Post by Eugene 2.0 on Nov 7, 2024 23:19:00 GMT
Usually we use language to think iff we think with language. This argument is usually held as basics, not in all respects, of course. /We can't claim there are no other deities taking part in the process of thinking/
Here's an interesting thing, that if we use language as metalanguage /language=metalanguage/ it makes an impact to the object language or the direct language of logic.
What is that object language? Is something like "S → P", "S v (P & ~R)", or "All x is P → some x is P", etc. Actually, as the object so the meta both are quite similar, while the former doesn't require semantics for usage.
The last one point can be explained in a way how computers calculate anything. The machines are changing the trillions of transistors' value, and that's about it. The calculators don't think, they calculate in a machine way.
However, no object language can be taken by itself solely. Impossibility of this necessitates us to interpret the objects of the object language in some way, for instance as some elements and sentences. This usually work well.
But why metalanguage? This language is the one by which we interpret object ones. And obviously there's a connection between them. What kind of relation it is? Let's think.
If what we think is nonsense and crap, what about usage of objects and elements within the object language? Isn't nonsense from metalanguage going to the object one? Sure, it is. Otherwise, if our metalanguage is senseful and rational, isn't our object language wrong? No, it's not.
Therefore, metalanguage (M) sense goes to the object language (O), and nonsense of M makes O be nonsense. In other words, if M is true, then O is true, and when M is false, the same is about O. M←→O.
However, we can interpret M partially as some models. In this case, M separates into some interpretations I1, I2, ..., Iⁿ. Each interpretation requires something from O. Depending on which values each variable possesses the total model can gain different general values. Primary or general values are different: the firsts are just symbols, elements, sentences, while the seconds are mainly True and False. For example, when we see or hear the phrase "2+2=4" we can say "oh, this is true"; when we see or hear something like "2+=4+" we may stick muted not knowing what to say about values here. The inner or primary values makes a phrase gains correctness, the outer or general requires the same as we speak daily.
So, I1→S, I2→S, ..., Iⁿ→S may give different results depending on as I so S. We're certain that I implies S or P, or R... In other words, the way how we assume something makes logic be controlled by language.
Here's an interesting thing, that if we use language as metalanguage /language=metalanguage/ it makes an impact to the object language or the direct language of logic.
What is that object language? Is something like "S → P", "S v (P & ~R)", or "All x is P → some x is P", etc. Actually, as the object so the meta both are quite similar, while the former doesn't require semantics for usage.
The last one point can be explained in a way how computers calculate anything. The machines are changing the trillions of transistors' value, and that's about it. The calculators don't think, they calculate in a machine way.
However, no object language can be taken by itself solely. Impossibility of this necessitates us to interpret the objects of the object language in some way, for instance as some elements and sentences. This usually work well.
But why metalanguage? This language is the one by which we interpret object ones. And obviously there's a connection between them. What kind of relation it is? Let's think.
If what we think is nonsense and crap, what about usage of objects and elements within the object language? Isn't nonsense from metalanguage going to the object one? Sure, it is. Otherwise, if our metalanguage is senseful and rational, isn't our object language wrong? No, it's not.
Therefore, metalanguage (M) sense goes to the object language (O), and nonsense of M makes O be nonsense. In other words, if M is true, then O is true, and when M is false, the same is about O. M←→O.
However, we can interpret M partially as some models. In this case, M separates into some interpretations I1, I2, ..., Iⁿ. Each interpretation requires something from O. Depending on which values each variable possesses the total model can gain different general values. Primary or general values are different: the firsts are just symbols, elements, sentences, while the seconds are mainly True and False. For example, when we see or hear the phrase "2+2=4" we can say "oh, this is true"; when we see or hear something like "2+=4+" we may stick muted not knowing what to say about values here. The inner or primary values makes a phrase gains correctness, the outer or general requires the same as we speak daily.
So, I1→S, I2→S, ..., Iⁿ→S may give different results depending on as I so S. We're certain that I implies S or P, or R... In other words, the way how we assume something makes logic be controlled by language.