A Survey on Retrieval of Mathematical Knowledge

We present a short survey of the literature on indexing and retrieval of mathematical knowledge, with pointers to 72 papers and tentative taxonomies of both retrieval problems and recurring techniques.Comment: CICM 2015, 20 page

Schematizing the Observer and the Epistemic Content of Theories

I argue that, contrary to the standard view, one cannot understand the structure and nature of our knowledge in physics without an analysis of the way that observers (and, more generally, measuring instruments and experimental arrangements) are modeled in theory. One upshot is that standard pictures of what a scientific theory can be are grossly inadequate. In particular, standard formulations assume, with no argument ever given, that it is possible to make a clean separation between, on the one hand, one part of the scientific knowledge a physical theory embodies, viz., that encoded in the pure mathematical formalism and, on the other, the remainder of that knowledge. The remainder includes at a minimum what is encoded in the practice of modeling particular systems, of performing experiments, of bringing the results of theory and experiment into mutually fruitful contact---in sum, real application of the theory in actual scientific practice. This assumption comes out most clearly in the picture of semantics that naturally accompanies the standard view of theories: semantics is fixed by ontology's shining City on the Hill, and all epistemology and methodology and other practical issues and considerations are segregated to the ghetto of the theory's pragmatics. We should not assume such a clean separation is possible without an argument, and, indeed, I offer many arguments that such a separation is not feasible. An adequate semantics for theories cannot be founded on ontology, but rather on epistemology and methodology

Schematizing the Observer and the Epistemic Content of Theories

I argue that, contrary to the standard view, one cannot understand the structure and nature of our knowledge in physics without an analysis of the way that observers (and, more generally, measuring instruments and experimental arrangements) are modeled in theory. One upshot is that standard pictures of what a scientific theory can be are grossly inadequate. In particular, standard formulations assume, with no argument ever given, that it is possible to make a clean separation between, on the one hand, one part of the scientific knowledge a physical theory embodies, viz., that encoded in the pure mathematical formalism and, on the other, the remainder of that knowledge. The remainder includes at a minimum what is encoded in the practice of modeling particular systems, of performing experiments, of bringing the results of theory and experiment into mutually fruitful contact---in sum, real application of the theory in actual scientific practice. This assumption comes out most clearly in the picture of semantics that naturally accompanies the standard view of theories: semantics is fixed by ontology's shining City on the Hill, and all epistemology and methodology and other practical issues and considerations are segregated to the ghetto of the theory's pragmatics. We should not assume such a clean separation is possible without an argument, and, indeed, I offer many arguments that such a separation is not feasible. An adequate semantics for theories cannot be founded on ontology, but rather on epistemology and methodology

Framework Confirmation by Newtonian Abduction

The analysis of theory-confirmation generally takes the form: show that a theory in conjunction with physical data and auxiliary hypotheses yield a prediction about phenomena; verify the prediction; provide a quantitative measure of the degree of theory-confirmation this yields. The issue of confirmation for an entire framework (e.g., Newtonian mechanics en bloc, as opposed, say, to Newton's theory of gravitation) either does not arise, or is dismissed in so far as frameworks are thought not to be the kind of thing that admits scientific confirmation. I argue that there is another form of scientific reasoning that has not received philosophical attention, what I call Newtonian abduction, that does provide confirmation for frameworks as a whole, and does so in two novel ways. (In particular, Newtonian abduction is *not* IBE, but rather is much closer to Peirce's original explication of the idea of abduction.) I further argue that Newtonian abduction is at least as important a form of reasoning in science as the deductive form sketched above. The form is beautifully summed up by Maxwell (1876): "The true method of physical reasoning is to begin with the phenomena and to deduce the forces from them by a direct application of the equations of motion.

