One reason for the " unreasonable effectiveness of mathematics " is that it is never compared to ... more One reason for the " unreasonable effectiveness of mathematics " is that it is never compared to nature itself, which is ambiguous, but to well-defined idealized versions (models). Math is consistent with nature in unfamiliar situations because it is consistent within itself. PART ONE: the Map and the Territory Nature and mathematics are divided by the same categorical gulf that has long plagued the relationship between the physical and the mental. Just as there is no mind without body, there is no mathematics without mathematicians. Mathematics and physics are alike cognitive activities undertaken by intelligent organisms. The relationship of one to the other—and of each to nature—must be considered in their context as embodied cognition. We moderns understand the universe through mathematical models, which are idealized constructs that correspond only approximately to reality. It is easy enough to mistake the model for the reality—the map for the territory—when one has learned to think of nature as literally consisting of such idealizations. This mistake parallels the naïve realism of ordinary cognition, in which we normally take our perception as a transparent window on the world. One can then even conclude that the universe is literally mathematics. It is perfectly reasonable for physicists to believe in the guidance of mathematics. Yet, if physics is a form of cognition, then it is also reasonable to believe in the guidance of cognitive theory, evolutionary psychology, and theoretical epistemology (the nascent science of possible cognitive systems). Such things are not a part of physics as we know it. The Scientific Revolution redefined natural philosophy as " first-order " science: study of the external world in strictly objectivist terms. Focus on the object excluded focus on the subject. Cognition in general is a form of map-making. So, then, are mathematics and physics. The map, however, is not the territory. At best it represents it selectively, symbolically, and adequately for specific purposes. In the case of ordinary cognition, these purposes are bequeathed by evolutionary history. Math and physics may be driven by other purposes as well, better described perhaps by sociology and anthropology. In any case, the map corresponds only grossly to the territory. There is always simplification and streamlining involved. Science tends to mask the real complexity of the world when it presumes simplicity or prefers tidy systems to messy facts. The complexity and messiness of nature are the signs of its reality, which (contra Plato) lies in its very " imperfection. " We vaunt the ability of mathematics to exhaustively represent natural systems, but the reality of nature lies precisely in its ability to resist such exhaustion. Mathematical laws generally describe ideal things and circumstances that do not occur in nature, and that could not even be stated without idealization, isolation, and experimental control. (Ellis 2002, p90-94) To single out a causal relationship, one must know how the process
Bruiger, Dan, 1945-Second nature : the man-made world of idealism, technology and power / Dan Bru... more Bruiger, Dan, 1945-Second nature : the man-made world of idealism, technology and power / Dan Bruiger.
This paper proposes the feasibility of a second-order approach in cosmology. It is intended to en... more This paper proposes the feasibility of a second-order approach in cosmology. It is intended to encourage cosmologists to rethink standard ideas in their field, leading to a broader concept of self-organization and of science itself. It is argued, from a cognitive epistemology perspective, that a first-order approach is inadequate for cosmology; study of the universe as a whole must include study of the scientific observer and the process of theorizing. Otherwise, concepts of selforganization at the cosmological scale remain constrained by unacknowledged assumptions and biases. Examples of limiting notions are discussed in the context of alternatives. To include the role of the theorist does not mean reducing science to subjective or sociological terms. On the contrary, second-order science would provide a more complete portrait of nature. The work of cosmologist Lee Smolin is discussed as a candidate example of second-order cosmology.
There is a categorical difference between natural things and artifacts. The latter we construct, ... more There is a categorical difference between natural things and artifacts. The latter we construct, whereas the former we simply encounter. The only certain knowledge we can have is of our own creations, because—like the constructs of mathematics—they are what they are by definition. Scientific entities and laws are made as much as they are found. Only products of definition can be truly deterministic. The immanent reality of nature implies that nature may transcend any thought system, however complete. There can be no final theory of everything.
The problem of cognitive domains is that one can conceive the territory only as it is portrayed i... more The problem of cognitive domains is that one can conceive the territory only as it is portrayed in the map. It involves conflating the domain of representation with the domain of what it represents. This is a category mistake: there are essential qualitative and quantitative differences between map and territory. The output of cognitive processes, both perceptual and scientific, is recycled as the input.
