# rag ## Squares of opposition

The traditional Aristotelian square of opposition is like that of first-order logic apart from existential import: For quantifiers (or other operators) there is a duality square: Outer negation is negation of the whole quantifier; inner negation is negation within the quantifier. For rates the inverse (reciprocal) acts like a negation: Outer inverse is the inverse …

## Lorentz transformation derivation fails

Attempted derivations of the Lorentz transformation in the previous post here, which is similar to the light wavefronts approach here, do not work. The reason is that independent and dependent variables are treated alike, but they are not. I suspect this applies to all derivations of the Lorentz transformation. Let us look at the first …

## Uniform rate of the rate of change

The Merton Rule, which dates to the Middle Ages, relates a uniform change rate to its initial and final rates. Because of its main application, it is also called the Mean Speed Theorem, which in modern language states that a uniformly accelerating body over a period of time traverses the same distance as the product …

## Moral and ethical distinctions

Moral truth, goodness, and beauty are defined as those that exist on their own, without the necessity of a contrary (inner) or contradictory (outer) opposite. What is moral exists without a necessary opposite. God is moral because God exists without a necessary opposite. Whatever is of God is also moral. Whatever contradicts God or something …

## Derivatives and quantities with units

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 …

## Two kinds of induction

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 …

## Converse physics

Velocity is defined as: where s is the displacement and t = â€–tâ€– is the independent time interval, the distime of a parallel reference motion. The inverse of v is the function defined by the reciprocal of this derivative: The converse of v is w, the lenticity, which is defined as: where t is the …

## Symmetry of length and duration

There is a symmetry principle for length and duration: Measures of length and duration are interchangeable and the forms of equations remain the same if all measures of length are interchanged with their corresponding measures of duration and vice versa. The three-dimensionality of length is fully reflected in the three-dimensionality of duration. This is a …

## Transformations with 3-dimensional time

Following the previous post here, we use Jacobian matrices to transform location and chronation vectors between inertial observers. As before, let matrices be written with upper case boldface. Let vectors be written in lowercase boldface and their scalar magnitude without it. Velocity = V, lenticity = W, displacement = s, distimement = t, distance = s, distime = t. …

## Definitions with 3-dimensional time

In order to combine the three dimensions of length space and three dimensions of duration space in definitions for motion in six dimensions (3+3), it is necessary to use Jacobian matrices. The 3+1 and 1+3 dimensional definitions are simplifications of these. Let matrices be written with upper case boldface. Let vectors be written in lowercase boldface …