Post by Eugene 2.0 on Sept 13, 2022 19:50:59 GMT
The predicates are to be defined by Aristotle as something attributed to substance, or this is something you can say about something. So, briefly the world can be divided into individuals like 'chairs', 'tables', 'lamps', etc and properties as 'wooden', 'round', 'metal', etc. Unlike just properties, predicates are everything that can be added to the substance or to the individuals. But there was another usual funciton - is a thought-model function. The predicates were supposed to be thought representations; it's like, an individual - is what you can see (directly), but properties or attributes are something you can say about them.
Much more later such a view was quite ruined by Russell, Wittgenstein, and the whole tradition of the most famous Analytic Philosophy followers. And that was a good point, because predicates were not serving their funcitons, nor explaining anything. How could we equal these words as "x bigger, than y" or " x such that laying down the street" as singular properties? That's why the role of predicates had been played already, and it was time to replace it with something more saner and more adequate. That was Predicate Calculus that allowed for predicates to wide their function just allowing them to utter a connection between individuals.
So, for that on the world had been divided into individuals (of different sorts), properties, different relations, and different classes. The classes are just names for groups of individuals. We constantly use them in pronouns or any other abstractions. But the abstractions are not such a problem if it can be difened. Briefly, a phrase like "Frank likes buying ice-cream to women" can be said using Predicate Calculus as "For all x, if x is woman, then Lfix", where 'L' means "__ likes to buy __ to __", 'f' means Frank, and 'i' - ice-cream. The function of predicate for now is just to connect individuals in a kind way. One may ask, what kind of connection is this, and are there any? - This is a good question. Predicates are still needed for this: if {a, b, c} is a set of individuals, then for them in this order there must be more, than one predicates. For instance, "a loves playing with b and c", or "a and b are chasing c", or "a gives b to c", etc.
That's why individuals only are supposed to have no independency without predicates. And that is something that bothers me. I don't think that individuals must be dependend of some thoughts (or anything else). I think there's a way to free individuals for this pit. How to try to make it? First of all, any predicate can be numerated: P1, P2, ..., Pn. An order of individuals is important. This can be seen on this example: "Mary loves John" is not the same as "John loves Mary". So we have to write using PC: Lmj =/= Ljm. A predicate may be replaced by another symbol, so L__ can be replaced with P__, or P1. Let's continue: "John wakes Mary up" :: Wjm or P2jm; "Mary hits John" :: Hmj or P3mj; and so on. We can replace P1, P2, ... to just 1, 2, 3 having: 1jm, 2jm, 3mj. Then let's say that 1jm, 2jm, and 3mj had been difined in a language before, so all we need to do is to check this out whether or not they are true, or to correspond with the world. If they are, then 1jm... are true, or else - they are false.
What is important is that it doesn't matter which symbols are using 1, 2, ..., or a, b, c... That's why 1jm... may be rewritten as ajm, bmj... If it's done, then all what we've got just sequences. To consider or not to consider them to be true or false is just a matter of consequences. The most important is to compare those sequences.
Therefore, the predicates are just kind of connections. Of course we may compare them as we do it with verbs like "to like", "to write", etc. However, it doesn't mean that "to write" in "I write this comment" and "John writes letters" are the same, and the so on in the other ones, so that's why to compare them - is just another new action which has to be checked further.
I think I've showed how individuals may be released from the chains of predicates, while we still are needed in some extra elements among the elements (or the individuals), because we do not see the individuals, but we see them connected or linked to each other in a certain way. We don't see a bird, but we see the one somewhere, and doing something. And so on. The more and more details, the deeper, and the deeper context.
By the way, if you're coding you can use even more plainer scheme to use predicates on your taste. Here's how can it be done: let's say that the maximum lenght of your predicate is 3, and you've got predicates as this: "Catherine asks John to visit Mary" or Acjm or P1cjm, or - in our version - 1cjm (or acjm). Anyway, you can code ordered sets using numbers in a certain way (it's totally upon you), and it seems that if you've got 3-lenght predicates, then you will require 3+3 set. (For x-lentght it's x+3 set.) 1 is reserved for the sign of the ordered set, another for the predicate, and the last one for the value.
Let's me introduce and example (it is not ASCII or binary):
0110 1011 0001 0010 0001 0001 = <P1aba=1> = ("a asks b to visit a" is true),
0110 1100 0001 0011 0000 0001 = <P2ac=1> = ("a pleases c" is true),
0110 0101 0010 0000 0000 0000 = <P3b=0> = ("b lurks" is false).