Framework Confirmation by Newtonian Abduction

The analysis of theory-confirmation generally takes the form: show that a theory in conjunction with physical data and auxiliary hypotheses yield a prediction about phenomena; verify the prediction; provide a quantitative measure of the degree of theory-confirmation this yields. The issue of confirmation for an entire framework (e.g., Newtonian mechanics en bloc, as opposed, say, to Newton's theory of gravitation) either does not arise, or is dismissed in so far as frameworks are thought not to be the kind of thing that admits scientific confirmation. I argue that there is another form of scientific reasoning that has not received philosophical attention, what I call Newtonian abduction, that does provide confirmation for frameworks as a whole, and does so in two novel ways. (In particular, Newtonian abduction is *not* IBE, but rather is much closer to Peirce's original explication of the idea of abduction.) I further argue that Newtonian abduction is at least as important a form of reasoning in science as the deductive form sketched above. The form is beautifully summed up by Maxwell (1876): "The true method of physical reasoning is to begin with the phenomena and to deduce the forces from them by a direct application of the equations of motion.

Framework Confirmation by Newtonian Abduction

The analysis of theory-confirmation generally takes the form: show that a theory in conjunction with physical data and auxiliary hypotheses yield a prediction about phenomena; verify the prediction; provide a quantitative measure of the degree of theory-confirmation this yields. The issue of confirmation for an entire framework (e.g., Newtonian mechanics en bloc, as opposed, say, to Newton's theory of gravitation) either does not arise, or is dismissed in so far as frameworks are thought not to be the kind of thing that admits scientific confirmation. I argue that there is another form of scientific reasoning that has not received philosophical attention, what I call Newtonian abduction, that does provide confirmation for frameworks as a whole, and does so in two novel ways. (In particular, Newtonian abduction is *not* IBE, but rather is much closer to Peirce's original explication of the idea of abduction.) I further argue that Newtonian abduction is at least as important a form of reasoning in science as the deductive form sketched above. The form is beautifully summed up by Maxwell (1876): "The true method of physical reasoning is to begin with the phenomena and to deduce the forces from them by a direct application of the equations of motion.

Schematizing the Observer and the Epistemic Content of Theories

I argue that, contrary to the standard view, one cannot understand the structure and nature of our knowledge in physics without an analysis of the way that observers (and, more generally, measuring instruments and experimental arrangements) are modeled in theory. One upshot is that standard pictures of what a scientific theory can be are grossly inadequate. In particular, standard formulations assume, with no argument ever given, that it is possible to make a clean separation between, on the one hand, one part of the scientific knowledge a physical theory embodies, viz., that encoded in the pure mathematical formalism and, on the other, the remainder of that knowledge. The remainder includes at a minimum what is encoded in the practice of modeling particular systems, of performing experiments, of bringing the results of theory and experiment into mutually fruitful contact---in sum, real application of the theory in actual scientific practice. This assumption comes out most clearly in the picture of semantics that naturally accompanies the standard view of theories: semantics is fixed by ontology's shining City on the Hill, and all epistemology and methodology and other practical issues and considerations are segregated to the ghetto of the theory's pragmatics. We should not assume such a clean separation is possible without an argument, and, indeed, I offer many arguments that such a separation is not feasible. An adequate semantics for theories cannot be founded on ontology, but rather on epistemology and methodology

Framework Confirmation by Newtonian Abduction

The analysis of theory-confirmation generally takes the form: show that a theory in conjunction with physical data and auxiliary hypotheses yield a prediction about phenomena; verify the prediction; provide a quantitative measure of the degree of theory-confirmation this yields. The issue of confirmation for an entire framework (e.g., Newtonian mechanics en bloc, as opposed, say, to Newton's theory of gravitation) either does not arise, or is dismissed in so far as frameworks are thought not to be the kind of thing that admits scientific confirmation. I argue that there is another form of scientific reasoning that has not received philosophical attention, what I call Newtonian abduction, that does provide confirmation for frameworks as a whole, and does so in two novel ways. (In particular, Newtonian abduction is *not* IBE, but rather is much closer to Peirce's original explication of the idea of abduction.) I further argue that Newtonian abduction is at least as important a form of reasoning in science as the deductive form sketched above. The form is beautifully summed up by Maxwell (1876): "The true method of physical reasoning is to begin with the phenomena and to deduce the forces from them by a direct application of the equations of motion.