Induction and Laws of Form

I wrote before here about the book Laws of Form. I’ve written recently about conceptual induction here. This post connects the two. In the book Laws of Form, Appendix 2, G. Spencer-Brown interprets the calculus of indication for logic and finds a problem when it is interpreted existentially. To avoid this problem he introduces “Interpretive

Induction and Laws of Form Read More »

Induction with uniformity

John P. McCaskey has done a lot of research (including a PhD dissertation) on the meaning of induction since ancient times. He keeps some of his material online at http://www.johnmccaskey.com/. A good summary is Induction Without the Uniformity Principle. McCaskey traced the origin of the principle of the uniformity of nature (PUN) to Richard Whately

Induction with uniformity Read More »

Uniformity without a principle

I have written about uniformity before, such as here and here. This post looks at the need for a principle of uniformity. David Hume’s principle of the uniformity of nature (PUN) asserts that unobserved cases closely resemble previously observed cases. This principle concerns the character of natural populations based on a sample as well as

Uniformity without a principle Read More »

Six dimensions of space-time

If one travels a distance X east, then goes a distance Y north, that is the same as going a distance √(X² + Y²) northeast. But if one travels for a time X east, then goes for a time Y north, is that the same as going for a time √(X² + Y²) northeast? No,

Six dimensions of space-time Read More »

Miracles and uniformity

The week before Christmas is a good time of year to write about miracles because it’s a time to be reminded of the meaningfulness of miracles. But what about their truth? Doesn’t the uniformity of nature make miracles impossible? Thomas Aquinas said a miracle is ‘beyond the order commonly observed in nature’ (Summa Contra Gentiles

Miracles and uniformity Read More »

Time scale maps

Maps of travel times have various names, e.g., time scale maps, isochrone maps, etc. Often a geographic map forms the background so that travel time is superimposed on distance traveled. Occasionally, the time scale replaces the distance scale and the map looks distorted from a geographic perspective, but is correct from a travel time perspective.

Time scale maps Read More »

A new geometry for space and time

This blog has described how as the distances between places cover three dimensions of space, so the durations between events cover three dimensions of time. One way of looking at this is as a map with the distance and duration given between places, such as this from the Interstate Drive Times and Distances: There are

A new geometry for space and time Read More »

Why time is three dimensional

The case for 3D time is very simple: space is based on the measurement of distance and time is based on the measurement of duration. As the distances between places cover three dimensions of space, so the durations between events cover three dimensions of time. As distance may be measured going from or toward a

Why time is three dimensional Read More »