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Bivalent Logic
A clear and succinct introduction to the two-valued logic pioneered by Aristotle. Associated topics covered include: the combinatorial basis of truth tables, Boolean Vector Arithmetic (an efficient implementation of truth tables utilizing matrices), rules of inference, the deductive argument form, as well as a brief logical analysis of Descartes' most famous argument.
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- GenresPhilosophy
30 pages, Kindle Edition
First published June 18, 2012
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About the author
Cliff Hays
8 books107 followersMusician and author from the USA, primarily influenced by mathematics, science, and philosophy. Has written two science fiction short stories
Dual Void
and
IHU
; one work of mathematics
Bivalent Logic
; two works of epistemology and philosophy of science
Aamrgan
and
On the Preservation of Enthusiasm
; as well as
Essays in Science and Philosophy [2004 - 2009]
(seven essays exploring and explicating various interrelated topics, such as: temporality, gravity, relativity, epistemology, agnosticism, metaphysics, existentialism, consciousness, music, art, physics, and cosmology).
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Displaying 1 - 3 of 3 reviews
June 19, 2017
I had this wonderful idea for an app that would use bivalent logic to evaluate and flag fake news.
Although bivalent or “missing middle” logic was invented by Aristotle (384 – 322 BC) in Organon (see the square of oppositions) and can be thought of as the basis for the microchip, where an electrical impulse can follow a circuit through different paths such as AND, IF (if and only if), OR or NOT gates (since replaced by the concept of negation as failure and yet to be replaced by quantum superposition), the main attraction for this purpose, the evaluation of text, is that it converts directly to binary code. Wa-hey! Low hanging mangoes. Digital evaluation of words can produce a quantified output, which can then generate a probability of (for example) bias, hoax or even a fake review, without being clouded by the interpretation of the observer.
This is how bias can be revealed in text:
Fake claims can be identified by frequency of first tier unproven statements and instances of the reinforcement of first tier claims citing second tier unproven supporting statements as factual. A fake review can be identified by an over-use of superlatives and low proportion of negative criticism.
Something either is or it isn’t; 0 or 1, so every statement has one of two possible truth values, true (1) or the negative of truth (0). Almost nothing non-mathematical can be proven to be true so the benchmark for this has to be what the accepted literature takes as “proven” to the current extent of our knowledge at this time. UFOs, for example, are proven – anything positioned in the air that you can’t quite identify. Aliens are not, so claiming a UFO = 1 but claiming it is therefore alien = 0. It cannot be both true and false, so that’s a bad mark for the trustworthiness of the text (unless it becomes the accepted reality later, when the literature catches up).
Statement: We build. Non-statement: Should we build? Opinion: We should not build. Command: Build! The truth value is assigned based on whether it happened or not, i.e. did we build (1) or not(0)? The assessment of whether something is a statement or a non-statement is important.
(With non-contradiction) that leaves seven sets of binary truth values shown as digits:
A (it is) = T, T, F, F = 1100
B = T, F, T, F = 1010
¬A (it is not) = F, F, T, T – 0111
¬B = F, T, F, T = 0101
A∧¬A = T, T, T, T = 0000
AV¬A (it is or it is not) = T, T, T, T = 1111
A∧B – T, F, F, F = 1000
To give you an idea without the numbers, lots of praise in a review and hardly any destructive questioning would leave a tally like 19 x F, 1 x T = 95% chance it has been written by a friend of the author. A high proportion of unfactual or unsubstantiated statements in an article would leave a similar trail, question mark count, for a fake or biased news report. A significant count of rubbishing the alternative would also flag as propaganda. This would initially need a human assessor until we can connect a database or encyclopaedia to match claims against. Results for tabloid newspaper editorials or scores for the reliability of individual journalists would be very revealing.
The app could be expanded to spot ideological leanings or favouritism being expressed by the writer for one nation or race over another. To clarify, using a particular word would not generate a result, e.g. “the foundation studied communism/fascism/racism for years”, but when the subject has been frequently referred to in conjunction with words such as “like”, “love” or saying the subject is “the best system” or “obviously correct” those would ring a bell, as would denigrating or stigmatising words against the subject’s diametric opposition. The only way a propaganda writer could avoid having their article flagged as propaganda and themselves as biased would be to take out the favouritism and stick to selective recounting of the facts, which would be a big improvement.
How should I rate this book? In mathematics, the result is either perfectly correct or it isn’t and in bivalence it is or it is not, so this book is either correct or it isn’t and I could give it 5 stars but that would be a world gone topsy turvy when there’s an unnecessary “of” in the Descartes section toward the end and also I’m a subjective human reviewer rather than a robot, so I’ve unilaterally deducted a star from this book because it gave me a headache. Clearly, I’m not bivalent. Byte me.
Although bivalent or “missing middle” logic was invented by Aristotle (384 – 322 BC) in Organon (see the square of oppositions) and can be thought of as the basis for the microchip, where an electrical impulse can follow a circuit through different paths such as AND, IF (if and only if), OR or NOT gates (since replaced by the concept of negation as failure and yet to be replaced by quantum superposition), the main attraction for this purpose, the evaluation of text, is that it converts directly to binary code. Wa-hey! Low hanging mangoes. Digital evaluation of words can produce a quantified output, which can then generate a probability of (for example) bias, hoax or even a fake review, without being clouded by the interpretation of the observer.
This is how bias can be revealed in text:
Fake claims can be identified by frequency of first tier unproven statements and instances of the reinforcement of first tier claims citing second tier unproven supporting statements as factual. A fake review can be identified by an over-use of superlatives and low proportion of negative criticism.
