I don’t think it’s fair to demand a full explanation of a topic that’s been around for over two decades (though a link to an online treatment would have been nice). Warrigal didn’t ‘come up with’ fractional values for truth. It’s a concept that’s been around (central?) in Eastern philosophy for centuries if not millenia, but was more-or-less exiled from Western philosophy by Aristotle’s Law of the Excluded Middle.
Fuzzy logic has proven itself very useful in control systems and in AI, because it matches the way people think about the world. Take Hemingway’s Challenge to “write one true [factual] sentence” (for which you would then need to show 100% exact correspondence of words to molecules in all relevant situations) and one’s perspective can change to see all facts as only partially true. ie, with a truth value in [0,1].
The statement “snow is white” is true if and only if snow is white, but you still have to define “snow” and “white”. How far from 100% even reflection of the entire visible spectrum can you go before “white” becomes “off-white”? How much can snow melt before it becomes “slush”? How much dissolved salt can it contain before it’s no longer “snow”? Is it still “snow” if it contains purple food colouring?
The same analysis of most concepts reveals we inherently think in fuzzy terms. (This is why court cases take so damn long to pick between the binary values of “guilty” and “not guilty”, when the answer is almost always “partially guilty”.) In fuzzy systems, concepts like “adult” (age of consent), “alive” (cryonics), “person” (abortion), all become scalar variables defined over n dimensions (usually n=1) when they are fed into the equations, and the results are translated back into a single value post-computation. The more usual control system variables are things like “hot”, “closed”, “wet”, “bright”, “fast”, etc., which make the system easier to understand and program than continuous measurements.
Bart Kosko’s book on the topic is Fuzzy Thinking. He makes some big claims about probability, but he says it boils down to fuzzy logic being just a different way of thinking about the same underlying math. (I don’t know if this gels with the discussion of ‘truth functionalism’ above) However, this prompts patterns of thought that would not otherwise make sense, which can lead to novel and useful results.
I don’t think it’s fair to demand a full explanation of a topic that’s been around for over two decades (though a link to an online treatment would have been nice). Warrigal didn’t ‘come up with’ fractional values for truth. It’s a concept that’s been around (central?) in Eastern philosophy for centuries if not millenia, but was more-or-less exiled from Western philosophy by Aristotle’s Law of the Excluded Middle.
Fuzzy logic has proven itself very useful in control systems and in AI, because it matches the way people think about the world. Take Hemingway’s Challenge to “write one true [factual] sentence” (for which you would then need to show 100% exact correspondence of words to molecules in all relevant situations) and one’s perspective can change to see all facts as only partially true. ie, with a truth value in [0,1].
The statement “snow is white” is true if and only if snow is white, but you still have to define “snow” and “white”. How far from 100% even reflection of the entire visible spectrum can you go before “white” becomes “off-white”? How much can snow melt before it becomes “slush”? How much dissolved salt can it contain before it’s no longer “snow”? Is it still “snow” if it contains purple food colouring?
The same analysis of most concepts reveals we inherently think in fuzzy terms. (This is why court cases take so damn long to pick between the binary values of “guilty” and “not guilty”, when the answer is almost always “partially guilty”.) In fuzzy systems, concepts like “adult” (age of consent), “alive” (cryonics), “person” (abortion), all become scalar variables defined over n dimensions (usually n=1) when they are fed into the equations, and the results are translated back into a single value post-computation. The more usual control system variables are things like “hot”, “closed”, “wet”, “bright”, “fast”, etc., which make the system easier to understand and program than continuous measurements.
Bart Kosko’s book on the topic is Fuzzy Thinking. He makes some big claims about probability, but he says it boils down to fuzzy logic being just a different way of thinking about the same underlying math. (I don’t know if this gels with the discussion of ‘truth functionalism’ above) However, this prompts patterns of thought that would not otherwise make sense, which can lead to novel and useful results.