One reason for the " unreasonable effectiveness of mathematics " is that it is never compared to ... more One reason for the " unreasonable effectiveness of mathematics " is that it is never compared to nature itself, which is ambiguous, but to well-defined idealized versions (models). Math is consistent with nature in unfamiliar situations because it is consistent within itself. PART ONE: the Map and the Territory Nature and mathematics are divided by the same categorical gulf that has long plagued the relationship between the physical and the mental. Just as there is no mind without body, there is no mathematics without mathematicians. Mathematics and physics are alike cognitive activities undertaken by intelligent organisms. The relationship of one to the other—and of each to nature—must be considered in their context as embodied cognition. We moderns understand the universe through mathematical models, which are idealized constructs that correspond only approximately to reality. It is easy enough to mistake the model for the reality—the map for the territory—when one has learned to think of nature as literally consisting of such idealizations. This mistake parallels the naïve realism of ordinary cognition, in which we normally take our perception as a transparent window on the world. One can then even conclude that the universe is literally mathematics. It is perfectly reasonable for physicists to believe in the guidance of mathematics. Yet, if physics is a form of cognition, then it is also reasonable to believe in the guidance of cognitive theory, evolutionary psychology, and theoretical epistemology (the nascent science of possible cognitive systems). Such things are not a part of physics as we know it. The Scientific Revolution redefined natural philosophy as " first-order " science: study of the external world in strictly objectivist terms. Focus on the object excluded focus on the subject. Cognition in general is a form of map-making. So, then, are mathematics and physics. The map, however, is not the territory. At best it represents it selectively, symbolically, and adequately for specific purposes. In the case of ordinary cognition, these purposes are bequeathed by evolutionary history. Math and physics may be driven by other purposes as well, better described perhaps by sociology and anthropology. In any case, the map corresponds only grossly to the territory. There is always simplification and streamlining involved. Science tends to mask the real complexity of the world when it presumes simplicity or prefers tidy systems to messy facts. The complexity and messiness of nature are the signs of its reality, which (contra Plato) lies in its very " imperfection. " We vaunt the ability of mathematics to exhaustively represent natural systems, but the reality of nature lies precisely in its ability to resist such exhaustion. Mathematical laws generally describe ideal things and circumstances that do not occur in nature, and that could not even be stated without idealization, isolation, and experimental control. (Ellis 2002, p90-94) To single out a causal relationship, one must know how the process
Bruiger, Dan, 1945-Second nature : the man-made world of idealism, technology and power / Dan Bru... more Bruiger, Dan, 1945-Second nature : the man-made world of idealism, technology and power / Dan Bruiger.
This paper proposes the feasibility of a second-order approach in cosmology. It is intended to en... more This paper proposes the feasibility of a second-order approach in cosmology. It is intended to encourage cosmologists to rethink standard ideas in their field, leading to a broader concept of self-organization and of science itself. It is argued, from a cognitive epistemology perspective, that a first-order approach is inadequate for cosmology; study of the universe as a whole must include study of the scientific observer and the process of theorizing. Otherwise, concepts of selforganization at the cosmological scale remain constrained by unacknowledged assumptions and biases. Examples of limiting notions are discussed in the context of alternatives. To include the role of the theorist does not mean reducing science to subjective or sociological terms. On the contrary, second-order science would provide a more complete portrait of nature. The work of cosmologist Lee Smolin is discussed as a candidate example of second-order cosmology.
There is a categorical difference between natural things and artifacts. The latter we construct, ... more There is a categorical difference between natural things and artifacts. The latter we construct, whereas the former we simply encounter. The only certain knowledge we can have is of our own creations, because—like the constructs of mathematics—they are what they are by definition. Scientific entities and laws are made as much as they are found. Only products of definition can be truly deterministic. The immanent reality of nature implies that nature may transcend any thought system, however complete. There can be no final theory of everything.
The problem of cognitive domains is that one can conceive the territory only as it is portrayed i... more The problem of cognitive domains is that one can conceive the territory only as it is portrayed in the map. It involves conflating the domain of representation with the domain of what it represents. This is a category mistake: there are essential qualitative and quantitative differences between map and territory. The output of cognitive processes, both perceptual and scientific, is recycled as the input.
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