On Second Thought

 

PREVIOUSLY ON NECESSARY FACTS

Open Secrets

NYC, Covid-19, and Conservative Business Interests 

All Volitional Beings Deserve Rights 

How to Start Your Own Country 

George Boole's Laws of Thought

Everyone who knows computing knows the Boolean operators AND, NAND, OR, XOR, and NOT.  They allow us to construct conditional statements, and programmatic branching.  Electrical engineers learn the rules of Boolean Algebra with two values OFF and ON; and with three operators,  PARALLEL, SERIES, and a simple switch for NOT.   0 and 1 are OFF and ON. The three operators  of Boolean algebra are + X and ~ corresponding to OR, AND, and NOT. They are the same as PARALLEL, SERIES, and SWITCH.  George Boole had a different view entirely.  His 1853 book, An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, is a treatise on epistemology.  

We learn that correct thinking by logic is a reduction by syllogism.  All men are mortal. Socrates is a man. Therefore, Socrates is mortal.  If A =B and B = C, then A = C. The middle or the mean term is factored out. Boole granted that syllogism is one kind of valid method. However, rather than reducing statements, Boole argued by expansion for a deeper and extended understanding of seemingly simple truths.  His algebra is deceptively similar to – but different from – the forms we learned in high school; and so the learner here must pay close attention to these laws of thought. 

If x is “red” then xx means “red red” which is nonetheless still “red.”  If the essential attribute under consideration is “red” then red red things with their redness removed do not exist: xx – x = 0. Taking from Leibniz, Boole lets 0 be non-existence and 1 be the universe.   If x is our subject, then (1-x) is everything else in the universe except x. Boole rewrites xx-x as x(1-x) = 0 to give Aristotle’s Law of Contradiction: A thing cannot both have and not have the same attribute in the same way at the same time.  Boole calls this “duality.”  Also following Leibniz, Ayn Rand delivered that as  “A or non-A.”  

In 400 pages, Boole carefully applies the essential truths he discovered. He extracts more meaning – and more exacting meanings – from common statements.  However, his insistence on closely laying every step of this long journey, couched, as it was, and, indeed, of necessity, both historical and personal, must have been, in Victorian prose, renders this important work so Germanic as to be nearly unreadable.  It is well worth the effort.

“Wealth consists of things transferable, limited in supply, and either productive of pleasure or preventive of pain.” 

w = wealth

s = limited in supply

t = transferable

p = productive of pleasure

r = preventive of pain

Boole specially defines 0/0 to mean the undefined.  He includes this to stand for the indefinite class: those things not included in the present statement but which exist nonetheless.

Given that this book is 400 pages and Ayn Rand’s Introduction to the Objectivist Epistemology is 164, Boole boldly goes beyond the orbit of concept formation.  He nonetheless is in the same material space: he identifies reality; and ties concepts to objects. Boole explores the relationships between the processes of thought and perception and the expression of them through language. 

Boole even applies his method to statements about God.  His goal is not to address God’s existence but to expand and analyze statements about God asserted by Baruch (“Benedict”) Spinoza and Samuel Clarke.  (“… considered the major figure in British philosophy between John Locke and George Berkeley.” – Wikipedia here.)  From there, he examines Aristotle’s logic and Fermat’s probabilities.   The last third of the book is about the logic of probability theory.

ALSO ON NECESSARY FACTS

Knowledge Maps

Visualizing Complex Data

Gregory M. Browne's Necessary Factual Truth

Understanding Objectivism by Peikoff and Berliner

Knowledge Maps

Now running on the Objectivist discussion site, Rebirth of Reason, is a set of multilateral exchanges comparing and contrasting the epistemologies of Karl Popper and Ayn Rand.  I believe that independent of partisanship many of the presentations are taxed by a lack of common vocabulary.  

Often, writers intend different meanings from the same word.  This is a hallmark of discussions with Objectivists for whom selfishness is a virtue.  One sub-thread differentiated “risk” from “uncertainty” with different assertions originating in the varied life experiences of the writers.  To engineer Fred Bartlett, a machined bolt of 8.5 cm +/- .03 is unarguably defined.  Is “authority” always unarguable?  Political authority is easily contradicted, but what about the “authority” of reason? 

 

From Frege's Lectures on Logic: Carnap's Student Notes (2004)

Certainly, the Objectivists are not alone in their quandaries.  Every non-trivial communication risks failure, from slight to partial to complete.  Common schooling left us all with the implicit belief that if you can look a word up in a dictionary, you can rely on an objective definition that everyone understands.  However, the important elements of our lives cannot be expressed in a handful of words, delivered as phrases, rather than sentences.  (Dictionaries do include pictures.)  On a different plane of understanding, the Austrian economist Ludwig von Mises acknowledged that capitalists and socialists often agree on the facts – in a certain place, at a given time, some commodity had a known price.  Where they disagree is on what the facts mean.  Such meanings cannot be found in a dictionary.  They require more complicated, nuanced, and subtle explanations, often including analogy and allegory. 

 

In the Star Trek: Next Generation episode “Darmok” 
we met the Tamarians who communicated in allegory. 
(See Memory Alpha here.) 
Tamarian Captain and Jean-Luc Picard.
Picard recites from the Gilgamesh before the wounded Tamarian dies.

Even if the philosophers could decide on a common vocabulary and a common narrative, the primary constraint may be the very dependence on verbal expressions: graphs might serve everyone better.  Outside of information systems, we do not study means of graphical representation, except, of course, for actual artists. 

Order Entry Program Code Documented
with Nassi-Shneiderman Diagram

Microsoft’s Visio delivers many graphical tool sets.  You are not morally obligated to engage the Database shapes and connectors only for the design of databases.  In the machine shop, we neither use screwdrivers as chisels nor calipers as clamps; but, a thousand years ago, when mastodons roamed the streets, my friend Geoff saw VisiCalc for the Apple // and said, “You could make a pretty good word processor with this.” 

 

From Carnap's Notes (2004)

Gottlob Frege developed a graphical representation for logic.  It presaged the notation systems of electricians.  The electrical schematics for series and parallel circuits, for Normally Off and Normally On, led to the circuit logic we accept today.  That much is all fine for planar arrays of linear logic.  What about events that unfold over time?

Star Trek Enterprise, "Cold Front"
Crewman Daniels shows Captain Archer
a map of their problem

PREVIOUSLY ON NECESSARY FACTS
Visualizing Complex Data
Readability is the only Metric
Documentation is Specification
The Genius of Design
The Art of Typography