Something either is or it isn’t; 0 or 1, so every statement has one of two possible truth values, true (1) or the negative of truth (0). Almost nothing non-mathematical can be proven to be true so the benchmark for this has to be what the accepted literature takes as “proven” to the current extent of our knowledge at this time. UFOs, for example, are proven – anything positioned in the air that you can’t quite identify. Aliens are not, so claiming a UFO = 1 but claiming it is therefore alien = 0. It cannot be both true and false, so that’s a bad mark for the trustworthiness of the text (unless it becomes the accepted reality later, when the literature catches up).
Statement: We build. Non-statement: Should we build? Opinion: We should not build. Command: Build! The truth value is assigned based on whether it happened or not, i.e. did we build (1) or not(0)? The assessment of whether something is a statement or a non-statement is important.
(With non-contradiction) that leaves seven sets of binary truth values shown as digits:
A (it is) = T, T, F, F = 1100
B = T, F, T, F = 1010
¬A (it is not) = F, F, T, T – 0111
¬B = F, T, F, T = 0101
A∧¬A = T, T, T, T = 0000
AV¬A (it is or it is not) = T, T, T, T = 1111
A∧B – T, F, F, F = 1000
To give you an idea without the numbers, lots of praise in a review and hardly any destructive questioning would leave a tally like 19 x F, 1 x T = 95% chance it has been written by a friend of the author. A high proportion of unfactual or unsubstantiated statements in an article would leave a similar trail, question mark count, for a fake or biased news report. A significant count of rubbishing the alternative would also flag as propaganda. This would initially need a human assessor until we can connect a database or encyclopaedia to match claims against. Results for tabloid newspaper editorials or scores for the reliability of individual journalists would be very revealing.
The app could be expanded to spot ideological leanings or favouritism being expressed by the writer for one nation or race over another. To clarify, using a particular word would not generate a result, e.g. “the foundation studied communism/fascism/racism for years”, but when the subject has been frequently referred to in conjunction with words such as “like”, “love” or saying the subject is “the best system” or “obviously correct” those would ring a bell, as would denigrating or stigmatising words against the subject’s diametric opposition. The only way a propaganda writer could avoid having their article flagged as propaganda and themselves as biased would be to take out the favouritism and stick to selective recounting of the facts, which would be a big improvement.
How should I rate this book? In mathematics, the result is either perfectly correct or it isn’t and in bivalence it is or it is not, so this book is either correct or it isn’t and I could give it 5 stars but that would be a world gone topsy turvy when there’s an unnecessary “of” in the Descartes section toward the end and also I’m a subjective human reviewer rather than a robot, so I’ve unilaterally deducted a star from this book because it gave me a headache. Clearly, I’m not bivalent. Byte me.
August 8, 2014
I ordinarily might have skipped over this title, but it was written by Cliff Hays, who is an author I admire. I decided to read it and I am glad I did.
Despite the daunting sound of the title, Cliff Hays manages to communicate an abstruse subject with amazing clarity.
He is conscientious about laying out basic terminology at the beginning and clarifying concepts with tables and charts, and he even includes some end-of-chapter recaps to review terminology. Each point proceeds logically to the next, so it is easy to follow.
Beyond the clear presentation,the content itself is fascinating. Although I took a philosophy class in college, my professor skimmed over the chapter on logic, and this book filled in some of the gaps.
What interested me about this book is how subjects I normally think of only in verbal terms were perfectly translated into the language of math.
The book starts off with verbally expressed logic, but there was a startling moment where statements completely left the verbal plane and entered the realm of mathematics. To someone who is used to programming this might not seem unusual, but it actually gave me a new way of looking at math, and I love books that introduce a new perspective.
Cliff Hays is an amazing writer who has given a great deal of thought to presenting an abstruse subject in a way that is clear and succinct.
Anyone who is interested in exploring the logical aspect of philosophy will find a lot to learn in this book, in addition to an enjoyable reading experience.
Despite the daunting sound of the title, Cliff Hays manages to communicate an abstruse subject with amazing clarity.
He is conscientious about laying out basic terminology at the beginning and clarifying concepts with tables and charts, and he even includes some end-of-chapter recaps to review terminology. Each point proceeds logically to the next, so it is easy to follow.
Beyond the clear presentation,the content itself is fascinating. Although I took a philosophy class in college, my professor skimmed over the chapter on logic, and this book filled in some of the gaps.
What interested me about this book is how subjects I normally think of only in verbal terms were perfectly translated into the language of math.
The book starts off with verbally expressed logic, but there was a startling moment where statements completely left the verbal plane and entered the realm of mathematics. To someone who is used to programming this might not seem unusual, but it actually gave me a new way of looking at math, and I love books that introduce a new perspective.
Cliff Hays is an amazing writer who has given a great deal of thought to presenting an abstruse subject in a way that is clear and succinct.
Anyone who is interested in exploring the logical aspect of philosophy will find a lot to learn in this book, in addition to an enjoyable reading experience.
December 10, 2015
What impresses me the most about this text is how adeptly Cliff Hays explains difficult concepts which might appear daunting if revealed any other way. His writing clearly illuminates the inextricable connection between philosophy, logic, and math, which I found to be quite intriguing. Even though the material itself is rigorous, the organizational flow and neatly arranged diagrams make this text easy to follow and refer back to. If only I'd had this available to use in college, I think it would've proven especially helpful in terms of constructing and evaluating arguments. Fortunately though, I have it now and I find it invaluable for use everyday, not simply as a reference source, but as a foundation for critical thinking.
Displaying 1 - 3 of 3 reviews