar ones, given the relevance of an analysis of everything that is conceivable. This leads to the treatment of associative ties that link different domains in creative processes, where, according to Peirce, a productive imagination in the search for uberty operates (MS 682, EP 2:463-474). Contrary to William James, as well as against the Cartesian foundationalist tradition of knowledge, Peirce will employ metaphors in such associative processes that do not fall into the dichotomy between chains or trains of thought (Descartes) versus fluidity of thought (James) but rather two differentiated levels of them, applied in different contexts. Our proposal interprets the Peircean pragmaticist approach by relating it to metaphorical fluidity, presenting an associationist model of creativity based on metaphors inspired on Peirce's writings. Download extended abstract.
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