Abstract Mark Wilson: Many authors, including Oswaldo Chateaubriand, maintain that "properties" should be structured in logical grades, where the least abstract quantities comprise the lowest ranks of a hierarchy that embraces more... more
Abstract Mark Wilson:
Many authors, including Oswaldo Chateaubriand, maintain that "properties" should be structured in logical grades, where the least abstract quantities comprise the lowest ranks of a hierarchy that embraces more abstract and mathematized qualities only at higher levels. But applied mathematicians warns that no quantities can be expected to possess crisp, real world extensions unless they have already been processed with a fair amount of set theoretic machinery beforehand.
Abstract response:
Mark Wilson argues that in order to make physical first-order properties suitable for inclusion in the bottom levels of a logical hierarchy of properties, their proper treatment must take into account the methods of applied mathematics. I agree that the methods of applied mathematics are essential for studying physical properties, and in my response focus on the nature of the logical hierarchy and on the requirements of classical logic.
Many authors, including Oswaldo Chateaubriand, maintain that "properties" should be structured in logical grades, where the least abstract quantities comprise the lowest ranks of a hierarchy that embraces more abstract and mathematized qualities only at higher levels. But applied mathematicians warns that no quantities can be expected to possess crisp, real world extensions unless they have already been processed with a fair amount of set theoretic machinery beforehand.
Abstract response:
Mark Wilson argues that in order to make physical first-order properties suitable for inclusion in the bottom levels of a logical hierarchy of properties, their proper treatment must take into account the methods of applied mathematics. I agree that the methods of applied mathematics are essential for studying physical properties, and in my response focus on the nature of the logical hierarchy and on the requirements of classical logic.
Research Interests:
Research Interests:
Explanations in physics commonly appeal to data drawn from different length or time scales, as when a “top-down” macroscopic constraint such as rigidity is used to evade the complexities one would confront in attempting to model the... more
Explanations in physics commonly appeal to data drawn from different length or time scales, as when a “top-down” macroscopic constraint such as rigidity is used to evade the complexities one would confront in attempting to model the situation in a purely “bottom-up” fashion. Such techniques commonly embody rather complex shifts in explanatory strategy.