Can a truth value be a relation instead of a function? (Law of Non-Contradiction challenged)

  • Thread starter Thread starter Ben_Sinner
  • Start date Start date
Status
Not open for further replies.
B

Ben_Sinner

Guest
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-…d-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.
 
Ben_Sinner said:
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-…d-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.
Click to expand...
I’m gonna kill the fun 😦

This old discussion, if it runs cogently, will turn into a debate about 1. the meaning of “truth” and 2. the underlying and unnamed assumptions in play when evaluating a truth.
 
How would one’s faith or agnosticism affect his answer about a logical question? There are no such things as “Catholic logic” or “secular logic.” The only theologian, moreover, I know of who works in such terms is the Protestant Albrecht Ritschl, who disliked the influence of Aristotle and the Scholastics and sought to base his views in what he called value judgments. In Ritschl’s view, dogma was not factual and could not be known, while the truths were assert about God could be known only by the practical experience of the relationship of the faithful community to him.

It’s not a very Catholic view, but it’s the closest one to putting your ideas here into any sort of theological context.
 
bardegaulois said:
How would one’s faith or agnosticism affect his answer about a logical question? There are no such things as “Catholic logic” or “secular logic.” The only theologian, moreover, I know of who works in such terms is the Protestant Albrecht Ritschl, who disliked the influence of Aristotle and the Scholastics and sought to base his views in what he called value judgments. In Ritschl’s view, dogma was not factual and could not be known, while the truths were assert about God could be known only by the practical experience of the relationship of the faithful community to him.

It’s not a very Catholic view, but it’s the closest one to putting your ideas here into any sort of theological context.
Click to expand...
I wasn’t saying that. I’m saying these forms of four valued logic are are held by orthodox Catholics due and would like know how these logics can be refuted as false.
 
I wasn’t saying that. I’m saying these forms of four valued logic are not held by orthodox Catholics due to this logic justifying eastern religions and would like know how these logics can be refuted as false.
 
Ben_Sinner said:
I wasn’t saying that. I’m saying these forms of four valued logic are not held by orthodox Catholics due to this logic justifying eastern religions and would like know how these logics can be refuted as false.
Click to expand...
To a degree, they’re different systems that attempt to model reality mathematically. I don’t know that there is a definitive mathematical disproof, though there’s not a disproof of more traditional logic, either. Not all mathematicians agree with this four valued logic.

It’s important to note that Aristotle and later the scholastically did not think formal logic rules (as a mathematical system) was the best way to argue everything. And I’d be more interested in looking at actual examples. Your article says that the statement ‘This sentence is false’ is both true and false, but to me it just seems to be neither true nor false. The PNC would not necessarily apply to all mathematical systems. You could have systems defined without it. The question is whether they best represent reality and are actually meaningful, and the PNC is about things actual, not just hypothetical or not clearly defined statements. Take your old example of the barber who shaves everyone who does not shave himself. Does the barber shave himself? A conclusion from the defined grouping is difficult, it seems like the answer is both or neither, but in reality, he has to either shave himself or not. It can’t be both. (Well, I suppose he could shave half his face and have someone else do the other half ;), but you know what I mean in the context of this example).
 
Wesrock said:
To a degree, they’re different systems that attempt to model reality mathematically. I don’t know that there is a definitive mathematical disproof, though there’s not a disproof of more traditional logic, either. Not all mathematicians agree with this four valued logic.

It’s important to note that Aristotle and later the scholastically did not think formal logic rules (as a mathematical system) was the best way to argue everything. And I’d be more interested in looking at actual examples. Your article says that the statement ‘This sentence is false’ is both true and false, but to me it just seems to be neither true nor false. The PNC would not necessarily apply to all mathematical systems. You could have systems defined without it. The question is whether they best represent reality and are actually meaningful, and the PNC is about things actual, not just hypothetical or not clearly defined statements. Take your old example of the barber who shaves everyone who does not shave himself. Does the barber shave himself? A conclusion from the defined grouping is difficult, it seems like the answer is both or neither, and we could debate for hours or days about the truth value. But in reality, he has to either shave himself or not. It can’t be both. (Well, I suppose he could shave half his face and have someone else do the other half ;), but you know what I mean in the context of this example).
Click to expand...
 
Ben_Sinner said:
I wasn’t saying that. I’m saying these forms of four valued logic are not held by orthodox Catholics due to this logic justifying eastern religions and would like know how these logics can be refuted as false.
Click to expand...
Catholic programmers would disagree. For instance, a system with multiple sources might have the four states:

false : all sources get false
true : all sources get true
both : some sources get false but others get true
neither : unknown (no sources available)
 
inocente said:
Catholic programmers would disagree. For instance, a system with multiple sources might have the four states:

false : all sources get false
true : all sources get true
both : some sources get false but others get true
neither : unknown (no sources available)
Click to expand...
Seems that True/False are the ultimate criteria of existence. IE,

has state 1 been achieved? (False/True)
has state 2 been achieved? (False/True)
etc.

peace
steve
 
thenobes said:
Seems that True/False are the ultimate criteria of existence. IE,

has state 1 been achieved? (False/True)
has state 2 been achieved? (False/True)
etc.

peace
steve
Click to expand...
That would be nice, but perhaps some questions don’t have a true/false answer. For instance, sources disagree on whether Guernica is the best painting ever. Or whether we have free-will. Or whether numbers have real existence. Perhaps such questions don’t have a true/false answer even in principle, and we then need the other states to describe them. Don’t know.
 
Status
Not open for further replies.
Back
Top