Can 4-valued logic be refuted?

[Ben_Sinner]

Some people reject the Law of Non-Contradiction that a thing can either be true or false, nothing in between.

Instead they believe in a system where there are 4 possibilities.

1. True
2. False
3. Both True and False
4. Neither True or False.

Here is an article that tries to justify this logic.

aeon.co/essays/the-logic-of-buddhist-philosophy-goes-beyond-simple-truth

At the core of the explanation, one has to grasp a very basic mathematical distinction. I speak of the difference between a relation and a function. A relation is something that relates a certain kind of object to some number of others (zero, one, two, etc). A function, on the other hand, is a special kind of relation that links each such object to exactly one thing. Suppose we are talking about people. Mother of and father of are functions, because every person has exactly one (biological) mother and exactly one father. But son of and daughter of are relations.

Now, in logic, one is generally interested in whether a given claim is true or false. Logicians call true and false truth values. Normally, and following Aristotle, it is assumed that ‘value of’ is a function: the value of any given assertion is exactly one of true (or T), and false (or F). In this way, the principles of excluded middle (PEM) and non-contradiction (PNC) are built into the mathematics from the start. But they needn’t be.

To get back to something that the Buddha might recognise, all we need to do is make value of into a relation instead of a function. Thus T might be a value of a sentence, as can F, both, or neither.

 

[AgnosticBoy]

Some people reject the Law of Non-Contradiction that a thing can either be true or false, nothing in between.

Instead they believe in a system where there are 4 possibilities.

1. True
2. False
3. Both True and False
4. Neither True or False.

Here is an article that tries to justify this logic.

aeon.co/essays/the-logic-of-buddhist-philosophy-goes-beyond-simple-truth

At the core of the explanation, one has to grasp a very basic mathematical distinction. I speak of the difference between a relation and a function. A relation is something that relates a certain kind of object to some number of others (zero, one, two, etc). A function, on the other hand, is a special kind of relation that links each such object to exactly one thing. Suppose we are talking about people. Mother of and father of are functions, because every person has exactly one (biological) mother and exactly one father. But son of and daughter of are relations.

Now, in logic, one is generally interested in whether a given claim is true or false. Logicians call true and false truth values. Normally, and following Aristotle, it is assumed that ‘value of’ is a function: the value of any given assertion is exactly one of true (or T), and false (or F). In this way, the principles of excluded middle (PEM) and non-contradiction (PNC) are built into the mathematics from the start. But they needn’t be.

To get back to something that the Buddha might recognise, all we need to do is make value of into a relation instead of a function. Thus T might be a value of a sentence, as can F, both, or neither.

I don’t have a refutation for the 4 values since I believe contradictions are possible through various psychological phenomena. I also believe that contradictions can exist on the level of belief in which belief would be based on a degree (less than 100%) of truth rather than being an all-or-nothing truth. I can expand more if that’s what you’re also looking for.

 

[Ben_Sinner]

I don’t have a refutation for the 4 values since I believe contradictions are possible through various psychological phenomena. I also believe that contradictions can exist on the level of belief in which belief would be based on a degree (less than 100%) of truth rather than being an all-or-nothing truth. I can expand more if that’s what you’re also looking for.

What psychological phenomena are you speaking of?

 

[AgnosticBoy]

What psychological phenomena are you speaking of?

Split brain syndrome. This can occur when the connection between the right and left hemispheres of the brain are surgically severed in a procedure called ‘corpus callosum’. This actually can lead to more than just contradictory beliefs but also to contradictory behaviors which is further described in my source below.
Source: nature.com/news/the-split-brain-a-tale-of-two-halves-1.10213

Here’s an excerpt:

Standing in the supermarket aisle, Vicki would look at an item on the shelf and know that she wanted to place it in her trolley — but she couldn’t. “I’d reach with my right for the thing I wanted, but the left would come in and they’d kind of fight,” she says. “Almost like repelling magnets.”

There’s also other psychological phenomena where contradictions can exist, like ‘cognitive dissonance’, ‘ambivalence’, ‘compartmentalization’, etc.

 

[surritter]

Are we talking about the Law of Non-Contradiction for very specific things? Because there are many statements that are neither true nor false.

For example, suppose I claim that “It rains sideways in California.” That is not absolutely true, but since it might happen there occasionally if the wind blows just right, then neither is it absolutely false.

 

[inocente]

Can 4-valued logic be refuted?

Yes. And no.