An article on Aeon published the concept of catuskoti, a principle in use during the age of Buddha. It states that for any given statement, there are four possibilities i.e. it might be true (and true only), false (and false only), both true and false, or neither true nor false.
I think the first two concepts are not that strange: "I am having a cup of coffee" is true and only true. "I am having a cup of tea" is false and only false.
But also "neither false nor true" is very common. For example if you have sentences with a wrong presupposition: "My cup of tea is cold". Since I don't have a cup of tea, it makes no sense to say if it is cold or not. It isn't true that it is cold. But also it isn't true that it is hot, or warm or has any given temperature at all. Also there is some debate if sentences about the future can be right or wrong. What about "Tomorrow the sun will shine"? Sure: Once it is tomorrow, you will know if the sun is shining. But then that sentence isn't saying anything about the future any more, but about the present: "Now the sun is shining." That wasn't the question. The question was about "Tomorrow the sun will shine". Is it now true or false?
Also "true and false" sentences are not that rare: If you are on a train, it is perfectly true, that the station is moving away from you. Someone at the station would object: He is not moving away, you are moving away. In special relativity there are dozens of examples like these. All of them not abstract at all but very commonplace.
The point of the Catuskoti is to discuss subjects outside the context of the context of the everyday, or Lebenswelt as the author of the article points out; even the ordinary formal logic of Western Philosophy isn't designed for ordinary discourse.
The broad message might be that all statements can't be assigned truth values; the standard sentence that displays this is the liars paradox.
Another example for the mathematically inclined is that infinitisimals can be made rigorous in a logic that denies the Aritotelian law of contradiction; and this in a geometrical manner.
The philosopher of science David Albert applied catuskoti to superposition in Quantum mechanics, in his book Quantum Mechanics and Experience:
So what we're faced with is this: Electrons passing through this apparatus, in so far as we are able to fathom the matter, do not take route h and do not take route s and do not take both of those routes and do not take neither of those routes; and the trouble is that those four possibilities are simply all of the logical possibilities that we have any notion whatever of how to entertain!
"I love you, I hate you..." is a little bit false, because hate is not the negation of love. Hate is a different situation. If I don't love somebody, it doesn't mean necessarily I hate him/her. Love is one side, hate is the other side, and the don't love is the middle, in terms of sense. I think this is the correct: I love you, I don't love you, I love you and I don't love you, I neither love you nor don't love you.
This logical form applies all the time in ordinary life. It is really just two contradictory pairs orthogonal to each other, so is just Aristotle's logic in an extended form.
Aristotle doesn't need to deal with 'neither/both' since he does so in his definition for contradictory pairs, leaving him with just A/not-A. The catuskoti approach is required where no definition is given for contradictory pairs. But in the end it's the same logic in both cases.
I would suggest not paying much attention to Priest in Aeon on this matter. He does not understand Nagarjuna, the most prominent user of this logic. There is a rebuttal of his article and his view published on the blog of Bernardo Kastrup under the title 'Nagarjuna and the Law of non-contradiction in Buddhist philosophy'.
It's usually best not to take too seriously those who write about Buddhism but do not claim to understand it.
With the attitudes of love and/or hate toward our fellow human beings (as ourselves, and God or Nature), we always default to either one mode or the other.
For those who automatically default to 'hate' mode, very little can change their attitude. Even if they "like" or "need" someone, they continue to hate them although they might not always show it. They're likely to lie about it, even to profess love for them.
Hate is a function of dominance, manipulation, and control.
For those who automatically default to 'love' mode, again very little can change their attitude. Even if they are terrified of someone, they continue to treat them fairly anyway, only acting defensively when necessary for survival, protection, or well being of self and/or others.
Love is a function of respect and appreciation.
Even when acting defensively, those who automatically default to 'love' mode are motivated by a sense of righteousness, justice, and morality -- not by hate.
Their actions might be swift and final whenever absolutely necessary, but there is no inclination to torture, vindictiveness, revenge, or harsh punishments.
With the modes or attitudes of love and hate for the human species and for God or Nature, there is no "might", "maybe", "neither", or "both".
But then the default mode of love I just described can't be compared to individual marriage, romance, familial, social, or even national relationships or loyalties; because people can and often do become romantically or legally involved with a partner or partners -- without love ever entering the picture.
Likewise, assuming the default mode of love doesn't mean we want to become somehow involved with everyone we meet.
Likewise, someone whose default mode is to hate may intentionally involve themselves with others for reasons irrelevant to love.
In logic, the value "neither true nor false" is used a lot in three-valued logic, interpreted as "unknown", "unknowable/undecidable", or "irrelevant". This can lead to logical conclusions and reasoning including unknowns. Reasoning with unknowns is common in everyday life. As an example, if you know one shop sells apples, but you don't know if a second shop sells apples, you can still be sure that you will be able to buy apples if you visit both shops.
Another common example are loaded questions such as "Did you stop beating your wife" where neither "yes" nor "no" may apply, because the premise is hopefully wrong.
The fourth value (both true and false) is less common in everyday life though. In law and morality (or whenever rules apply), situations can occur though where the same action is both required by one rule and forbidden by another rule. In such cases reasoning can still be possible by weighting the different rules. Like when you have the duty to help a person in danger but are forbidden to enter the restricted area where the person lies. But I am not aware of any useful everyday inference that could be done other than realizing a system of rules is inconsistent. Other examples for this value (true and false at the same time), just to illustrate:
I created the article 'Catuṣkoṭi' on English Wikipedia. Some people have built on what I started, but how the article now stands, is pleasing. I feel the work showcases the relevance that the Catuṣkoṭi has to practical living and forming a sound worldview. I hold that the article could do with restructuring and for a section on the relationship and intersection of Apoha Theory (and the nature of the gestault), coupled with the hermeneutics and exegesis of the Catuṣkoṭi. Hopefully, someone will follow my lead and iterate as appropriate. Does anyone have any comment on the piece?
