g) the function of a mordant is to fix the dye h) the function in steel-making of trace metals, e.g., molybdenum, is to make the metal stronger (tougher, less brittle, stainless, etc.) Next, and more unusually but I think relevantly, these last two instances. The first is in physics where the system invoked is fundamental physics, a yes/no system of laws of physical necessity rather than a system of more/less, better/worse relations of the sort found in complex and derivative causal systems such as the biological. The second is the system of roles of mathematical objects in mathematical systems, which is also a yes/no system because mathematical roles and relations are a matter of mathematical necessity. i) mass in Newtonian physics functions to generate the gravitational field And then in mathematics, consider the function of squaring. Think first about my calculator. One of its functions is squaring: j) my calculator functions to square numbers Then think about the abstract mathematical object the function squaring: k) the function squaring functions to square numbers This sounds clumsy, but parse it carefully and you will see that it makes sense: the function squaring is the thing, and it has the function of squaring, and it functions to square numbers. I will devote considerable effort to getting all this laid out in clear and distinct ways. But back to the gravitational force function l) F = g(m1)( m2)/r2 If we look just at the function with its variables removed we get: m) f( ) = g(…)(…)/(…)2 of which we can say f( ) is an inverse square function and inverse square functions are important in field theories. I will return to this question at the very end of Section 2.5 where I attempt to articulate the conceptual structures of functions both empirical and mathematical. I will also argue that Frege’s conception of function (Frege 1952, 107-116; is a fits my account of “What Function?”) function. His conception of function is as a type of abstract object that has the capacity to “map”, that is, to take one object as input and yield another object as output. Input-output talk is metaphorical, but it can be made literal and I will show how. 2.3 The problematic features and ‘for’ ‘supposed to’
g) the function of a mordant is to fix the dye h) the function in steel-making of trace metals, e.g., molybdenum, is to make the metal stronger (tougher, less brittle, stainless, etc.) Next, and more unusually but I think relevantly, these last two instances. The first is in physics where the system invoked is fundamental physics, a yes/no system of laws of physical necessity rather than a system of more/less, better/worse relations of the sort found in complex and derivative causal systems such as the biological. The second is the system of roles of mathematical objects in mathematical systems, which is also a yes/no system because mathematical roles and relations are a matter of mathematical necessity. i) mass in Newtonian physics functions to generate the gravitational field And then in mathematics, consider the function of squaring. Think first about my calculator. One of its functions is squaring: j) my calculator functions to square numbers Then think about the abstract mathematical object the function squaring: k) the function squaring functions to square numbers This sounds clumsy, but parse it carefully and you will see that it makes sense: the function squaring is the thing, and it has the function of squaring, and it functions to square numbers. I will devote considerable effort to getting all this laid out in clear and distinct ways. But back to the gravitational force function l) F = g(m1)( m2)/r2 If we look just at the function with its variables removed we get: m) f( ) = g(…)(…)/(…)2 of which we can say f( ) is an inverse square function and inverse square functions are important in field theories. I will return to this question at the very end of Section 2.5 where I attempt to articulate the conceptual structures of functions both empirical and mathematical. I will also argue that Frege’s conception of function (Frege 1952, 107-116; “What is a Function?”) fits my account of function. His conception of function is as a type of abstract object that has the capacity to “map”, that is, to take one object as input and yield another object as output. Input-output talk is metaphorical, but it can be made literal and I will show how. 2.3 The problematic features ‘for’ and ‘supposed to’
Function.%20rev%20of%206.28.17.docx