There are numerous ways to code it. The idea is simple, but there's an important idea that can tell that there may be no thoughts. It's possible to talk to each other using only the objects, while only in a right sequence. If the sequence is correct, then the talk is success.
Much more later such a view was quite ruined by Russell, Wittgenstein, and the whole tradition of the most famous Analytic Philosophy followers. And that was a good point, because predicates were not serving their funcitons, nor explaining anything. How could we equal these words as "x bigger, than y" or " x such that laying down the street" as singular properties? That's why the role of predicates had been played already, and it was time to replace it with something more saner and more adequate. That was Predicate Calculus that allowed for predicates to wide their function just allowing them to utter a connection between individuals.
So, for that on the world had been divided into individuals (of different sorts), properties, different relations, and different classes. The classes are just names for groups of individuals. We constantly use them in pronouns or any other abstractions. But the abstractions are not such a problem if it can be difened. Briefly, a phrase like "Frank likes buying ice-cream to women" can be said using Predicate Calculus as "For all x, if x is woman, then Lfix", where 'L' means "__ likes to buy __ to __", 'f' means Frank, and 'i' - ice-cream. The function of predicate for now is just to connect individuals in a kind way. One may ask, what kind of connection is this, and are there any? - This is a good question. Predicates are still needed for this: if {a, b, c} is a set of individuals, then for them in this order there must be more, than one predicates. For instance, "a loves playing with b and c", or "a and b are chasing c", or "a gives b to c", etc.
That's why individuals only are supposed to have no independency without predicates. And that is something that bothers me. I don't think that individuals must be dependend of some thoughts (or anything else). I think there's a way to free individuals for this pit. How to try to make it? First of all, any predicate can be numerated: P1, P2, ..., Pn. An order of individuals is important. This can be seen on this example: "Mary loves John" is not the same as "John loves Mary". So we have to write using PC: Lmj =/= Ljm. A predicate may be replaced by another symbol, so L__ can be replaced with P__, or P1. Let's continue: "John wakes Mary up" :: Wjm or P2jm; "Mary hits John" :: Hmj or P3mj; and so on. We can replace P1, P2, ... to just 1, 2, 3 having: 1jm, 2jm, 3mj. Then let's say that 1jm, 2jm, and 3mj had been difined in a language before, so all we need to do is to check this out whether or not they are true, or to correspond with the world. If they are, then 1jm... are true, or else - they are false.
What is important is that it doesn't matter which symbols are using 1, 2, ..., or a, b, c... That's why 1jm... may be rewritten as ajm, bmj... If it's done, then all what we've got just sequences. To consider or not to consider them to be true or false is just a matter of consequences. The most important is to compare those sequences.
Therefore, the predicates are just kind of connections. Of course we may compare them as we do it with verbs like "to like", "to write", etc. However, it doesn't mean that "to write" in "I write this comment" and "John writes letters" are the same, and the so on in the other ones, so that's why to compare them - is just another new action which has to be checked further.
I think I've showed how individuals may be released from the chains of predicates, while we still are needed in some extra elements among the elements (or the individuals), because we do not see the individuals, but we see them connected or linked to each other in a certain way. We don't see a bird, but we see the one somewhere, and doing something. And so on. The more and more details, the deeper, and the deeper context.
By the way, if you're coding you can use even more plainer scheme to use predicates on your taste. Here's how can it be done: let's say that the maximum lenght of your predicate is 3, and you've got predicates as this: "Catherine asks John to visit Mary" or Acjm or P1cjm, or - in our version - 1cjm (or acjm). Anyway, you can code ordered sets using numbers in a certain way (it's totally upon you), and it seems that if you've got 3-lenght predicates, then you will require 3+3 set. (For x-lentght it's x+3 set.) 1 is reserved for the sign of the ordered set, another for the predicate, and the last one for the value.
Let's me introduce and example (it is not ASCII or binary):
0110 1011 0001 0010 0001 0001 = <P1aba=1> = ("a asks b to visit a" is true),
0110 1100 0001 0011 0000 0001 = <P2ac=1> = ("a pleases c" is true),
0110 0101 0010 0000 0000 0000 = <P3b=0> = ("b lurks" is false).
There are numerous ways to code it. The idea is simple, but there's an important idea that can tell that there may be no thoughts. It's possible to talk to each other using only the objects, while only in a right sequence. If the sequence is correct, then the talk is success.