Science particularly as related to creation and the creation-evolution controversy
The purpose of science is to discover laws, which are then applied to predict and explain phenomena, develop technology, and make things. This occurs through a cycle of material induction and formal deduction. Induction consists of making observations, defining terms, and proposing postulates. Deduction consists of taking the terms and definitions from induction, possibly with …
The traditional Aristotelian square of opposition is like that of first-order logic apart from existential import: Or in words: Outer negation is the contradictory, i.e., affirm/deny, and inner negation is the contrary, i.e., all/none. For quantifiers (or other operators) there is a duality square: Outer negation is negation of the whole quantifier; inner negation is …
The units of quantities are conveniently ignored in the definition of a derivative, but they should not be. A derivative should be defined as a function of two quantities, both with their own units: where r’ is a vector function of two quantites and r is a vector functon of one quantity. The second derivative is …
Historically, there are two kinds of induction, called here the postulational and the hypothetical. Postulational induction (cf. material induction) is the induction practiced in ancient and early modern times in which empirical induction leads to essential definitions and universal postulates for subsequent deduction. This is the Socratic view of induction: “in modern philosopher’s technical terms—the …
Kinecosm is the world of motion, which is the subject of kinematics. Since the extent of motion has two measures: length and duration, the kinecosm has two subworlds: Length space is the three-dimensional world of length, which is commonly called space. Duration space is the three-dimensional world of duration. Chorocosm is length space with time. …
This post is based on the article Deriving Lagrange’s equations using elementary calculus by Josef Hanc, Edwin F. Taylow, and Slavomir Tuleja (AJP 72(4) 2004), which provides a derivation of Lagrange’s equations from the principle of least action using elementary calculus. A tempicle moves along the t axis with potential lethargy W(t), which is location-independent. …
The traditional ratio, x : y, represents both x / y and y / x. In order to represent a ratio as quotients, both forms are required. Let us define a ratio as an ordered pair of quotients: For vectors this means One can either exclude zero or include infinity as follows; A rate of …
This is the latest post in a series on science and metaphysics; the previous post is here. The one and only metaphysical postulate of natural science is this: Everything has a fixed nature. This postulate allows the study of classes or kinds or types of things with a common fixed nature. For example, it allows …
This post is a slight modification of section 2.0 “The Parallel Sum of Vectors” from W. N. Anderson & G. E. Trapp (1987) “The harmonic and geometric mean of vectors”, Linear and Multilinear Algebra, 22:2, 199-210. We will consider vectors in a real N dimensional inner product space, although some of the results given herein …
The difference quotient is the average rate of change of a function between two points: The instantaneous rate of change is the limit of the difference quotient as t1 and t0 approach each other, which is the derivative of f(t) at that point, denoted by f′(t). Derivatives are added by arithmetic addition, i.e., if f(t) …
